File "SL-paper2.html"
Path: /IB QUESTIONBANKS/5 Fifth Edition - PAPER/HTML/Math AI/Topic 4/SL-paper2html
File size: 1.07 MB
MIME-type: text/html
Charset: utf-8
<!DOCTYPE html>
<html>
<meta http-equiv="content-type" content="text/html;charset=utf-8">
<head>
<meta charset="utf-8">
<title>IB Questionbank</title>
<link rel="stylesheet" media="all" href="css/application-02ef852527079acf252dc4c9b2922c93db8fde2b6bff7c3c7f657634ae024ff1.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-9717ccaf4d6f9e8b66ebc0e8784b3061d3f70414d8c920e3eeab2c58fdb8b7c9.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">
</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../../../../../../index.html">Home</a>
</li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Help
<b class="caret"></b>
</a>
<ul class="dropdown-menu">
<li><a href="https://questionbank.ibo.org/video_tour?locale=en">Video tour</a></li>
<li><a href="https://questionbank.ibo.org/instructions?locale=en">Detailed instructions</a></li>
<li><a target="_blank" href="https://ibanswers.ibo.org/">IB Answers</a></li>
</ul>
</li>
<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>
<div class="page-content container">
<div class="row">
<div class="span24">
<div class="pull-right screen_only"><a class="btn btn-small btn-info" href="https://questionbank.ibo.org/updates?locale=en">Updates to Questionbank</a></div>
<p class="muted language_chooser">
User interface language:
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=en">English</a>
|
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=es">Español</a>
</p>
</div>
</div>
<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="https://mirror.ibdocs.top/qb.png" alt="Ib qb 46 logo">
</div>
</div>
</div>
<h2>SL Paper 2</h2><div class="specification">
<p>A wind turbine is designed so that the rotation of the blades generates electricity. The turbine is built on horizontal ground and is made up of a vertical tower and three blades.</p>
<p>The point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is on the base of the tower directly below point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> at the top of the tower. The height of the tower, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math>, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo> </mo><mtext>m</mtext></math>. The blades of the turbine are centred at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and are each of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo> </mo><mtext>m</mtext></math>. This is shown in the following diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The end of one of the blades of the turbine is represented by point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> on the diagram. Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> be the height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> above the ground, measured in metres, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> varies as the blade rotates.</p>
</div>
<div class="specification">
<p>Find the</p>
</div>
<div class="specification">
<p>The blades of the turbine complete <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> rotations per minute under normal conditions, moving at a constant rate.</p>
</div>
<div class="specification">
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>, of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> can be modelled by the following function. Time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, is measured from the instant when the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> first passes <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math> and is measured in seconds.</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>90</mn><mo>-</mo><mn>40</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mn>72</mn><mi>t</mi><mo>°</mo></mrow></mfenced><mo>,</mo><mo> </mo><mi>t</mi><mo>≥</mo><mn>0</mn></math></p>
</div>
<div class="specification">
<p>Looking through his window, Tim has a partial view of the rotating wind turbine. The position of his window means that he cannot see any part of the wind turbine that is <strong>more than</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="bold">100</mn><mo mathvariant="bold"> </mo><mtext mathvariant="bold">m</mtext></math> above the ground. This is illustrated in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the time, in seconds, it takes for the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> to make one complete rotation under these conditions.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the angle, in degrees, that the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> turns through in one second.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the amplitude of the function.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the period of the function.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>5</mn></math>, clearly labelling the coordinates of the maximum and minimum points.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> above the ground when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the time, in seconds, that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is above a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mtext>m</mtext></math>, during each complete rotation.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At any given instant, find the probability that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is visible from Tim’s window.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The wind speed increases. The blades rotate at twice the speed, but still at a constant rate.</p>
<p>At any given instant, find the probability that Tim can see point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> from his window. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows values of ln <em>x</em> and ln <em>y</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The relationship between ln <em>x</em> and ln <em>y</em> can be modelled by the regression equation ln <em>y</em> = <em>a</em> ln <em>x</em> + <em>b</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</em> and of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation to estimate the value of <em>y</em> when<em> x</em> = 3.57.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The relationship between <em>x</em> and <em>y</em> can be modelled using the formula <em>y</em> = <em>kx<sup>n</sup></em>, where <em>k</em> ≠ 0 , <em>n</em> ≠ 0 , <em>n</em> ≠ 1.</p>
<p>By expressing ln <em>y</em> in terms of ln <em>x</em>, find the value of <em>n</em> and of <em>k</em>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In the month before their IB Diploma examinations, eight male students recorded the number of hours they spent on social media.</p>
<p>For each student, the number of hours spent on social media (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>) and the number of IB Diploma points obtained (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>) are shown in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_07.43.52.png" alt="N16/5/MATSD/SP2/ENG/TZ0/01"></p>
</div>
<div class="specification">
<p>Use your graphic display calculator to find</p>
</div>
<div class="specification">
<p>Ten female students also recorded the number of hours they spent on social media in the month before their IB Diploma examinations. Each of these female students spent between 3 and 30 hours on social media.</p>
<p>The equation of the regression line <em>y </em>on <em>x </em>for these ten female students is</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="y = - \frac{2}{3}x + \frac{{125}}{3}.">
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mi>x</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mn>125</mn>
</mrow>
<mn>3</mn>
</mfrac>
<mo>.</mo>
</math></span></p>
<p>An eleventh girl spent 34 hours on social media in the month before her IB Diploma examinations.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and 2 cm to represent 10 points on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar x}">
<mrow>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean number of hours spent on social media;</p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
<mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean number of IB Diploma points.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar x,{\text{ }}\bar y)">
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo stretchy="false">)</mo>
</math></span> on your scatter diagram and label this point M.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> for these eight male students.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line, from part (e), on your scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a reason why this estimate is not reliable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A medical centre is testing patients for a certain disease. This disease occurs in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> of the population.</p>
<p>They test every patient who comes to the centre on a particular day.</p>
</div>
<div class="specification">
<p>It is intended that if a patient has the disease, they test “positive”, and if a patient does not have the disease, they test “negative”.</p>
<p>However, the tests are not perfect, and only <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>99</mn><mo>%</mo></math> of people who have the disease test positive. Also, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> of people who <strong>do not</strong> have the disease test positive.</p>
<p>The tree diagram shows some of this information.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Write down the value of</p>
</div>
<div class="specification">
<p>Use the tree diagram to find the probability that a patient selected at random</p>
</div>
<div class="specification">
<p>The staff at the medical centre looked at the care received by all visiting patients on a randomly chosen day. All the patients received at least one of these services: they had medical tests (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math>), were seen by a nurse (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>), or were seen by a doctor (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math>). It was found that:</p>
<ul>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>78</mn></math> had medical tests,</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math> were seen by a nurse;</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> were seen by a doctor;</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> had medical tests and were seen by a doctor and a nurse;</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math> had medical tests and were seen by a doctor but were not seen by a nurse;</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math> patients were seen by a nurse and had medical tests but were not seen by a doctor;</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> patients were seen by a doctor without being seen by nurse and without having medical tests.</li>
</ul>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the sampling method being used.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>will not have the disease and will test positive.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>will test negative.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>has the disease given that they tested negative.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The medical centre finds the actual number of positive results in their sample is different than predicted by the tree diagram. Explain why this might be the case.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a Venn diagram to illustrate this information, placing all relevant information on the diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total number of patients who visited the centre during this day.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 800 students answered 40 questions on a category of their choice out of History, Science and Literature.</p>
<p>For each student the category and the number of correct answers, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, was recorded. The results obtained are represented in the following table.</p>
<p><img src="images/Schermafbeelding_2018-02-13_om_14.11.54.png" alt="N17/5/MATSD/SP2/ENG/TZ0/01"></p>
</div>
<div class="specification">
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test at the 5% significance level is carried out on the results. The critical value for this test is 12.592.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span> is a discrete or a continuous variable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, the modal class;</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, the mid-interval value of the modal class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to estimate the mean of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>;</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to estimate the standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected frequency of students choosing the Science category and obtaining 31 to 40 correct answers.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null hypothesis for this test;</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value for the test;</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the result of the test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Fiona walks from her house to a bus stop where she gets a bus to school. Her time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> minutes, to walk to the bus stop is normally distributed with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>12</mn><mo>,</mo><mo> </mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfenced></math>.</p>
<p>Fiona always leaves her house at 07:15. The first bus that she can get departs at 07:30.</p>
</div>
<div class="specification">
<p>The length of time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> minutes, of the bus journey to Fiona’s school is normally distributed with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>50</mn><mo>,</mo><mo> </mo><msup><mi>σ</mi><mn>2</mn></msup></mrow></mfenced></math>. The probability that the bus journey takes less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> minutes is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>941</mn></math>.</p>
</div>
<div class="specification">
<p>If Fiona misses the first bus, there is a second bus which departs at 07:45. She must arrive at school by 08:30 to be on time. Fiona will not arrive on time if she misses both buses. The variables <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> are independent.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that it will take Fiona between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> minutes and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes to walk to the bus stop.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the bus journey takes less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math> minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Fiona will arrive on time.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>This year, Fiona will go to school on <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>183</mn></math> days.</p>
<p>Calculate the number of days Fiona is expected to arrive on time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A company performs an experiment on the efficiency of a liquid that is used to detect a nut allergy.</p>
<p>A group of 60 people took part in the experiment. In this group 26 are allergic to nuts. One person from the group is chosen at random.</p>
</div>
<div class="specification">
<p>A second person is chosen from the group.</p>
</div>
<div class="specification">
<p>When the liquid is added to a person’s blood sample, it is expected to turn blue if the person is allergic to nuts and to turn red if the person is not allergic to nuts.</p>
<p>The company claims that the probability that the test result is correct is 98% for people who are allergic to nuts and 95% for people who are not allergic to nuts.</p>
<p>It is known that 6 in every 1000 adults are allergic to nuts.</p>
<p>This information can be represented in a tree diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.31.34.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c.d.e.f.g"></p>
</div>
<div class="specification">
<p>An adult, who was not part of the original group of 60, is chosen at random and tested using this liquid.</p>
</div>
<div class="specification">
<p>The liquid is used in an office to identify employees who might be allergic to nuts. The liquid turned blue for <strong>38 </strong><strong>employees</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this person is <strong>not </strong>allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that both people chosen are <strong>not </strong>allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy </strong>and complete the tree diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this adult is allergic to nuts and the liquid turns blue.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the liquid turns blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the number of employees, from this 38, who are allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A survey was conducted on a group of people. The first question asked how many pets they each own. The results are summarized in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The second question asked each member of the group to state their age and preferred pet. The data obtained is organized in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test is carried out at the 10 % significance level.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the total number of people, from this group, who are <strong>pet owners</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the modal number of pets.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down the median number of pets.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down the lower quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the ratio of teenagers to non-teenagers in its simplest form.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the null hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the alternative hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected number of teenagers that prefer cats.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion for this test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">i.</div>
</div>
<br><hr><br><div class="specification">
<p>Sila High School has 110 students. They each take exactly one language class from a choice of English, Spanish or Chinese. The following table shows the number of female and male students in the three different language classes.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test was carried out at the 5 % significance level to analyse the relationship between gender and student choice of language class.</p>
</div>
<div class="specification">
<p>Use your graphic display calculator to write down</p>
</div>
<div class="specification">
<p>The critical value at the 5 % significance level for this test is 5.99.</p>
</div>
<div class="specification">
<p>One student is chosen at random from this school.</p>
</div>
<div class="specification">
<p>Another student is chosen at random from this school.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null hypothesis, H<sub>0 </sub>, for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the expected frequency of female students who chose to take the Chinese class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether or not H<sub>0</sub> should be rejected. Justify your statement.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the student does not take the Spanish class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that neither of the two students take the Spanish class.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least one of the two students is female.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>There are three fair six-sided dice. Each die has two green faces, two yellow faces and two red faces.</p>
<p>All three dice are rolled.</p>
</div>
<div class="specification">
<p>Ted plays a game using these dice. The rules are:</p>
<ul>
<li>Having a turn means to roll all three dice.</li>
<li>He wins $10 for each green face rolled and adds this to his winnings.</li>
<li>After a turn Ted can either:<br>
<ul>
<li>end the game (and keep his winnings), or</li>
<li>have another turn (and try to increase his winnings).</li>
</ul>
</li>
<li>If two or more red faces are rolled in a turn, all winnings are lost and the game ends.</li>
</ul>
</div>
<div class="specification">
<p>The random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="D">
<mi>D</mi>
</math></span> ($) represents how much is added to his winnings after a turn.</p>
<p>The following table shows the distribution for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="D">
<mi>D</mi>
</math></span>, where $<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> represents his winnings in the game so far.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of rolling exactly one red face.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of rolling two or more red faces.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that, after a turn, the probability that Ted adds exactly $10 to his winnings is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{1}{3}}">
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Ted will always have another turn if he expects an increase to his winnings.</p>
<p>Find the least value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> for which Ted should end the game instead of having another turn.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Don took part in a project investigating wind speed, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, and the time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> minutes, to fully charge a solar powered robot.</p>
<p>The investigation was carried out six times. The results are recorded in the table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> is the point with coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><menclose notation="top"><mi>x</mi></menclose><mo>,</mo><mo> </mo><menclose notation="top"><mi>y</mi></menclose><mo>)</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>On graph paper</strong>, draw a scatter diagram to show the results of Don’s investigation. Use a scale of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>cm</mtext></math> to represent <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> units on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>cm</mtext></math> to represent <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> units on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate <math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>x</mi></menclose></math>, the mean wind speed.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate <math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>y</mi></menclose></math>, the mean time to fully charge the robot.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot and label the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> on your scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, Pearson’s product–moment correlation coefficient.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the correlation between the wind speed and the time to fully charge the robot.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the regression line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>, in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>c</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw this regression line on your scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise estimate the charging time when the wind speed is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Don concluded from his investigation: “There is no causation between wind speed and the time to fully charge the robot”.</p>
<p>In the context of the question, briefly explain the meaning of “no causation”.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>It is known that the weights of male Persian cats are normally distributed with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>1</mn><mo> </mo><mtext>kg</mtext></math> and variance <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup><mo> </mo><msup><mtext>kg</mtext><mn>2</mn></msup></math>.</p>
</div>
<div class="specification">
<p>A group of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> male Persian cats are drawn from this population.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a diagram showing the above information.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the proportion of male Persian cats weighing between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>kg</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>kg</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the expected number of cats in this group that have a weight of less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>3</mn><mo> </mo><mtext>kg</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>It is found that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> of the cats weigh more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mtext>kg</mtext></math>. Estimate the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Ten of the cats are chosen at random. Find the probability that exactly one of them weighs over <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>25</mn><mo> </mo><mtext>kg</mtext></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>In a company it is found that 25 % of the employees encountered traffic on their way to work. From those who encountered traffic the probability of being late for work is 80 %.</p>
<p>From those who did not encounter traffic, the probability of being late for work is 15 %.</p>
<p>The tree diagram illustrates the information.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The company investigates the different means of transport used by their employees in the past year to travel to work. It was found that the three most common means of transport used to travel to work were public transportation (<em>P </em>), car (<em>C </em>) and bicycle (<em>B </em>).</p>
<p>The company finds that 20 employees travelled by car, 28 travelled by bicycle and 19 travelled by public transportation in the last year.</p>
<p>Some of the information is shown in the Venn diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>There are 54 employees in the company.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>a</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>b</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee encountered traffic and was late for work.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee was late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee encountered traffic given that they were late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>y</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {\left( {C \cup B} \right) \cap P'} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mo>∪</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> <mo>∩</mo> <msup> <mi>P</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>In a school, all Mathematical Studies SL students were given a test. The test contained four questions, each one on a different topic from the syllabus. The quality of each response was classified as satisfactory or not satisfactory. Each student answered only three of the four questions, each on a separate answer sheet.</p>
<p>The table below shows the number of satisfactory and not satisfactory responses for each question.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.16.22.png" alt="M17/5/MATSD/SP2/ENG/TZ2/01"></p>
</div>
<div class="specification">
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test is carried out at the 5% significance level for the data in the table.</p>
</div>
<div class="specification">
<p>The critical value for this test is 7.815.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>If the teacher chooses a response at random, find the probability that it is a response to the Calculus question;</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>If the teacher chooses a response at random, find the probability that it is a satisfactory response to the Calculus question;</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>If the teacher chooses a response at random, find the probability that it is a satisfactory response, given that it is a response to the Calculus question.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The teacher groups the responses by topic, and chooses two responses to the Logic question. Find the probability that both are not satisfactory.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the null hypothesis for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the expected frequency of satisfactory Calculus responses is 12.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> statistic for this data.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion of this <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Mackenzie conducted an experiment on the reaction times of teenagers. The results of the experiment are displayed in the following cumulative frequency graph.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Use the graph to estimate the</p>
</div>
<div class="specification">
<p>Mackenzie created the cumulative frequency graph using the following grouped frequency table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARQAAADQCAYAAADGfp5vAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAC6aSURBVHhe7Z0NWFRl+v+/f9bLWgf9K5ESxoQaiZA2jkpbsKZ28bKs0oRbuZlGgeVLkbjuWpCuP7JYyyDRzF9ZTCK77pYwP3ZjVVLIv1YLMvLTwJdJHVnlJQ0JGFKDOf/nnDkDA54ZBj0oh70/1zUXZ57zzJzn9Xvu5z4Pc/8fjgGCIAgZ8BD/EgRBXDckKARByAYJCkEQskGCQhCEbLQ7ZdXqO4UEgiCInlJVdVb42+kpDy8q9hME0Zegsdk36dovtOQhCEI2SFAIgpANEhSCIGSDBIUgCNkgQSEIQjZIUAiCkA0SFIIgZIMEhSAI2ZBJUFpRa3hB2OQi+YpKQbaxFlYx9w2l2YRifTr0xmYxoaOsmgwje3cjsLJiFEOfmg1j+wX/DUPCBFaOSGS0l00hWI9DHzMW6hg9TK461d18vUGrERkaibEovm5c3/9ncWMslMqPkaJbhPXGBjHhRsEm7dLZmL9qFy6KKTeF2nwsffgprMo9LyYoGSsa9+VgbTmgiX0AY1yNII+7EBo7GSjfAv2+C2Ii0Z+RX1AiNqKk6qywHVd4mUuwNW4iO1GK93eUo9GW6yYyAD66jULZypO07N3Nwg+6LYdZOXYhSesppvUNrLVf4l39l9J9ZTUhN/2vsGAyYkPv6mYA3YoxoeHQwIzs9H/ceCtFQIfMEnPHeBRfN7fv+y+9b6F4+CJMNx1e7NBS14AWWyobtEYYMuIxTjBBxyIqRY9iU+chbK0tRXbKrA5TdVw8MvaY0LFAEJcS7Xkcv4dfUvwaibvr2XEFMnSBUGvS2ZLD2ZLnCmqNBmQkhDh8Vw6MtVfE84xaAxL4c5q3UHy0sCOvqyUd/5mQF7CbP65Ph260/bpdlzz29xOQoC/Enva2mYVVxdWwWmtRmtmRlmI47tAOXcvOzuuLYWru6Qzm29OAlXELsQu3QUrmrCe/Qm65hZkn4Qgdc6uY6hyPMQ8gVqNiVkohDpy8JKb2FZphzIgU2/zv0AvtF4aUYt6acqdNbe2VEsWWdcI4WAXD0T3iUusFGGr50SW1tJUeg67nhONn9uDonkwkjLPn6zJO2a3AVKzvKJdj2e3L0PZ62rkEk36u8H0x+uPSY9kNel9Qmo/jHzuKUA8VNGHjMFxIK8X6uN8iMWMXu9PxWFCZ/Srmx6yEoVpsGFbxrc89hZTsQ7b3PJZdyHjmGaSJDWGtzsfyGLaUaM9j/551KG7sSZOwgWHcjDjdC8jYXS2m8d+1Arrpv+8ok5369Zgf+UxHXn5JN3cT9vXoms6ox+5Vz+CZ9rY5BP38Z/Dcc09j9rqOtOzEVHxq4ieoVNnZ+VVPIWZ5PqrdLRLrJ0PKIwh6+AVkV9ajfG2ORH1a8V3FQbDVDlTj/THCPnqEzzoIf/tkYnjcBv/xt7ODI9hf0VeXfHybL8Iqof1U8B4y0K02tY0/vr1svYLKj5AY+TQy+HtYT3FnTojUZzyNyGfexG4ho22czt1gtyivoNqwEjHzX+0ol73safvQ6DEKEc9GsVqakVv4TYcVaj2DA7kH2YE7lqdz5BeU3S8gpH1gsVfQw0jkJ7wqCs9GjGIXZBX+fBverwSC4j5GiZk3QStRmDoTKstObP7r/wp33tbyz/AOuxOqojfiaz6P+UtkRvuyM+dxxPw9m0YXsO/ddShgbaaKSENhZVVHHstfkZ57CTFbPkNmBG8bBSPJcAxV5cuglbJzmRn/6ep3UQlfRCz/m61MlXuQOY8t1Sw78Mq7Xc1/li91FyqZ6Wz+eiOi2Q0Yln/h0Ld2+8sBHx22lGxEBH/stQyGU26Y20ELsbXkFCtDHpKC+C+vwO6zv+ySJk5Q61l8/v42VvaJiNtaAjNv0lfuQmqELywFH+Ov5W76rTzZnSluNluesPactw3fHE3FtCFdh8clVJ82sb8qBATcIVow7M72aSoScydi6zesDyqLkJUUiJ8J53g8MTLgLva3HgdPn2+/G984DEgM8XcQO/YSLFXxtJ32Ns/Gb+/+3o02dRx/r2IH/1nzQexYHslap6e4NyfaUc1EamEly3MKX2fOFq5n+cyIb/k6NbLl6is7mMxcPUYt2R8gl607fWc8ilj+fe5eGMWbht3yVEU/hgg3LE9n9L6FEvQ0UjP/jD2lGdD5DmQJjThRWsYqzJRV/zRC/PlODkL4qn/Y0ooqUMPqOEC7DOVVVSj9nRdK8nOhX7kEiQX83cKCqosWtgT4HuYj/B3PH7FP/QpjPVlVPNTQbS5hDX0c+XFj3a5cuxnvNQeLFz8IH/6DbILpXowXhMCx4QWYOD4VO06YUB6+kxAVyouWXDBLbs5jmOrD2spzFCZO4u/ujmnj8FCkvy0rT/MplH7BtwtvyYTAXxDxSPFuW4miw3Vumq+XcPJAIbM+vBA6ZQyGiKmduYiqihr29xYMHzqoc/uygb9N/zVqBwXg4aQXMMvHLpkDMHjoMOGovqKKTcO+iVdkNMKE9h0OH5zpvk07jb/fYAr/WQ8fTImbJ0zWnuHenLCjip2D2LF8Dw2E7y+mI9SWLGCtM+MIb5h0GqM6bD7Ki1QO4gKYWAy5F+GxbAxZ9qLQyJtT9r5ndZkTBt/rUIXr+KgTRKesueRjxPF30spPsb3U0Qb8EQ11ne/3naiqRxNrPN4xmJnwC2aCP4nExESHZY2I1YKLVULLMRP12hWVx9pUjyr+YPJo+DqaDt5qBAvOn3o0tDj06C1DMWSQ/E1nw3Gy3ooh3vzolJjAdloaUMc3gySi+IrvXNOMc6Yz7O94hAXzIuYut2JM1LOsr3/A7nWPIyR6FQxdfGE3Fwmn7FWWqgrqYaqO9nWnTZ2Nv0FD4H2LeOw27s0JO7d4D8Eg8bgr7WPZ5Rj1gjZ8Biu5uOxp/Br6tV+wqsxAuPb6bo69NSuYWE/HH95YgiBeYdka78UPykSz7ecYOoJXVy9EZH7VuaPbO5sp5s53sY7dEVQRy/DOu/nMDDwGQ1Iw+5zY+R4qDFPzk82CC43X5+zzGOwFNX9w8BSqHU3hC1Wo4LVQ5YWhvSYg18mgoRgh3BGv82lG4zcozDW77Wx1xMPnYaR++g+21GHmPu9HePhpZEhsEVCNGOp0Itxcugi2O2064HaMmizcbTqPv5ZGXLgsHjulFU0NjhsZ3JkTtpzd0T6WLzeg0fEm2AkPDNHOEJc9hfj880LkWlQIem4WJl+1zO0ZvThLPOCpnY83kqawYyYqGe+ITsSONfXuzR+jmPdOW6tgWMh70+0e5vOo2H+E5VHhruBfImKWFsO/+xcMu9iAt9Pu7GMqu+2fOC543xtgzHhUWCePSylmhuQwqIPvYOk1qKhyvhPF445gTOetqfrt2LTpS9TyX8U7Gjd8KDydUcXOgPZ6Gtpu6dSzdfYFmb0InncgIIAf/YXYvOkLoezWagMWCk8A5kIvtHl3WNFo3MsGFauro7P1KuzteRnfNbR0tnw8+aXOBygtTEOEqhQff3FK9Jd0TB5Xd9Y+hVttejuCw8azvw7jz1qN4nVvI1vSujFj1xdHhZuqtfYAsrfzDlA77swJ9/AY4Y/xfNH5JWiu7Xq8wzdDeOLj8GSnfdnzMZYu/ZjN0MmYM3O8sES6HnpRUHiGQrsgWXQifoG1b+9EtfVWBPxmqS2tcjPmh4yG2v9Bm3+k3XFr7yxeiB5FEBMI/5CnoRe81nYz3htTlyy3OZt2v4LwIDVrsHuhyyhleabgudkaBz8A66jEB6SdcTye9+G3L89j1lS1zWzn17DtzuTZSFvyoBOfQk+xOQhl3aXpEYDfrBYtQXH97f+LF2zOwnYHm/3xqLMdoldQZz7JvoGtocP9ULev3CaqVzEId0+8n8m8BSZTjWhxtqL27xvFx/nsJjIyEMF3+eMXo7zFwWVfSvnj1xPVytj74VabsqVexGOdx59/CObruyzNXY5lO+7MCTcZ8iCWpPGOWjaWV0UK11MHPYoM/npBj2O2YFXxsPkTlyA44QWuwTKVopcFheE5CQuEpQ9r0oI3kJpfBavnFLyk/wsyeRPZlostbf6ArPzXRMcta+D5bzt4zCdi3ut5+LpwjdAA9UWHcZoNeA/fGKzL34ZU/mmMCL9EyjS8h5e0Q9k7T2h++0csj+CfDjF4R+ElqZkyED7T/gC9YSOS7HnZlYPmrYWh6C2xTNfBgHvx2w9eZXdu/o0KPmjD9S3SHOEtwYVdyu6LiKQs5K+L6aGD7TzKCpllqJ1gc0xfBS8YoxHAjixHzKizN+X/1SB63Hl8xO/ZCFqCiug3sTpGbRtc7c7LuxAw8nrvfzcK99rUNv42Yp5wwxTH8K6PkdTJDcGLxWrbclB4z4/lv8Hwjk541063c8JdBsJX9xryt65pL5et7Bth0C+Eln94IdK+R4hdUdPdrmd34X+k2o6f30jxiOh//MidyHqam5V1jGsTU66JtmNc1qx72FhZwuXV/CQmuqAmj4tn48pvVhZ34jourJix+VMZl34fq6+77XMTaav5nFsZyfflk1zWiR/F1J7RtV/k0CRCAdjW7T9i+oQR12eWsuVA7LIn2D2tHKXHutvjYkXjMSMOsOXOvGUzEUCjrW8g7vi2L71U8xYgln+cLAPUxf8R8E/NdqNtYSoWCEvB68EDQ6bOxQrNeeRu3+96J679/340CYib6i0mEjed9qdYtmV9zoty+QgpLg+hEGhs9k269gtZKARByAYJCkEQskGCQhCEbJCgEAQhGyQoBEHIBgkKQRCyQYJCEIRstO9D4Z8nEwRBXAv2vSi0sY1QBDQ2+ya0sY0giF6DBIUgCNkgQSEIQjZIUAiCkA0SFIIgZIMEhSAI2SBBIQhCNkhQCIKQDRIUgiBko18Kii2MKR8k6U6oo1KQbax1O1DSjaERpmI9UmIzpeMECVxBbelmJAjBpcYiKiUHRj4AlAs61dvNzxA3CGstSjPjMU7omzsxLiETe/pUyFZ56H+C0lyK9XELUeCbhhLzKZS8/HPkzE1DfnVvTawrqDasQaaxU3x8JzCRMOYgJSoMLxYC4WvjnISYtKLZuBlxsz+D73slMJuL8PLPtmPu6gLnPwrN1/vVQqhXfA4+Kn/JjiTcmbsCurjNMApRFYmbRwOMG/8bXz3wOiqqbHG/Hzv7Lp75XS5M/a1r+P/lsaP8uDx87JknOb/AlVzRD2IQGDGOTGByEfeDLcVN2rimE0VcVvLzXHpZk5jWlctcTcl7XPx9DteThOUry+PS40O5yOQsruhENyWRKHPbiSxull8ol1x0XkxxpI37oeg9bn3ZRfE9j9gWfhEuyq8c+lfMqJ+4mrwlncepQunfcXmsZ3Ag9yAQqkWgPRaxx10IjZ0MS+5eGBvdux1Ya0uRnfIIggQz4ndYoJWIeCfEng1DyOw12F3/Eebf+ytkXGWl8BaJARkJYZi+6RRGLf4UBa/HYVqA66AF1pNfIbf8FoROGdMe3sAW5e28LVq+mNaBB4ZMW4jETiEyBmDw0GGA6n5MvFsREYX/g2jAsdIziE5LwNTrDE7e1+hftWmugclkgVewGh1RYMSJZTkJc113PggjDBnxCI4zoC08HZU7X0fctADpANIeaug2ZSNV4wVN6h6Yq3YhqZPw8PGEZyFE9wI+Dt6MI1uWQaf1caPB2XLn3CmYcAeC1azcdjwGYejwWzqHAHUJP2jLrz/QOyEvzSbsyViBpfgd3tSJ4Vr7Ef2rPi0NqHOMQd2JC7jYJO0B7RCSHWiY+DJKXQmJAzZLYjxiQ++SaEhPaJP+jhLDRjxdsRDj3XbCWVk16uG0GlX1aHJDUKzV+7H9s0kyBnonrpdWYzo0QdPxTMYu1Gc/hfsXGlwHSlMg/0G3Lm8MG3y1B5TvZG1IDBKLfon8AveExIZoSXhNwoRRzsI4DoSPVoekLftRtFiNw2ujEZWiR/H1ePfVXhjcXa+x5Vh+qgFjP/qv6w/0TsjGAO0ylPMOczEIu6VgHd7dd0E82z/oX4IyfBzCNCpcvtCIFjGJD8NZfdoEqMbAf8TVk4vvZGNJPjKn/z/EBMcjw2BErVt3jXoYC/cCv9bibsknNY7YhaUAG8KBwhfDXAjLAAwPngwNs1EuNF4S0xit53H6YD1U4/0xwmWvNeL41iwcnvMGXrrusKOE/NjGwksrFrM+bkRdw49iev+gfwmKlAPWeg6Hi8wufQkePlrokj5ERdFCeJf+ESHRKdAXm+DyQXBrFQ59BsSG39uDJcUQBEyLw+s799uEZYVech+KlAPWevowiur9u7neFdQWb8FW/AbLpvn+J5mfisNjhD/Gs5tcsHqwmNJPEJ/2CPSHR3Nt5/K45wOncPFZ33BN3A/cibyVXGRgIpd37rKYozvsj4tncn6RyVxW0Qn2PVcjPMblH/ud+18ua+VfuBOyPv27zJ3LS+QCA5/nso79wHFNx7g8Vp7A5/O4c06vc5mrKXqbSxbq3UFbzefcf6V/0cNH5n2PfvXYuO0cV7RSx0Wu/JyrUfZT46v6pd8Jik0Q8rjkyHuE+vhFruTyutv3IYnrfSg2QXmce/7NLK6kRkqsmriy9AhbGZy97nubK/tJzH4VohgKee/hIpPzuBNNDqOvJo+L58/F53E1gpi8Jubt+nK2d0VZ8HVRLE0lXLp9PPIv/kaVX6Z4MeHp2i/0I9WEIqCx2Tfp2i+0zCYIQjZIUAiCkA0SFIIgZIMEhSAI2SBBIQhCNkhQCIKQDRIUgiBkgwSFIAjZIEEhCEI22nfK8jveCIIgrgX7blnaek8oAhqbfRPaek8QRK9BgkIQhGyQoBAEIRskKARByAYJCkEQskGCQhCEbJCgEAQhGyQoBEHIBgkKQRCyQYJCEIRsKFdQrLUozYzHOPWdUKtnISW7tJuIf1dQW7oZCeP4/O5+5ibQbEKxPgWxGUZIR2Lmq/4lMhNCbPWISkG2sRZuV8NajeJVs6DWpEsGGSOI60GhgtIA4/pFmF0wCu+VnIK5ZCl+lpOE1flVTiaWFc3G9/GqwQcrSqtQZT6IHcuHIzflKcStL3UdIfA6sFYbsDTTuTB0ggmkMTsFUUHLUIhwrF2ggWSE0+ZSrI9biALfNJSYT6Hk5Z8jZ24a8quviBlccQXV+WuxSH9IfE8QMsP/c6AdpQRTEoJsdQpg9SN3IutJzo+P5PeDVPSk81xR+hauzDFQVtsxLmvWPd0E23JC0wmuKCuZezS9jHP20baaA9z6+JndB9lqq+HK8t7m4gNZ3qyizsG8rkKinmI9ApOLuo0OKERVvG8GF/nwNdb7JqLoQF/9mK79okAL5RJOHihEOTSYEmgPBn4rxoSGQ2PZi0JjvZjmiDemJcVD6+lQXY9BGDr8FqjcCnYu4pYVwawAw0sIDnkc63YfQvZ8DTRSyxf+uwzpSAiOwabTo7G4aAdej5uGAMcydsV6BgdyDwKhWgTa4zRLxXOWorkCW1cZMPajDCz0v0VMJG4sjsvuR/GnjOXQqMOQUnxBPK98FCgozThnOgN4jYbau2M6ewweiuE4jyPm793zJzSeROmBIe4FO2+f/Auwoy0cGyr/x8XkHwhf3Vrkpz4EaNZgj/ksypO0nYWn1YgM7WToEnchOGcvtiTpoPUZKJ50QXMNTCYLvILVTCLtDMDgocMAy0mY65wte9gS8YO3sD/s91igZXmJm0AjjusTMX1+KSZsPQhzZTJu2fV31KtmIFzrJeZRPgoUlB/RUNcoHnfFgqqLFjcEhVkRe/Pw2UPLsWRqx9S8CkchadBiRakrIXFAsCSOQBP7AMZIZR2gRZLxIAyZkaiYOwMJGYUwNbshgy0NqLOIx1dxARebpLw1vP9oGzZdnIc184PhKaYSNxK+D/R4aVUdnst5G4lTfODh6YNRdzJLMWA0RnY3nhRE/6mJgArqYapuK2WtLkDqR2Pw0boY+DrL3G5FlCEs/xP3hMSOYEncgekTRjovi4cPtLpl2FKRj8WjjmDtlEeQoi92T1gk8cawwVcvwKy1RXhzE7D4D9Ph0896WzFYz+Lz97fhzLyXEK8Vl+nWFjR8x4xYZzcdhaLAqtyO4LDxwOUGNLZ0TL7W6lM4yM6N97/NdaV4X8K7pzDn/YWdfSpdabciJmF/zFRmRRhgrHXnSYoVjca9yMX9mHj3IDHNBXZhKU1HOArxYpALYRk+DmEaFS5faESLmMT7lKpPm5iWjoH/iK7LplZ893Ue9Lv/BF2QWnxc/gASd9cD9enQjZ6ABMO/xbxEb2E9uRcfFQx0WF4zi6V8F7aXD+l+vCoMBdZFygF7CacPl3W/HuX3YKR/CsxPwDR3fBaOVoR3KZJDZrthRbTg20P/AmJnQGt3nLqDZwCmxb2OnZU2YVnxQfnVjlwpB6z1HA4XmaGSvN4A+Og2Cj/R1/H6CpkRrI28lsFw6jC26PzEvETvwMTj3CmYHB8iNB/Fp5u2obKf+U94FCmOHmNm4NnoK8jd9k8cb25Fs2kn9NvPIDotAVOdTWJeTNZ8APMTSYgba3fDXkFtcSYyuvOy88Iyr2Oyu7QihAneyu5GfqjRv4Vs0yXxhJuIwpLb1ZErwMQ04jFEYye25R5FMxphys/BdlMU0pY82L1zmbiJnMPp6ma2BP0SmWnvYf/ZH4CAwWgwHu57myuvA0UKCjzU0K3LRtqIvyE8yB9BD38ILPwQ63RqsUKtqDW8wMx70aTnxWT185i/5QOsCg8STX/+NRohiy5gort3CXesCIHLOLf9L/g8eB7mBtwqpjnA+2c09jJIvyQfNTM8fGOwLj8ZI7bHIkgdhIc3s6rnvwadr93i+jcMCRPYd7wAQ6106YgbiQeGTH4CKyLOIUN3P6I3fIdfvfIHzLzzFqiunEH9EP9+5duiX70nFAGNzb5J137pR9pIEMTNhgSFIAjZIEEhCEI2SFAIgpANEhSCIGSDBIUgCNkgQSEIQjZIUAiCkA0SFIIgZKN9pyy/440gCOJasO+Wpa33hCKgsdk3oa33BEH0GiQoBEHIBgkKQRCyQYJCEIRskKAQBCEbJCgEQcgGCQpBELJBgkIQhGyQoBAEIRskKARByIZyBcVai9LMeIxT82EnZiElu7QH8U34eDxrEKWORIaxWUzrIzSbUKxPQayTMBo8QmyXhBBh27M6KgXZxlq4V3Ur+/p9yM2wtxuF2ug9bG1tYH0ZJdnObAyWbkbCODF0yrh4ZOwxoY+Nxh6jUEFpgHH9IswuGIX3Sk7BXLIUP8tJwur8KrcmFh/bePWizagU3/cW1moDlmY6F4ZO8IHZs9ngC1qGQoRj7QKNRKAvRnMp1sctRIFvGkrMp1Dy8s+RMzcN+dXdhUlthMmwGr95eAHev/Ag3jQchLlqI3Q+klchrpfGfUiLeRKJqz6WGGe24OkbvpqANRVnUWUuwdbHvkPGM6vxaU8Dw/U1+H8OtOPnN1I86tu0ncjiZvmFcslF58WUH7kTWU9yfoEruaIf2sQ0J7Sd4fKen8FFRoay+kZw6WVN4oke0HSCK8pK5h5NL+N+EpO60lZzgFsfP9OhjE5oq+HK8t7m4gNZ3qwi7kSTq/JL1LPtGJc16x4uMLmI+8GWIsFl7lxeIhfoN4WLz/qGu4Ya33SUMjY7I/aX3xIur8bZSBGpyePiO41pZdC1XxRooVzCyQOFKHeMFSsZ71iKRhzf+iY+GvsaNizUiGk9wC0r4gqqDS8hOORxrNt9CNnzNdJRAPnvMqQjITgGm06PxuKiHXg9bhoCXAVwt57BgdyDQKgWgfaQq1LxjrvAW2Spr+wAopOROj8YnmI60dsMwOChw8RjV1jReMyIg9HLsWSqt5imTBQoKM04ZzoDeI2G2rtjOnsMHorhOI8j5u+dLHtsZubv99+PtxZMxmAx1S3aJ/8C7GgLx4bK/3Ex+QfCV7cW+akPAZo12GM+i/KucYr5UKTaydAl7kJwzl5sSdJB607w9uYamEwWeAWr0THsxEFrOQlzndSyhwnw7k9QYPFF6JhvsCrYtmYfl7AZpbXdLZOI3octRfdsxLKlwDtvxsBXgTPSEQUW/0c01DWKx12xoOqiRVpQmsvwwaYWLFvzBMa6sgIccRSSBi1WlLoSEgcES+IINLEPYIxU1gFaJBkPwpAZiYq5M5CQUSgdeL0rLQ2os4jHV3EBF5skvDV2qyYoHA89nID3j55CyY5XEXpgDWY/92eY3HE6Eb2DEOM6CA8/8yZ213+E+fcnwdCtL6xvo3A97IoK6mGqqyvFB0t/cxuweCGmuWMJ8LRbEWUIy//EPSGxI1gSd2D6hJHOG9jDB1rdMmypyMfiUUewdsojSNEXuycsknhj2GAJB6vVgotVFqgmheMRrQ8rz0D4TJmDxc9NAcoLceCkwp2ASoa/sZSfhbkkH5lJkVBZduCVd79kNotyUaCg3I7gsPHA5QY0tnRMvtbqUzjIzo33v+3qSn1Xgm36HcjQ3Wt7RKf2R0iigZ2oYGmBUCcYUGvL2UG7FTEJ+2OmMivCAKNbSwS2HjbuRS7ux8S7B4lpLrALS2k6wlGIF4NcCMvwcQjTqHD5QiNaxCR+SVN92sS0dAz8R7gplvCE76iR7K8Tq4a4oXj4aKF76Q9YwfrWUtfg0LfKQ4GCIuWAvYTTh8tQr5qBcK2XmOaAjw5bqs4KP1Vne5lRkqljJ4KRZDiGqi06+NhydsbRivAuRXLIbDesiBZ8e+hfQOwMaO2OU3fwDMC0uNexs9ImLCs+KL/akSvlgLWew+EiM1TOrjdAjYm/9pd22qrcFD2i9/G4Df7j70RQ8EhFO80VKCis0GNm4NnoK8jd9k8cb25Fs2kn9NvPIDotAVN7MondhReWeR2T3aUVIUzwVsSG+6FG/xaye7qvQBSW3K6OXAEmphGPIRo7sS33KJp5h15+DrabopC25EEMEXN1xhtTlyxnn/kr/rSuSNj8Z639Aps2lyNixROY3BvtRYi0oqnhIvt7EQ0uLUF+o+Vm/KlsOl7+7X3KfgonPj4WUNSz/qZjXF7yTKHMfn4zueS8Yw77K37iavKWsPTxXHxelZjmiP18L+xDEfaFhHJPP/8at7GkhpPcVfJTGZd+H19u56/7nO5xaWOXz+OSI++x5Y1cyeWdcNyBUsXlxY9n5xz3PnT5DN9eW0u4mm627PQl+HIrCok+7ujTi1xZus7hHL8H6TOurOaycFZJ8OV3hH71nlAENDb7Jl37hexdgiBkgwSFIAjZIEEhCEI2SFAIgpANEhSCIGSDBIUgCNkgQSEIQjZIUAiCkA0SFIIgZKN9pyy/440gCOJasO+Wpa33hCKgsdk3oa33BEH0GiQoBEHIBgkKQRCyQYJCEIRskKAQBCEbJCgEQcgGCQpBELJBgkIQhGyQoBAEIRvKFRRrLUoz4zFOzQfumoWU7FIhRIRbNJtQnJuOhHH8ZycgwfBv8UQfgC+bPgWxUgHWRay1XyIzIUTYpaiOSkG2sdZJPGcRe5B3oa2uob2Ia8DKunIfDKwvo9QvwFDbXRiNNSxfJDKMzWKaMlGooDTAuH4RZheMwnslp2AuWYqf5SRhdX6V64kldLIBKb+Zifnvf4+wN/NRYj6MLTo/8by8WKsNWJrpXBg6YZ/0QctQiHCsXaCRiMvDaC7F+riFKPBNY2U/hZKXf46cuWnIdxoT9wqq89MwN+UwJmXuQWVVFSoLH0fdG0/hua3Hu2kv4ppp3Ie0mCeRuOpjVIpJzrBWF2D1os3d5lMCihQUKxOF1RnnMe9lW6xiD59QzJtzFwpe2YJ9XaPjOWCtzsfymBeQe+erKPz0NcTN0sLnWlrATSti46oPoZqglhYGO44B2dvCsaHSVUD2SzB9+g4yzujw8vLprOwD4TP1McwJ2OkiJi67+50+BotqIsJnBMCTdbnn2GmYGXoLTKYaKPt+2IcZMg2vH/0We1IfEhOcYK1CfuoGmO/yFxOUjQIF5RJOHihEOTSYEjhUTJMKT9oFoePeQAFmIy31CYx1N/C5I25ZEcwiMLyE4JDHsW73IWTP10AjJTztQhKDTadHY3HRju4DslvP4EDuQSBUi0B7xD+p8KSdYKIzKhAqy05s33vWZpFYW9Dw3e2IDb/XSbRBQh4GYPDQYeKxFI04vvVNfDT2NWxYqBHTlI0CBaUZ50xnAK/RUHt3TGePwUMxHOdxxPy9pBlvPbkXHxVUQxV6O0yrwmy+hHHxyCztxv/A0yMrYiB8dWuZeLE7k2YN9pjPorxrWNFWIzK0k6FL3IXgnL3YkqSDllla3dJcw6wKC7yC1fAWk9oHreUkzHVSyx6+PK/BkKrF1//4AqbmS6jd9wlyh8dh/mSJONDEDYItv416/H7//XhrwWQMFlOVjgIF5Uc01Ekb92xWoeqiRUIg7FbNRMQ+FIl575fAXPI3LA89gnWzf4etzuIPOwpJgxYrSl0JiQOCJXEEmtgHMEYq6wAtkowHYciMRMXcGUjIKOwmALtISwPqLOLxVVzARafxc4cgIGo+nr3tH3hpyt2Yvu0uvPXO3Guz0gh5aC7DB5tasGzNNVrLfZR+NqJUUA9TSVSqFU0XL7DTExH+yCTBb+Lh8ws8u/gpBOEgcg+cuVqE2q2IMoTlf+KekNgRLIk7MH3CSOcNzAdg1y3Dlop8LB51BGunuAjA7hbeGDZY2ltjrd2D1XHr0fbEf6Og6G9YhA0ID3oEq4qru7fOCPmxVqP4zW3AYpsPsD+hQEG5HcFh44HLDWhs6ZgOrdWnmDTcjvH+t7lZKQ94+qpxpzOrpt2KmIT9MVOZFWGAsdbZkxRHrGg07kUu7sfEuweJaS6wC0tpOsJRiBfZRHcqLMPHIUyjwuULjWgRk3jrq/q0iYnlGPiPkBqcF7Bvwx+hH/grzNQMZZd7EInvZCE1og769N04SYpy4/muBNv0O5Chu1d8jO+PkEQDO1HB0gKhTjCg1pZTcShQUKQcsJdw+nAZ6lUzEK6V8gsMwt0T74dK0mnrj19PdPIkxtGK8C5FcshsN6yIFnx76F9A7Axo7Y5Td/AMwLS417Gz0iYsKz4ov9qRK+WAtZ7D4SIzVM6uZ/0e5iPnxTcinmMRNTMEqKpHEwnKjcdHhy1VZ4VfOrO9zCjJ1LETwUgyHEPVFh18bDkVhwIFhRV6zAw8G30Fudv+iePNrWg27YR++xlEpyVgquQk9sCQqQlIY5/J/tNmFPOWBm92bvoQByKe7945yQvLvI7J7tKKECZ4K2LD/VCjfwvZzvwzzhCFJberI1eAiWnEY4jGTmzLPYpmNMKUn4PtpiikLXlQ+omNKEIo34S1WyuEx8TW2i+wafM+BD39S9wjvUoiZIEttRsusr8X0eDUv9XP4H9T1o6f30jxSAE0HePykmcKZfbzm8kl5x3jmsRTHPcTV5O3hKWP5+LzqsQ0RqfP3MNFJm/jymouiyd7QNMJrigrmXs0vYxdqQttx7isWaHc08+/xm0sqeHaxORO/FTGpd/Hl8H56z6p7xZoY5fP45Ij77HljVzJ5Z34QTzHU8XlxY9n55ZweTXiN7TVcGVbk7nI9u9n7bW1hKuRLFzfhC+3opDoY+d9ah+vEVx6WccoVgJd+4V+pJpQBDQ2+yZd+0WRSx6CIPomJCgEQcgGCQpBELJBgkIQhGyQoBAEIRskKARByAYJCkEQskGCQhCEbJCgEAQhG+07ZfkdbwRBENeCfbcsbb0nFAGNzb4Jbb0nCKLXIEEhCEI2SFAIgpANEhSCIGSDBIUgCNkgQSEIQjZIUAiCkA0SFIIgZIMEhSAI2SBBIYgbwr9hSJgg7CxVqyORYeQDmvQ/lCso1lqUZsZjnNBBs5CSXYpal0GrrqDWmIOUqLFip45FVEqOm9EAbyDNJhTrUxCbYbw60JcdPo/hQ1aXECQY/i0musZa+yUyE0JsdY9KQbbRjSDxhIz4QbelBHv4IPoqN6NKKhCFCkoDjOsXYXbBKLxXcgrmkqX4WU4SVudXOZ0k1uoCrJ6birJJa7GnsgpVlbmYU7ceuuf+DFMvzSxrtQFLM10IgyN8YPbsFEQFLUMhwrF2gUY6miEuoDjtGcxP/COyK90MItZcivVxC1Hgm4YS8ymUvPxz5MxNQ351HxPT/o4QRP+g8yiP/QBF1spqMmB1xnnMe9kWbNrDJxTz5tyFgle2YJ89RGcXrLWn8LXldkwKD7MFPbeH4zSdwrmeBih3w4rgLYKNqz6EaoKTMKd2eCExpCMheAF2tIVjQ+X/dBOY3RvTXt8P85410IgprrkE06fvIOOMDi8vnw4fj4HwmfoY5gTsxCvvfolGMRfR+1hPfoXc8tsRG36vdJTHfoACBeUSTh4oRDmbTlMCh4ppUvGOO+PhMxq/UJmRu30/qgX9sIWJ7NHdwi0r4gqqDS8hOORxrNt9CNnzNdBICU+7kMRg0+nRWFy0oxsh6YzH4KEYLh67RLwrIlSLQHs9pWIkE72MOG5Vv0DAT9uRME5cdq/a081SXVkoUFCacc50BvAaDbV3x3S2TbDzOGL+XnLZ4+Ebg3WGNIR+vRO7TY1sPh9Adu4wrJiv7f5u0SMrYiB8dWuRz6+VNWuwx3wW5V3jFLcakaGdDF3iLgTn7MWWJB20zNLqFZprYDJZ4BWsZraNnQEYPHQYYDkJcx0te24M4ri1HIfJEo53jn4DQ1IQKvV/xIZ9F8Q8ykeBgvIjGuqcGeoWVF20OPGjeMAzIBzPP+uJ3JfC4D/9E4x+6w3EjXUhJ45C0qDFitLuliMiglVwBJrYBzBGKusALZKMB2HIjETF3BlIyCiUDrwuBy0NqLOIx1dxARf/U4J432wav0Fh7nkEJa3CK7qx8MRQTHjol/Bii866hh/FTMpHgYLiChXUw1TSlbJWo3j1IqxsewJ/LtiNHYt+wtrwKc5NznYrogxh+Z/0aDliswruwPQJI503sIcPtLpl2FKRj8WjjmDtlEeQoi/uPWGRxBvDBrv08BCyYEWjcS9yLZMxZ+Z4Jia2tJbGBlzGHQhWM2uxn6BAQbkdwWHjgcsNaGzpmHyt1adwkJ0b73+bRKVYh+7bjEX6QbYOZZN5SmIGDKnTcUb/EXaelHha0m5FTML+mKnMijC4+YhZHDxw89GgXVhK0xGOQrwYJLOwDB+HMI0Kly80okVM4tfz1adNTH/HwH9ELy21CAfqYSzcC4smHKFjbu2cFvRrPHRP/3mErEBBkXLAXsLpw2WoV81AuNZLTHPkCurMJ9mCyJEhGBsVhVBXZr+jFeFdiuSQ2W5M9hZ8e+hfQE8fDXoGYFrc69hZaROWFR+Uu/e4uTukHLDWczhcZO7Xjy/7FK1VOPTZ+U5LYGv1fmzPvYLohTpo3LV8FYAia+IxZgaejb6C3G3/xPHmVjSbdkK//Qyi0xIwVXKCiCKEL7B27SfsM2xi8UugTR9itzt3CF5Y5nVMdpdWhDBZWxEb7oca/VvINrm5V8SOKCy5XR25XbA2NeA7ZjB/19DixGdkh9U94jFEYye25R5FM1uzm/JzsN0UhbQlD/bbx5d9Cevpwyiqn4zY0LvYhLNtsFz57CqYn3sX63RqZU5CZ/A/Um3Hz2+keKQAmo5xeckzhTL7+c3kkvOOcU3iKY77iavJW8LSx3PxeVVi2mWupmwblxx5j/iZe7jI5G1cWc1l8XwPaDrBFWUlc4+ml7ErdaHtGJc1K5R7+vnXuI0lNVybmNyJn8q49Pv4Mjh/3Sf13QJNXFl6ROf8973NlbVnruLy4sez9CVcXo09sY0VOa+j7pErubwTP4jnlAFfbsUijpdIe39FJnNZRSccxqty6dov9Kv3hCKgsdk36dov/craIgji5kKCQhCEbJCgEAQhGyQoBEHIBgkKQRCyQYJCEIRskKAQBCEbJCgEQcgGCQpBELLRvlOW3/FGEARxLdh3y3baek8QBHE90JKHIAjZIEEhCEI2SFAIgpANEhSCIGSDBIUgCJkA/j8DtdbDLDpEUgAAAABJRU5ErkJggg=="></p>
</div>
<div class="specification">
<p>Upon completion of the experiment, Mackenzie realized that some values were grouped incorrectly in the frequency table. Some reaction times recorded in the interval <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>t</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>2</mn></math> should have been recorded in the interval <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>2</mn><mo><</mo><mi>t</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>4</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>median reaction time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>interquartile range of the reaction times.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the estimated number of teenagers who have a reaction time greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>4</mn></math> seconds.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mtext>th</mtext></math> percentile of the reaction times from the cumulative frequency graph.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the modal class from the table.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find an estimate of the mean reaction time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest how, if at all, the estimated mean and estimated median reaction times will change if the errors are corrected. Justify your response.</p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A pharmaceutical company has developed a new drug to decrease cholesterol. The final stage of testing the new drug is to compare it to their current drug. They have 150 volunteers, all recently diagnosed with high cholesterol, from which they want to select a sample of size 18. They require as close as possible 20% of the sample to be below the age of 30, 30% to be between the ages of 30 and 50 and 50% to be over the age of 50.</p>
</div>
<div class="specification">
<p>Half of the 18 volunteers are given the current drug and half are given the new drug. After six months each volunteer has their cholesterol level measured and the decrease during the six months is shown in the table.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAj4AAABUCAYAAACCwj25AAAgAElEQVR4Ae2d3+8VxfnH1296qxbkigtiChc1mJRY2hqqTbwAjPSiJhoKF00vCIbSmGBSMFRiDPUHVbmiUElJjFGsRWNiQlMhgQuqCSgJRky9gMYY9MrKrz/Ab16j783zmTO7O7tnz+ecw3meZD+zO/PM8+M9P8/OfHZu+uabb74pnBwBR8ARcAQcAUfAEZgBBP5vBnx0Fx0BR8ARcAQcAUfAEQgI+MTHK4Ij4Ag4Ao6AI+AIzAwCPvGZmaJ2Rx0BR8ARcAQcAUfAJz5eBxwBR8ARcAQcAUdgZhD4XuzpTTfdFEf5syPgCDgCjoAj4Ag4AlOPAP/PNTDxwSv/R6+pL1t3wBGYKAT4QTXOfmXc+imMcdvg+me7Ds56+asNEvpS10QND26MI+AIOAKOgCPgCIwSAZ/4jBJdl+0IOAKOgCPgCDgCE4WAT3wmqjjcGEfAEXAEHAFHwBEYJQI31MTn73//e1hHZy3TaXYQWLZsWSj3f//7352d/t3vfhdk/PnPf+4sY1wZVe/vv//+cZngeseMAPXXyRFwBPIQ6DTxWbhwYRgkfv3rX8/RwjOTDgaicRD6d+7cOQ7VSZ0akMBEF9jQSf33v/9N5rlRI/F/VJOK06dPDw3b/v37i5UrVw4tZxwCJq3e94HBRx99VNDPpCaz1CP1QT/5yU8KePug//3vf6GOaiKNjj/+8Y9zRNNuab/SDy/tvC9K2RC3G57Vnyg8cOBALyak9Odg8M9//rMX/VZIXR0Qn/pYPfcZNuknnfoHZn1RDv7o1VhL+fODh7g+KKU/rn+xftpAzNPVlpT+uP5J9lD4c1aXpW//qcvGDN6fOnXqmwULFnDG1zdHjx6dw0DcxYsX58TN58OePXuCXfOps07X2rVrv+ESgdfKlSsDfufOnVP0DR9SLyibURHyqZfDEOXUl41btmzpTVaOT9ht61lOnvnkoXxy6auvvgptJFWm+EnfQ9uBb/369eGZ+zrK0Q9+lJtkoYt8r7/+eima57/+9a/hWfqJy+nzutiAPeSzdbtrWXfRn4OB+jPhVoIV3eToVxZkITf2XemE1AGNQza+6r5P/cKljcwc3qY6CC74rHrKM/dLly6tcruM76I/rn/Sv3PnzrKd0D6QbdtJqdTcdNEvnGPZis+RaUwIdvI80BvlCKIRUkBcFAJgiHLyi3cUoQAZhewuMoWTzavKk1NZbT6/r0aAemcHh2rO6hTKivrTB9Fp9yUrxx50Yf+kUpt+gc6WyUWqTGkzdLoiBj/44o5R6Qrb6Fce6hP56n6ggDt9YA51sYG+gny2LnUt6y76czDgxxyym9pfG/11dQCswYU2pnrSN/51+ql/+CxscnTD08Z/yZQO1UFNMpROqDoSv4SwPNx30S/Zqn+yh3hLOX1nF/3SJ//R2RV/i0GnpS69amJ5ANq6dauiBkJeXdlXw7yiIw7SK2VC0UsvvRReI+uZ11y8zrM8SiPkVTivG+Hh9fORI0dsctBNGq/ieC2qV9R6RWr3Rcge+3qd12nwIMNeNt8chRkPt912W7Fly5bi4sWLc5a8sFE2xK/wwQwsZD8hPmCf4uCRrXr1aF9Lwhe/NuQVtcUPmSKbF9+xjThRnb3iIaT8VQY8W5u5l82Eqhs2v+6pG8IHebEv8Km+CB/lJbT2prCwvNxjS1XdJd1ihz3gCBF++OGHxY4dO8o6ExIiG2wZW0xS5Rjrsu1Ism+EkPr39ddfF4888siAOywz0WZ+/vOfl2k/+tGPwv3nn39exg17A/7gvW/fvuL1118vpMPKxRZsPXHiRHHy5Emb1Ov91atXg7w777yzV7lNwnIwkIxr166F2zvuuENRQ4V1dUCCd+3aVWzatKlYvny5onoLm/Q//fTTxQMPPNCbvpSgKvxT9ZzxBDp//nxK1FBxcf2jjBcsWFCAPzZCjJdnzpwpHnrooaF02cxV/sPTC/521mZnRHG8fWYWpl+XmnFrthnP6pg5MzNnhshFPuIgzSbtrzW93pQ8+JAZzzCJ5/UyafbVs/IHBd/9gUe/DmQvScwc5QfPsgf/RPzClL3oi39xkt/KUD6FVenMoLFLusCAX46a2WKbfSPEMz5gA3byil+zcMnCTuTBp7TYfnQIb7AgXa/ptWwg23nmgtCJ3Fx7JUMhvsom4mQzfiEbv21ZKp9C6gO2Sz/5Le7k5Rk5yOMee0XCV/kJkWdtIo99rqu7yCW/6h56eRbFsoiXDVVlLEzicozrOc/4hg5RjIfiJyWkfJpIflF+EHlUXjxzH8eJz2IRMkd/cvRbHfAj0+qXSJUTPJSV2o/Sq8JcG2x+2wYVr3pE20Umoe0vxReHufqFM/xVGEg2ZYV+tQPFp8Ic/U11ALn4qn5Jtqb0xXF96ZfcNrrJk6MfPslN4a9+0vZT1Ad4bZxstGGufpsnVf9U5sjjot9Tn2bzxve5+uv8tzLFZ+Oa7mXDQG+khDoBKLQdDZ0wzgOIza9n2yjVaCXfAgt4dCTEMSBC5CUuRZoM2DR1SjYOmyTPxsNr/SANXvwTxc9xHvLHMpSXsCpddkoXGFob6QDQDSYpHK0OyYLPEtghw8YLX8une8nRM+WAXbJR8YR19lo+3WMH8kWxLuKRaXnEqzSLj03jHvm2nsXyY3vJgzw6bRFlJf0pzOO6S50Ho9TAZ2VJfmyDLWN4ZLMtL+Kxk7yWVLbSTd66emjzjuOe8mkifLQdKHmoe/hGyKU4K4s4yqGOcvTb/OBKW0npEx+2YrP6PsVXhW1twG/kx/XByidNdqou2HR731Z/DgbUuar+2ermPkd/Ux3AJouJ6gTym+p/H/qtT1a3ja+6z9Fv81bhr34IefRf6jds/2fl6L6t/qr6R1ujzFUv9TIBPOqorf4q/6WjLf7kkw1DLXXp1dTf/va34vLly8XevXvDazDF/+c//wm369atK1/5b9iwIfCK51e/+lXxxhtvhNdm//jHP4pf/vKXxX333Rfi4HnllVeSr71JO3v2bKHXfJJXFd56661VSbXxS5cuDa+8efXGdfDgweIHP/hBmedf//pXwdWW9ArxnnvuCVlZGnnmmWdKnNALXb9+vRCOt9xyS62aGAu9+ly0aFEpl//+uHLlSimH5SOWTbhYmrH0l7/8JSzb3HvvvWGJidf/ojp7xdM2jO23+dHXVIZ1+KTyI4+lkxQJ87q6yxIHWFJWLNPZZcCUzFzMYhxS9Vy+fvnllylVUxdHPQSfFStWlHUVJ6h7qpc333xz8EtLK9bJu+66yz4OfU8b3717d5Dz/vvvJ+WxBPbUU0+F/kz1JcnYIZLlls8++yz0LXF9sOJIk53Hjx+3SUPfN2HAMvCDDz5YaMvDsApz6gD/tUs9UZ9G/YBYan733XeHMiFH/1AKWmauwp++muVgxvELFy4Ua9euDZJ/+MMfttRQzV5V/1jWYrymzFUvWZbmP2JZGu6TqvzvQ0cvEx86gD179oSB2xq1ePHi8Hjq1KlQSBSULvGtXr06TJZotHTwrJ0Sx4DEQMvAklpjJz/AjJpefvnl4tixY6Gh0djWrFlTdjRddTOBovKsX7++FMHgCYbCRyETI+FYMmfeLFmyJHBKlkJN1Oi4GLyp5Fzot0TFpoJ/9dVXxR/+8IeCSYAG9zp7rYy+7jUR7CqP/JpsSgbPVf/CLszr6i71Eiypq9RFJux11BUzZFNnLGnw72tfhZU9jns6T9VPhdgh/GkH4M3+gvfee680UZ+FGMUeGHXspbLEjSagiaTOUbRF+h0NLrQ57dlLCY3rdYqna1wVBvQdt99+e/mjlEmD3RvZRV9OHQAb1Q9C6gekuC56lSdHv3jnK6zC3+p/9tlnw57RvsbDnPoX90fYY39QW/uGuc/xv4v8zhMfZpqWtm/fHgYR3vyIKAhmo9u2bSs38TKZsZtScYwZLA3pxz/+cchKPgakRx99tPjtb38rcQPhL37xizDLV4MjZLNhG+JXAh0LBSm7Ll26VIrA9nfeeadsWOqMxMAvfa5cwn/4mbHzhke0efPm4rnnnis7D2wCF0g4MqNWhaOjoYLWkSaVYEs+LptPgwYyuI+xYwMwdlBGd999d1DFGyiozt7A0OEP9lV14ujjbZtspqxVXsJEk4GUavLztsvWFZ7ZIClCDr+yIWFeVXeRw+Zk8sDLoGzrPjKEJ/hjd1fMNm7cGH7lUnYQsp588skwcVbHAG62TTJQ8it4WkllatsivvBPAZSb2uwLL7wQ+oo+NpuCl51g6F6bNilzeFSHsJE2yYRWb26HxRu/XnzxxeK1114rRcVvMrBBb1+xAQyYEMrOMmOHmyYMEKl6SJ8vevvtt3XbW1hVB6wCtXn1CzZt2Psm/aPQnYO//NIYwQ8vvfVTWtewqf6lNjdTH3gLx3g9LLXxfyj8tV6mUGtgek6FrGnDF6/tptbcWAdnTRB+5dHaoGTH+xWIZ90QPU3E/gfkwsuapNY7tXdD69/wsDZqCTtYFyaNkDVFydJeA6UTr4s1Zngh0rlShD7lUYhddn1U+bRWL2yRKRvg4V62yFfFK498lkxCsMVe9Nt8pNm1YnBUOWi/hPQpLzyiJnvFR2jLAD+4ZLN0WZ64nJAhfcLRYojfslHyLZ9swX7pJQ91RZTSj6yqukuacEUX8qzdYIkuLsXLB9lgy9hikipHZFg/rf+kxf7iG3omhbCvDVlfwUYkDOUv5aO2KJ5UmKOfMrPlTfnG+xbol2y55+rHphwbrGz5SGjrKjqFD2k8W4xS/ufqb8IArFV/rX3cx1jFdsDThuQj+lL+NbWZWFdf+mlvcd9o23KsV885+pvwlyzVAeoFbSKHcvTn1D9wRz/yuMiD3U2Uoz/H/674Y59suOm7h3Kixozr2/QyamZvmP3yRoDlDP2y5lcAb2wefvjhwv7imVmQ3PGJREBvw/jXz0mgcfcr49ZPGYzbBtc/3rHN8R8v/rYNdl7qmoTOdNQ28IqZ5Qv7up1NjMRp/8yobXD5jkBbBHjtTx2dlElPW/ud3xFwBByBUSLgb3xq0OXtDh9qYi+N9m+w94i3QGyEc3IEHIE8BGb91y4ozToG7v9433jMOv62DfrEJ6/fdi5HwBEYAgHvdH3iM+t1wP0f78SP7ktl4EtdQ3TmntURcAQcAUfAEXAEpgsBn/hMV3m5tY6AI+AIOAKOgCMwBAI+8RkCPM/qCDgCjoAj4Ag4AtOFgE98pqu83FpHwBFwBBwBR8ARGAKBiZ748GVcfSU09nHZsmVho5K+rhqnt3lGBvLafIG5ST7/CcZGKsnkm0B8CZk4p34R6LMuxJbF5Rinj+KZOoJPfdTtUdjnMh0BR8ARmGYEJnbiw0SBz2BXfYb99OnTA7hrANRRCwMMiQg+9HbkyJFwHpfOsEqwZUUxYGmw4rgJDtQTcaTBq6++qscytHnKSL9phUCqLrQSEDEzWdWENS5HsY6y3PiAKGc1cYSJ6pP0eugIOAKOgCMwHAITO/HhTQ/n8uiLybGbqXgGC4iztZhoNBEfeuO8LE5Y5rylvik+TXwUBxr2bfM0ykvVhT79iMsxJZs3Q5ospdLbxnH2E4cPMvlxcgQcAUfAEegPge/1J6o/SXw4kIGECcwo6dNPPw3i+zjgEEFdjvrokmeUmLjsIhxR0oRDXG4ff/xxU5bW6RwMy4czORSzr0MwWxvhGRwBR8ARuMEQaP3Gx+5V4Z5fubz2J2TCwqt5lpq4mLyISOOUanjjSzwKjx8/HvLbzp78LEtpn0wfv67Pnz8fTjWWXoVaMuMEZNlMHP4Sp3Sdh0Q+8bVZmkjlsZhanPDXYg8ewl46sY19UeSL8be64jKyOlWOwgJe+Ytc67N4KGf0CSPxI8uemqw6oDJkGYk4CBnIl5+SoZOwpYswpy7gE/KFRWw3coUVPNzHdlid9t5iSTyyeXPIESfI4pLdFj90YJfI+ogM8uG/KOetpXg9dAQcAUfAEchEID5RVaeXxvH2mRNh4eO0a06G5bRWnjmhVif0cs+prSJOk+YZfi5Od7Xp4iMknhNYLSm/TmLWidT21GJ0Y4dssPlT9+TFzpgkhzT0YS8nBWMXpzNDwoA0EbqtPbF8yRU/YZwHPfgKoZtneyq69MKDPGwiDrvgFT7gG5/OjS54hI9O+FU5yj6dtKtyJYR0Km54iP5gg2wFE+zANnSIVIakc4GvfIWHZ8nABuyXrZJBKDnyNVUXkCPZ8CFLdUrPKkv5LR3YwSWKy5H4uNxSPOizJ0uDM3aJpBdd+Iu9Vm9Kj/JOWwhe46Rx68f3cdvg+me7Ds56+ds2OFATcsChk4/5eCZeFPPQodt0dfriV8ggy2BhJxTcI18DsnhjnZJJmEPYEw805EvJgc/ypnhie2L5ymNti/PwbO2PZfAMj8XHytO9+PRMGOtq4tHEB74u+phYoBNKlaEmBrIRfJks1VFKDvzWN+pJjBGTCk3CmIDU6YnLGv9t2cf6eE7xoMNOWplwYZcmkqoPcb22/lu/bPy03ePHOGnc+vF93Da4/tmug7Ne/rYNtl7qynyRNMDG5uGDBw+WSx/79u0rli5dOsDHpmaWKOyGVU5Eh2ZhczCYgA3LOVxgltp4bfERiMIO/Hbs2KHoziFLLUePHg02LFq0KCznaWkqR+jy5ctLNpXhunXryuWgDRs2lIe/ijHll9IIJaeuLrCECWGzlp4OHDhQXLlyJcSfPXt2Tv0KkSP4w38lsgQmG1Tfr1+/PkdbnS9zGP3BEXAEHAFHYGgE5m3is3v37mAsnT8DAYPQW2+9NccBBlUGqPjk88WLF8/ha/vA3oo2A3Zb+X3y859px44dC4M2A/eaNWsKYVenh30nJ0+eDHtl2C+zZ8+eOvbsNDZ+X7hwoTh37lzxwQcfFFu3bs3O+8knn5R7qFSGp06d4mfXnCtbYFEUklOXZ8mSJSE51qPPFaQmknXyuqZR1ymH2A67d62rbM/nCDgCjoAj0A2BeZv47N27t9i8eXM5CDAIxZs333zzzWLlypUD8QxU8ZsQNoPqF3Sd62z45Zd31ZsENqSOiq5evRomDZJ/7dq1cGs3/CpN4bZt28J/s2mw3L9/f6XtykNoZXJ/4sQJm9zpno25TKggygq89dakSiB4Q9jw/PPPh08S8EwZrl27tsA/2QpvvOm4Sq7ic+rC6tWrw4QL25nwcvE2TJvtN27cGDYiawMy9vCWrIricqziO3PmTNCFHi7qO/+OLj3acF2Vvyp+1apVVUke7wg4Ao6AI9AWgXjdvWkdUHtw4NOeCfZP8MxFuvaG8KwNptpPIj5CNnra/Q08awNqbBcySScf+y2sDuVRutWh+1gez6m9IMRLDnuNIORLjjbEkkYcvFCMgc1DGvY25UEOvkmXQvaKsD8kJSMo/85GyWdfiXyrKyPxi4cQncSjCx+EBfHYQXyKVL6yHxn4bfcGkVc6kGfTY7xSOhSHHNlVVRfwH3vlD/ZZ4ln+Swbp1g7K2j5jL0SIXC7hQfnIJu3rwXd4U3qQI37hHYSbP8hGh93zZZKn6hY/xknj1o/v47bB9c92HZz18rdtcKAmjAIcBoDUoMmgwKAD0bkzANiBMiSM8I82mzK4TQIx0IGTxUDYxQP3JNhrbdDEx8b5/XAIUC9pEzcCjaJfaYPLuPVj67htcP0Dw12bKjQ0r+M/XvxtG5yXpS42pLLc9MUXX5QvpFhe4NJ+i8OHDw9sai6ZR3SDbr4O/cQTT5TLESNSlSWWZTc+WHfp0qWSH+yI076VMsFvbmgEWB5jqe7xxx+/of105xwBR8ARmG8EbvpuFlTqZePxtz9Oyqhebtgvwn8oXbx4Mchjv8j69euLxx57LDyzkZcNtPG+n16U1whh/8ehQ4eCbXxQThtga7KMLAlbdu3aFfaHMNmB2PO0adOmgQ3fIzOig2D2rqxYsSLkpFzZDO3UHQHaIDiyR2j79u3dBU1QzlH1K7kujls/do7bBtc/mrFtWurgrJe/bYPJiU9uQTqfI+AIOAKOgCPgCDgC04IAL3aSZ3WN4o3PtIDidjoCjkD/CPivTX/jM+t1wP0f7xs3ejXKAJqXPT79d6Mu0RFwBBwBR8ARcAQcgfYI+MSnPWaewxFwBBwBR8ARcASmFAGf+ExpwbnZjoAj4Ag4Ao6AI9AeAZ/4ZGDGfy0tXLgwrA/qK7wZ2ZxlyhHgv/xYEx6mzPmCMzLuv//+qUPD1vupM94NdgQcAUegAoHOEx/+9ZrvjGhCQKgjAip0TW00/2L/6quvToz9dkBiUOUCf45dGGaQnhgHWxiC73wqYRR0+vTpocVSJjt37hxazjgEzHe9p0+hLDXhpE7HZcu3v2y/A6+OIukTI7WxqvZE+ijPAAQL6o6OgEn5Bg9HvoBB3ZErqbxNcXX68R196nvQH5dTk/yq9FQdSB1rgz6NPZQDNvVJdf6n6mBdObWxK+V/jK1wj0PaxbCU0p/CHz2jaAMp/bH/1kf9sLRxWffx5yhzvi7J14T53D5fGebrxxCf9yfvNHxeny9Gt/0SMn5Nkn/xl5L56rOOg5iUL1HHdWsUz5RJ27JsY0cfZY59+kJ5G90pXsq2L1kp+XGc6n0c3/YZHJsIv2ib+nI59zH+POvYGPhU59UPVenI0a+8+lp6rFvpanttZJI3l5/jVnTMSVV/SnuHB1u4z6E+9IMNejmWReVEnUR2U7+Toz+uA8LayiYOG/BbdYBn2VOFRY5+8jbhjxxbBxkH+9If+59qA/HX/dVG+2gDsf4U/mCk+FxMyZPDG+tP+a/yVRvIkas84h3ojZQgxlSIMamCpkCqGmpKzrjisJOCa0OqXJPinype7AMVhzJsagRxPn9OIwCWw5Y5ZUW59EEMOH3JyrFH9T6Ht44np1+J8zOQka+urZJGX9REbfTTv1X9kNM5eF1wybGBAV7+wp+qe+rw7WSgyX/S+9Avv+NJBnVSdlfZkqM/zit9dnLHj26dhwc/achuwiNHfw7+sY06FzFVVpY3R7/l5z6nDTD552qiLvpT+HdtA130V/lPPOO42mmT70qXDZ0mPlS8OqCpPCiwHbQOZFTlsDxUXJuuWR4NCT46NhmMw5p4EYcdxEHqEIjnHv2yQzyARZy9BIoNmTggW3ySJfurbLQ2SJ7lVZy1TzoILWbiTYVgA39MaoTgJoJX+OI/ukXgQkUWxoTKqzz4DI+1DxnChzy2I0I2dghrK5O0uAzj9Dp7ZTdhjKvF3uILpip/m1/3+Cdb8ZF7Ec/W/9hW+Kyv8Ns6STr+xOVa52MsT/aoDNChS/WxSp7FBAxUj+GHbDkiE13EiZBP/LDURQZtkHzgERNp1FP8sfbGfHrO1Y9Myg8ij/CVHIVdcMm1QTqq9GNfXJ+Upy7sQz91iDZA21ObAgvimn5stdGPbModX9Uf4VtVnUC26nQVBm30IwP+qvK3OrAPXuFh0+x9W/3krfJXcpWeY2cb/VX4Sy9h2zbQRr/0yL+4D6D+MenpasNAj5ZjHDxNlYxO2jZOgCSfLSDSGVzhxTEaj9LhpRPGOTurw2HikceFDOJE2EVeZJJOp8gzMkTkabIfu2zj5j62v8pGfCHNEjZbnZIPD4UrHJRHfug5DqvSVRGki0YJrhocwAVdIp6xDRvAi45GeSULvPAJDLiHYvvRoQ4KrElHJoRM0kVKRx+EXOlsslcyFIKz8hLHPXF15a+8hNiIbaof8lk8yMJn8FN9Ay8R+eFRfp5JF07wYZN9bvLR2oNei10sC/lN8oQJOOOfrYsqR3zjggd9KpsYD/ndNgSjtkS94YpJ/iATe1XPYj77nKNfZSffyYP/KeqCS44NVldKP7YRj99gw72ebd7UPXxtCP6U/9hAvZFu6ov6lzr5ufqFLfy0G2uD0mwcOsXbh37JQGasR2kKhYXav+JTYa7/Nm9VGxAP9cD2LYpPhbn6hbEwrcJAfCldqbhc/TZvyn/GIvULXW0YaAk5xsFD51NHqQ6afBZECswOIlYevAxeltTocVykTl/P6hT1TGg7ep7RW2e/Ji7oEwlga3/KRvjFq7yEsc4YixivlB9WXlW6dMs/fLc4aqDWQI4dFk+rQ7Li9BQ+6ohtft3HttJJ0FlSdjHV2Rvz8oz98pXnWBdxcflbOZr42Th7H+MTy0/lFz4akMljO6cmH8GGhq381p5YFmlN8mSzrc/kk502Xm1MZaM6YG3ocg+ObQib8cvaFuenDsNjJ2oxj55z9CPLDuDkwX9sIbTUBZccG6wO6bdx0msnfMSBQdPg24d+bKFuol9lg96UrdZu7tvqp/6jx8qW/4SW4NFgaOPtfVv9Vq+VY+9p19iYQ231N7UB9eVx/1xlS1v9KfytbJWFjau7b6s/5T822X7B2mD72Co7ZEPn/+r67LPPsjZPNzHddtttlSy33nrrnDROKofWrVtX/kfBhg0bwunlcxijhzodEWt4PH/+fAhz8sU2puSl4jiEct++fQW72Lk4wFUn1cPP4ZTf9hWp3NVx165dC4mrVq0K4Ycfflg888wzJV7oha5fv14Iz1tuuSXEVf2J04UPB8vqPwsOHDhQXLlypRTx0ksvhf/84L8/duzYUcZz88gjj4RTx/XfOXbXfp29c4S0eKgrx7NnzxZ16aiJ/beqU/nF/+WXX1rW8r7Jx5MnTwYsKSv+Db7pP1aa5Elx7KfK0cbr/vPPP1e2eQ/5Tw36Fw4Mlj0pI/ivs6eeeiq0f9XlFF9OHPUVHDlsV3WafPfee+9A/c2RN2qejRs3lv3FPffcU/z0pz8t3n777VGrDf81+sYbbxT79+8vy4b2zGHK9Gd9Ev3h7t27g8j3338/hDfffHMI1c9ZfXfddZd9HPk9/deDDz4YsOhbWU4beOGFF8Jhxg888EDf6oO8FP4jUZQQWuU//yFLO9XYQ/uEaLPvvvtuQlI6qtPEh1PVMSwm/q2w6t8/Y94uz4sXLw7ZTlxAfgQAAA2iSURBVJ06FSYFTAx0dZFXlWfJkiVVSb3Fv/zyy8WxY8dCAVKIa9asKRv5MEpeeeWVYsGCBQWdIcTguWfPnhIn4UW68GyrT/hIlkKdbE+HwOBNHeFCf0xM7L7++uvwmYDnnnuuYOCB6uyNZfTxbCebXeSRn4mrJXXKd9xxh40u75t8ZEAHy4sXL4bB7b777ivzpm6a5KXyEKdytPbr/s4776zKNtJ46gttQwMrkz47MY6Va5IZx7d9ZvBWPVaIDPU1ak9t5fbNrzZ76dKlAdHf//73B+JGFaF6YuXbHz42fpj7eOJL26B/e++990qx/Hs5NJ91lj7u9ttvDz/i0E3/1dfYl9MGwB++P/3pTyUOo7iJ8R+Fjlhmnf+kqX0S0j4hxcWyqp47TXx+//vfh19ZFL4agH4xWUXMwOi44NG3AFIN1uapu2eQWbt2bbFt27ZClZ3vJ0h2VV70X716dU7yiRMnwjM+SJYY+PUEqcMl/fDhw0rODjWYE545cyb8ilVmfHjnnXfKAlNHr3R0M4vNJXDm7Qq/xuw3hzZv3lwwsVCjFB9yhafePBGHrVSuOlq9enXofFT+4GvzWTy5F9aSyVsM6fjZz34Wvseh8qmzV/nbhqnylwx+OVNPhQ/26pso5IM0kVEeG5KfXyAqa/I/+eSTBT8O1Gng24ULF8psdT5ih74PQ/nQ0V++fLnMyw11CdvAkKtO3pyM0YPKcdeuXUEeMrlnIkW5QPJdZdq2XkYqax+pmy+++GLx2muvlXz2VxzY0CZUVthL3cXevicmKvuq/irGpTS4p5sq/Wqz4KQyAQ9w+s1vftOT9qLs12P/mcwz8VCdQSF1nzbw6KOPDq2f8lW/izDdP/TQQ6XsLVu2FLxh1tjCmw/eOPX55qMKf/lLyI83UV9v25ragPQdOnQo3KqvUvywYQ7+0jGKNpDr/9A2xGthWgOL4+Nn1hVZa4Ofi81u7HfQui8ha26kEWo9krVo1tHZQ6C88Rqp1nVJ114D6Scva7k2r3SShnzStN6bkoXt8HHF8qWHeMlChvZDEIeelFzlJQQL7AAX1iGFhfTpWX4Qgic4QaxvEpci66fyYxc+k2YJbLBVvqDX8nAvW+BBr0gbGOWz4glt+cf5LHbgIOxUJsTJHuwnXmXYZK+1wZYBfnBJrnRZHmFvZXCPz8pn8Yn9R77wRq4IuZaXNPlDWpynzkd0xO3K2k39kC5whJrkyTfyxRTrs3XI4qm8wiqW0/QMBk1k/RZmhLZOsp/E8mGv2kyd/Bz9Nr8wBjtwEFEWai/IJN3WGfGlwhwb0IU8lRl5eLZ1QOVNGhd40MaaqC/92Ajuo9CPH7HseD9P7H+fdaAJf+qaLRthQBjbGZdHDv62blvZtg0gFxviuFhf/JyjPwf/rm0gR3+u//hGWaks1D/FPsfPsuEmEjR7ImTGF0XZZL/vAQFmtZs2bZqzh4FfGLwJefjhh+f8kuhBnYtwBHpDQG9Xn3766VYyx92vjFs/YI3bBtc/3rHN8R8v/rYNdlrqatXjOfMAAryWZvnCvkZmcyZx2ncxkMkjHIExI8DSCnW07aRnzGa7ekfAEXAE5iDgb3zmwDE/D7zdYY2c/Rnav8EaNW+B2GTp5AjcaAjM+q9dynPWMXD/x/vGY9bxt23QJz432gjj/jgCE4iAd7o+8Zn1OuD+j3fiR7eoMvClrgkcJNwkR8ARcAQcAUfAERgNAj7xGQ2uLtURcAQcAUfAEXAEJhABn/hMYKG4SY6AI+AIOAKOgCMwGgR84jMaXF2qI+AIOAKOgCPgCEwgAhM98eELtvoibozdsmXLwkYlfdkzTm/zjAzk8R2dvoj/2GIjlWTy7Z6FCxeGuL50uJxvEeizLsSYxuUYp4/imXqDT33U7VHY5zIdAUfAEZhmBCZ24sNEgc+g20+VW6BPnz5tH8O9BkAmGOTPIT7IduTIkXBuls6aysmX4mHA0mDFp8Q5UE3E0QP2KAnF2zyK87AdAqm60E7CXG4mq5qwxuUozlGWGx8Q5bwqjhpRfZJeDx0BR8ARcASGQ2BiJz686eFMFp13FLuZimewgDgDi4lGE/FBNk4u54RnzsDpm+KT2/s6ULFvO6ddXqou9OlTXI4p2bwZ0mQpld42jrOnnn322TD5aZvX+R0BR8ARcASqEfheddL4UvjAHwMJE5hR0qeffhrE93W4XZejPrrkGSUmLrsIR4k04RCX28cff9yUpXX63XffHT5wySGUfR/C2doYz+AIOAKOwA2CQOs3PnavCvf8yuW1PyETFl7Ns9TExeRFRBqnecMbX+JRePz48ZDfdvbkZ1lK+2T6+HV9/vz5cNKw9CrUkhknv8tm4vCXOKXr3CLyia/N0kQqj8XU4oS/FnvwEPbSiW3siyJfjL/VFZeR1alyFBbwyl/kWp/FQzmjTxiJH1k6QRpe1QGVIctIxEHIQL78lAydxC1dktNUF/AJ+cIithu5wgoe7mM7rE57b7EkHtm8OeQoEmRxyW6LHzqwS2R9RAb58F+U89ZSvB46Ao6AI+AIZCJQdXppHG+fORWWU045HZqTcjkllWdOEdYJtdxz0qqIE6t5hp+LE3VtuvgIibenEROn/DqJmXR02hNq0U2cbLAyU/fkxc6YJIc09GEvp79iF6dDQ8KANFFsTyxfcsVPGOdBj07+RjfPOoUbfumFB3nYRBx2wSt8wJeTay2hCx7hA4/k44fs00nPKldCSKfyWpm6xwYrCzuwDR0ilSG6uMBXvsLDs2RgA/bLVskglBz5mqoLyJFs+JClOqVnlaX8lg7s4BLF5Uh8XG4pHvShV/hRjtglkl504S/2Wr0pPco7bSF4jZPGrR/fx22D65/tOjjr5W/b4EBNyAGHTj7m45l4UcxDh27T1emLXyGDBIOFnVBwj3wNyOKNdUomYQ5hTzzQkC8lBz7Lm+KJ7YnlK4+1Lc7Ds7U/lsEzPBYfK0/34tMzYayriUcTH/i66GNigU4oVYaaGMhG8GWyVEcpOfBb36gnMUZMKjQJYwJSpycua/y3ZR/r4znFgw47aWXChV2aCKk+xPXa+m/9svHTdo8f46Rx68f3cdvg+me7Ds56+ds22HqpK/NF0gAbm4cPHjxYLn3s27evWLp06QAfm5pZorAbVjm5HJqFzcFgAjYsAXGBWWrjtcVHIAo78NuxY4eiO4cstRw9ejTYsGjRorCcp6WpHKHLly8v2VSG69atK5eDNmzYUB7SKsaUX0ojlJy6usASJoTNWno6cOBAceXKlRB/9uzZOfUrRI7gD/+VyBKYbFB9v379+hxtdb7MYfQHR8ARcAQcgaERmLeJz+7du4OxdP4MBAxCb7311hwHGFQZoOITyhcvXjyHr+0DeyvaDNht5ffJz3+mHTt2LAzaDNxr1qwphF2dHvadnDx5MuyVYb/Mnj176tiz09j4feHCheLcuXPFBx98UGzdujU77yeffFLuoVIZnjp1ip9dc65sgUVRSE5dniVLloTkWI8+V5CaSNbJ65pGXaccYjvs3rWusj2fI+AIOAKOQDcE5m3is3fv3mLz5s3lIMAgFG/efPPNN4uVK1cOxDNQxW9C2AyqX9B1rrPhl1/eVW8S2JA6Krp69WqYNEj+tWvXwq3d8Ks0hdu2bQv/zabBcv/+/ZW2Kw+hlcn9iRMnbHKnezbmMqGCKCvw1luTKoHgDWHD888/Hz5JwDNluHbt2gL/ZCu88abjKrmKz6kLq1evDhMubGfCy8XbMG2237hxY9iIrA3I2MNbsiqKy7GK78yZM0EXerio73yLR3q04boqf1X8qlWrqpI83hFwBBwBR6AtAvG6e9M6oPbgwKc9E+yf4JmLdO0N4VkbTLWfRHyEbPS0+xt41gbU2C5kkk4+9ltYHcqjdKtD97E8nlN7QYiXHPYaQciXHG2IJY04eKEYA5uHNOxtyoMcfJMuhewVYX9ISkZQ/p2Nks++EvlWV0biFw8hOolHFz4IC+Kxg/gUqXxlPzLw2+4NIq90IM+mx3ildCgOObKrqi7gP/bKH+yzxLP8lwzSrR2UtX3GXogQuVzCg/KRTdrXg+/wpvQgR/zCOwg3f5CNDrvnyyRP1S1+jJPGrR/fx22D65/tOjjr5W/b4EBNGAU4DACpQZNBgUEHonNnALADZUgY4R9tNmVwmwRioAMni4GwiwfuSbDX2qCJj43z++EQoF7SJm4EGkW/0gaXcevH1nHb4PoHhrs2VWhoXsd/vPjbNjgvS11sSGW56YsvvihfSLG8wKX9FocPHx7Y1Fwyj+gG3Xwd+oknniiXI0akKkssy26XL18uLl26VPKDHXHat1Im+M0NjQDLYyzVPf744ze0n+6cI+AIOALzjcBN382CSr1sPP72x0kZ1csN+0X4D6WLFy8GeewXWb9+ffHYY4+FZzbysoE23vfTi/IaIez/OHToULCND8ppA2xNlpElYcuuXbvC/hAmOxB7njZt2jSw4XtkRnQQzN6VFStWhJyUK5uhnbojQBsER/YIbd++vbugCco5qn4l18Vx68fOcdvg+kcztk1LHZz18rdtMDnxyS1I53MEHAFHwBFwBBwBR2BaEODFzsBZXaN42zMtgLidjoAj4Ag4Ao6AI3BjIzAve3xubAjdO0fAEXAEHAFHwBGYFgT+HzIA5bRldNhkAAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>Calculate the mean decrease in cholesterol for</p>
</div>
<div class="specification">
<p>The company uses a t-test, at the 1% significance level, to determine if the new drug is more effective at decreasing cholesterol.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the name for this type of sampling technique.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of volunteers in the sample under the age of 30.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The new drug.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The current drug.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State an assumption that the company is making, in order to use a t-test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the hypotheses for this t-test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the p-value for this t-test.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion of this test, in context, giving a reason.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows a probability distribution for the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}(X) = 1.2">
<mrow>
<mtext>E</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1.2</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.18.09.png" alt="M17/5/MATME/SP2/ENG/TZ2/10"></p>
</div>
<div class="specification">
<p>A bag contains white and blue marbles, with at least three of each colour. Three marbles are drawn from the bag, without replacement. The number of blue marbles drawn is given by the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>A game is played in which three marbles are drawn from the bag of ten marbles, without replacement. A player wins a prize if three white marbles are drawn.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability of drawing three blue marbles.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the probability of drawing three white marbles is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{6}">
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The bag contains a total of ten marbles of which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> are white. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Grant plays the game until he wins two prizes. Find the probability that he wins his second prize on his eighth attempt.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Two events <em>A</em> and <em>B</em> are such that P(<em>A</em>) = 0.62 and P<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {A \cap B} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩<!-- ∩ --></mo>
<mi>B</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> = 0.18.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find P(<em>A</em> ∩ <em>B′ </em>).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that P((<em>A</em> ∪ <em>B</em>)′<em> </em>) = 0.19, find P(<em>A </em>|<em> </em><em>B</em>′<em> </em>).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The weight, <em>W</em>, of basketball players in a tournament is found to be normally distributed with a mean of 65 kg and a standard deviation of 5 kg.</p>
</div>
<div class="specification">
<p>The probability that a basketball player has a weight that is within 1.5 standard deviations of the mean is <em>q</em>.</p>
</div>
<div class="specification">
<p>A basketball coach observed 60 of her players to determine whether their performance and their weight were independent of each other. Her observations were recorded as shown in the table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>She decided to conduct a <em>χ </em><sup>2</sup> test for independence at the 5% significance level.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a basketball player has a weight that is less than 61 kg.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In a training session there are 40 basketball players.</p>
<p>Find the expected number of players with a weight less than 61 kg in this training session.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a normal curve to represent this probability.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>q</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that P(<em>W</em> > <em>k</em>) = 0.225 , find the value of <em>k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For this test state the null hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For this test find the<em> p</em>-value.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a conclusion for this test. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>On one day 180 flights arrived at a particular airport. The distance travelled and the arrival status for each incoming flight was recorded. The flight was then classified as on time, slightly delayed, or heavily delayed.</p>
<p>The results are shown in the following table.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAvQAAAEJCAYAAAD7OLNMAAAgAElEQVR4AeydD3yT1b3/PwnIEMsfq9zxBBlIK3+2Is52MP9cTYu0KlNZK+BU0ppeL2yg/Mal7cqFzU0m16a3TCYb6G2lRRkgyVDGtIGE6kUdmDCVOkhtuYAlwYGFNpW/Tc7vdZ78e5ImJf2XJuk3r1ebJ+c5f77n/T158n3O8z3fI2OMMdCLCBABIkAEiAARIAJEgAgQgZgkII9JqUloIkAEiAARIAJEgAgQASJABEQCZNDTQCACRIAIEAEiQASIABEgAjFMgAz6GFYeiU4EiAARIAJEgAgQASJABMigpzFABIgAESACRIAIEAEiQARimMDAGJadRCcCXSIgk8m6VI4KEQEiQASIABHoKgGKQdJVclQuHAJk0IdDifLEFQF+UeVGPV1c40qt1BkiQASIQNQSoImkqFVN3AhGLjdxo0rqCBEgAkSACBABIkAEiEB/JEAGfX/UOvWZCBABIkAEiAARIAJEIG4IkEEfN6qkjhABIkAEiAARIAJEgAj0RwJk0PdHrVOfiQARIAJEgAgQASJABOKGABn0caNK6ggRIAJEgAgQASJABIhAfyRABn1/1Dr1mQgQASJABIgAESACRCBuCJBBHzeqpI4QASJABIgAESACRIAI9EcCZND3R61Tn4kAESACRIAIEAEiQATihgAZ9HGjSuoIESACRIAIEAEiQASIQH8kQAZ9f9Q69ZkIEAEiQASIABEgAkQgbgiQQR83qqSOEAEi0DMEvoQuNxl8q/Z2f4pclG6vQV2rU9KUJ38ycnVfStLDOGytg3F7KRauMaMtjOzRl8WJ1roabC8twhpza/SJhyC6semQK+p2IXS27lNvM5cimdeXXApz96uLQoYkEhEgArFAgAz6WNASyUgEiEB0ELBVoWBOOpSLNuGIn1HfFfFaYV6/ADPmFGCPoyvlo6BM29+x/sF0zCk4gFjtQhRQJBGIABEgAt0mQAZ9txFSBUSACMQngSSotCfAGHP/XYLVVIVCpQBbVTGWbKuDa55+DLIr68FYPSqzx8QnCuoVESACRIAIRDUBMuijWj0kHBEgAtFDYBCE1CewsrQAStigX1GFmhZu0gdx60AL6owVKEpX+Nx20otQYayDyzGFl7kNaQU1YvcaCtJwjSwdpR63ldY67C7NhcLr9jMFuaU6mG2X3TgkbW7/G8y6UuQqXC5Citx1OODN58rutJmhk9bHXYd2e2RxV8ndfyqKkO5p009edx7pG3dduSYNBQ08sQYFaUPdbidtsOkWiv1O/q/tqF6e5WKQVYE68Q6oBXW713jl5W5NitxS6Mw2OOFEi3G5q9+K5TCKfN2NthhRJPYxDUXGM67Ezsosld/vmLsOGVFR5JZVpkB6UQWMdS1+ueCnF66TatQ1k5+NPyT6RASIQJ8QYPQiAv2QAMAnXelFBIIROMG0qiQGJDGV9kT7DFdMTJMEBsxh5ZYLjLHA/A5mN5UxJXiewL9ZTGM6KykjPa9kGpOdMccxplWnBCkLJqi1rNHBRfK0KS0vOc4sZxYxH2PMvp9plEKQ+lKYWnuMidlCtpnCVOWHmL09BcasWqYK7F+ShpmuXGFW7YJ27QmFBtbMLrFG7SImBJbjn4VFTNt4iTHHYVaeyeVNZYWG0+6WHazZUOwqpyxjJrujA05SmT2cJLr0yr2Aaa1XxPodjVqmFiT8PPIJalZ+uNklQ0hG7nJi34OBojQiwMTvA3EgAr1JgGbo++Q2iholAkQg9gmcRpM92OzseVj2vg0+9y4UGtAsuuychUkzC8AuFCzXoc7J3XQ+gUmjFDEkaUy4wvZiWWoCnPUGbKioBZRlMNkdYOwSGrWLIACwvXcUp6TrcXlpZTG0lma/fNAfQO1XXLaLqNtWioIaG6B8DgbrJTGf1fAclKhFxeINqGlpQ0vNBiyuqIWg2ojDYpsO2A9vhEqoRdWKzTggnSn3KE7IRuUVEzRJohDQmOxg9cuQOtCTgb/PgsZ0FoxdQd3KOzHMeRTVG3SwedMZHI1aqMXOfY6jpy4D8nG4e97dAMzYVP0ZXHPkTTBV62GDgMz5D+D7CeiazFLRvMdnULP2BVTYUqAqPwS7qK9mHC5XQ7BVYMVrJrTwJwduRkAmig2NcDAGh3UfylQp3progAgQASLQVwTIoO8r8tQuESACcUpgEEaN/57LAC+ZgUm5pdiuM+L4Lb+G1cHAqtWY0MGVVz5BjWpuLG6+B436HdBVrMSTOetg47TON6H5vNSi5wauCrMnDAMwCKPvyMBMP6qnUfveQQBJUD2jRoYwSMwnZPwKe7nhan0BGcMu4ouDH4n126ryMHnoAMhkAzB0ch6qeKM2PapNTX61hv0hMxsPf38EgIFISBgMyCdBXW0Fc7yK9EYjdLpXUfzkYlSInbPjdPNFAIORfPf9yORNb9oDE7+ZaPkM1ZvMAO7GvLvHQY7zPSdz23Ec1PK6a1GVPwVDRZej4ZicX+FiIspwEaeO1bt0oFqAZzJGg6tQLtyB/NyHRF2HzYQyEgEiQAR6gYDfXEov1E9VEgEiQATilMBIJA4NdgkdhNGz/xM7N16HZXklqKkqwJwqD4JMFGpfwsrsSUjwJAW+t9aiYtFPkF9VG3gGGJKI4UOkdwNDMGrEdaJxKWYeORZT+Iy56NcOoO2fOPoB/yBOo7evT0w5i+OHOgq3eQ6nzl0IUbbjZOG2cRglFRctOFLxc2S4jWX/0kMxcvhgMUk+4WEUFaZCX8JvJv4f0rAHm2yAoH4MWck8z5c9J/Pp4zjk4eUvkOuTrQnnvrmM4U2nxc/CqBG4zptPjiHDEzHE+5kOiAARIAJ9Q8DvUts3IlCrRIAIEIHYIeA8+il2cwNQSMa4UXzGO8hLLiA190XsZQ7YLXuh1WrxpkYFAXqU5PwS2+r4THSwF3eR+Y3LmFcWoly7CybrJVwxaTo0yYPVJKYN/BeMv4sb8+dx6tw37qg8gbmvxYhRfBYdcLn+eKL6eN67Hr1nyMjhfsaus247lojGfCYKy9/EDpMVDq/bjlSuRKRlZUIQ3W6qoRfdbVIx/4l7MFr81epBma8bgVHc5QdKl9uQN6qRp//rkS0MxtDEkaKAtk+OSdyenDjf3ITzUtHpmAgQASLQBwTIoO8D6NQkESACsUiAR0KpRtlv10DPfblXqaAcFuQS6jwOXf4UyHiklOUG2JOVyM7ORvZPHsEDouHYUd9b0Wg5KmYQxk9H1uwHkfrt03hfu9s76d5R6fbnRiLl3tu58wr0m7aiRox+40TrkUp3lJm5qKgb4jaegYayP6DqCPdavwyb8deuiDeB0WbaNxJmihOtjfU4xHMLt2B61sN4JPUGfPX+X7Cr3Qy5HMOmzcZSHiK0RIU5JWZAyERWWqK7LY/B3wMyD7sVWfNTxUg9ZWu1rv0FnCdhdEfnURQZ0SJxA4J+KzbWnBRvjpy2j1BeudPlihMmBcpGBIgAEegVAr254pbqJgLRSoCi3ESrZqJBLk9klCBRT9zRTwTVRnaYR1oRX578nkgqHUW5kUaqucAs5XMk0WB4lJuvg0eBuVPJlDwKi1DMDM283cA23aJ4I/D4IriEjnIjMGWxnll5dfZDrFwVLLKONGKMuw3pmzcijTTSiy/KTZLGxFxxZFyFgkeTSWVKJY8qJI1qw/NL+QhMqdnvH20nLJmDcGoX5cbB7Ic3MhVFuZFqlo57mAD95vQwUKquHYEg00u9ct9AlRIBIkAEYp+AoIJGa4L5tVxMSgh1+ZQjIXUJdloMKC/kSzs9L+5mYkDNS7PdbiODkfzAEkmUFO6ZLXf73xfCFf9GgLKwCqbt/4NnZiZ1bYFqwjQs3bwTWtHlxy2L2I+d2LxqJgTejYQUqNdpYSj3tMtn0VXQ6LVYp04J7e8vH48Hnv9PqDxPHsYMAC5KF+16+u56l4/+EVbtdG3OJaYoC7HR9Ge8/sx9AVFt+Fnf4li+GHb+w7f6y9FVmf1FEpknTJqPdTX++hJUZdDXrIF6El9wzLONRfZLWui9HFOg0ryLzw2ru+YO1U4OSiACRIAIdJ2AjJv4XS9OJYlAbBLgm9nQ0I9N3ZHURIAIEIFYI0C/ObGmsdiTN9QUU+z1hCQmAkSACBABIkAEiAARIAL9kAAZ9P1Q6dRlIkAEiAARIAJEgAgQgfghQAZ9/OiSekIEiAARIAJEgAgQASLQDwmQQd8PlU5dJgJEgAgQASJABIgAEYgfAmTQx48uqSdEgAgQASJABIgAESAC/ZAAGfT9UOnUZSJABIgAESACRIAIEIH4IUAGffzoknpCBIgAESACRIAIEAEi0A8JkEHfD5VOXSYCRIAIEAEiQASIABGIHwJk0MePLqknRIAIEAEiQASIABEgAv2QABn0/VDp1GUiQASIABEgAkSACBCB+CEgY4yx+OkO9YQIXJ0A34KbXkSACBABIkAEiAAR6G0CkTKzB/Z2R6h+IhBtBPiXixv1kfqSRVv/+6s8pPP+qvno6jeNw+jSR6SkIb1HinR0tcP1HqkXudxEijS1QwSIABEgAkSACBABIkAEeoEAGfS9AJWqJAJEgAgQASJABIgAESACkSJABn2kSFM7RIAIEAEiQASIABEgAkSgFwiQQd8LUKlKIkAEiAARIAJEgAgQASIQKQJk0EeKNLVDBIgAESACRIAIEAEiQAR6gQAZ9L0AlaokAkSACBABIkAEiAARIAKRIkAGfaRIUztEIBQB5xFUZCnEUJo8xJWiyIiWYHlb62DcXoqFa8xoC3Y+6tKcaK2rwfbSIqwxt0addF0VqM1cimSZzKsvrjPfXxaKKg/A5uxC7TGn3zD62GJEkULKhx+noch4xle4tQ67S3Oh4BwVuSjdXYf2o6UFdbvXIFesawpyS6tR19oesp9ukkthjo0vio9FnxxdRF3FXN8YViyHsaU9W6AFdcatKF24rmOuNh1yxe/EQuhsfaWAMGXtE97UKBHoHQJk0PcOV6qVCIRNwFn/Ibbqbd78tpL12F530fvZddAK8/oFmDGnAHscAaei9WPb37H+wXTMKTiAWBG5+yj1KMmbjcfLDgQxSjuqPQb121F3xHNOtJj2YJNvaLtKKJ/A3GmJrmPnceiW5CBz972ocThg33kbdmXmYInuOHwm5WWc1C2HMvMj3FtzAcxejim7noJyyQ6c9GUS6xuYuhBbNUpX3fQ/PALOY9i3dZ8vr20jXtxeJ+HvOtVmfgUPzngMBXsu+PJG6VEsyRqlCEmsGCRABn0MKo1EjicCF1G/713oAQhLX8Yr6hQA+7B137F2P6jx1Ou46ItKCytj4gZlfJMyxi6hUbsIAmyoKduBA0FnOeOi52F2ogmm6iasslyQMGJge3+O1AT+0+NES80GLK6oRdLMqRgvlyNh6j2YlVSLisUbUOPh17IPaxevgy1pGqaOHwwkfBfpsybCVvEC1tZIZvpFqQZDMX5imPJRNk7AO6EgLMErrywQx69+64eoD7hZIlpEgAhENwEy6KNbPyRdvBPwzo6lYv6sOZj3xENBflC/hC73NqQV1Ig0GgrScI0sHaVB3VhaYS5NFx+fJ5fuxj+8bgoKpBfpUNfahta6apTmTnE9Yk8vQqXZ5n/z4Hb9cLk3cBeJLBRVGP1dHHieiiKke91NeP0VMNa5nYX4Y/dr0lDQwEWuQUHaUMji3gViEEbfkYGZvMu2Jpz7RmIRBfJKL0KF0eNaEky/d+I/ivJFNxSpC5azrgJZIvO5qPA8xfG6bEnSOmzP86XibgkVKEr3uHsF6rkNNt1C1zjJ3QyzWecbN4pcrDkQMG481brfnSffxxubNiB/4rWQ8f7qavzHELjBr4cNApISr4Pfj5HtIxz84rzL6PfM8iclYqhfJjO0B4/HiPtZAJyo+SiZUJj/MObNm4v5AgD9u9hX73lK6BoH16QVQPw6NxQg7RoZkks74/rH3e+MqCjKcrv2BFwvPDyk7lfiOOfuVTqYbZc9oyqgnsDrU0/I6hGG3olAjBFg9CIC/ZAAwCcN+/7lsJSzTIBBKGaGZgdjzQZWKIABs5jGdNYt4AmmVSUxLrPvT8k0JnuQDtiZSaOU5JOWEZhy6VKmEuuXpHva5rXZD7FyVUrw8soyZrI7GGNnmUkzq+M8Vi1T+ckLhiQNM10JInKEknpK51dMGpbE+6bSMquf7M3scLmaCQAT1FrWyFHxl+MY06qDMU1hqvJDzM5C6Fevc40Fr34uMEv5HDf3JKbSnnDV72HtyXfV9nixS6xRu0iU1TemXGNCUG1kh0U9X2FW7YLgehZ1O4eVWy64ZGj3XyqrdKypWfnhZldux2FWnikwQNKXKyamSeL5PWmSery8JWPcm+YRQCKze7x59SXK7KrXP03Nyg07mcYz7pXPMYPVzqyG55jSPYZ9TDztdP29p8Zh1yWQlPTqIJUVGk4zxk4zQ2EqAwSm1OxnriuMhKmbB+9DksbEgn6dPeMRC5jW6srhaNQydeB1h9clSMdDqO+J5Ptk3880Sj5mJGNKPPbI20lZJSh6+zCq9N7bnaX6vQQiqffosGq8XacDIhAZApH8koXukc9YEQoNzGXmeH5QwXxpvAafERPyh1RsyJfP92MpNcA9RqSD2U1lboPFc3Pgk8dXljGHVc+KxR9R94+m1+jyGAFcPM8PrcAyyw8z0Zb15vPUH5pEJM70lM79jcFAwwJMUL3M9lsvubvkYM2GYpeR7zWUHcx+eKPrxspjhAfVr2cseDj7G/6u8SGpXxxDks8dtee5cZQaVN6bOU97UuMokxVqD4sGns848xjdQbTnNRTb8/HevHrHh6Qeb5rHYJSMZ6/xLklrd5MokdlzzmFl+8sWMbVGy0xevUjGOtzfCcmNkKBUsjs5m4/edN9gS8Z1kO52JqmnxmFn2gyVt92EAvONH6+e3IW9497DNVSl7Qx6zzj2XHt4QcnNr/va55XFO3EguekMvDnzfm+k1zHfDWbYsobqQy+kR5Pee6F7VGUIApHUu98DzBh7uEDiEoHYJtD6Gd7exBejpWJ+1q0YJvYmEWlZmeBPvW2b9sDk8SPuQk+F+U/g0Um81hGYmq5EEq9DeAi5j34XCfD4K0sq9rr/CMhcVYA8sSwgF2bgFyvzXL7h69+HxXkjxt/Lff3NKJmRjtzSzdDpG3FLqRkOZkW1epK/+4Skif5waKtaj3VbPnZHujmPLw5+BL4u1FaVh8lDB0AmG4Chk/NQJSbqUW1qCoFlBCZPTwNgxSfHzsDZ8gX2724AlI9DpRRg0x7EF20etxXPGAqvvbYvDkIrtl+B/MnDXW4QQ6cgv6pW1Oum6s/8Iy1lzkP+7ElIACAf/QPMmimOphBy80yToK62unzn7RYYtK+gUMlHNQexDZV7ToYu25NnWo9AV7wEG8YW4NVl2UgVBrlrH4ihI9wLc3EXHnlgEhLkN2Ds5BvF8zbLeOQb10D9w+mYLvbVhoamb/xd03pSzj6p6xz+/rbOtX5n/n1IG8bNATmGpd3ncruxdTQ2OyFw23Ec1JoB1KIqfwqGiq40wzE5v8L1vXBf5+QT1KhmDI7N96BRvwO6ipV4MmedmAfnm9B83gn5qPG4V7w4rsaMSU+hdPsO6I9PRKn1EhjbBvWEwZ0QjLISgfgiQAZ9fOmTehMzBJxoObADZTXcquKG8Ui3b+kADJ+x2vUj1s0f1CEjh2NIII8hiRg+JMTX3vkNmhq4PBMxc+pNEqNcjiHDE111NdTj+NejMXtVOTYWZrp+pAueQE5ODmanKTAgfTl0Hj/6wLbj7XO7RbEO2C1aFCq/RtXSJfiduGDzLI4f+rKDnp/DqXOhooYMxLdTpiETNvBFikeOcCNcQOb8p/HkNAXQcACf1h12GUtCJrLSuIEaTnt2nD5e7/KHDiGZ7dQ5fCM9N2qExH/9eoydMkZ6tuPjhAnIyH4aLxo+hqGYj5kGfHD0n2iTX4fEJLeR366GJNw1/l8wEAMxNHFku7PehLvGQzHQ+8n/4PwHWLtoDnJK3sQ7u8ydCyU6cxYecN/Q+lcaR59aDmJb2S6xQ7aSGRjuWQ8zfAZK+GUAZrS7setK908fxyHR+T5EYc96k9ZaVOROwQBFGmbn5CAnvwSuVUMA3Nct+egfYdXOKtfNoa0KBXNykJMzC2mKce41QpJ1KyGao2QiEK8EQvyyx2t3qV9EIFoIeGZWO5LHjE1vvN8uNF9HJbp1zmtgWbD700bJbKQT55ubwJcoIikZY0cOhFyYhtwXq8FYMyyGHdBq34BGlQLUrEbOM9tR1y9/V+VImJCJubN4lBXPgs1rMWLUCFEtSRoTrvhFxeGRcepRmR3aOJYn34l5mYK4SLFSW4MG8WbrdkwXn+IchKFSCz5pL3hnWMNpbyyuG5EoPgVCkgamK9JIPe7jymzX+W4NqIDC8tHI+EURCoVU5Nw+FgPlN2LcbQoA53HqXODs9xhMGXs9gEEYNS7ZJcupc7AHjKukKWMR2twfjYeeKYZaAGwVv8Ivd0hDYQbI1u8+hggpGsDBtkmHPSc9C1IDTob78boRGCXetymhMdn9Ix6J34f1yBbaULftN64nRMpClGt3wWS9hCsmjevJoretQRBS5+PFvVYw8cmPFto3NVAJNtSULMYz29qH2/QWpQMiEOcEyKCPcwVT96KUQMtnqN7EH0OnotBwOuBHzoFmQ7HL7aZiC6q90SZ6uS/ycbh73t3cJwL6FRpsPOKKWOO0GfBfz28Uo5EoF96DW77SIV/c4CcLy412JGc8guzsR/GTR+7teSOwl7vc09U7bR9Bu8vC73zcM8w+F6qGsj+gSmR6GTbjr10RgkJu4uOWzKuTN1FSsgsQ7sDttyRg2OQ0zEQDNpe8BD2SMHP6Le1ctkK3B59bRUMl1lbVijHznbbdWC5GvAnY+KkrkHh8+fwpUOSuwwFvhBI+0zocI2/wPE3wsAniziL2kz9fkriANDQFGPTuG4NQ8g0Zh5vTHsNLO8ugBA+FqcGO7hqnodqKuXTfhIJQaEBz4I1mswGFomuLDhuqj0pu7rvQ0WG3Imt+qhjtqmytFkf4hmDOkzAud0W8cUVxakWj5ahYuTB+OrJmP4jUb5/G+9rdkidJfD+Cxa4NyNJ/DaN9HDKys5GdPQePPMBdAOlFBPo5gRB+/JRMBOKaQCQXqrQHKVl4JokE4ZfPs2gRnsV40kV8fKFhqIWmvgWD0sWzQReJeRcgSuryLm4NspjRu1hNusg2MF8KU2uPuRbFBi6MvNpiOj8APf+hp3TuZdku0oaEhZdVR5GDpIsEQ+vXu1iQt+dZGOrH1rcYUKTmXdwqkUeUVdqeb1Ei5yL980V0kSww9bTrasAdSUmymDVQXd6xBQZlMdNa+JJv3uZzrMwbvUkSASiznFkcngWOkjEk1utZHOnup3uM+kUS8rbvG/++RZ2S8SpGsOELlqW8PdFYPIs3wSDKw+XzROIJXKTubbDTBz01DjvdsLSA9/oSSoftWfiNw05FuZEsAg8Ya77F9x4d+49F3KlkSh4dx7MItqPrk7CIaRtdi9HDllXKpJePo0LvvdxHqr49gUjqnaLctOdPKf2AQCS/ZO1xtv+xDCePw7qPlXlC6/mFtZSW9hk0XTLoeVV2CzO8qZGEt8xkheUGZhFDGXraamYWQzkrlIaQUxaycoPFHeqO57vErPtf9tUjNXI91UTwvad03rFBn8JUftFU3B3kTMsLvWEQIaiYRi9lxaMJhdCv16j03NzxOiUGqcf4lLIMoz1uYPvrkMv+rkTP3TDomYPZLVrJ+OB1b2EG0bCXCsrH22GmLcx03VQE4eLK3cws2mI3v0A5ffW10w2/EZHeXIgG5QK2RbvKFXrUY2AmrWLaLf4hOpM0W9gWv3CxoYxfX/vhHPXUOAynreB5pBMKATeD3gJB8ojRglTuUKeeMJHeAr6DdlFu+Ck+Hgys3KNnHtpVVcb00vHgsDLTRs93RGDKwipmsta7Q/Z6Ii+5r0/S7xIPsVlY7j+2wpXVJ3WvH/W93v272O674vku+L1LJnu4Fq0mtsPvt4HfsBeycu1eyXWDsc7XLbme8fY9N3D+Ivvq7ePJoQCxOvwYSb3LuCT9/CEFdb8fEpDJZKKbSz/ser/tMum836o+qjpO4zCq1BExYaJN723mUkzybBYWkgJf97ATy1KHoPXIJizKcEfnCpZf+RwMm4uRIQxC5+pOAPjmeA9kIF8vrsbm4diQWW7EOwER07z18rU/R5YhNdSC+GDy9VFaJPVOPvR9pGRqlggQASJABIgAESACfUFgYOoy1HvXTthh0ihFMfwX7+/FstQEoNWE9T8tFkPtCqoy6C3N7nVfl2A1uaMO1TyHGXmviwEROlU33w+6/kNs5ca8sASvvLIgyG7pfUEo9tokgz72dEYSEwEiQASIABEgAkQgAgQuom5bKQp4iGWhGK//fglmTnDtmsKjUPGoQ6tff1mMJgX9H1AuhuvtjFgXUb/vXfd+CA9j3ry5rn0Q9O9iX6QCQnRG3CjOSwZ9FCuHRCMCRIAIEAEiQASIQN8R8EUgSlqag3vEDcj8pZGPvgdPiJGMPOF6/c93+Mm7oaF7czxvVKR92PT2Z2IErg7L00kvATLovSjogAgQASJABIgAESACRMBH4ALOnTonCcXrO+M7SsBNE8eLHxsOHcdp34mrHvncbdqHs60p24ED3dgt/aqNx1kGMujjTKHUHSJABIgAESACRIAIRD+Bc/j72zq3u819SBNn/yV7T3Rzt/To73/PSkgGfc/ypNqIABEgAkSACBABIhAnBDy7Tzfgg6P/RFvQXknccjrcvTmgcMtBbCvbJSbaSmZguEwGHhVGNnwGSsSAN2Zsqv4Mri0OA8rSx3YEyKBvh4QSiAARIAJEgAgQASJABACJO03Za3g7yG7LzpPv4w33zuc5t49FeNEknWgx7cEmT6TKEKhtm3TYE6TNEOJ95jsAACAASURBVNn7dTIZ9P1a/dR5IkAEiAARIAJEgAiEIjAYE+Yug0YpALZ1yHlyJSrNNjjF7JdhM29C8ZOLUcENc+UTmDstMVRFAelNMFXrwYsJhQY0e0NoMldIzGYDCgUANh02VB91txdQBX30I0AGvR8O+kAEiAARIAJEgAgQASLgJZCQhoV/XA0VN7BrSpCXpsAA0T3mW1CkqVDCQ1qKG0stQmpCmGZly2eoFmf1kzBz+i3wBML0tumNdmODfuuHqHfdQbhONxQg7Rq3e47HTUd8XwidLbhTkLfeOD4Ik3wcE6CuEYGoIXAGxqI0lw+h5CKlKDJKfAhbULd7DXIV/GI2Bbml1ahrlV7peGecaK2rRmnuFLEuRe4a7K4L4oXYZkZpsueimI5Sc2vUkCBBukHAq9er6dSJFuNyKCRjTfRfVSyH0RtZIsyx1FqH3aW5rroUuSjdXdc+3Fw4eQBxl8lkj0zJpTD339/nbgyCqxRtMaJIvIZ4vv/8PQ1FxjOSguFca8LJE+YY8o5bLsvVxq5ETDqMAAE5EiblorLOAsObGpdh72lVWYhy7V5Ydq4Ud4n1JHf8LnW3uR33powMkj0RaVmZ4PcQoJj0QfgESWL0IgL9kADAn+pF2avZwAoFMC6b728W05jOugW9xBq1i5iAOazccoEx+36mUQpMUGtZo8PXF0ejlqkFgWWWH2YOdpaZNLMYhEVM23jJl8l9dMWkYUlie0qmMdnbnY+nhKjUeW8AvmJimiQ+hq6m09PMUJgqGWu8jMCUmv3MMxLCGkuOY0yrTmHILGcWh4PZTWVMiRSm1h5j3mEZTh4vCzszaZQuuZI0zHTFeyIuDvp+HDpYs6GYCX7XGTAoy5jJ7tFYONeacPIwFtYYcms2nq9Hfa/3uPj6xFwnIql3mqEPcpNDSUQg8gT4jEUNPl91GA4/X8K/YFnqCJc4LfuwdvE62JKmYer4wUDCd5E+ayJsFS9grXd3vjOoWfsCKmwTMXPqTZBjBKamK5FkW4fFa/dJZvpdVQ5UjMddke8stRgNBPgj789/BovD7bMqjjsr9i6bhgRRvnDGkhMtNRuwuKIWSTOnYrxcjoSp92BWUi0qFm9AjTjTH04eKZDBUIyfKE2g4x4lwH2Xm7DKcsHlq+y53uz9uc9dIpxrTTh5EM4Y8nWOrkc+FnREBDpLgAz6zhKj/ESgNwg4v8SeN/6MXfmTMUCWhaIKHYx+bjKSR5RJiRjq982V7M7n9UscicSh/rEGbNqD+ILcF3pDe52o09/9wOXikotSnRk2j+eUTYdctz/odvPfoPO4snAXqzUf+PKJrUpdHmRwuVc1hSHPZZzco8OmXfmYOECB9KJXoTMGuMmENZY8C9sEJCVeB79hafsIB784DyCcPGGITFl6hIArIskG5E+8FrL0IlToagLc9sK51oSTB0BYY6hHukWVEIF+T8Dv+tvvaRAAItBHBJz1BmyoqHW3rkdJfg5mTLwLuRW1bl/kyzh1rF6MCIBRIwIMesCzO5/z1DF8IoYBS8SIAIMeDfU4fvoqFr2fH6sMslwdbH5pycitqPb5S8uysNx4Em223ViernD5/yvyUXEkiM9+H7GNpmadJ3dgifJ+FFR5dM2jOFShICcPK3YcD4jksAFz0u5ATkGVS++oRdXSOcjbeMQbYeKkbjmUmUtR5Q79ZqtaiszvZaKg4Sq9dh5F9Qadu14bakr+HTkzJmJCbiWOuNdkhDWWnGdw7BMrgCEYNSLAoMeXOHT8LBBOnquI22YuhdevXpaMXN2X/r72snxUGP/iXTciS/81jLZW2Iy/RrrbH18h6dtVmovj0xdRX73FFZGE97KmBPk56Zg44WnJdzaca004eYCwxlBHtP2uPe7rEVphLk33rTXKfRVG77oiBdKX74at7SSMy7PceaZIrqMdNUbniEBsEyCDPrb1R9LHBYGLqN/3rrhbnn93alGVn4fnxYVqbbA3dbCh9gdHYW0DnPYmhLblLDhqvejfROCngVPwxOaXoVZroDVZ4ajMhjAwFUv/Wo5MMW8Ddr93CmMWbsDH2kUQoMfqJ+di5qPFODm/EtrCVMBWgfwl21HnmXEObKPffvYYUwKUmv2wc1cHxzFo1SkAavHe0TMBBr0AZaEWFrtDks8G/Xv/wFecocflAQKUxXpYueuMw4r9ZSrXQrIOOHu3Ww/IY6vKQ8bzNaJrVlhjyfkNmhrcdxMBdQHujWjCydOurH/CwO8/gc1li6DWaGGy/gOV2WMwMHUx/lo+x53xAN47Ng4LX/uLi2fNc3jy8Yfw6JMnMP+jN8Xwd7aqYizZVhfA2L+duP/kPIZ9W/e17yb/zmb8l3sxdDjXmnDy9NL1CAlIXfpHlGeKyyWB3X/DsTH5eO1jLdSCDTWrf4rHZz6CJ0/Ow0faQgj8Rjj/N9hWd5VrX3sqlEIEYooAGfQxpS4SNj4JDMYE9Ta3P2szLAYtygtd5jNgRknl++6Z1N7ufTPqdM8hb4OA37y6DNmpgteFQj50BEaJzSdh5iMZmJQwGN8eOw5DeJqtBd/J34h16nTcMT3NJWRDE+xk0AcozKPnY9icfgZ63XZUFP87ctxPZs6fbgZ3UPG97sb8/AcxgYeBk4/GHbP8Vzv4Zj8fxjPPpEPgV3O5gGn5uZjvtnV8dfkfySeoUS36Tjtgt+yFtrwQSncWW8k27Imm0G+tR6ArXoINYwvw6rJspAqD3JIOxNARnpjXd+GRByYhQX4Dxk6+UTxvs4xHvnEN1D+cjukzk/hARUPTN/3boJdPgrra6rrW2C0waF9BIY8vzl+2bajcc9J1HBX/Q1+PIL8OI0aJVx9g5iw8MGkY5N8ei8liUgMs33kGxnV5+OEd0zFT7MtpNNmv8nQyKvpMQhCBrhMgg77r7KgkEegFAsMwISMb6hd3wmp4zmVkibPvAzE0MVhoL7cId42HYiAgH5oIbroEf03EeMXg4KdwBn9fuxjKnNXQv2PEftvlEPmCJbuNqWCnKE1CwInWI5XIVfDYzbOQkzMH+SV67/khI4e7bpC8KVK3qYEYOTbZT7feGXQhESOuk1zKhwzHSLet460q5IEcCROUyFa/CINVj2LRuHM9yQlrLMmvQ2JSqLuHJNw1/l8wMJw8oeQ7/wHWLpqDnJI38c4uyTqDUPml6W5DT5pExxICCROQkf00XjR8DEMxn0BwP1FBONeacPL01fXIM+kg+U5Iuk2HRCBeCdCIj1fNUr9inMAgCBmLsLIwFULO7bhl4CCMGpfscqU4da7d7HfSlLHg5r581DjcJtpXTTgXOCOVlIyxI/0XykohDX7oGazl7h88Is4v/4KTNMMuxdP9Y2cdti0pRpWNu9K8Au0OE6wOO0waz9x455rwGty2ehw7JbkBO9+M0/5T/WFVLBdm4Bcr8yAId+D2W4aEN5bkN2LcbQoA53HqXODs9xhMGXs9EE6ekBKOxkPPFEPNN6ms+BV+2W6dQciCdCJcAvLRyPhFEQqFVOTcPhYDEc61Jpw8dD0KVwWUjwj0BAEy6HuCItVBBLpF4DJO6hZDocjFmgOeLbV5hYMxfOR4zM+6FcMgx7C0+1yuFO3cWTw/xAC8u+u1f8TsujEIJeiNmHzzNDz6Urm4xTcZT6E4dSO91QrLIe5vfgPGT8/E7EdS8e2vPoJ2l6VLlcqT78Q80Y94HzZt/F9X9BunDQfKK7EplFu7uyXnSR3yFYFRc+QYMjwRN8y/D2nD5GGOJc/mL0HcWdw3BkA4eUIgGDION6c9hpd2lkEJHgpTgx0nJTcvIYpRcggCzuPQ5U+BIncdDkifwvGnOjdkIiuNuzCFc60JJw9dj0JogZKJQK8QIIO+V7BSpUSgMwQu49TRz2GzVWHp9DwU646gle/2euTP2DZgGVZmuHyCMexuPPvyIggNB/Dp0YtA6z+wd5cFgno5nlW68+BGKJ9dDrVgwe5PG+HEOXy6twYNwiK8/Ozd7bbXbrMexQeiqHacbr4I8C2+SwtcxlPOv2OF8aToc+y0n8Mpvy45cb65ye3z7Xka0Ab7OXfIxPNNaD5PU/x+yBKSMP0B1wLYipxx4tbpAxS5eA83i09e2vvQ+5Vu/0E+HlkLsiGALwTMhGKADLIBCkxf6omK076IJ8V56ijes7mi5jxerHOFLWytRdW2BGxcqXSPk3DGkhzDlAvwsjoFDbs/xVGnE62fvo9dDSlQv7wASn5jwA3Eq+bxSMbfL8J61H2TI44jICH1KZRqZolPj3KeXA2jaIxKxpu3+EU0n7a7PnmeZDm/wblTrkcWnWbsrTdODpxncPS9WtiqFmP6489BJ4bGbcGRqr9gwMZCZIj64oZ4GNeacPL00vUIEp16NeN9MuV7WuS7brmvb97MdEAE4pBAzG27RQITgR4gEMnd28IS136YaQszvbt2CioNe9Ng8e7Y6aujmVm0xUwp7vKYwlSad5nFu7ujJ5eD2S1aVqgUxPoEVRnTW5o9J33v3h1FPTvTLmBaK99Z1r1Lp9hGElNt2eLeedSTT8k02nKmku40mbSKabcs8MrP+UKlZVZfa31+FA06d1j3s41ePWeywo37mbVR62IpFDNDs4Mxq/szuD5826R6d9H049rMLPoypnLvMCzq+nN9GDvFSscRGAQV07y5t+tjSTp+eV36IGM3nDyMMW8/PeOL9zfIWN2iXeXe5dg9LoOMwSTNFrZFlSQZl0lMpT3Rp2Oxb8eh/7UB4NeQLcwQ7PrApGMk1LUmnDz+bXb7eqT9POAaBdZez0GuUQHfp0gPgr7Ve6R7S+15CERS7zLeaBzep1CXiECHBPiGPjT0O0QUdydJ53Gn0pjsEI3DmFRbt4UmvXcbYUxWEEm9k8tNTA4REpoIEAEiQASIABEgAkSACLgIkEFPI4EIEAEiQASIABEgAkSACMQwATLoY1h5JDoRIAJEgAgQASJABIgAESCDnsYAESACRIAIEAEiQASIABGIYQJk0Mew8kh0IkAEiAARIAJEgAgQASJABj2NASJABIgAESACRIAIEAEiEMMEeiRsJQ/LQy8iQASIABEgAkSACBABIkAEfAQiFSJ7oK/Jrh9xYSMZa7PrkrYvGatyt+8JpXSGAOm9M7TiIy/pPD70GOu9oHEY6xrsmvyk965xi/VSXO+RepHLTaRIUztEgAgQASJABIgAESACRKAXCJBB3wtQqUoiQASIABEgAkSACBABIhApAmTQR4o0tUMEiAARIAJEgAgQASJABHqBABn0vQCVqiQCRIAIEAEiQASIABEgApEiQAZ9pEhTO0SACBABIkAEiAARIAJEoBcIkEHfC1CpSiJABIgAESACRIAIEAEiECkCZNBHijS1QwSIABEgAkSACBABIkAEeoFAj8Sh7wW5fFWyy7h4eSAGf0uGtnNf4KN9/0DzdeORekcKhMF0P+IDRUdEgAgQASJABIgAESAC/ZFAFFvEDG2297BWPQfFNaeB83/HH+beh3se+jEeyrgL9/50Ez5vdfRHnVGfiQARIAJEgAgQASJABIiAl0D0GvRXDqPqp3lYsvFj/OPkaZwyVuG53V8CSfdgllLAFxufx293nQDzdoUOiAARIAJEgAgQASJABIhA/yMQtQa98//+hq1vHcP18/4Tzz0wFJ//7z6cRQoW/m4zdm4tw8LrG/DuR3U4G0c6c9rMeGt7KXIVMvDtgsW/9CJU6GpQ1+rswZ62oM64FaUL18Hc5qn2S+hykyGTJSNX96Unkd6JABEgAkSACBABIkAEopxA9Br09iY0IAkPzX0YdySext+rLQAm4wcTboAsUUBSInD27De4FOWAwxPPidYjlXgqNQ2z5xSgyiYpVVOC/Jx0THzoeRhtlyUnun7YZn4FD854DAV7LnS9EioZ3QRa62DUbUZpbhaKjGeCyHoZNvMmFKUrxBtHRe4a7K5rCZKPkvofASda62qg45MLycthbAmcTHCixbgcCs+kg9/7XFTUXex/yKjHEgJXGz+SrODXob9ie2muOJ4URUbQVUjKJ5aOz8BYlOabjJQpkFVxBL6rRwvqdq/xTVimF6HSbJOcj6W+RqesUWvQywYOwjA0ob7xDFqPfIQ/f9oKTJ2GqWO/hbYTR2D6ChBGjcB10cm1c1K1mrD+p8WiIS+oyqC3NIMxBsYuwWqqQqFSAGqew4y811Hn+3Z0ro2r5h6D7Mp6MFaPyuwxV81NGaKYgPMIKh5bgUrtahRUfR1EUCdazeuQt7YFOZuPgbFmGO+tRa5yOXQne+amMUijlBQjBJx1G/HYr1+D9tkCVJ0PJnQTTNV6SOcdvLky78fdyYO9H+mg/xG4+vhxM3HacGDN00h9aCuOjXsKNXYHrC9mYFj/QxYXPXaefB9vbDJL+nI35t09Di4j8zJOvrUJuzAL66wMzGHF/odPoTjtaZSZz0nK0GG3CLAeegHcBu3BV/N7bOWkBO4i7/5LYCmrPmT2hjfZv/1AYMAk9pT2OHN2s8kel7vT8lxglvI5rj4KxczQ7GhXg6NRy9QC55DKCg2nGWNXmFW7wFVG9QYzmbRMo0px16FiZfutrH0tvFpJOS9XsCSNiV1hJ5hWlcSAJKbSnhBluGLSsCSeL2k1M3z+rq8NZTHTWpoZs1uYXqNiglhXJivcuJ9ZvQ07mN1iYOWFmW79CUxZWM4MvFwUvPpe770PwWEpZ5neMSNpz3GYlWfe6R5L7nTHMaZVpzCh0MCiQ0MSeXvosD/ovIdQMcbc16Vg16TmvUyzUi/5rvNWHazZsJLNKj8c4trTc5LFek39Yxx2MH5EBZ5lJs0sJqheZvutl2JdpWHJH9965/pU+f+mSKk4jrK9e0/4XxvE3yEhrn9zOIJI6j1qZ+gxbBr+reRn+EGC634l4Qc/wwvzv4+Ea+W4/LEdt+StwC8eHANZt25noqFwKxotR0VBkpbm4J5h7VUiH30PnpifCsAM7cHj8Lq981JVTyAtLQcFVbWuztiqsHT6EmzsycfeDcWY8b37fW3UrEbOguUoWpSDzIIq90ydHiV5P8PvalzuHc6TO7BEOQP5JXo3ZBtqSvIxQ/lzVByhh6puKH3y5qz/EFv1ozHxJveXi0sh/zZS7poM26Y9MLVzsegTManRKCXg/GYMflw4A4L0UuWsw/YXG5DtnZGLUuFJrCggwJ8QvoZlZePw8gtPY5owKApkIhG6RaDlILaVVaHkeU3wNX/ym6FUjnHP1rtbkt+IcbcputUsFfYnIL0k+5/p80+D8Z2HfgvjPz6HyfQ5/mH8LR76zmDghqnIe6sG7/3xJ5gwOPbNeeACzp3ij5yScNf4f0HwjQEScNPE8aJGGg4dx2k/3WSiUHsYdsbgaNRCLfCTB/FerX8uV5GBELLX44pJgySekKSB6QpD/bLUEO16GkqBqvwQ7MwBu6kMSp5csw6bsAyH7Q4w+35ouFuQ94bjDGrWvoAKm6ccdx9qxuFyNQRbBVa8ZiI/SQ/aiL870dpYj0Pt2h2EUeOSIdjqcewUud20w0MJXgJyIQlJCf4/HfwmUXdTDrLI3cbLiQ5CEHDWYdvydcD8qXD+6WnXWgxFLkp316E1RBFKjmYCF1G3fT1KuA+ed83fCujCWpN1Ax6YngTJ1FI0dzTqZfO/KkeTuG2tOGM7DfvA66FQXI+B9tOw2WywfT0Ek36gAM5+hVPnLlLYysx5yJ89SfxCyEf/ALNmiqZ6z2pSeAi5j34XCZAjYeo9mCU2kYr5ubMwif+wJ3wX6bMm+tpsO46DWu5LV4uq/CkYKi6aG47J+RXibD7NAvtQRf5IjoSbkjEF+7B137H2C5KEZIwbRTNmkddLLLd4EfX7DuB7T9yD0dH7ixLLgONKdtcTwiRM++5U3LW0ElY+2bNqIMoyl2I9+VPHoK4HY4J6m3vN306UF2YC4lP8cpg7is7X8hmqP7kfP8sMmLmPQQLRInL0Xn5P6/EfCgUUHfzd/T+fI/a3lroWI0aNANCAD47+09+dxjtKJG45U8ZipDcdwKgRGOrV4vUYO6UXFrQOScTwId5G3K0PxcjhIRa/nT6OQw1SIQOObU04902vre4NaIw+BhKQT3gYRYUK6FdosNHt/uS0mfDnajNsU5JxU8Dsa2B5+kwE/Ag4j2Gf7l+QlZbol0wfiEB7Au4nhEIqsn6c5nbbGoZJeQVYlXkQBct1vRj4ob00lNKTBAZBSP0R1C/uhNXwHJQ1b2DbgaYQDZyD+ZW3MfKFp5BKvzchGHU+OdBK63wNVKKbBCTuNGWv4e0gUUZ8q8dTkXP72Ku4x3RTnJ4oft0IjBJdf5TQmOzuiD3c7cbztx7ZQnDnop5onuq4GoEbkbFyM/RL27Bi8nDIFLko++BT/ONAAzLn3YlkuipcDSCdlxAQ3W2+p0RakPU/kmx0SAQAXMapY/XtIyTJx+HueXcDh+rR2NGsLjGMAQKDIGQswspCYFP1Z0Hca/kaii3YlvhvWJjKJzPp1VMEovene2Qm/ttqhTXg74RlH/5U9AAm5ZVja+73MKCnSPRZPYMxYe4ylw+6bR1ynlwpic3qihVe/ORiVHD/NOUTmDstBmbBht2KLHERbw3K1mpxhF+gnSdhXJ7linlOsYb7bLR5G06YgJnL+ONuBmatxNJbB+ATy1wUPTrBf+GStwAdEIFgBNzuNlm3UrjBYHgoLYDAVdbq0BPCAF6x+pFPVE7ElImKdv7xzpPv4tXau7FSndLuXKz2Nlrkjl6DfmACbhQECAF/YybchXmFS3B/tQbr/vef0cKxe3IkpGHhH1dDxWe1a0qQl6bAANHv/FtQpKlQUmMDlM/BsHlRjzyekg9NdC2KbShA2jUyJJeaQ7j6dLVbiZj21DNif2xVeZg8dABkA27CjNV6QFBj1VNp9OPfVbS9UM5p240VC3Zi5s5CZNAsay8QjuMqyd0mjpXbG12TY1jafZgvHMYHtV9J1vBwt9KT9ISwN5D3SZ2taKyf0m6CyGkz4qVtg/HYfI8xzzfV3I4Kd3S8PhE1jhqNXoO+A8iybw3B0IFH8Kb+MwTbA7ODolF6So6ESbmorLPA8KbGZdh7JFUWoly7F5adK5HRQ+G95MkP4PkyFUSvGAgYAwd6dm9H3p/5WFdjcC2QcfdF3DSrZg3Uk2jrEI96+/Sd7ya7vRRP/evrGPniH7CUHn/2qTpisXFyt4lFrfWxzMPuxrMv34t3Fv/GvYbnMmwHtqLyk0fxwlx6QtjH2ul8804bzG/9FWbPTvbihmFlqLlvPpTeCSK+e7AOxY8/iaVLZ0AxQObeUXYAhk7eBigozk3nwQcpIY39353jHg+eb7cwg1bLtIF/W15hz6vuZAkAS1iwk/2zO0JHOOh/N0Wl4j1IoMfHaw/K1v2qTjNDYap7Qy/3xmyZ5czi2fSr2cAKxY3KMllhuYFZ7J4T3W85mmuIb533IHnv+PBs6iewzKAbRvHNgwqZxnS2BxuP/6rifhyGNX6amUVfxlTidYhvOljFTHG+wVTc6t3RyAzFng0kU5hKs6XdBpK+zTE91xTJu/S3KQ6//pHUu4zzC2LndzpJJpOJix47XTBUAZsOuYocVIU6j1T8dOefse5H3dtcqsflDikvnYgmAqT3aNJGZGQhnUeGM7XSMQEahx3zidezpPd41WzH/Yqk3qM31Mg1IzBBpYKqHSs5rh31Pdx1/4/xY2X3jPl2VVMCESACRIAIEAEiQASIABGIMQLRO0PP/Xv1tbCPvQMPpQr+kTdaP8XW9btx5va5+GnGd/zPdVIBkbx76qRolL0XCZDeexFulFZNOo9SxfQzsWgc9jOFu7tLeie99zaB6F0Ua69FZU4O/mOvVbIS3o3jmguoX1eAX2z7DF/3NiGqnwgQASJABIgAESACRIAIRDGB6HK5uVIP3S9fxFvWy8CFE/gAwFdbfoWnDt3gNwvv/Ppz7DgGtF643MPhFqNYUyQaESACRIAIEAEiQASIABEIQiDKXG4caDI+h7tmrMKRIML6J92Cx7e8i03zxvsZ+/55rv6JHoNdnVE85iC9x6NWO+4T6bxjPnQ2MgRoHEaGc7S1QnqPNo1ERp5I6j3KDHoe4Oc0Pn3nAzSc+gi/zy+BRaXB2kcCjfZvYcTY7+L2qeMwYqCsW1qJJOxuCUqFe5QA6b1HccZEZaTzmFBT3AtJ4zDuVRy0g6T3oFjiPjGSeo8ulxuuWtlITH1wNqaeG4Nvmkbi6yk5+HHWzRgQ92qnDhIBIkAEiAARIAJEgAgQgc4TiL4Z+s73oVslInn31C1BqXCPEiC99yjOmKiMdB4Taop7IWkcxr2Kg3aQ9B4US9wnRlLv0RvlpkM1t6HV9jneM5+Eo8N8dJIIEAEiQASIABEgAkSACMQ3gehzufHybsMZUxVKnv8D/vi2Ga3edN9BksaEI6mjfQldPOJ3UPTqfwRI76Tz/keAehwNBOjaEw1aiLwMpPfIM+9PLUavQX/+Y2x4agk0tcFMeSAhdTYeGT8CPWGKM8b6k86pr3yphkwG0nv/Ggqk8/6l72jtLY3DaNVM78pFeu9dvtFaO9d7pF5R63LjOPYp3q1txfVzNPjrh3/GqnQBuGMltPv34k9F9+OaYXfi0fRxtFg2UiOF2iECRIAIEAEiQASIABGISgJRa9CzC62wIQkPPTYPD9yRgfsfTAGOtWHEpHvw2PICPH1kNZZtOoTLUYmVhCICRIAIEAEiQASIABEgApEhELUGvezaBAhowhdHGtHCEnDL7WkQbH/HwS/sYG1XcBln8aH5KL6ODCdqhQgQASJABIgAESACRIAIRCWBqPWhH5B8J57ITMBP/zMHc0YZ8df7pkKZsBq/XvAT/G1oPbQ2QBg1AtdFJVYSiggQASJABIgAESACRIAIRIZA1M7QY9D38OTv1+KXD0/E5NHXY8CYGXimeBZgfgfami+AhHn4pWoahkWGE7VCPM47BgAAIABJREFUBIgAESACRIAIEAEiQASikkD0GvStDThQ68TtK1/DC8qRgOxG3FG4CZ9+VI0/lxfhRw+MRdtXTXBGJdYuCuW0wawrRa5CJkZh4aujZelFqDDWScJ2tsGmW+g6n6uDTWzqS+hykyGTJSNX92UnG+9M2RbUGbeidOE6mNs8zXSmvKcMvRMBIkAEiAARIAJEgAj0FIHoNejttajMycF/1HyNQd9yiznweoz/YSZmPzEbP/y4BMXbPosfH3rnSRhX5CEtpwBVLivdpeOaEuTPUOKh0gMSo76n1N+5etrMr+DBGY+hYM+FzhWk3ESACBABIkAEiAARIAK9RiC6fOiv1EP3yxfxlvUycOEEPgDw1ZZf4alDN0B65+H8+nPsOAa0XrgM70RxryGKTMXO+mq8uFoPIAWq8j9hnToFCaKRr8aM1XrUFJRi28NVUE8IprIxyK6sB6uMjKzUChEgAkSACBABIkAEiED0EJDayX0v1TU3QzlzFA5UVaHqzRo0AGg178Lr/LPk7/VdfOfYW/D4g7fh230vdY9I4LQ3if0FbsSUqeOQwGuVj4Yybx4yxRaOwtIYfJMtIITbS2sddpfmQsFdd2RZKKo8gC8PlCKZf04ulbjNeLpwGTbzJhSlKyCTKZBetAlmGw8M6nLzuSatwCVjQwHSrpEhudTc7obKWVeBLLG9uaiou+ipGMBF1FXMFV2FFEVGtEjO0CERIAJEgAgQASJABIhA1wkEm+7tem3dLjkAienPYsuuVDSc+gi/zy+BRaXB2kfG+83QA9/CiLHfxe1TxwWkd1uAPqtAPjQRSQAaUIOCZc8j8ZkHcHfmPZgwQY1qppbIFeYzCedx6JbkIKei1l1Wj5I8KxpVyTgvqc13eB4n3volHq/ajBp3Yk2JCmmfXIHlHRWG+jJ2eCSf8DCKClOhL9mHrfuOIW/CJJeOnMewb+s+AKmYn3UrLWbukCKdJAJEgAgQASJABIhA+ASia4aeyy0biakPzkZ29lyoNRoUPp6DH2dnI9vvbxYyUm/GiIGR21I3fKRdyymf8CheKldD4MW533xOOiYOHQCZIhel2//qnikPv25nvQEbRGM+E8WGRjgYg8NahrEn9rsX0gbWZUPNibF4xtIMxi7BangOSp5FfwC1XwFC9npcMWnEmw4kaWC6wlC/LBXt7wgTkZaVCQE26Ld+iHr3qmVn/YfYqrcBmT9DvvLGwMbpMxEgAkSACBABIkAEiEAXCUSfQe/pyIhUzF+2DP8v62YM8KTF9fswTFL/EWbTTpQXupxsxO7aqlAwZxbSUn+KiiPhOqpcRP2+d8E98pE5D3nK0eIsuVyYgV+szHPdNLRjKSBzvgqzJ/BAoIMgpP0rpol3F+0yXiVBjmFp92E+L6t/F/vqudvNOfz9bR30EJA5704kR++ou0rf6DQRIAJEgAgQASJABKKPQIyYVgxtrTbUfWqG+dMGnLkYV8EqJaNiEITUH0H9YjUYc8Bu2QtteaFrptxWgRWvmcL0PW+Dvem0WK9w2ziM8mpZjiHDEzFE0qLvcAhGjbjO58I0ZDhGBs/oKxLqaNjtmLt0FgCX242z5SC2le3i0/xYkBXoPhWqEkonAkSACBABIkAEiAARCIeA19QLJ3Mk8rCLJ7DvjVIUle7FGbHBS7C9/xKevH0CJt6WhrTbkjHyVhVK3z/ZbkFmJOTrnTbOwFiU5ootn1WBOvF+RY6ECUpkq1eiVCM6v8CmPYgvwnKhH4ihiSNFUW2fHMMp7/2PE+ebm0L40Pdkz0bg+w9nI1N0u/lfmPbvwSa+s+/8bNw3elBPNkR1EQEiQASIABEgAkSg3xOILoO+7f/w559n41+fLEDJWxb80wEwmx7P/9tKbP1CEuHlizdQMHsl/tQQfHln7GnV43fO3VTW4LcvfQCbaIQ70XpEi7VlrmWqQs7tuKW903qQ7g5G8t33u6Lj6LdiY81JcQMup82A/3p+Ywgf+iDVdCNJnnwn5mUKgH4Dil7YBhsthu0GTSpKBIgAESACRIAIEIHQBKLIoGc4b9qCX603AwnpWDj3u7hedgn/t2cbNnFj/vqn8Xp9K5wXjuIvRUrg7A68svsoHKH7FkNn5BimXICX1SkAalG19G4oBvBQkwMwdHKea6MpQY1VT6WFHR1GnjwDC8T69Fg94yYMkMkwQLEUx78zPYQP/dVxeSLxoIOwld5a5OORtSAbAsyoqWmgxbBeMBE6aK2DUbcZpblZKDK6nnX5t3wZtgPr3LsS8xClOtS1eh/l+GelT/2MgBOtdTXQbS9FbvJyGFuCjYsW1O1e49vVmi/e3y3d0bqfIaPuSgiEM36k2Y9Dl5+GrIoj8bXzu6SL/evwMk7qFkPh9TaQ9t6JFuNydyhtbuPIIAuaT1qGjsMlEEUG/QUc+2Q/apGEeX9Yj98/cw8EmRUfv/ORuEOq8PRjeCjpOsgG34wH1PORibP45JNjaAq3p9GeTz4W2a/qYdrxCgqV0tWoKVBptsBQswbqSXzBapgvXt9LWug1KpcBL6ig0Wux7tm7QvjQX71eefIDeL7MXR8EjIED0kjz/jUMwuj7sl2LY2kxrD+a3v7kPIKKx1agUrsaBVVfB2nNida/vwM9svGalUc/ehMPn/oVlM/XhLlGI0iVlBQ3BJx1G/HYr1+D9tkCVAV9CMp/sJdDmVuLe408KhaDw/wkml54Cs8HvXmMGzTUkTAIXH38SCu5jJM7NFhcYZUm0nEME3Ce/At+uXhdcE8A55fY88ZOyTkKlNGjqmY99AL4db07LzszaZQMUDKNye6q6Ot32ZLrwYAUtnBnI3N6qrdqmQpgUGmZ1ZPWxffuy93Fhnu52BWThiVxRkhhau0x5hDbO8tMmlmM97kn2HXcBQezH97IVAKXYQ4rt1zoOHuEz8ar3qUYHZZylolUVmg4LU1mzHGU7d17wj0m+CkHazYUM0EoZoZm10jxLxAfn/qDzntOUxeYpXwOQ7Ax4TjMyjMFJhQaWLO3QVd+/zTvSTqQEOgf47CD8eNl4WB200tMtXQpUwkCyyw/LLkmeTPFzUG/0Lt9P9OolrBCVQpDZjmz+P2ccH2XsUy/60bcqDdkRyKp9yiaoZfj2oThAM6gwdYMhjb888N3UHUWQMI0KG8dCVfUeYbzxy04COD666/Dt3r09iZ+Khs48R4sFGf6a1GRM050uZHJrkdawS4AKVA/ktpLu+y6dpWVugsJhQvx6ITB8QM31nsivxlK5RhfRCNcxqljxzFx6WxMGxZFl4RY5xyv8stvxLjbFLAd+BRfeN20WtFoOU+bxsWrznujX60mrF8LPLv0fozqjfqpzggTOAfz+s3Asz9D1qhgllkTDmx7A/qSF/HbCh2MdeGG4Y5wN2K4uSj69R6Mm773fUxCLV7/71Ks3/RHvPDfOnB7/vo5s/CvYwYBbS04YdqK3yz/o+iac/8dE3B9DMPvVdETpmHp5p3QelxuPI0pC1Fu0OKl7LESg85zsifeB2Lk2GTXBlQQoCzUomalMmzf/56QgOroBAHua1/xG/y2Pg+bl05DQieKUtb+SiAR0+Y+AWXNUjy0aBOOtF6EzbgR1aOK8f9o07j+Oig62W+P8adC6tD+sdNMJwHFWHYnWs1VWIvHsTA1Majszrq38WKJmUf+QEl+DmZMnIMi3RHRpTpoAUrsNIGwYqZ0utYuFZBj2A8fx3NPvYXHXvsdfuYK7AIkzMZzS+6DQtYG29uFGJuzQaw9Ib0Ez2R+xz1r36UG476QXEhF9rJK8S+SnR2Yugz1bFkkm6S2Ok2AL05agUkzVrv8GZXAI/XTkS1uLNbpyqhAvyIgR0LqImzePwi/mJ2HyUOLkVluxDs/n9RLkwT9Cm4/6KzP+FuXOgK0cCcOVO552rIuDQkhVjbKJ6hRzdRw2szY+c42/C6/BCU5yzDS9DqW8XFAr24TiKIZegDX3IK5a9+EsfIFLMnLw4Kil7Hzb/+Dn03li0EHIFHxHYyDgB/krcVbG3+GH15Pd/bdHgFUQT8lIMewjBdgZZdgNVWhEBuRo1wO3cnL/ZQHdbtzBAZi6IibMGXpahQqAX3+EqwwusLjdq4eyt3vCLSa8Kp2LF6gJ4JxovpzML9qxPgXFiI14eomJZ9ofET9IgxWPYqVB1G27SDd0/XQSIiiGXpXj2QJSUhXFSNdFdhDGQZNUmG39VmMExIQdYIHikufiUBMEOC7E8/H6g1X8MnEP2C/pQXZo2+MCclJyL4iwPfH2IQlvxuK3/zhFxi9dD6yVqgxY8YCJNJsW18pJUbadRl/Yxctxeir234x0qf+LCZ/2rIF2rE/wapObhopF2bgFyvzsPHJPTD9pxIZtH6r2wMppr5SshE3IZmM+W4rnSogAoEEXBuBBVvIFJiTPvd7As46bFvyPBqnfRcC/wWRj0bGC1th0gAFy3Xuna77PSUCEIxAy0Fs0xQj56ZvuWKQ8zjkw2egxGaDPn8yBsjmoqIudDDkYFVSWl8S4Atd/wervYE3eGz5kZjBfeX1+Zg4QNHB/gJyJNyUjClTknFTGDP7fdnLWGk7pgz6WIFKchKBmCPQaoWl4fuYPrETex3EXCdJ4B4hwMfKocAA9cNwy+23dnnTuh6RiyqJfgLDMvCilYl7F/D9C8S/ZgMKBQGZ5YfhYNugpoho0a9Hr4Q3IuNFk78+2WkYClOBzHJYHFZUq0OtrXGitfGfSC16GBPIEvUS7c4BYewOvV4t2wpzabo4i5FcakZb2G19CV1uMmSyZOTqvgy7VCQytplLkcxnZJJLYQ6/Q5EQrV+14TypQ74iC0WVB2Djm4A6T8L4X+txavlCZHbysWm/AkeddREYdjvmLr0d+hUabDziDj3X+g9sr/wIDyyYgWT6VaGRQgSIgB+By7CZ/4q3zDb3bsB8p/JX8NuaVDxDkbH8SHXnA116u0OPyhKBqCRwBsaiNAyYmA89zCiZMdJve2358Am4a6YVJXnToRggg+KpP+Fczkt4TZ1CYSujUp8RFqrFiCLFtZiY/yZgW40Zw28KeGw+AqlLX4Vp9Y3YNHm4y3ViggZNT27oxXC4EWZAzXWdwFXHT9erppIxTKD5Y/wuTSHuiaPIXYsPWjOw8jczXW57MdytaBJdxre36gmBZDKZ+NilJ+qKZB3RKzefoX8IaQU1SNKYcGRZapgLgfkMfTpyqgCVdi8qs8dEEmeHbfEZ+klpBWhI0sB0ZBlS+3Blc/TqvUOEdLIbBEjn3YBHRXuMAI3DHkMZUxWR3mNKXT0mbCT1HkUz9E601tVAp9OF/ed7fNNj7PuoIt73apTmTnHNdilyUbrbguZg0ogbARUhnbuu8L/0IlQY666+OUNrHXaX5kLhKSebgtxSHcy2y4DzCCqyFJDJ2i9gcdZVIIuXUSyHsUX0z0BrnREVRVmu9mUKpBdVtN/1za893lY16prJzyaYSimNCBABIkAEiAARIALdIsBn6HviBfAJ+u68rjCrdgF/WhD2X5LGxK50p0nX04lu1tD94o5GLVMLofvt7afjGNOqU4LwSWGq8kPMLopygmlVSQxIYirtCZdwIcuBCWota3Q4WLOhmAmcfWY5szg8fbrALOVzxPaEQgNrZoyFlFVQs/LDPAfPFEpOdx+TNMzUXcV5ROzie/fHaxcbpmJ9RoB03mfoqWEJARqHEhj96JD03o+ULelqJPUeRTP0MlwzIgkqlSrsv4xvXxsHO8WeQc3aF1BhA6B8DgbrJTC+2c/+l6ESpPdqTrTUbMDiiloIqo04bHeAMQfshzdCJdSiasVmHBBn0KVlXMfOegM2VNQCyjKYxHKX0KhdJEaksL13FKeccgxLuw/zeXv6d7Gv3h02zHkM+7buAzAHq/LvxDB4ZE2BqvwQ7GKUgmYcLldDsFVgxWsmtMAnJ5CJYkMjHIzBYd2HMlVKe+EohQgQASJABIgAESACRKBbBPrQizlQ7gG4MaMAlRmB6XH+2XkGxz6xAkiC6hk1MoRBYoeFafOQO/81VPF4ruLrPL44+BG43Y+qPEyuynOne970qDYtRUYQfn5bLut34Pi5/fh9/jpXXeeb0HzeCQy7FVnzU1FSsg9b9x1D3v9v71zAojrPff9niMYYRMqjOy4w1SMUsZFchJLEupMRzKA1JlaiphqGBE6PaYxJw1GIRnuamzbAJjUt2dqUiUB1R5Nhm9hUGQNOsslFMiQm2ioU3RiV8RytFZh4C8w6z1pzYWYcEi7DsGbmP88Dsy7f5f1+7zdrvetb7/d+CQm48PluVBrMgGY2ZsSPADr/is/0NnkqcpNQkeuo2/5dKS0QcQfGtzTbytYuw4q0WNty8MKdyM2eh6KKQ7ZzHlm5SwIkQAIkQAIkQAIk0D8CChqh70sDOmEx/xXvN5xCV1+yKTGt9WucOyqZ6VEYF3Wdi4QjMHrsKJf9f+L4wW8LQ3kep89fdEnvsmk5BF12EsJjUjA/MxOZuYUwOk6PjMbokVI3iEbqoqVQwwzD9o/QbJUWjNgKI6YixxGK7sxxHDzqyOjl23wO57++go5zZ+STwrgoXO9MpsLI0dEY6dznBgmQAAmQAAmQAAmQgC8IKNig78RZkw7596dglHMip30iaNgwjIqZitx9p2WnbF+AGLIyVNcjOk7ydWnFgZaz9hitkjSX0Hamw0Ws6xA1Lkrel6LefONYlMP53dxDRJtLaNrxHHIrJJebfJTp34Wp9TK+MRUhzqV0QIWI2+YgSyPY3G5Mn6C6sgEQ5mHprBtto+zXR2Gc7AakRpGpw2MxCWmRkE1YIIzAqOixcsnmAy04Lc2jlT9WXGg7B8/laBxn+U0CJEACJEACJEACJNA/Aso16C98is2PPImidxq8RnCJSJ6P+ydFBb4PvWoiZiyeAUgj45XbYZSizkBadGE7yiWD2vmJRkqGRvZ7P1ryKirkBV2uwFz7rC3ijTMKjTODfcOCk43H5G1h0u3ImP8TJN9wBh/o9+KqwXanLHUoK9iASjMgZM1CSqS9m9jdcgAjSl7R44jFaluUaI0t4k1MQS3aMQLxM2ZDI9Vo2I4txlPyQ4rV/DHKynfR3cZTPdwnARIgARIgARIggQESUKxB39XyBfYcsuB7C4vwl4/+Ey/MFIA710G/fx/+o2A2hkVOxwMzJyJ8gACGPvsIxGc8iBxp5Nv4a6THXIuwsGsRc/vjqJAd5h0SqhCZugQvSBNLzTrkygu6XIuY9F/LbjHaF5Yg1WF4O7LI35GYfPsdtgmwukyMDw9DWPh4pL9/BWqpTocPvZzWIYsZHxk/gtk5GdZRYDRSH1khT9Y1S378o8JtZW0wAEIOXngkBZEAVPHpWJYjTYA1YEP6eHkhifCYGciT3hLwQwIkQAIkQAIkQAIk4FMCijXoxYsWmBGHeQ8uxpw70zD7J1OBlk5EJd6FB9esws+PbMDKyoOQxrMD/aOKnY+Nxj0ockSBEbQoMphQU6R2b1rEVOSU6lFTlg/nGTmtHqU9rvI5HLHzn8GuLY48AtT5FTC99UesuCcOMEuTac8561HF3oWlWcm2fcdk2O6ziEjMQqmxBmX58hi8fEbQlsBgfBk5iZI5L1n0E7Bgox6GIq38IAFMhbZoD/5as8HDzceWnP9JgARIgARIgARIgAT6T0CxK8V2/W0T1DetQdeL72LP6tuBfWuRmP458kxv4H//j0+QN3U2fnuPHq3lC+xGY/8g+HMVr/5J6Odc0gTa5T9DbsU/oCmrxe6cRJv/vJ/FGOzqqPfBJqy88qlz5ekkFCViPwxFrUNeiNG29E1otj9UW+3P37uCwla6qzs8fjqWaiLwi2cysXBcLf4y6xaoIzbg2WU/wyejmqGX/Lvdoqi45+deHwmYq5Adk4kKRzZhNQoeSAhKY97RRH6TAAmQAAmQAAmQQDAQUKzLDYbfhId+9wp+dd9kTIn9HsJvTMeK1XOBht3QG/8ORCzGr7Spss92MChiyNswdgKSHGFv1KuhNz6NNK8++UMuKQUgARIgARIgARIgARJwIaBYlxunjOIVXLpyDUZcqwI6/4ljpk/x5WlAmDYdqd+PGHCUG3++DnG2iRtDToB6H3IV+F0A6tzvyFmhFwLsh16ghMAh6j0ElOylif7Uu/INei+AfHnIn7B9KTfLGhgB6n1g/AIxN3UeiFoLPpnZD4NPp71pEfXeG0rBl8afeleuy835z7Gz6mM0nb0U+ItHBV8fZYtIgARIgARIgARIgAQUQkCxk2Jx8b/xn5mZ+GnEj7DwsSw8OD8Dd90WjzEjfP8MIj1B8RN6BKh36jz0CLDFSiDAa48StOB/Gah3/zMPpRqV63Jzvh6bnl6H4s0G54qmEcmL8Vj2IszP+Ffc9oOxGOEDO1z6gTGUVCh1eVtbqXfqPPQIsMVKIMBrjxK04H8ZqHf/M1dCjf7Uu3INelkTVlw624zPP6jGzjcq8eqbn8IiHxeQvDALj6x4Ar/419gBhVb0J2wldC7KYCNAvYdeT6DOQ0/nSmwx+6EStTL4MlHvg89YiTX4U+8KN+hd1dOJ9qb/whtl/4bCwnflUfu4IhOOrEzGQPyG/AnbtTXcHloC1PvQ8h+K2qnzoaDOOj0JsB96EgmNfeo9NPTs2Up/6n0gtrCn3IOz39mOr76ow3t73sGfXt+KfUdtY/SS+82ixO8NOGzl4AjNUkmABEiABEiABEiABEjAPwSUa9BbjuDPutdRUVGJNxvMdhqJmPvLx5CzaPAmyPoHO2shARIgARIgARIgARIgAd8QUK7LjbkK2TGZqEAE4ub+HE9k3Y9Z6bdjypgRPh2V9+frEN+ojKX4ggD17guKgVUGdR5Y+gpWadkPg1Wz394u6v3b+QTrWX/q3fcxIH2llWHRSCnahpovmnBoVwmeWHw3fuhjY95XovqmHAsaimdCUn58cQM63QrthLnqUflcWHYVHO8r3JIM+o43GU6gKjseYWHxyK46MegSsAISIAESIAESIAESIIGrCSjI5cYKS9MHMBxqQ9TUmUiLicFNk87hfPPH+Evz1YJLR8In3Il5ycKAotx4L5lHSYAESIAESIAESIAESCAwCCjKoO849AYyM9+DVr8PaaMOoTxTcrnp+SNFuZlLg75nQD49cw2EBZsgipt8WioLIwESIAESIAESIAESGBgBBbnchGFYVBy02jQkRA0DhkUhQauF9lv+0m64zqf+9ANDORS5pbcatdAVZNjcccJiMLNAh9qmdndhLE3YW5yNmLAwe7okZBdXocF8BcBZ1BakyMdjCmrRndOK9to1tjwxa1DbfuU73X6sTTpkyHUsgq7pkosMl9CkW+SlDpck3CQBEiABEiABEiABEugXAQWN0IdjTNoqlKc52jEOz3TvOA7y24WA9dROPKnOhM7pVG+GsTAXxsoPUVb7MnISIwHrcVQ9mYlM3SGXnIdQsSoTew/r8elrC6DOfQyawlwYKt+D6Rk10iKl57xzMFUbYIYAdd58pEaq0OFSgrdNVcJ9KMhPhqGwDtvrWvBwQqLNHcragrrtdQCSkZVxMyK9ZeYxEiABEiABEiABEiCBfhFQ0Ai9h/yXmlC9dSf2fdGCf16yepwM7t2jq1IwzDmaLo2qD0NM5maPRp+F8ZX10JmnQlt2EB2iCFFsw+GyHAhmHda+bpJH263NNdgsGfPqEpg6uiCKl3FSvxwCAPP7x3DaCqjip2OxRgDMBlSbztnqaf8S1ZUNAGYg676bEeFRu/fdaKRkaCDADMP2j9BsV5u1+SNsN5gBzWPIVY/xnpVHSYAESIAESIAESIAE+kVAsQZ9V+MerH7op0ib8yrqL4j9alxQZ+o8js/0ksF9CBW5SRglPwCMxpRcnRwFxyyNtrdboUrIQbUoomvbXThp2Ikq3To8lFlqi5Rz4RzaLkgW/UTMWDwDQAMqq79EO6xoN72HSmnkXzMbM+JH9BKlCpEps5AlPS0Y9qCuWXK7OY/P36mCAQI0i6cjXrE9rpdNZDISIAESIAESIAESUBgBxZpXqhtvgiaxd+PCCmM6YHGkyb7fyCPu0qi79PcNWvXL3Ms9cxwHj7ofctszn8P5r62A5RB02UkIj0nB/MxMZOYWwuhIODIao0dKXWAEEh54FPnSIL38IHDW7m4zFTnL0vtmhEdOw6K8uQBsbjfW9s+wo+RdQFiAZRmTGJHIwZ7fJEACJEACJEACJOAjAgryoXdvUdjwG6F+9CHUri3CA7P/L3659G5MvTEKw1yShXTYyuujME72m1GjyLQLK5O9PfxIk1GfQ26F5HKTj7IVd+OWO2fhltZXkJiyCm7PA5E3IyMrGYWFBlQbpgCSu42wGktn3dhHIzwKt923AJpV78Kw/b9guvG/5ZF+IX8BZsUOd9EeN0mABEiABEiABEiABHxBQLEGPToO4T9+uQmfSq38tAIvfHp1AMuQDlvpNMCNKHlFj3tLs5A40ozatTlI32CAkF+DIy/djJONx+R+Iky6HRnzf4JYnELt7/a6G/NyimikLloKdWEeChdqbXnyZyFFniAr7/b6n8Mn32DYjIIr52FGMvI5GbbX/JiQBEiABEiABEiABPpCQLEuNwxb+V1qjEbqIyugldxkKh7GlFHhCAsfLxvzEHLwwiMpiEQkJt9+h20CrC4T48PDbGnevwK1NLrv8KGXq1Ih4rY5yJImx8qfuchbNK1/EWlUk5CxbAEENMBoPMrJsHaifvtyC1MqhTKttIcodZWgHU17X0Z2jD2UaUw2ivc2weKahNshSkAKh2tE1VvFyI6XQtb2FJSgO+SttMJ1WFgMMnRH0FPqEIUZ2s2WoqzlpnjpF1dgbqhEwcwYhIUlIfvlD2FmxwngvtK7+4nV/CFezk6yhc+euQZVniG2A5iAEkRXrkEfMR4pmp/i4bxn8dvNr6O8vPyqvz9k/RDhSqA4JDKoEJGYhVJjDcryNU7sVW9EAAAdL0lEQVQJBG0JDEZ7yEoMR+z8Z7BrSz7UcgoB6vwKmN76I1bcE+ce1UY675wcK02GXYD7botyltu3jeGInbXANjmWk2H7hm6gqa3H8fZrtcB9v0OrNBm69U3cd7oQKUtK0WBx3DGv4FTVGqizD+Hu2jZ5nkZXw0M4t/4RPF97dqASMH+AE7A2bcGDz74O/ROrUHGh58ZYT32ArXIkLEeaGVg8Y2IfXfQcefkdfASu4NTOIjyua/VomhWWhlIsWXkMGdtaIHbtQfaZDVhSUs8BBQ9SgbHby/uJ5QvsNITjwdcPQuxqxf77TuFx9W++ZcAgMFqvKClFH30AyS7w3afzwEbxNkCEsErc849O3xXsUZKv5fYoPkR3u8SOw1tErQARWCiWNV5UHIdg1XtXc5247+RlN95djWWiBslifs0Z2/Guw2KZRhCF/BqxzZnyothYttDjmPNkUGwEq84HRzm2/gBhtVjT1uWlin+KpiJtd5/ykoKHvBMIjX7YJXaYNoravDxRKwiipuyw6OxF8vVnunvfaasR8wVl3iu8a7HvR4NW7726n1wUm/d9LJ50dgJRFGWdu9yX+o40IHL4U++KHaEP5Sg3inri65MwnfbVZMMxasrDqDADQv6jeCCht2Ev+1QZE3shoIr7MdQek49V4ybiVocnlZRHNQYTb42Buf4L/N05am/BycYLXPjLC1Me8kJAjl5VgcLni6CrMqLJ2Y+8pOWh0CNgMWHTK8ATebMxzqP1tnVJYjF5vEsgB3lO2Cl5QULHe0SPbNxVKoFe3U9GIE59B2JdLE7r6RYcmLwUi1KjldqygJPLBa+yZHdEuflRhxTlJgfrNuqwvaoKVS5/bzeY6a+pKLVdg7ET4hEnyyS59+hhXKfunx++otoVBMKMvAO3T3as0WufAG3Mw7zllThiuQRz7RZUj1uNX3LhryBQ9mA34RKa3tqEQmmdCmMhcjNnYvK8tfSHHWzsAVP+eTRs2gY8oUXyKE+n2EtortsDgxCPieM8o55ddluQMGCaG/KC9vV+0o6mWh1Wv2hGwbblSI5QrBkacJpllJuAU5myBb4meSWaxZXKFjKkpJMWCTPiwKNarHOO3KsQkbwc2/YPx9PzpQnVq6Epq8XupxLp/xxSfaO/jR2BhJwdEHOkiY0G7N7xO+QWbkDmsrEw7XqSN+j+Yg2KfJJ/fAVewRKUJkdBXq7crV3Sm8BjQNJsjKch50YmcHf6cD9pr0VBYrptMAAa4P5MpC5I7OVK9IFLyF+SK9egHxaFBK0WtgCK3nFce8N1CPN+ikdJgAQkAhYT/lA+ButLUzwumtdgVNR4JOVtQP67r6Aw90msnajDC2mxNOrZc3pJYDiE5HuRk6zBnIwNWJK+FTvqs5CcNqaX+Zks6AhYTHhNPwHrX0j1uN4EXUvZIDcCvbyfRKbhpVYRG8z1qPztOjycuRBn9X/Gawsm8L7jxrN/O8o16Mek4ZnytP61irlIgAQAnEfDa7sRvfopj1FTKyxHKvHkb0fhuVefRmxeFjKk9QvSlyHa9CeslEbW+CGBXhMYDiFtOdbl78JD1V/imbQ0utn1ml0wJZSuN7WYsDzPzVfavYURGD95ElDZjJMWKxL6sc6Je3ncG3oCfb+fqIRUZG/YiK4DaVi7/ygsCybwmuEDRQao85KITssJHPr7P+hD74NOwCKCkcAVnHr7DRya8xRyEh2+8/Z2Wpuw48nncTL1hxCkK4AqFmnrt8NUBKxaU4UmzkoLxg4xyG2SDLXJSJocw5HZQSat2OKlidJFq5E5/lpbnHFpbYLRknuFGYbcKQgPWwRdExA/Y7bkbOH+sZ5Fy4Hz0CyejvgAtUrcGxRCe/29n7iGyQ4hXIPZ1MD66XS248QXe1Hx4i+gufWHmP92Cw36wewdLDtACVyBuVaHHaPmIctpzLfjSHkljNIiQZZWNB70DDAeiR9Mu1lehCxAG02xh5SABSebk1DwQAJfnQ+pHoawcrs7hSiK8toW8ndbDfIFAZqyw+gSdyAnYQTklcST3ke16Vy3sPI1aRrXMegmEjhb/b6fSPMp2jDn9jgOAvhI2wFg0HfCcuILGCrW41FNCr5/qwbZazdj39FgX9PSgobimfJIR3xxAzp7rfATqMqOR1hYPLKrTvQ6lz8SdjYUI14atYkvRkPvG+QP0YKojnY0Vf0aS9J/gbz08QiXV/CUVvEcjSnbvkGMNBEtchoW5U2DYW0Rthxpt7Xd8je8Vf4x5ixL5whZEPWGQWmK1YyGt//Svfqw1Yz6l0tgnJUFNV0oBgV5UBWqSsCi9Q+g/vlS1JqvANZTqP1NCerzVmIRQxwHnqp7cz+xrxjcvWq5NOhUipdOL8EqzY0cBPCR1hVq0EsuNV+h4V0dXnx0Lm79/q3IyH4Gm/f9HYj4ERbmvwL9R4345PHboNxJAD7SEIshgV4TsK/Yl7kBxqvyCC6vs6OQnPcaTBvGoHLKaNvr8YQinHtoMzZyctJV5ELugBSJIuY6TM59EzBvQPro8cjQHXF5G2pF2/6NSImRXCuSkF3yASxzn8ZznFAdcl2lfw22R0V5aQzKk69FWHgOqif/CtvyOJG2fzyHOlcv7ieq7+GHP74FjYVa23Uj5ufYev5ebHk9G4mMduQzBYZJS235orSwsDD5NduAyupsx1df1OG93W9i00tb8KlzEP4HmLkwHuff3I3PtXq0li/wmWuAT+QeUKN7yiyN0M9Dyioj4opMOLIyuZcPL9II/UxkVgBa/T6UL7ixpwr8flwaoU9MWYWjcUUwHVmJ5CF8GlOu3v2ulpCpkDoPGVUruqHsh4pWz6AJR70PGlpFF+xPvStohL4T5nfyMSFlLnLXScZ8BOLmPoWNb9TgwFcmGDb+TyQpWm0DEc4KS1M1irOTbKOlMdko3tuINm9FWppQqyvATIcrxcwC6Gqb4Hz28ZZHOmZpwt7ibMQ48kkja8VVttfm1iPQZcQgLCzGYyQOsDbpkCHliVmDWsn/GpKstdAVZNgnPsVgZoEOtU121w1H/W71SXVVo6mNfjYOPPwmARIgARIgARIgAZ8RkEboffEBpAH6gXy+EVv1y6S3BSIQIcbdky+WGQ+LZy522Qpt1Yta6ZxWL7YOpBqPvAOX26PAfux2ndSLOYLUbu9/cUUm8Rup3K4WUZ8z1Uu6qaK27KDYIdf9lajXxolAnKjVf2WTpsd8EIUcvXiyq0tsq1ktClL9mjKx0Y5cFC+KjWUL5fqE/BqxTRKhJ1mFHLHssJTi2+S0ty+uSDTJDbIlH4r/StD7ULQ7lOukzkNZ+8ppO/uhcnThT0mod3/SVk5d/tS7gkboVRgVdxfyF/4IEbDg6N5C5KqnYOzUOXj0xQoYvjyBr332GKOkgs7C+Mp66KRl1NW/Rk3rZYjiZbTu/z20gqucVrQbN+Nx3SEI2i043NEFUexCx+Et0AqHULF2G+rlEXTXPLZta3MNNusOAeoSmOR8l3FSv1x2WzK/fwynrSpEpsxCllSfYQ/qmi/ZM7agbnsdgIV4IXc6IuGQdSq0ZQfRIUczaMPhshwIZh3Wvm5CO7rlBDRYXXMSXaKIrtY6lGinXi0cj5AACZAACZAACZAACQyIgKIM+ohbluClHR/ixNFPsGvTGixMFoCjBmxem42M2b+EXmrqiSP4sukMLknjxsHwkePvtgKIg3ZFDtKE4QCGQ0hdjOysZJcWXsDfP/sYkt1vrngYU0aFIywsHKOmPIwK+aDBPQyYS05VQg6qJaN62104adiJKt06PJRZKpeFC+fQdsEKRN6MDLm+Omyvk8KBWmH5fDcqDWZAMxsz4kcAncfxmb4BwCFU5CZhlOy+MxpTcnU2uSrfg6n9Ek63NNvK1i7DCvtEOZVwJ3Kz5/ls7oNL87hJAiRAAiRAAiRAAiFNQEEGvUMPwxA16Xbcu+xF7Pjkrzj68S6UPf8wfhRhP7/vGcyePAlT0x/Dyx+ccom84MgfYN/Wr3HuqGSRR2Fc1HUuwo/A6LGjXPb/ieMHvy0M5XmcPn/RJb3LpuUQdNlJCI9JwfzMTGTmFnZHQRkZjdEjpW4QjdRFS6GGGYbtH6HZeg71O7bCiKnIcYQyPHMcB4+6lOu5aT6H819fQce5M/IZYVwUrnemUWHk6GiMdO5zgwRIgARIgARIgARIwBcEFGjQuzTrmu9h0h33ImetDh+Zj8P05zI8r51uc8nZ9+8orT8d+Aa96npEx0m+Lq040HLWpT2X0HamwwXGdYgaFyXvS1FvvnFdvEPebu4hos0lNO14DrkVkstNPsr078LUehnfmIoQ51I6oELEbXOQpRFsbjemT1Bd2QAI87B0lj1O7PVRGCe7AalRZOroXjzEKcsmLBBGYFT0WLlk84EWnHauOmrFhbZz8FzOyE0E7pAACZAACZAACZAACfSZgLINemdzwnBNxPeRPDcHa8vfh/mrA6gufxH3Rg9zpgjYDefyx2YYKrfDKC20gSsw129HuWRQOz/RSMnQyC4rR0teRYW8IJC0OMOztog3zig0zgz2DWk1tmPytjDpdmTM/wmSbziDD/R7cdVgu1OWOpQVbEClGRCyZiHFsViM0y3HiJJX9DhisdoWBVlji3gTU1CLdozoXtrbsB1bjLa3KFbzxygr32VzxfEUkfskQAIkQAIkQAIkQAL9J+CrucD+nMnrK5mlcpQgd4+RY+xRb5xRbjoOimXavka5uSye1C+3RbBxjaIzXS2qpcg6wmqxps0Z1sYjis1CsazxogvuLrHj8BZR6y0iD6PcuHDiphIJKOG3rkQulMm/BNgP/ctbKbVR70rRhH/l8KfeA2SEvv8PLIGQUxU7HxuNe1DkiAIjaFFkMKGmSO0ufsRU5JTqUVOWD+cZOa0epTlT4Zhm4J5pOGLnP4NdWxx5BKjzK2B6649YcU8cYHafTKuKvQtLHZNxHZNhnQWqEJGYhVJjDcryNc6jgrYEBuPLyEmMtB1TTcCCjXoYirT2SbBToS3ag7/WbPBw83EWwQ0SIAESIAESIAESIIF+ElDWSrH9bMRAsvlzFa+ByOm3vNIE2uU/Q27FP6Apq8XunEQE41Mf9e63HqWYiqhzxagipAVhPwxN9VPv1PtgE7hmsCtg+QFCwFyF7JhMVDjEFVaj4IGEoDTmHU3kNwmQAAmQAAmQAAkEA4FgHHwNBr34vw1jJyDJEfZGvRp649NIc0yG9b80rJEESIAESIAESIAESKCXBOhyExYmh1/sJS8mCxICfP0ZJIrsQzOo8z7AYtJBI8B+OGhoFV0w9a5o9QyacP7UO0foB02NLJgESIAESIAESIAESIAEBp+AT0bopScQfkiABEiABEiABEiABEiABLoJ2CKkd+8P1pZPJsX6S9jBgODP1yGDIT/L7B8B6r1/3AI5F3UeyNoLHtnZD4NHl31pCfXeF1rBk1bSu78+dLnxF2nWQwIkQAIkQAIkQAIkQAKDQIAG/SBAZZEkQAIkQAIkQAIkQAIk4C8CNOj9RZr1kAAJkAAJkAAJkAAJkMAgEKBBPwhQWSQJkAAJkAAJkAAJkAAJ+IsADXp/kWY9JEACJEACJEACJEACJDAIBGjQDwJUFkkCJEACJEACJEACJEAC/iJAg95fpFkPCZAACZAACZAACZAACQwCARr0gwCVRZIACZAACZAACZAACZCAvwjQoPcXadZDAiRAAiRAAiRAAiRAAoNAgAb9IEBlkSRAAiRAAiRAAiRAAiTgLwI06P1Fupf1dDYUIz4sDNJywT3/zURxg8VZotXcgLffKkZ2jEuemQXQVRnRZLE606GzAcXxLml6qCO+uAGd9lzWJh0ynOlSUFB7trs8x5azXHe5HKf5PXQE3PpGzBrUtnf3B6u5HuUFGXI/i8kuRb35ytAJypqVRaC9FgWu15OwRdA1XXKTkf3HDQd3ZAJnUVuQ4v3elaFDk/PycwXmhkoUzIxBWFgSsl/+EGbnOaJUPgErLE1GVEl2R7z7fcUpu6UJe4uzEWO3H2KyX8bepnbnaccGryMOEgP/pkE/cIZDWIIVliPleCQ5BfMXrkKF2UUUYyFyM2di8rznUdtvQ+0Smuv2wOAstgGFL73jclF2nuCG4ghcgbm+FI8kP4yqlhuRbWyD2LoeaZH2n7ylHiVLnkNjhg5d4mU0ZJ9FwZJSNLg+ACquTRTIPwSu4NR7Vah0vZ5oZmNG/Iju6tl/ullwq5tA+5eormzo3nduCdAsno54+fJjhaWhFEtWHkPGthaIXXuQfWYDlpTUo3uYypmRGwokYG3aggeffR36J1ah4oIXAa3HUfVkJrIPpqG2owuifI9px3r1b9wGlcDriBd4AzgkhvgHgIIJdIimIrUoyRhXZBK/8ZS0Y79YpBbk84K2RDQ0ttlTXBZbTRVivv0cNGViY5dnZlH8xlQkxgEi4opE01WFi6LYdVgs00jlJ4t5f9go5ggQgYViWeNF98K+MYlFcdI5tVhk6nA/p9A9Zet9oNC6xA5TiagWtGLJ/lbxatVfFBvLFopCfo3o6DGieEasyZ8uasoOe0k/UHmUkT+4de5DxtJ1RbNOrGm7uufYagnN/uMrwsHbD7vEtpqN4rqakx7XEOnasqz7viHfV6aL+TVnupG21Yj5gpd7S3eKgN8KPr3brgMQVl91rehqLBM1SHbX8VV6D43riD/1zhH6ATwMDW3WS2jaUYxVRjMgrMaffvck7kmItIs0HEJyFjb86ffIEQAYXkWZ0YurzHc0wNr8EbYbpPI1mLv4QSzNSgZQh+11LeDb0e+AN5SnLSZsWrkVk37/HJ5MFXDVj9zagrrtnyFpcgwinHJGIyXjbhzc/hGaqVwnldDbsKK9fidKDH/E8y+Woaq26epRU/af0OsWvWpxJ74efz/y02LdrjnWpnfw0oFU5xse230lFpPHd199EHkzMrJO8d7SK87KT6QaNxG3Cq2o/+xY9/XD0orGo3cjIyXa1gBeR3yuyKvu9T6vgQUOEgELTjYek8uOy8vEXQ5XCpfaVLF32Y3wBug/O+70i3dJ8i2b3e42QtYspESOQUqGBgLMMFTuxud0zfgWdkN5yv6gh3T82PomHpH9oJOQXVztnE9hu6FG4daJY9xuvLLUhj2oa3b3lR7K1rBuPxOwNuGtl7bADDOMhf8LmelqzCuocvYdSRr2Hz/rJGCqGw4hYYLLIIEkuHQf+RDjl6Xb3W3s9xUhHhPHDfdo2WUYOKDgwSRAdyOnYVHeNBhX5WK57hAs1lOoLX4P47atgNpuq/A64nvd0qD3PVM/lXgR50+fBxCHH0/6F1zjtdYIjJ88ST5z9OBxnPGapoeD8tNzHYBkZGXcjEioEJkyC1nSiL9xK3bUn+shIw8PKQH7qIc6dSpu+fETKG/tQsfhlUDJI1i2yQQLrLCcbMZBTHIfIRtSoVm5YgioEpFT3QqxqxWmnX9AvhowFj5u7zuSlOw/itFVIAgiXY+qYrF01o32wQP7QFRSPMZH0PwIBBX2T8YoJOe9hv0l07A3Nwmjwp9Cy0O/wlPON8a8jvSP67fn4i/q2/mE6FkrLJ/vRqXd3cb5ikx+LSq53TSgsvpLXD1fPURxKanZ0mvNg1FIzZiDZEEaAVMhInExnnlhBoyrirHDI1KJkkSnLAoioBKQfP/P8VLNp6hZnQRjyU7Uu0RIUpCkFEXBBKRR2Kqb1Ejx8gZZwWJTNF8QUF2PqAnJyCvKgxpvInfZSwMI0OELgYK/DBr0Aavj6xA1LgrAUXx47P/14E7j4paTNAFje93Wc6jfsRVGKb15A9JHh9vDkI1FeqEtgoG58j2YeIPvNVF/JbSebsEB1+gkcsUjED9jNjQ4hsaTFxAxPh5J8jZjSvhLLwFbjyoWaU8XIB8GVJukt3Iq9p+AVaa/BZfca+pxk/yG11G3/a3xwWacpNumA0oQfrfjiO5XKMH9yFv5b6hpNWA1NiPdGUmN15HBUDoN+sGg6pcyXdxpSl7HO6eujiFuPfUBtsohxJKROW1CD245XoTtMfSYS1rzLmx97wQnx7ogUcKmYzLSgZazXnRjc7NRxU/HYs21HuJewemWZpg9wxN6pOJuCBKIiMHkpMlOFy32nxDsA/1psuxu8y/dkyDlMhyDCx4FWs+i5cB5l9CWHue5G1AErE1v4cncVqROvUF2tVIJ92D9rp0oQinW7GiS7028jvhepTTofc/UTyWOQMKilShSC4C5FJkPrUN5g9luxNkW7Vj90OPQSaO16qVYlGqfWf6d0lnRbnrPFoNaWI2aNimGrOjydwY1+ZLbzSHoNtcwIsp38vRzAtktKgYHP/yby0Itdn9Fh7GumogZi2M93KaktzmneEP1s7oCojpLK5qTc/FAgj0OPftPQKhtqIXsyd1GNuSS3re/8bFLKbsKTsPiGROvnqg/1A1h/X0k4PCP98gWMQnTUm/oPsjrSDcLH23RoPcRyCEpJiIFj/77BmjliaqFeDglBuHyqmzXIiZFi0IppKX616jZthzJvZ6AdA6magNkr417UjDlKt9HKbyhFO1GCofpGRHFiFUpo7ysEhiP7KoTQ4Io9CodA/UTazBn9//Bmi2H5JBhVvPHKCs/jrz1C5Ag/+JtD4N59SX4Te0pWHEF5tpSPF//ANYvSuANNfQ6jbPF8srCbzc4Hwat5g/x8oufYdaKGXAExQXYf5zAuNEDAW/uNvakqgQsWv8A6p8vtflUSxFQflOC+ryVWOR4aOyhVB4OBAIqRKbOR566Dmtf3I4jsmuVtAjmuyjX34ZlGZPs9xheR3yuzYBfrWGADfBn0P++i/odC0s5CuxoFGveLBK18sJP0gJPEKHOF8v0+8TGjp4Wh+lhYSl5gQ+pDKHnRYY80zgXlrLXLdXv9hcnavVfOaRVxLey9T5QRF1iR+MesUg71dkXtpiuXmCqq7VOLJHTCKI6v0I0tV4eaMWKzh/cOvcN+q5Wg7jasSCdoBWL3uz5GhJq/cc3hEX5N+mrshRbjrSIUM5G0dTj/eey2Lr/9/Z7lkbM37JfbO35VqXYZvZFsKC6/jhtAMe9/mp7oat1v7glX+O0BdwXv+wmF+zXEX/qPUzC6vOnhAAqMCwsTHYnCSCRKaoPCFDvPoAYYEVQ5wGmsCAVl/0wSBX7Hc2i3r8DUJCe9qfe6XITpJ2IzSIBEiABEiABEiABEggNAjToQ0PPbCUJkAAJkAAJkAAJkECQEqBBH6SKZbNIgARIgARIgARIgARCgwAN+tDQM1tJAiRAAiRAAiRAAiQQpARo0AepYtksEiABEiABEiABEiCB0CBAgz409MxWkgAJkAAJkAAJkAAJBCkBGvRBqlg2iwRIgARIgARIgARIIDQI0KAPDT2zlSRAAiRAAiRAAiRAAkFKgAZ9kCqWzSIBEiABEiABEiABEggNAjToQ0PPbCUJkAAJkAAJkAAJkECQEggTRVEM0rb1qlnSsrz8kAAJkAAJkAAJkAAJkICvCfjLzL7G14IHWnn+Ah1oXCgvCZAACZAACZAACZBAYBCgy01g6IlSkgAJkAAJkAAJkAAJkIBXAjTovWLhQRIgARIgARIgARIgARIIDAI06ANDT5SSBEiABEiABEiABEiABLwSoEHvFQsPkgAJkAAJkAAJkAAJkEBgEKBBHxh6opQkQAIkQAIkQAIkQAIk4JUADXqvWHiQBEiABEiABEiABEiABAKDAA36wNATpSQBEiABEiABEiABEiABrwRo0HvFwoMkQAIkQAIkQAIkQAIkEBgEaNAHhp4oJQmQAAmQAAmQAAmQAAl4JUCD3isWHiQBEiABEiABEiABEiCBwCBAgz4w9EQpSYAESIAESIAESIAESMArARr0XrHwIAmQAAmQAAmQAAmQAAkEBgEa9IGhJ0pJAiRAAiRAAiRAAiRAAl4J0KD3ioUHSYAESIAESIAESIAESCAwCNCgDww9UUoSIAESIAESIAESIAES8Erg/wP22U8gza8+bwAAAABJRU5ErkJggg=="></p>
<p>A <em>χ</em><sup>2</sup> test is carried out at the 10 % significance level to determine whether the arrival status of incoming flights is independent of the distance travelled.</p>
</div>
<div class="specification">
<p>The critical value for this test is 7.779.</p>
</div>
<div class="specification">
<p>A flight is chosen at random from the 180 recorded flights.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the alternative hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <em>χ</em><sup>2</sup> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the associated <em>p</em>-value.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State, with a reason, whether you would reject the null hypothesis.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that this flight arrived on time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that this flight was not heavily delayed, find the probability that it travelled between 500 km and 5000 km.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two flights are chosen at random from those which were slightly delayed.</p>
<p>Find the probability that each of these flights travelled at least 5000 km.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A transportation company owns 30 buses. The distance that each bus has travelled since being purchased by the company is recorded. The cumulative frequency curve for these data is shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAg8AAAJkCAYAAACWFsI7AAAgAElEQVR4AeydC1hVVfrGX9QxLeziZQqzMjXMytQEk9TJS2pmhWlmWYOOMaUVpc0govafLuJ91MTKcdQRMhslLDIrNS8VlSmKZo6CZhcVMxVLSQyF/X/WUejAOZy1Dqx9zt7nvPt5jHP2+vb3vd9v7eRz772+HWIYhgFuJEACJEACJEACJKBIoIaiHc1IgARIgARIgARIwEGAxQNPBBIgARIgARIgAa8IsHjwCheNSYAESIAESIAEWDzwHCABEiABEiABEvCKAIsHr3DRmARIgARIgARIgMUDzwESIAESIAESIAGvCLB48AoXjUmABEiABEiABFg88BwgARIgARIgARLwigCLB69w0ZgESIAESIAESIDFA88BEiABEiABEiABrwgEbfGwbds2pKamegWLxiRAAiRAAiRAAkBIML7borCwELfffjs2b96MzMxMdOrUiecCCZAACZAACZCAIoGgvPIwc+bMMjyjRo2CKCa4kQAJkAAJkAAJqBEIuuJB3K4YN24cJkyY4CAkrj44FxNq2GhFAiRAAiRAAsFLIKhuW4grDA899BAaNWqEf//73wgJCUF6ejoGDBiAnJwchIeHB++ZwMxJgARIgARIQJFAUBUP4gHJIUOGYP/+/WjSpImjeDAMA3/9619x5MgRvPnmm6hbt64iOpqRAAmQAAmQQHASCJriITc3Fy1btnRcaejfv79jtsWVB1E8lI6lpKQgJiYmOM8EZk0CJEACJEACigSCpnhwd3WhtHgQrCpelVDkRzMSIAESIAESCDoCQVE8LF++3O1zDc7FQ8XnIYLuTGDCJEACJEACJKBIIGhWW4gHIz09ECmedZg6dSratGmjiI5mJEACJEACJBCcBILiykNlU+t85aEyG+4nARIgARIgARIoTyBorjyUT5vfSIAESIAESIAEqkqAxUNVyfE4EiABEiABEghSAiwegnTimTYJkAAJkAAJVJUAi4eqkuNxJEACJEACJBCkBCxWPBTh0KZXMKRxCEJCGqNbwnLkFpS4TE3JoU1ISejt6BDZeMgr2HSoyMWGO0iABEiABEiABMwhYKHioQQF2R9gNfrjP3kGivPScO+P/0DXlzbghHPuBZswY/CLyOm9EMXGb9gy5CgSBr+CLW6KDOfD+JkESIAESIAESEAPAesUDyXfI+uXW/DnDmEQomqEReHRIfcAr3+ErBOlVx9OI3fZdMzo8CzGdL8SNVAbYd2fxHMd3sLYZbkotdKDhl5IgARIgARIgATcEbBO8VDjWnTtepWjcDgntAg/fvc9Wj7bDx0uPi+z5DtkLt2K1i0bI7Qsm/qI6H07diz9HHtZPZRR4QcSIAESIAESMIuAdYoH5wwLcrFu4YtI2jsUS57tUFYolOz9HEtXX4q2TRs6FRnnD1z9ITL3nnb2ws8kQAIkQAIkQAImEKhlgs9quCzBiXXjcX2PSTgkvHQFovfeiv7hFwMoQcGBvdiBZhjU5PfrDtUIxkNJgARIgARIwHYExJugjxw5glatWqF+/fp+0W+x4qEGLu4+EXnG8zi0ZSlm/T0BA7qeQPrmGeh/pfdSo6KipFBVbKROaEACJEACJEACGgmUlJSgqKgIv/32m+OneHnjiRMnUFBQUBbllltuwZYtW8q++/SDYeGtOGeB0QvtjdFrjzhUVvx+Tnqx8cvaRCMMA40FOYVeZQPAo31GRobHcTGow0bFR8eOHautRSWODhsdWlXY6tAq4sj06ooj8yMbV9HqS24yvTKuKlpVbGQ6VHwIG5leHXF0+PCVVhVuKvnIuOqKo6JFZqNDa1XyOXXqlJGTk2Okp6cbSUlJRnR0tCF+P4k/kZGRRnx8vGNs1apVDjthLzYVvQ5DE/7j/T/nfVja1GhxGwb1WoCc8zErfj+3WzxYuReHet2Jzi3q+FAdQ5EACZAACZCA9wTy8vKwevVqZGVlYdOmTcjIyHA4iY2NdbzZ+YknnsCdd96JIUOGQLzx2YqbpYsHFOQh55t2uLWleOZBrN9sis6DrsT4VV9hXPfuOLe3AAdyDqLXoNvQwpqPf1px3qmJBEiABEjABwTE7YacnBzs27cPGzduxLRp0xxRo6Oj0aFDB4hCYerUqQgPDy+n5t1337Vs4SCEWqZ4KDm4HH+N/BcaTnoJI//cAWE4iHWT5+LHsf+HXlfWPg+1DsIf+DuevedFTF7XEhO6N8Lhda/gpU33Y/pz4a4rMMpNBb+QAAmQAAmQgPkExJWF5cuX44MPPsD8+fMdAcVVhS5duiA7Oxs7d+7Eww8/bL4QEyNYpniocUk4OvXMw6NDb8XUoUBYzDTMefpl/Kf9uaZRZQxCO+DZJYl4ecydqNnjGLqOnoLpSwahfSgvO5Qx4gcSIAESIAGfEcjPz3fcghC3IcaNG+eIW1osPPnkk2jZsmW5qwg//PCDz7SZFcgyxQNCb8KwlB0YliJPtUZYJ4xK2YFRCrZyb7QgARIgARIgAe8IHDhwAOvWrXNcYRDPLERGRiImJgaZmZn47rvvbH9lQUbDOsWDTCnHSYAESIAESMCPBLZt24aVK1diwoQJ2Lx5M8RzC/3793d5ZuHYsWN+VOmb0CwefMOZUUiABEiABGxIQDRkEisjUlNTHQVDz549HcVDRESE3xo0WQFjiFj+aQUh/tAQEhJStkTGH/G9iTlp0iQkJiZ6c4jfbO2kVUCyk15qNe+0Jltz2NqRq7hy8NVXX+GLL77Al19+CVEwdOrUCS1atEC9evXMAVUFr4Kt0OiXzYTeEbZxySZRrlMla6IijpDZqDQukflQiaPDh4gj06srjsyPbFxFqy+5yfTKuKpoVbGR6VDxIWxkenXE0eHDV1pVuKnkI+OqK46KFk82ovHSjTfeaMTGxjqaM4lGTaJp07Fjx4TEss2Tj1IjmY1sXPhRsVFhW6pJ90/etvBLycagJEACJEACViBQelsiLi4OoaGhGD58uKMvQ8W+C1bQaiUNXN9opdmgFhIgARIgAdMJiMZNn332Gfr16+dYRrl9+3bHKokbbrgBTz31lEvDJtMF2TAArzzYcNIomQRIgARIwHsCJ0+edDz4OGfOHMfBYmml+NykSRPH9xo1+O9pVaosHlRJ0Y4ESIAESMCWBJxvTYjllWKppej2aNX3RtgBMsssO8wSNZIACZAACXhNQBQNo0ePdtyaEF0dJ0+ejHfeeQe9evVi4eA1zfIHsHgoz4PfSIAESIAEbE5APM/w17/+1VE0iFTEi6nEy6datWpl88ysI599Hs6/CtU6U+JeiR3XSrvPxHp7ydacObETV0HATnqp1f05u2vXLrz99tuO3gyPPfYYOnbsiAYNGrg3drPXTlxLz1n2edC9CFXBH/s8uEJSWVsss1FZeyzzIZTJbGTjKj6EjUyvrjgyP7JxFa0qOavE0WEj46qiVcVGh1YVtjri6PDhK6262Os4D2TccnJyjJ49ezr6MyQnJ7v0ZhC5iE3mR4dWlTgyHSo+hI2KXmFnxsbbFm6qT+4iARIgARKwPgHnZxpEjwbRGVIstaxfv771xdtcIYsHm08g5ZMACZBAsBEQr8CeOHFiuWcahg4dyqLBhycCiwcfwmYoEiABEiCBqhMQzZ2WL1/ueI5h06ZNZQ9Cshtk1ZlW9Uj2eagqOR5HAiRAAiTgMwJiBcWoUaMc8VatWuVYbumz4AzkQoDFgwsS7iABEiABErAKgQMHDji6QK5ZswYpKSkYOHAgezRYYHJ428ICk0AJJEACJEAC5QmIWxSpqam46qqrHC+s2r9/P0Q7aXaFLM/JX9945cFf5BmXBEiABEjALYFt27ZB9GkQW2ZmpmMVRen7J9wewJ0+J8AmUWwSpf2ks2OjlcTERO0czHBoJ7Z20irmyk56A1VrUVERMjIysHjxYkfx0LNnT9SuXduM/5Xc+rQT19Jzlk2izOhiIfHJJlGugHQ0L1FpXKIjjg4fgoBMr644Mj+ycRWtwkbmRzau4kPFRsZVxYeKja58ZHp1xNHhQzDxhVZd7GVaS+NkZ2cbkZGRRnR0tCGaPjlvurjJ/Khqddbm7rMsjmxc+FSxUdHrTp+Ofbxt4bb+5E4SIAESIAFfEBDPNqSlpTmuNvCBSF8Q1xODxYMejvRCAiRAAiTgJYHSZxtq1Kjh6NnAfg1eAvSjOYsHP8JnaBIgARIIRgLiasOCBQsQFxeH5ORkXHHFFWDhYK8zgcWDveaLakmABEjA1gRE34YXXngB27dvR3Z2Ntq2bYt3333X1jkFo3j2eQjGWWfOJEACJOAHAqtXr3b0bbjsssvw4YcfOgoHP8hgSA0EeOVBA0S6IAESIAESqJyAuE0xc+ZMjBs3Dunp6ejfv3/lxhyxBQEWD7aYJookARIgAXsSEL0bnn76acdtipycHD7bYM9pdFHNJlFsEuVyUlR3hx0brbBJVHVn3fV4ngeuTHTtsQvbXbt2YcKECYiKinI0ffJlw6eqsLYL19LchF42idLRtcJLH2wS5QpMpTGJzEalcYnMh1Ams5GNq/gQNjK9uuLI/MjGVbSq5KwSR4eNjKuKVhUbHVpV2OqIo8OHr7RWl31KSooh/o5t3ry5cOVxk3GRjQvnOmwC7Zz1CL2ag3xgsrSE408SIAESIIFqExDPN4wePRpDhgxxvJeiUaNG1fZJB9YjwGcerDcnVEQCJEACtiTgvAxTvAWTL7Oy5TQqieaVByVMNCIBEiABEvBEQBQOpasoPv74YxYOnmAFwBiLhwCYRKZAAiRAAv4k8Nlnnzn6N8TExGD27NmoW7euP+Uwtg8IsHjwAWSGIAESIIFAJbB8+XJ07twZ4qVWTz31FAuHQJ3oCnnxmYcKQPiVBEiABEhAjcDKlSsxb948x4ORnTp1UjuIVgFBIKD7PIi1xdxIgARIgAT0EigpKcFPP/2Eo0eP4pprrkG9evX0BqA3ZQLs81DNNadVOZx9Hlypca20OUyEVxlb2bjwoWMdukocHTY6tOrippKPTK+KD5mNbFwlX5XzQFccd35OnTplxMbGGpGRkcbChQuFHI+bjKs42F0cZ6eycRUfKjY6tKrE0ZWPil5njjo/85kH5fqOhiRAAiQQ3ARED4fSVtPiWYcGDRoEN5Agzp7FQxBPPlMnARIgAVUCpYXDkSNHIAoH9nBQJReYdnxgMjDnlVmRAAmQgDYCpYWDcPjmm29yRYU2svZ1xCsP9p07KicBEiAB0wmI5k8PPfSQIw57OJiO2zYBWDzYZqoolARIgAR8S+DYsWOOrpHi/RQsHHzL3urRWDxYfYaojwRIgAT8QEBccRCvfG7Tpg0LBz/wt3pIFg9WnyHqIwESIAEfExDPOLzwwgto2rQpCwcfs7dLuIBuEiWbhJCQEGRkZMjMLDEu/gWQmJhoCS0yEXbSKnKxk15qlZ19VR8n23PsioqKHF0jxbfHHnsMtWvXrjpU/v9VLXayg8U5yyZROrtXKPpikyhXUDqal6g0LtERR4cPQUCmV1ccmR/ZuIpWYSPzIxtX8aFiI+Oq4kPFRlc+Mr064ujwIZiYpbW0AZRoAiU+y/TKxlW0+nKOZXplXFW0qtjIdKj4EDYqeoWdGRuXaspKO46TAAmQQBAQKF2OuX37dohXavPNmEEw6dVIkc88VAMeDyUBEiCBQCHg3DmShUOgzKp5ebB4MI8tPZMACZCALQjMmTMH4ooDO0faYrosIZK3LSwxDRRBAiRAAv4hIAqHuLg47N+/ny2n/TMFtozKKw+2nDaKJgESIIHqE1i9erWjcMjMzGThUH2cQeWBxUNQTTeTJQESIIFzBHbt2oXevXtDFA6dOnUiFhLwigCLB69w0ZgESIAE7E9AdI8cM2YMkpOTWTjYfzr9kgGbRLFJlPYTz07NdkTydtJLrdpP1zKHwcJWvK9C5NqtWzf07du3LH+zPgQLV7P4efIr2LJJlBldLCQ+2STKFZCO5iUqjUt0xNHhQxCQ6dUVR+ZHNq6iVdjI/MjGVXyo2Mi4qvhQsdGVj0yvjjg6fAgmVdXq3AQqLS1NuPK4yfTKxoVzmVZhI/MjG1fxoWKjQ6tKHF35qOgVeszYeNvCU1nHMRIgARIIIAL/+Mc/HEsyxRsyq9t2OoCwMJUqEGDxUAVoPIQESIAE7EZALMncsGGDo5cDm0DZbfasp5d9Hqw3J1REAiRAAloJfPbZZ1ySqZUonfHKA88BEiABEghgAmJlRefOnZGens6VFQE8z75OjcWDr4kzHgmQAAn4iIB42VX//v2RlJTk+OmjsAwTBARYPATBJDNFEiCB4CQgXnbVpk0bjBo1KjgBMGvTCLDPA/s8aD+57LSuWyRvJ73Uqv10LXMYaGzXr1+PlStXIjExEQ0aNCjL09cfAo2rr/l5iifYss+DGQtRJT7Z58EVkI71xyprj3XE0eFDEJDp1RVH5kc2rqJV2Mj8yMZVfKjYyLiq+FCx0ZWPTK+OODp8CCYyrbNmzTLE32+ZmZnC3O2mQ4uKD5lWIU7mRzau4kPFRodWlTi68lHRK/SYsfG2haeyjmMkQAIkYDMC4gHJV155ha2nbTZvdpPL4sFuM0a9JEACJFAJAfGA5AsvvICmTZviqaeeqsSKu0mg+gRYPFSfIT2QAAmQgCUILFiwwNFBcsiQIZbQQxGBS4BNogJ3bpkZCZBAEBHYtm2boxFUdnY2fvjhhyDKnKn6gwCvPPiDOmOSAAmQgEYC+fn5eOyxx5CSkoK2bdtq9ExXJOCeAIsH91y4lwRIgARsQyAhIcHRz2HgwIG20Uyh9ibA2xb2nj+qJwESCHICy5cvx/z587F//37whVdBfjL4MH02iWKTKO2nm52awojk7aSXWrWfrmUO7cj22LFjGDZsGJ5//nm0a9euLBcrfbAjVyvx86RFsGWTKDO6WEh8skmUKyAdzUtUGpfoiKPDhyAg06srjsyPbFxFq7CR+ZGNq/hQsZFxVfGhYqMrH5leHXF0+BBMhNZTp04Z0dHRRnx8vNhVbtMVR+ZHNi5EybgKG5kf2biKDxUbHVpV4ujKR0Wv0GPGZq1nHgpysWb6EDQOCUFISGN0S3gdWw4VuSm8jmJdQgRCHHbnbHsv3I0SN5bcRQIkQAKBSCAtLQ15eXmOvg6BmB9zsjYB6xQPJd8j49/rgHuTkWcYKM5Lw70/TkXE4FewpaB8WVBy8BO88foWJ7KdMahzU1gnGSdp/EgCJEACmgmcPn0aopfDvHnz+JyDZrZ0p0bAMr9vS749gEseGIae4Rc7lNcI64Rnxo1Crw1vYNmmfKdsfkb2mxlouPgIDMM4/2cZhoXXcbLhRxIgARIITAKii+TevXsdr9nmsszAnGM7ZGWZ1RY1mndC1wrEalzRFG3DKuw8sRXLZqRiassr0PLnPujc608ID7VMDVRBLL+SAAmQgF4CM2fOdDjka7b1cqU37whY/7fuhR1xa8tzVyOA08h9ay6mHgKwYSoeHdANLe8Zj+W5J7zLmtYkQAIkYEMCoovkuHHjcO211/J2hQ3nL5AkW7h4KMGJrA3YNjwGva6sfZ55HYQPWwbD+A15WSuwYHQvYMMkDHh8gctzEYE0ScyFBEiABMTtCtFFMikpCRdddBGBkIBfCVi3eCjIwryUhpg4PAKhLohqI6z93Rg2ZQXy1j6Pri7PRbgcwB0kQAIkYGsCYnWF2Hi7wtbTGDDiLdok6mdsmfkytvcZhWHXl96yqIy5WLZ5Jx7BVOye0h3O1lFRUZUd5Ni/ceNGdOzY0aMNB0mABEjA3wTE6gpxy6J169a86uDvybBYfDaJKuti8Ztx4J3XjEW7finb4/lDoZGzYLDRa8Euo9izocsom0S5IJE2axFHyBqcqDQukflQiaPDh4gj06srjsyPbFxFqy+5yfTKuKpoVbGR6VDxIWxkenXEqYqP0mZQSUlJQqZj84VWEUimVzYufMi06oqjokVmo0OrL/NR0Sv0mLFZ7LZFEQ6tW4hl9e7Bn8uuOJzA7pTXseFE+V4Pvxd/BTiwtzUS7g9nn4ffofATCZBAgBD44IMPHM2ghg8fHiAZMY1AIGCh4uEEcpc/j8E9RuDZHk1Qs6x75CVoteQMGovlmCWHsCXj/d+7TpYcwqaZM7Dhjj+j68UWSiUQzgzmQAIk4HcCBw4cwIABAzBhwgTUr1/f73oogARKCVjkN24RDi4fi64DJmFDqbKyn2HoNeg2tHAoLcEvX76MiMYXICSkNYbM+AQFfcfgxe5X8qpDGS9+IAESCBQCs2fPRnx8PHr16hUoKTGPACFgkSZRtXFl/znIM+Z4xlrjSnSfuArGRM9mHCUBEiABuxNYvXo1pk2b5njVtt1zof7AI2CRKw+BB5YZkQAJkEBVCYieDuPHj0d6ejqaNGlSVTc8jgRMI8DiwTS0dEwCJEACVSOwYMECNG7cGH369KmaAx5FAiYTsGifB5OzPu9evNI7IyPDN8GqGWXSpElITEysphffHG4nrYKInfRSq3nnsFXYitdsjxgxArNmzXK0oXaXsVW0utNWcR+1ViSi77tgyz4PZixElfhknwdXQLJ10OIImY3K2mOZD5U4OnyIODK9uuLI/MjGVbT6kptMr4yrilYVG5kOFR/CRqZXRxwVHz179jTi4+OFpEo3X2gVwWV6ZePCh0yrrjgqWmQ2OrT6Mh8VvUKPGZtFHpjUV4nREwmQAAnYlYB4SHLNmjX473//a9cUqDtICPCZhyCZaKZJAiRgbQKlD0mOGTOGPR2sPVVUB7A9As8CEiABErACAfGQpNjat29vBTnUQAIeCfC2hUc8HCQBEiAB8wmITpJxcXHIzMzEsWPHzA/ICCRQTQK8bVFNgDycBEiABKpLoLSTZKdOnarriseTgE8I8MqDTzAzCAmQAAm4JyBetS06Sebk5Lg34F4SsCABXnmw4KRQEgmQQPAQeP7555GUlITw8PDgSZqZ2p4Am0SxSZT2k9hOTWFE8nbSS63aT9cyh/5gm52dDVE8LF68GPXq1SvTIvvgD60yTZWNU2tlZKq/X7BlkygzulhIfLJJlCsgWRMVcYTMRqVxicyHShwdPkQcmV5dcWR+ZOMqWn3JTaZXxlVFq4qNTIeKD2Ej06sjjrOPU6dOGZGRkUZ6eroIX7Y525TtrPDBF1pFSJkW2bjwIdOqK46KFpmNDq2+zEdFr9BjxsbbFtUv/uiBBEiABLwm8MEHHziO4fsrvEbHAyxAgMWDBSaBEkiABIKLQH5+PiZPngzREKpu3brBlTyzDQgCLB4CYhqZBAmQgJ0ILFmyxPHWzP79+9tJNrWSQBkBLtUsQ8EPJEACJGA+AXHVobQhlPnRGIEEzCHAKw/mcKVXEiABEnBLYO7cuYiOjgYbQrnFw502IcArDzaZKMokARKwP4G8vDyMGzeODaHsP5VBnwH7PLDPg/b/Cey0rlskbye91Kr9dC1z6Au2ixYtcsQbOnRoWdyqfPCF1qrocncMtbqjomefYMs+D2YsRJX4ZJ8HV0CyddDiCJmNytpjmQ+VODp8iDgyvbriyPzIxlW0+pKbTK+Mq4pWFRuZDhUfwkamt7pxcnJyDPF3jvjpaVOJY7bWUn0yLbJxFa7CRuZHNq7iQ8VGxlXFh4qNrnxU9Ao9Zmx85kFPAUgvJEACJOCRwPz583HfffexDbVHShy0CwEWD3aZKeokARKwLYHc3FzHy6969epl2xwonAScCbB4cKbBzyRAAiRgAgFx1SE+Pt7R28EE93RJAj4nwNUWPkfOgCRAAsFEoPSqg3jl9u7du4MpdeYawAR45SGAJ5epkQAJ+J9A6VUHvnLb/3NBBfoI8MqDPpb0RAIkQALlCDhfdSg3wC8kYHMCvPJg8wmkfBIgAesS4FUH684NlVWPAJtEsUlU9c4gN0fbqSmMkG8nvdTq5oTTtEs3W9FNcsSIEXjttde0PyipW6smhG7dUKtbLFp2CrZsEmVGFwuJTzaJcgWko3mJSuMSHXF0+BAEZHp1xZH5kY2raBU2Mj+ycRUfKjYyrio+VGx05SPT622c+Ph4Q/xx3rz14Xys82fdWp19O3+W6ZWNC18yrcJG5kc2ruJDxUaHVpU4uvJR0Sv0mLHxmQct9R+dkAAJkMDvBPisw+8s+CkwCfCZh8CcV2ZFAiTgRwJ81sGP8BnaJwR45cEnmBmEBEggWAjwqkOwzHRw58krD8E9/8yeBEhAM4HVq1cjNjaW77DQzJXurEWAVx6sNR9UQwIkYGMCJ0+eRFxcHDIzM22cBaWTgJwArzzIGdGCBEiABJQIfPLJJ4iOjkanTp2U7GlEAnYlwCsPdp056iYBErAUgfz8fMybN49XHSw1KxRjFoGAbhIVFRXlkdvGjRvRsWNHjzYcJAESIAEVAqJ4EI2hbrrpJhVz2pCAFgJsEmVGFwuJTzaJcgWko3mJSuMSHXF0+BAEZHp1xZH5kY2raBU2Mj+ycRUfKjYyrio+VGx05SPT6ynOqVOnjMjISGPMmDFCcqWbJx+lB6nYVEerN3FkWmTjIpZMq7CR+ZGNq/hQsdGhVSWOrnxU9Ao9Zmx85kFL7UcnJEACwUzg008/daTfvn37YMbA3IOIAIuHIJpspkoCJGAOgVdffRUxMTGoXbu2OQHolQQsRoDFg8UmhHJIgATsReCzzz5DRkYGBg8ebC/hVEsC1SDA4qEa8HgoCZAACYjCITk5GfXr1ycMEggaAlyqGTRTzURJgAR0E2Arat1E6c8uBHjlwS4zRZ0kQAKWI8BW1JabEgryEYGA7vMgYxgSEuK4Vymzs8L4pEmTkJiYaAUpUg120iqSsZNeapWeflU28JataEX9yCOPYPLkyWjVqlWV41blQG+1ViWGrmOoVRdJVz+CLfs8mLEQVeKTfR5cAelYf6yy9lhHHB0+BAGZXl1xZH5k4ypahY3Mj2xcxYeKjYyrig8VG135yPRWjJOenm5ER0cLiWVbRXYX0PAAACAASURBVJuygfMfZOPCTMXGW60VdajGkWmRjYs4Mq0qWlTi6LDRodWX+ajoFXrM2HjbwrWY4x4SIAESkBIQVxzE8kxuJBCMBFg8BOOsM2cSIIFqERDLMzdv3ow+ffpUyw8PJgG7EmDxYNeZo24SIAG/EVi0aJFjeWbdunX9poGBScCfBLhU05/0GZsESMB2BMTyzPnz52P//v22007BJKCLAK886CJJPyRAAkFBoHR5ZpMmTYIiXyZJAu4I8MqDOyrcRwIkQAJuCIjXbsfFxSEzM9PNKHeRQPAQ4JWH4JlrZkoCJFBNAhs2bEBkZCQ6depUTU88nATsTYBNojIybDGDbLRi3jSRrTls7cRVEFDRO3HiRERFRaFbt27mQFP0qqJV0ZXpZtRqHmLBlk2izOhiIfHJJlGugNhoxRwmwquMrWxc+FBpCiPzIxtX0apio0OrShxd+cj0zpo1yxB/Zxw7dkzIcrvJtMjGhVMVG5lWFR86bFR8yLSq5KwSR4eNDq2+zEdFr9sTVcNO3rYwryikZxIggQAikJWVhfj4eL49M4DmlKlUnQAfmKw6Ox5JAiQQJATEg5KLFy9GdnZ2kGTMNEnAMwFeefDMh6MkQAIkAPGg5K233oq2bduSBgmQAAAWDzwNSIAESEBCIDU11e8PSUokcpgEfEqAxYNPcTMYCZCA3Qhs27YNGRkZuOmmm+wmnXpJwDQCLB5MQ0vHJEACgUDg/fffdzwoWa9evUBIhzmQgBYCLB60YKQTEiCBQCQgHpQcN24coqOjAzE95kQCVSbAJlFsElXlk6eyA+3UFEbkYCe91FrZWVf9/e7YigY86enpmD59evUDaPTgTqtG91pdUatWnOWcCbZsEqWhaYW3LtgkypUYG62Yw0R4lbGVjQsfKk1hZH5k4ypaVWx0aFWJoysfd3qjo6ONlJQUIUM6fyo2Zmp1iDz/H11xZH5k40KOO67OWsVnmR/ZuIoPFRsdWlXi6MpHRa/QY8bG2xbl6jh+IQESIIFzBMSrt8WDknfffTeRkAAJVCDA4qECEH4lARIgAUGg9NXb9evXJxASIIEKBNhhsgIQfiUBEiCBwsJCvnqbpwEJeCDAKw8e4HCIBEggOAls3brVkfgtt9wSnACYNQlICLB4kADiMAmQQPARWLRoEZKTk1G3bt3gS54Zk4ACAd62UIBEExIggeAhIHo7zJ8/ny/BCp4pZ6ZVIMA+D+zzUIXTxvMhdlrXLTKxk15q9XzuVWe0lO369esda+fHjh1bHXemHluq1dQgmpxTqyaQbtwItuzzYMZCVIlP9nlwBaRj/bHK2mMdcXT4EARkenXFkfmRjatoFTYyP7JxFR8qNjKuKj5UbHTlU6rXubeDiF+66Yijw4fQU6q1VFvFn7riyPzIxlW0ChuZH9m4ig8VGxlXFR8qNrryUdEr9JixWeuZh4JcrJk+BI1DQhAS0hjdEl7HlkNFLvVWyaFNSEnojZCQEDQe8go2ubFxOYg7SIAESEBCgL0dJIA4TALnCVineCj5Hhn/Xgfcm4w8w0BxXhru/XEqIga/gi0FJb9PWMEmzBj8InJ6L0Sx8Ru2DDmKhIo2v1vzEwmQAAkoE2BvB2VUNAxyApYpHkq+PYBLHhiGnuEXO6akRlgnPDNuFHpteAPLNuWfn6bTyF02HTM6PIsx3a9EDdRGWPcn8VyHtzB2WS6cSowgn1amTwIkUBUCqampGDhwYFUO5TEkEFQELFM81GjeCV2vrF0Ofo0rmqJtmNOuku+QuXQrWrdsjNCy3fUR0ft27Fj6Ofayeiijwg8kQALeETh58iQ2b96MLl26eHcgrUkgCAlYpniolP2FHXFry3NXI0r2fo6lqy9F26YN4SJ89YfI3Hu6UjccIAESIAFPBE6cOIGkpCT2dvAEiWMkcJ6Ay+9g65ApwYmsDdg2PAa9HFckSlBwYC92oBlaNvn9uoN19FIJCZCAXQmIdtT79+/H7bffbtcUqJsEfErAusVDQRbmpTTExOERTrcofMqGwUiABIKEwKefforQ0FCwHXWQTDjTrDYBizaJ+hlbZr6M7X1GYdj1525ZiExLcheiT8tX0Xbth5jSveH55EtwYt14XN9jLybkpGJYeJ0yKFFRUWWf3X3YuHEjOnbs6G6I+0iABIKIwL59+3DhhRfiiiuuCKKsmWogEGCTqLIuFr8ZB955zVi065eyPWUfincZC3rdZoxee6Rsl2EUGjkLBhrotcDIKXbarfCRTaJcIeloXqLSuERHHB0+BAGZXl1xZH5k4ypahY3Mj2xcxYeKjYyrig8Vm+rmc+zYMUP8XdC6dWsRrtKtunGEYx0+hB8ZW11xZH5k4ypaVbioxNFhI+OqolXFRodWVbbCzozNYrctinBo3UIsq3cP/lx2xeEEdqe8jg0nSoAaTdF50JV4fdVXOFFWMhbgQM5B9Bp0G1pYLJsyifxAAiRgWQJZWVmIjIzERRddZFmNFEYCViNgoV+3J5C7/HkM7jECz/ZogpqOLpOi0+QlaLXkDBqHCql1EP7A3/HsphmYvO4gSiCKjVfw0qb7MfGBcNcVGFajTT0kQAKWI5CWloaYmBjL6aIgErAyAYsUD0U4uHwsug6YhA0utMLKX1UI7YBnlySiUcqdqBnSFINXNcP0JU+ivaO4cDmYO0iABEigUgIHDhxwvEGzX79+ldpwgARIwJWAF6/kPotfC4pxYegFCHH1U809tXFl/znIM+Yo+RHdJ0el7MCoFCVzGpEACZCAWwLr1q1DdHQ0mjRp4nacO0mABNwTUL/ycHY7XmvbFveMehlL123H/oKz7j1yLwmQAAnYhMDy5cvRv39/m6ilTBKwDgH14qFGA1wf3RS7Z43Egz3a4uq2fTE8aSHe2/gNfj4rHlbmRgIkQAL2ISBuWWRkZKB79+72EU2lJGARAl4UD01x9z9X4usjOfg8fTZG33Icb4x/FPdEtcBVHR9CQvJyfJF7BKdZR1hkaimDBEjAEwHesvBEh2Mk4JlANZpEnUXBD9vx8UcfYsXiFPxr/R4AoWje7c8Y/uQQPNA7AleH1vQc3c+jISEhjn95+FmGUvhJkyYhMTFRydbfRnbSKljZSS+16ju7J06cCNFIrlu3bg6nZKuPrbMncnWmofezYGuzJlElxpmTPxjb1v7XeHn0IKN9KBxNVkLb/8n4U/PQc5+7vWR8lHfajN4U2nyySZQrSh3NSwKt0YoOJoK0zI9sXPjQwVYljg4bHVp1cauYz/79+x1/T4mfpZtMb0Ufpcc5/5TZyMaFLxUbX2hV0aJDq644KlpkNjKuKlpVbGQ6VHwIGxW9ws6MTf22hfhNe/oIcjeuwL+eexgdw65G2x4P4plX9+PGhAVY8cVe7N+4ARu+/gY708eg1foZeD5jD4r1Flr0RgIkQALVJsBbFtVGSAdBTkB9qWbxdiTf1hnPZBcAuA7dhk/DmwN7olOHG3FVqJObWn9Eq8i2aIZL8NtFZizrDPIZY/okQALVJsBVFtVGSAdBTsDpt76MRAhCI57Eywl9cEePW9GqYZ1K+z2EhPXFK8ejUf/Sym1k0ThOAiRAAmYQKF1lMWeOWl8ZMzTQJwnYnYB68VDzZgybd7O4d4Gj3/+MXxtcgVDRLer099iS9SsaR1yPsDrn74LUCkWDS+2OhvpJgAQCkQBvWQTirDInXxPw7pmHgq/w+hM9ce1ts7HpZIlDa/G+DzCyy40Iv2si1h76zdf6GY8ESIAEvCLAWxZe4aIxCbgloF48GD9h/YQRiJl7En2f6oKmtc81qa5xdS9MTElA5Obn0G/EG8g9w0YPbklzJwmQgN8JlN6yYGMov08FBdicgHqfhxPrkHB9D/z7znR8vaA/Gpd7wUUBts9+EG2fuRALclIxLLyOLbCwz4M502Sndd2CgJ30Umv1zlmxJn79+vUYO3asiyOydUGiZQe5asHo1olga/0+D3npRgxgNJ+WZZxxWTR6xshLf9wAuhrTsk66jFp1B/s8uM6MjvXHKmuPdcTR4UMQkOnVFUfmRzauolXYyPzIxlV8qNjIuKr4ULHxJp/Y2FgjJSVFuHXZZHq9iePi/PwOHT6EK19oFXFkemXjKlp1xVHRIrORcVXRqmIj06HiQ9io6BV2Zmzqty3qX43WbULxzeos11sTxlF89ekmIPR6NGtsj6sObss47iQBEghYAvn5+Y7Xb3fs2DFgc2RiJOArAuqrLS64Afc+fS9eePQFDH3sFzz7SBdcd2ltGKcOYst7CzFt1h5cnzANXa9Qd+mrJBmHBEiABLKyshAZGYnw8HDCIAESqCYBL37TX4jwmKlYmZ+A2PgEPLTIOfJV6DpyPl4Z3xX1yz0L4WzDzyRAAiTgPwJpaWmIiYnxnwBGJoEAIuBF8QCg1pX4099T8dXD47F91zc4+PNvqHHRH3Fts5Zo2aIR6rBwCKBTg6mQQOAQOHnypOOWRXZ2duAkxUxIwI8EvCseYOBswWH88NOvqHXJFbjmknPKz574ATu3/gDgYlzTpgUa1mIV4cc5ZWgSIIEKBMQSTXHLom3bthVG+JUESKAqBLwoHopRsHMx4u57Cov2iPdbuNseR3reHPQP88KtOzfcRwIkQAIaCXz99dfo16+fRo90RQLBTUD9t3zRDix8bBQWHboZMS8NxV03NMAfKrKr8Ue0u6xmxb38TgIkQAJ+I1BYWIjFixcjMzPTbxoYmAQCjYB6k6hDyzGk8QCsGfkhvp7ROyAejGSTKHNOZzs1hREE7KSXWr0/Z7/99luMHDkS4oHJ2rVrV+qAbCtFU60Bcq0WPo8HC7bWbxL1y1pjdBiMq577xCgwo+OEH3yySZQrdB3NS1Qal+iIo8OHICDTqyuOzI9sXEWrsJH5kY2r+FCxkXFV8aFiI8snOTnZuO+++4Qrj5tMryyOcC6zkY2r+BA2vtCqokUlH5lWXXFUtMhsdGj1ZT4qeoUeMzb1JlEXd0DM/w3C8bQMrPnhV/ANFh4LQg6SAAlYhEBqairatGljETWUQQKBQUD9mYfiPHy95Sdcvnsp7rtmCdr37YYbG1Q4vEY7xM6IQxc+9xAYZwezIAGbE8jNzcXmzZvxzDPP2DwTyicBaxGo8Nvfk7hCHN6yGd84TA5hy8ol2FLRPPQSDJxacSe/kwAJkIB/CGzcuBGxsbGoV6+efwQwKgkEKAH14qFmGzy99SSeDlAQTIsESCDwCCxfvhz9+/cPvMSYEQn4mYD6Mw/nhRqnD2LLykWYnjACQ/4yC58e/xV7VqZi+fafcNbPyTA8CZAACZQSEC/CysjIQPfu3Ut38ScJkIAmAl4VD8bxL/DPQXcg4u6/IH7qXKQu2o0jp3/GvjUzMKDzULy09gALCE0TQzckQALVI1D6IqwmTZpUzxGPJgEScCGgXjwYP2H9lL8jft2NmPbJTnw8tet5Z5ejR8JkJLTaiBdHvo6sU1yH4UKZO0iABHxO4KOPPuKLsHxOnQGDhYB6k6gT65BwfQ/8O3oFdr/aFfv/eQ8i4lueb0d9FrkLY9Dy0SK8tnMJht9woS34sUmUOdNkp6YwgoCd9FKr2jlbVFSEgQMHYtasWbj22muVDiJbJUxeG5Gr18iUDxBsrd8kKi/diAGM5tOyjDPGSSNrWlcDeNxIzztjGMYZIy/9cQPoakzLOmlGPwpTfLJJlCtWWRMVcYTMRqVxicyHShwdPkQcmV5dcWR+ZOMqWn3JTaZXxlVFq4qNOx3Z2dniEqhx6tQp4UJ6zgobmV53cRzOnf4js5GNW0mrihaVfGRcdcVR0SKz0aHVl/mo6BV6zNjUb1tcEobwm0JxeOte5FW8M2EcxVefbgJCr0ezxnWUqyYakgAJkIAZBMR7LOLj41G3bl0z3NMnCQQ9AfXi4cLW6PdkX+DNKfjHvE/x3S9FAH7F8e+3YVXyWMTN2oPr/nwXoq5QX/0Z9PQJgARIwBQCoqvkHXfcYYpvOiUBEgC8+E0fihtjp+OdQ4+h3/C7sMhB73PERi0GEIrrBiUh5YU+CAshVhIgARLwH4EDBw44ukrecMMN/hPByCQQ4AS8KB4A1GqCHs+/hdwBm/BF1g7sy/8NCA1Dyxsj0SXqOlxai5VDgJ8vTI8ELE9g06ZNiI6OBpdoWn6qKNDGBLwrHkSiIRci7Oau6H9z6VJNG2dP6SRAAgFH4IMPPuAti4CbVSZkNQLqxYNRgP07cvDTGU8pXIxr2rRAQ16B8ASJYyRAAiYRKCwsxPz585GdnW1SBLolARIQBNT7PJzdgunXRyD+3JuxKqH3+Pm+D+o1SSWOtOyOiory6Ee8NKdjx44ebThIAiRgHwInT57Ezp070aFDB9Soof48uH0ypFISKE/A+n0eSn4ytq1820hPTy//57/zjWnP3Gs0D+1sPP7yGmNfYYkZS0pN8ck+D65YZeugxREyG5W1xzIfKnF0+BBxZHp1xZH5kY2raPUlN5leGVcVrSo2zjqSk5ON+Ph4cVi5zdmm3IDTF5leFR8yG9m4kKNi4wutKlp0aNUVR0WLzEbGVUWrio1Mh4oPYaOiV9iZsalfIghphDZ39UOb8kXPuW8P9EXrkLvw0MbDiB/hzoD7SIAESMB8AqIl9RNPPGF+IEYggSAnoOe6XkhD3NylA46/mYY1ewqDHCnTJwES8AcBsURTvEWTSzT9QZ8xg42AnuLh7GF89eWOYGPHfEmABCxE4H//+x+XaFpoPiglsAmo37YozsXSkZPw/omSCkRKUPjDl0jbsAehPWcjqinbwVYAxK8kQAI+ICBuWbCrpA9AMwQJiLZP6hQKcfizt5CaXeB6SGh73PvMq/hbwjC0uZCNolwBcQ8JkIDZBKZNm8YlmmZDpn8SOE9AvXio2QZPbz2Jp4mOBEiABCxGYNu2bQ5FLVu2tJgyyiGBwCSgXjwoNYlyhlQT9a5phfCGFzjv5GcSIAES0E7gq6++QmxsLN+iqZ0sHZKAewKam0Q5B2mOmPT1SOl/lfNOS30OCQlxPJ1tKVGViJk0aRISExMrGbXWbjtpFeTspJda3Z/rEydORLdu3SBrDOf+6HN7ydYTnaqPkWvV2cmOFGzt0SRqcYLRLRRGaGSM8dyrqcZb6enGW6lzjOdibjNCcZXRbfS/HPvONZJ61/hkX4EZvSm0+WSTKFeUOpqXqDQu0RFHhw9BQKZXVxyZH9m4ilZhI/MjG1fxoWIj46riQ8Vm8eLFhvh/OScnR5i73VRylulV8SGzkY0L8So2vtCqokWHVl1xVLTIbGRcVbSq2Mh0qPgQNip6hZ0Zm/ptC5zBj1s+wfpW4/Fhxnj0Dvv9dsSAh+7EjTXuxoPr8zHxuVh0DNWzAlRWdXGcBEiABER/h8jISISHhxMGCZCAjwio/5Y/uhVv//sLNI3ui65OhYNDZ61r8Kd7bgc2r0JmzikfSWcYEiABEgD27duHfv36EQUJkIAPCagXDzX/gDp/AH75Jg/HxEVC5834BXu37wLQCPXreXExw9kHP5MACZBAFQisX78eERERVTiSh5AACVSVgPpv+sva4d7HbsPLU17Esy2K8WR0BFrUr4OzJw9i59qF+L8ZW3HdiCXoc12dqmrhcSRAAiTgFQFxy2LPnj1sSe0VNRqTQPUJqBcPIX9Et/GvYcHhoXh03ANYOs45eBgih8/F21PvQhh7RDmD4WcSIAETCYiW1LfeeiuaNGliYhS6JgESqEhAvXgAEBJ6M4b9ey26Pr4JWf/LxQ/5v6F2/WvQ8oZbcGtEM1xai5VDRcD8TgIkYB6BrKwstGnj9l2/5gWlZxIgAag/83AelnH2FI4fO4Qfcv6HHTtrod19d6HZsc+wbucRnCVQEiABEvAhgXHjxqFZs2Y+jMhQJEACgoB6kyixkPr4F/jn0GGIf3f3eXqPIz3vOVw0pS/uXNAY//fOPDzXo4k3L8zw6yywSZQ5+O3UFEYQsJNeav39nM3Ly8OIESOwePFi1KtX7/eBKn4i2yqCkxxGrhJA1RgWbG3QJOqwsTbhNgOhA4xpn+w0Pp7a1QAeN9Lzzhhn8j4wEiIvM3DTROOLX0vM6Edhik82iXLFqqN5iUrjEh1xdPgQBGR6dcWR+ZGNq2gVNjI/snEVHyo2Mq4qPjzZpKSkGLGxsdJ8PfkQY6WbTK8Objp8CL2+0CriyPTKxlW06oqjokVmI+OqolXFRqZDxYewUdEr7MzY1G9bnPwaq1I/x2WPDEVM56txkdPjDbXCumLY8DuAr7/Etu8Kq1FH8VASIAESUCPw6aefokuXLmrGtCIBEtBKQL14+PVn/HgIqN88DPWdCodzamqh3qX1AfyCgsISrQLpjARIgAQqEigsLMT8+fNx8803VxzidxIgAR8QUC8eLglD+E2hOLx1L/JcmkQdxVefbgJCr0ezxuzz4IN5YwgSCGoCW7dudeTftm3boObA5EnAXwTUi4cLW6Pfk32BN6fgH/M+xXe/FAH4Fce/34ZVyWMRN2sPrvvzXYi6wqvVn/7Km3FJgARsTCA7Oxvx8fE2zoDSScDeBLz4TR+KG2On451Dj6Hf8LuwyJH354iNWgwgFNcNSkLKC33YJMre5wPVk4AtCHz00Ud44oknbKGVIkkgEAl4UTwAqNUEPZ5/C7kDNuGLrB3Yl/8bEBqGljdGokvUdWwSFYhnCHMiAYsREC2pMzIyMGfOHIspoxwSCB4C6n0eSvbgjb9OxO7uz+Bvg9viUpeHJu0HjX0ezJkzO63rFgTspJdaAXHL4oMPPsDYsWO1nsBkqxVnmTNyLUOh/YNga/0+D3npRgxgNJ3whXHajEWjfvDJPg+u0HWsP1ZZe6wjjg4fgoBMr644Mj+ycRWtwkbmRzau4kPFRsZVxYc7m/j4eCM5OVkMOTZd+cj06oijw4dI2hdaRRyZXtm4ilZdcVS0yGxkXFW0qtjIdKj4EDYqeoWdGZv6A5MNW+Ouv7TD0U2bkX3kNCouuNBeUtEhCZAACVQgIJZoTps2DZ07d64wwq8kQAK+JKD+zEPNC9DwmnCE/edpRP1xEtr37YYbG1Q4vEY7xM6IQ5fLavoyB8YiARIIEgI5OTmOTFu2bBkkGTNNErAmgQq//T2INI5jZ8ZK7HGYHMKWlUuwpaJ56CUYOLXiTn4nARIgAT0EMjMzHUs069atq8chvZAACVSJgMfbFsaxXHyZ9TX2FxQDNdvg6a0nYRhG5X9OzsbdjXjVoUozwYNIgASkBMQSzTvuuENqRwMSIAFzCXgoHopx9Is5uCMyDktzCoHiXCyN+wv+Mv1THDdXE72TAAmQgAuB0iWaN9xwg8sYd5AACfiWgIfbFgbOFhWhAMfxzd59OHT5Iex8bxEWRXbByEMtcNqdzpC6uOzyS1EnAJZxukuP+0iABPxH4H//+x+io6PRpEkT/4lgZBIgAQcBD8VDLVwe0RPDrnsDcx9sg7mlwL57FG3TSr9U/Pk40vPmoH+YB7cVD+F3EiABElAgkJaWxlsWCpxoQgK+ICBpElWMgtzVeOPdnThZcgAbJr+Mlc1i8NyDrXGxW3VN0XN4f7QJ9XA3xO1x/tnJJlHmcLdTUxhBwE56g1VrUVERBg4ciFmzZuHaa6815cQNVramwHRySq5OMDR/FGyt3yTq7Dbj5XahRujjK4yfzOg44QefbBLlCl1H8xKVxiU64ujwIQjI9OqKI/MjG1fRKmxkfmTjKj5UbGRcVXyU2mRmZorWMsapU6fErnKbrnxkenXE0eFDJO8LrSKOTK9sXEWrrjgqWmQ2Mq4qWlVsZDpUfAgbFb3CzoxN/RLB+dUWJ+fejUaaq6dy7gpysW75Ekwf0hsJ646WG/r9y1GsS4iAuHJw7k9j9F64GyW/G/ATCZBAABEQLamTkpLAJZoBNKlMxdYE1IsHX6RZshsLHxyPlPRJiE89VmnEkoOf4I3XnbtMdMagzk1hrWQqlc8BEiABLwmkpqYiIiLCy6NoTgIkYBYBaz3ZWON6DHtvGYbmLsSPS16tJOefkf1mBhouPgKje8NKbLibBEggUAjk5eVh8+bNLB4CZUKZR0AQsFbxoIL0xFYsm5GKqS2vQMuf+6Bzrz8h3CYPaKqkRxsSIIHyBERL6tjYWNSvX7/8AL+RAAn4jYDNrvSfRu5bczH1EIANU/HogG5oec94LM894TeADEwCJGAuAfE0eZcuXcwNQu8kQAJeEfC6eDBOH8SWlYswPWEEhvxlFj49/iv2rEzF8u0/4axXoatiXAfhw5bBMH5DXtYKLBjdC9gwCQMeX4AtBXxcsipEeQwJWJmA6Cr55Zdfonv37laWSW0kEHQEvCoejONf4J+D7kDE3X9B/NS5SF20G0dO/4x9a2ZgQOeheGntAR8UEGKOaiOs/d0YNmUF8tY+j64b3sCyTflBN3lMmAQCnYDoKnnrrbeyq2SgTzTzsx0BSZMop3yMn7Au8T70eCUM095/ER02PonbR7d0dJS8Fx9hfPRgTCmMxxdfjkHHC6vXn7okdyH6tHwVbdd+iCnShyLFss078QimYveU7uWaV0VFRTkl4Ppx48aN6Nixo+sA95AACViCwL59+3DhhRfiiiuusIQeiiABqxGwfpOoX9Yao8NgXDZ8hXG45KSRNa2rATxupOedMQyj0MhZMNAAoo3Xdv5a7X4UxTkLjF5ob4xee0TBl4g92Oi1YJdRrGDtbMImUc40zn3W0bxEpXGJjjg6fIisZXp1xZH5kY2raBU2Mj+ycRUfKjYyrjIfx44dczSGmjVrljCtdNOVj0yvjjg6fAgQvtAq4sj0ysZVtOqKo6JFZiPjqqJVxUamQ8WHsFHRK+zM2NRvW/z6M348BNRvHob6LhcWaqHepeJJ6F9QUOjrZw8KcGBvayTcH84+D1YriamHBKpBYNeuXYiMjDStHXU1pPFQEgh6AurFwyVhCL8pFIe37kWe+PeA82Ycx6uKDAAAIABJREFUxVefbgJCr0ezxnWcR/R+LjmELRnvY8uhonN+Sw5h08wZ2HDHn9H1YvVU9IqiNxIgATMIfPzxx4iJiTHDNX2SAAlUk4D6b9wLW6Pfk32BN6fgH/M+xXe/iF/gv+L499uwKnks4mbtwXV/vgtRV1SndcS5ttM1Wz6K1diCqT0aIaT3QuSWXcwowS9fvoyIxhcgJKQ1hsz4BAV9x+DF7lfyqkM1TwQeTgJWIlBYWIhx48ahXbt2VpJFLSRAAucJePGbPhQ3xk7HO4ceQ7/hd2GRw8HniI1aDCAU1w1KQsoLfRDmckvDG9YN0X1KFowplRxT40p0n7gKxsRKxrmbBEggIAhs3brVkcctt9yCNWvWBEROTIIEAomAevFgHEPuV4Vok7gMuQOy8EXWDuzL/w0IDUPLGyPRJeo6XFqrWpVDIHFlLiRAAtUgIG5Z8EVY1QDIQ0nAZALqxUPxd3j3gQjEoxeGDx+KgT37YfiNTRDKgsHkKaJ7EgguAqW3LDIzM4MrcWZLAjYi4EWfhyPYnpaCuXPnYe76PY4UQ9s/hJF/fQh9u3VE2+saoY7NLjyI13lnZGTYYromTZqExMREajWBANmaABVAVbl+++23GDlyJNLS0lC7dm1zxLnxWlW9blyZvotazUFsJ66CgNBr/T4PpQtFSwqNIzmfG+mzRxsD24c51mEDoUbzvqOMl5duMvLOlJRaWv4n+zy4TpGO9ccqa491xNHhQxCQ6dUVR+ZHNq6iVdjI/MjGVXyo2Mi4VuYjOTnZSEpKEsOOTaZXNi6cqNjI9Kr4kNnIxq2kVUWLSj4yrrriqGiR2ejQ6st8VPQKPWZs6qstSgu9kDpoGB6F/nFTsGzjbnyf9TamxbTG4ZUz8cygBfjiSHGpJX+SAAmQgNcEUlNTcfvtt3t9HA8gARLwHQH1Zx7KaSrB6aN7kf3JKrzz39fxatpmFCAMkUM7oHk97+uRcq75hQRIIGgJbNu2DZs3b4ZYZcGNBEjAugS8Kh6M04ew4/NPsGHFEsye9S6+EYs0I4ciYcHz6HNHZ7S5+mJ45dC6XKiMBEjADwTEQ5Lx8fGoW7euH6IzJAmQgCoB9d/1xduRfFtnPJNdICoGDBz/L8zq2wOdI5pxiaYqbdqRAAl4JCBuWUyYMMGjDQdJgAT8T0C9eEAIQiOexOzx0ejbPQLNLv2D/9VTAQmQQMAQKL1lERERETA5MRESCFQC6sVDzZsxbN7NgcqBeZEACfiZgLhlIRpD1a8vXrLHjQRIwMoEPBYPxblLMTJpA66JfRF/v+04lo6chPdPlL1owjWvGu0QOyMOXS6r6TrGPSRAAiTggYC4ZTFz5kwPFhwiARKwCgGPTaKKt89GZNvX0GHFWsztcwSzI88/81CZ+tA4rNg3E3c3skfxwCZRlU1k9fbbsdEKG3BVb87dHe3NeeCvxlDOur3R63ycPz5TqznU7cRVEBB6rd8kquQnY9vKt423P9lnFLp0nCgxCvd9bCyeu8zIyj/rMmrVHWwS5TozsiYq4giZjUrjEpkPlTg6fIg4Mr264sj8yMZVtPqSm0yvjKuzVtEUyrkxlBgr3WRxZOPCj4qNTK+KD5mNbNxKWlW0qOQj46orjooWmY0Orb7MR0Wv0GPGpt6UofgHrHn6Ptw3PxvHXYq+sziyaREeGf4q1u8rdBnlDhIgARKojEDpuyzYGKoyQtxPAtYj4PGZBxgH8d4Td+KeuV//rvybAWic+vvXcp9CH8Hll3EVRjkm/EICJOCRgPPrtz0acpAESMAyBDwXDyGN0Tv+JYw5/Tbyzh7DzndWYsvlXTGw09VwaeFS90pE3BOD+669wDLJUQgJkID1CfD129afIyokgYoEPBcPCMEfmvXDpP/0A4q3Y3bkx8jp8De8MvduNKroid9JgARIwEsCRUVFGDduHPj6bS/B0ZwE/ExAUjw4qavZBk9vPYmnnXbxIwmQAAlUh8A333yDyMhIvsuiOhB5LAn4gYB68eAQZ+BswUHk5hxGxccijVOHkbPtOJo/8iA6ss+DH6aSIUnAfgTWrl2LmJgYvsvCflNHxUFOwIvioRjHNyZj6CPP4d1vCtxjE30eHnzQ/Rj3kgAJkIATgfz8fKxZswZTp0512suPJEACdiDgsUlUuQRKdmNhn+549PNrETOyO+pmpuBfWS3w+OgoYH0a/rX+SiR8mIoJva+yzZs12SSq3Axr+2LHRitsEqVt+sscyc6D7OxsvPHGG5g+fXrZMf78INPrT20VY1NrRSJ6vtuJq8hY6LV+k6ifVhiPh8K4bPgK43DJaWNf6sMGMNBYkFNolJzMMmbf29y4bsS7Rl6JGe0ozPHJJlGuXGVNVMQRMhuVxiUyHypxdPgQcWR6dcWR+ZGNq2j1JTeZXhnX6OhoY+TIkUKyx00WRzYunKvYyPSq+JDZyMatpFVFi0o+Mq664qhokdno0OrLfFT0Cj1mbOpNos4WobAAqN88DPVDauOPTVvgKuxDzoEChITehLvv74g9ry3FR9/9pqcEpBcSIIGAJXDgwAFkZGTg5pv5sr2AnWQmFtAE1IuHixvhmquA/G8OId8IQd3Lr0Yr/IScgz/DQA3Uql0bwEEczj8T0MCYHAmQQPUJrFu3DtHR0WjQoEH1ndEDCZCAzwmoFw8X3YCeQzvj+OJJSJjzGY5d2Qp/uuk41i5dhve++Ahvv50JhDbDVY1EEcGNBEiABConMGfOHDzxxBOVG3CEBEjA0gTUiwc0QOe4SZje91csei8Hx+vegmGzEhD58Tjce9tdeGbpaXRL/At6XcXiwdIzTnEk4GcC27Ztw+bNmxEREeFnJQxPAiRQVQJeLNUEQhp1xt8Wf4JBh87iihoXoFaPBCzf3hNffvUjENYWnTpcg9CQqkrhcSRAAsFAQHSTjI+PR/369YMhXeZIAgFJwGPxUJy7FCOT3scJpdSXY8ncdoidEYcubBKlRIxGJBBsBMQbNOPi4tiOOtgmnvkGHAGPfR6Kt89GZNtnkK2atmgStW8m7m5UU/UIv9qxz4M5+O24Vpp9HvSfC+7Og127dmHBggWYOHEiajsestYft6oe3emtqi+zj6NWcwjbiasgIPRav8+DGQtF/eyTfR5cJ0C2DlocIbNRWXss86ESR4cPEUemV1ccmR/ZuIpWX3KT6XXHNTY21khOThYyHZvMhzCS2cjGVXwIG3d6HSLP/0dHHB0+fKVVxJHplY2raNUVR0WLzEZ2DqhoVbGR6VDxIWxU9Ao7MzaPty3Mqe3olQRIIBgJiN4O8+fPR05OTjCmz5xJIKAIqBcPRgH278jBTx7bOFyMa9q0QMNafGoyoM4SJkMCGgiU9nYIDw/X4I0uSIAE/ElAvXgozsHS/hGI/8aT3MeRnjcH/cPU3XryxjESIIHAISB6O4wZMyZwEmImJBDEBNR/y9e8Gj1nv4300yXlcZ05jn1fvIu5C/JxR9L9aMeVFuX58BsJkABKezt07dqVNEiABAKAgHrxENIIbe7qhzbukn6gL1qH3IWHNh5G/Ah3BtxHAiQQzATef/99JCUlsbdDMJ8EzD2gCHjRYdJD3iENcXOXDjj+ZhrW7Cn0YMghEiCBYCOQn5+PcePG4fbbbw+21JkvCQQsAT3Fw9nD+OrLHQELiYmRAAlUncCGDRsQGRmJTp06Vd0JjyQBErAUAY9NosopLc7F0pGT8P6JCs88oASFP3yJtA17ENpzNjLfeQptLrTGaouoqKhyKVT8snHjRnTs2LHibn4nARLQSEAszRStqBs1aqTRK12RAAkIAtZvEnV2m/Fyu1BDNFZy+RPa3rj3mVeNj/NOm9GLwjSfbBLlilZH8xKVxiU64ujwIQjI9OqKI/MjG1fRKmxkfmTjKj5UbATX7Oxsx98Xx44dE4e4bDq06PAhhPniPLCTVsFEplc2rsJVVxwVLTIb2TmgolXFRqZDxYewUdEr7MzY1B+YrNkGT289iadZ7JEACZCAIgHxoCRfgqUIi2YkYCMC6sVDWVIlOP3zURwvLC7bU/YhpC4uu/xS1LHGXYsyWfxAAiTgewJnz551PCgp3qLJjQRIILAIePHAZDEKcjOQ9GBHNLrscjRu3Nj1T9gYvP/j2cAixGxIgASqRODEiRN8ULJK5HgQCVifgPqVh5J9eDthJMa/8wd0HRSHLu2vxsUuVxiaonk9L+oR6/OhQhIggSoSOHLkiOPKQxUP52EkQAIWJqBePBzegY/e+Q5hIz9E+ozeqO9SOFg4S0ojARLwKQHRUfL48eO4++67fRqXwUiABHxDQP0ywUWX4oowoFa9C3EBCwffzA6jkIBNCYgHJcWtTbFEkxsJkEDgEVAvHi7uiMdnjkCd/y7F8p354JMNgXcyMCMS0EGgtKNkgwYNdLijDxIgAQsSUG8SJZoinPgS/7x/IOLX7HefSmgcVuybibsb1XQ/brG9ISEhyMjIsJgq93ImTZqExMRE94MW22snrQKdnfTaQev69esdjWvE/192OWd5Hpj3l4gdztnS7O2ktfSctX6TqJIfjBUj2p9rEBXa3uj7SIwRE1Phz9CZxif5Z83oR2GKTzaJcsWqo3mJSuMSHXF0+BAEZHp1xZH5kY2raBU2Mj+ycRUfldmcOnXKiIyMNNLT06VcK/Mh9jtvMr2yceFLxcYX54GKDhUbX2hV4aZDq644KlpkNjKuKlpVbGQ6VHwIGxW9ws6MTf2ByaPb8d7rW3DZ0Dew+bUH0byO+h2P0qqOP0mABAKbwNatW7F582b06dMH06ZNC+xkmR0JBDEB9QrgggtxST3gkhbN0ISFQxCfMkydBConsGjRIiQnJ6Nu3bqVG3GEBEjA9gTUi4eLO+DRKY/jDxkr8NEPvzpecGH77JkACZCANgK5ubmYP38++vXrp80nHZEACViTgPpti+I8ZH95CBfv+hfuvnEV+va7EQ0qlh412iF2Rhy6XGaPByatOSVURQL2JLB69WrHeyyaNGlizwSomgRIQJmAevGAQhz+fB22FAjfW7By8RbXIKGXYOBU193cQwIkENgExPLMuLg48D0WgT3PzI4ESgmoFw98q2YpM/4kARKoQGDDhg2Ijo5Gp06dKozwKwmQQCASUO/zYBRg/44c/HTGE4aLcU2bFmhYyx4tKNnnwdNcVn3Mjmul7dKPwIpsi4qKMHbsWAwYMABRUVFlJ44VtZaJc/PBTnqp1c0EathlJ64iXaHX+n0ezmQZ05o7npM81+sB7j4/bqTnnTFjSakpPtnnwRWrjvXHKmuPdcTR4UMQkOnVFUfmRzauolXYyPzIxlV8ONtkZmY6/k4QPR6cNxlXZx/Ox1X8LNMrG1eNI9OrI44OHyIfX2hV4aaSj0yrrjgqWmQ2OrT6Mh8VvUKPGZsXty2uRs/ZbyP9dEn5+u7Mcez74l3MXZCPO5LuRzs+LFmeD7+RQIATEP0cuDwzwCeZ6ZFABQLqxUNII7S5qx/aVHDg+PpAX7QOuQsPbTyM+BHuDLiPBEggEAmIt2eKFu8LFy4MxPSYEwmQQCUEKi62rMRMsjukIW7u0gHH30zDmj2FEmMOkwAJBAqBJUuWOJZn8u2ZgTKjzIME1AioX3nw5O/sYXz15Q4AjTxZcYwESCCACBw7dszRgjonJyeAsmIqJEACKgTUi4fiXCwdOQnvn6jwzANKUPjDl0jbsAehPWcjqinb0qqApw0J2J3Axo0bERsbi/DwcLunQv0kQAJeElAvHkSTqM/eQmq2o0tU+TCh7XHvM6/ibwnD0OZCeyzTLJ8Av5EACXhDQDSFmjdvHptCeQONtiQQQATUiwc2iQqgaWcqJFA9Au+99x5uvfVWNoWqHkYeTQK2JeBFk6ginC6qhToXOD1jefp7bNn+27nGUDZ80yabRJlz3tqx0QqbRKmfC6VNoR5++GG0a9eu0gN5HlSKptoDdmJLrdWe7kodCLYWbhJ12vgp6w0joW97Izp1j1Hi1G3i7M7XjM6AERr5lLFg84+GfdpDnUuCTaKcJvP8R1kTFWEms1FpXCLzoRJHhw8RR6ZXVxyZH9m4ilZfcEtPTzciIyONtLQ0Ea7STcZVHKiSs8xGNq4aR6ZXRxwdPkQ+vtCqwk0lH5lWXXFUtMhsdGj1ZT4qeoUeMzanywjuipuzOPLJPzGo68OYsjIPx46fRFGZmYEzdZrhgZH34vLNc/Bot8cxKyufr+ou48MPJBB4BAoLCzF58mSMGTMGtWvXDrwEmREJkIASAc/Fw4nPkfz4JKwPi8XcLzZjTVw7XFDmNgR1mvVC3My3sHnzbNyLDLww4R3sOSM61XIjARIIRAJbt251pNWnT59ATI85kQAJKBLwUDwY+HX7OizafTkeemksHut4Jeq4XUjxB1wW8TD+PioKBRnr8OWB369NKGqgGQmQgE0IiFbUMTExqFuXS7JtMmWUSQKmEPBQPBTjxJEfsR9X4ZYWjeC2biiTdDFatL0ZwEEczvf42s2yI/iBBEjAXgQ+++wzRyvqwYMH20s41ZIACWgn4KF4CMEFF4XiMvyGE6dkVxPO4uTP+QDqoLZNXsetnSQdkkCAEyh9ARZbUQf4RDM9ElAg4KF4qInLWkXiztAdSFuZjXxPjzKc2YfMdzcDYe1w07W8nKnAnSYkYCsCvOpgq+miWBIwnYCH4gEIuaobYp+8GbunxONv877AoYqv40YJTh/ZjvTn/oZnMorRc8z96HixR5emJ8QAJEAC+gnwqoN+pvRIAnYmIG0SZRR8hf/EDcWji7IB0Yb6L3eh89UXI8Q4gQNbPsV7SzfgG4TiuqFz8HbyI7gxtKZteLBJlDlTZaemMIKAnfT6Q+u3336LkSNHYvHixahXr57ySeMPrcri3BjaSS+1uplADbvsxFWkK/RauEmUYZSc3GusW5Bg9G0eKm5eOP0JNZp3G2FMS882fjrj3D7KjJYU+n2ySZQrU1kTFXGEzEalcYnMh0ocHT5EHJleXXFkfmTjKlrN4BYfH28kJSUJ1+U2mV4ZV+FM5kPFRocPEUemV0ccHT58pVUXexlXXXF0sNWh1Zf5qOgVeszYlO4xhIQ2R7dhk7Hi6/3I27cTWVlZyMraiX15+/H12lfx9/5t0UjXg5IFuVi3fAmmD+mNhHVH3daSJYc2ISWhN8SVg8ZDXsGmQ7IHOt264U4SIAEJgdzcXMdrt++//36JJYdJgASCiYBS8VAKJKTOpQi79ga0b98e7dvfgGvDLq2k90PpEV7+LNmNhQ+OR0r6JMSnHnN/cMEmzBj8InJ6L0Sx8Ru2DDmKhMGvYEtBxVeFuz+ce0mABNQJzJ8/H/Hx8XzttjoyWpJAUBDwqngwnUiN6zHsvWX4zz9GoZfbYKeRu2w6ZnR4FmO6X4kaqI2w7k/iuQ5vYeyyXLB8cAuNO0mgSgRKrzrExsZW6XgeRAIkELgErFU8yDiXfIfMpVvRumVjhJbZ1kdE79uxY+nn2MvqoYwKP5BAdQnwqkN1CfJ4EghcArYqHkr2fo6lqy9F26YN4SJ89YfI3Hs6cGeKmZGADwnk5eU5nnXgVQcfQmcoErARAZffwdbVXoKCA3uxA83Qssnv1x2sq5fKSMC+BJYvX46kpCQ+62DfKaRyEjCVgLTPg6nRK3FekrsQfVq+irZrP8SU7g3PW5XgxLrxuL7HXkzIScWw8DqS/UBUVFQlEbibBEigMgInT57Ezp07ERERgVq1alVmxv0kQAIWIGDpPg9mrBH15LM4Z4HRC+2N0WuPlDNzv7/Y+GVtohGGgcaCnMJy9rIv7PPgSohrpc1hIrzK2MrGhQ+Vdd0yP7Lx6Oho47HHHnMFUWGPzI8Orbq4ybSqsFXxIbORjavk6yutKlpU8tFxHqjE0WGjQ6subir5qOgVeszYbHTbAqjR4jYM6nVBhVqvCD9+txeHet2Jzi1Kr0ZUMOFXEiABJQKl77D405/+pGRPIxIggeAkYKviATWaovOgK/H6qq9womy+CnAg5yB6DboNLeyVTVkG/EACViFQ+g4Lb9pQW0U7dZAACfiOgM1+3dZB+AN/x7ObZmDyuoMoQREOrXsFL226HxMfCHddgeE7joxEArYnUHrVYfDgwbbPhQmQAAmYS8BixcNRrEuIQM2Wj2I1tmBqj0YI6b0Quc79G0I74NkliWiUcidqhjTF4FXNMH3Jk2gfarFUzJ03eicBrQQKCwsxatQoJCcno379+lp90xkJkEDgEbDYo9QN0X1KFowpnkHXCOuEUSk7MCrFsx1HSYAE1Ah88MEHDsNHH31U7QBakQAJBDUB/nM9qKefyZMAIK46TJ48GWPGjEHdunWJhARIgASkBFg8SBHRgAQCm0DpVYc+ffoEdqLMjgRIQBsBSzaJ0padxJF4pXdGRobEyhrDkyZNQmJiojXESFTYSatIxU56dWsVDaEeeeQRPP/882jXrp1kZr0b1q3Vu+jeW9tJL7V6P78qR9iJq8hH6GWTKDO6WEh8skmUKyCVxiQyG5XGJTIfQpnMRjau4kPYyPTqiiPzIxtX0aqSs3Oc5ORkQzSFqrg521QcK/0us5FxFX5kPlRsdPgQcWR6dcTR4cNXWnWxl3HVFUcHWx1afZmPil6hx4zNYg9MqtSGtCEBEtBBQLxyOy4uDpmZmTrc0QcJkEAQEeAzD0E02UyVBJwJlL5yu1OnTs67+ZkESIAEpAR45UGKiAYkEHgEtm3b5njldk5OTuAlx4xIgARMJ8ArD6YjZgASsB4B8YCkaAgVHh5uPXFURAIkYHkCLB4sP0UUSAJ6CWRnZztWGbENtV6u9EYCwUSAxUMwzTZzDXoCoiHUG2+8gfT0dLahDvqzgQBIoOoEWDxUnR2PJAHbEUhLS3NoZkMo200dBZOApQiwSRSbRGk/Ie3YaCUYGnAdO3YMw4YNc7SibtWqlfZ5r+iQ50FFIvq+24ktteqb94qeBFs2iTKji4XEJ5tEuQJioxVzmAivMrayceFDpSlMZX7i4+ON2NhYqQ4VrSo21dEq/JduleWjOi7sZD6EjUyvig+ZjWzcSlpVtKjkI+OqK46KFpmNDq2+zEdFr9BjxsalmhVLOX4ngQAk4Lw0c/fu3QGYIVMiARLwJQE+8+BL2oxFAn4gIB6S5NJMP4BnSBIIYAIsHgJ4cpkaCQgC4q2ZeXl5ePTRRwmEBEiABLQQ4G0LLRjphASsSSA/Px8DBgxwLM2sW7euNUVSFQmQgO0I8MqD7aaMgklAncDkyZMRHR2N/v37qx9ESxIgARKQEOCVBwkgDpOAXQk4PyRp1xyomwRIwJoE2OeBfR60n5l2WtctkreTXlWtRUVFmD59Otq0aYO+fftqn2MVh6paVXz5wsZOeqnVnDPCTlwFAaGXfR7MWIgq8ck+D66AZOugxREyG5W1xzIfKnF0+BBxZHp1xZH5kY2raC3llp6ebkRGRhqnTp0Su8ptKnF02Mi4ClE64ujwIbTI9OqIo8OHr7SqzI9KPjKuuuKoaJHZ6NDqy3xU9Ao9Zmy8bWFOAUuvJOA3AqWdJFetWgU+JOm3aWBgEghoAnxgMqCnl8kFI4EVK1YgNjYWvXr1Csb0mTMJkIAPCPDKgw8gMwQJ+IrA6tWr8fbbb2P//v2+Csk4JEACQUiAVx6CcNKZcmASEJ0kx48fjzFjxqBJkyaBmSSzIgESsAQBFg+WmAaKIIHqE5g5cyYaN26M9u3bV98ZPZAACZCABwK8beEBDodIwC4ERE+HcePGIScnB3zxlV1mjTpJwL4EeOXBvnNH5STgICBuVzz22GNISkpCeHg4qZAACZCA6QTYJIpNorSfZHZstJKYmKidgxkO3bFdv349Vq5ciYkTJ6J27dpmhK2ST3daq+TIRwfZSS+1mnNS2ImrICD0skmUGV0sJD7ZJMoVkKyJijhCZqPSuETmQyWODh8ijkyvrjgyP7Jxd1pzcnIMcR5nZ2eLYccm8yMbF0502Mi46oqjQ6vQItOrI44OH77SqjI/KvnIuOqKo6JFZqNDqy/zUdEr9Jix8baFOQUsvZKA6QTE7YrRo0c7ble0bdvW9HgMQAIkQAKlBFg8lJLgTxKwGYG0tDTk5eVh1KhRNlNOuSRAAnYnwNUWdp9B6g9KArm5uRgyZAiys7PZgjoozwAmTQL+JcArD/7lz+gk4DUB3q7wGhkPIAES0EyAxYNmoHRHAmYT4O0KswnTPwmQgIwAb1vICHGcBCxE4Ndff+XtCgvNB6WQQLAS4JWHYJ155m07AuJ2xbfffsvVFbabOQomgcAjENBNoqKiogJvxphR0BI4ePAgjh8/jhtuuAE1arDuD9oTgYmTgBMBNokyo4uFxCebRLkCkjVREUfIbFQal8h8qMTR4UPEkenVFUfmx9N4ZmamoxlU27ZtXSetwh5PflS46rKRcdUVR5avahyZXh1xdPgQ+fhCqwo3lXxkWnXFUdEis9Gh1Zf5qOgVeszY+M8XpwqOH0nAigTy8/MdvRxSUlJQp04dK0qkJhIggSAjwOIhyCac6dqPwOTJk9GmTRsMHDjQfuKpmARIICAJcLVFQE4rkwoUAsuXL8e0adOwf/9+NoMKlEllHiQQAAR45SEAJpEpBCYB0UVywIABWLVqFZo0aRKYSTIrEiABWxJg8WDLaaPoQCdQ2kUyPj4evXr1CvR0mR8JkIDNCPC2hc0mjHKDg8DMmTMdL7168803gyNhZkkCJGArAgHd50E2EyEhIcjIyJCZWWJ80qRJSExMtISW/2/vfICjqvI9/02sZcRBRgF37QCvGB+byNQwghj8Q2qMoIks48qEcRh9mrgEcHZFB11NCOhT5g//wmINwcEBk0fA0RFMBH2+IcHEMBVeFWwiIL6CTlHKvIQO+xwwhBQINemzdW7STf+/J51zO/d2f7sq1d33/u7vfH+fc7r7l3vP+V0zEU7SKmOxm155s6tXX30VmzdTZ1xxAAAgAElEQVRvRkZGRhBuu2kNEhfyxkla7TgOQnAGvXUSW2oN6jqtbyRb1nmwYiGqiU/WeQgHZLYOWh5hZqOy9tjMh0o7OnzIdsz06mrHzI/c397eLrKzs0VNTU145yhoTSQ3s3jMuKpoVbEx06HiQ9qY6dXRjg4fidKqwk0lHjOuutpR0WJmo0NrIuNR0Sv1WPHgnAeteSCdkUD8BK5cuYKVK1cayzILCgrid8QjSYAESMBiApzzYDFguicBVQL79u3D0aNHsXfvXtVDaEcCJEACQ0KAycOQYGejJBBM4MCBA9iyZQvkfIdRo0YF7+Q7EiABErAZAV62sFmHUE7qEejo6EBOTg6WLVuGKVOmpB4ARkwCJOA4AkweHNdlFJxMBGQ9hyVLlkDWc+BdYJOpZxkLCSQ3ASYPyd2/jM7mBHz1HOREST5IgARIwCkEOOfBKT1FnUlHQN63YsWKFbxvRdL1LAMigeQnwCJRLBKlfZQ7qSiMDH4o9H755ZdYunSpUQxq6tSpyn0wFFqVxYUYOknrUI2DEGTKb53EllqVu3XAhpIti0RZUcXCxCeLRIUDMiuiIo8ws1EpXGLmQ6UdHT5kO2Z6dbXj83P27FmjEFRFRUVQB/j2B20MeWOmVZqb+THbr+JDxUaHVpV2dMVjpldHOzp8SCaJ0KqLvZlWXe3oYKtDayLjUdEr9Vjx4JyHAed6PIAE4icgJ0iWlpYahaCKi4vjd8QjSYAESGAICXDOwxDCZ9OpR6CystJfCGr48OGpB4ARkwAJJAUBJg9J0Y0MwgkE5LXJNWvWwO12sxCUEzqMGkmABKIS4GWLqGi4gwT0EThy5IiRONTV1SEzM1OfY3oiARIggSEgwORhCKCzydQiICtILl682PjLy8tLreAZLQmQQFISYPKQlN3KoOxCwFdB8rbbbsOcOXPsIos6SIAESGBQBJg8DAofDyaB2ASeffZZw2Djxo2xDbmXBEiABBxEgEWiWCRK+3B1UlEYGbxVej/66CN88sknKCsrw+jRo7VwtkqrFnEhTpyk1cpxEIJFy1snsaVWLV0e0YlkyyJRVlSxMPHJIlHhgFhoRQ+TmpoaIceX2+32OzRja7ZfOlIpCmPmx2y/bEeHjQ6tKlp0aFVhq6MdHT4SpVUXex3jQBc3Mz86tOriZqZVZRxIG6sevGwRMZ/jRhKIn8CBAwcwb948NDc3c2VF/Bh5JAmQgI0JMHmwcedQmvMIyJUVOTk5qKiowIwZM5wXABWTAAmQgAIBJg8KkGhCAioEZOJQUFBgJA5LlixROYQ2JEACJOBIAkweHNltFG03AleuXIFMGOSSTN6zwm69Qz0kQAK6CTB50E2U/lKOgKzlsGXLFtx0002QSzJ5z4qUGwIMmARSjgDvbZFyXc6AdROQtRxOnTqFqqoqJg664dIfCZCALQmwzgPrPGgfmE5a1y2DH4xeK2o5xOqQwWiN5deKfU7SOthxYAW/WD6dxJZaY/Xk4PZJtqzzYNVi1Bh+WechHI7K2mIzm2RbKx0t3oqKCn8th2g2gYTNbMz2S1862Kq0o8NGh1YZs5kWs/0qPlTY6mhHh49EaVXhphKPjnGg0o4OGx1adXFTiUdFr9RjxYNzHgaX+PHoFCVQW1uLZ555hrUcUrT/GTYJpDoBhyYPf0Vj6R1IS0vr/8tAftUJeFO9Nxl/QggEFoFiLYeEIGcjJEACNiPgyOTBe/rP+MOO1gCUOZifMwGODCYgCr60PwGZOMgiUHV1dSwCZf/uokISIAGLCDhwtUUXDr+zB2Pe+gpi5hiLsNAtCYQT8CUOsnpkXl5euAG3kAAJkECKEHBe8tD9KXZu2I51WTcjq2s2cvJ+iMwRPOeQIuN1yMIMLDvN6pFD1g1smARIwCYEHPar+w3a3nsD6zoBNK1D8bz7kPXQS6ht67YJTspIRgJnz55l2elk7FjGRAIkEDcBhyUP1yJzwU4IcRmelg9RWZIHNK3GvKcq0drD6ZJxjwIeGJWAPOMg11IXFhYa5aejGnIHCZAACaQQAYcXibqCzsbVeGzWh5jesBdrQ+ZA3H333SnUlQxVNwF5v4q2tjbceOONGDt2rG739EcCJEACgybAIlFxV7H4SjSUTBOukgZxfoA+WCQqHJhKYRIzG5XCJWY+pDIzG7P9Kj6kTSS97e3tIjs7WyxcuFDs2rUrHFTIFh1aVHxE0hoiJWHczPTq0CpjM2vHbL+KD2ljpldHOzp8JEqrCjeVeMy46mpHRYuZjQ6tiYxHRa/UY8XDYZctIiVpIzAuKwuTszIwItJubiOBARLw3Vpb3iFT3uhq2LBhA/RAcxIgARJIbgJJkDz0oOPkZJT+JJN1HpJ7rCYkutDEgXfITAh2NkICJOAwAs5KHrydaN3zL2jtvNKH2duJQ69tQNP9TyB3pLNCcdg4SQm5TBxSopsZJAmQgAYCDvvF9eL8wd/ijoxvIS1tMoo2/Bk9c5bhlzPH8qyDhsGQyi6YOKRy7zN2EiCBgRJwVpGo9LGYuaoOYtVAw6Q9CUQnIFdVFBQUwDfHgZcqorPiHhIgARKQBBx25oGdRgJ6CcgzDnI5pqzjsHXrVjBx0MuX3kiABJKTAJOH5OxXRqVA4MiRI8YZhzFjxrAAlAIvmpAACZCAj4DDi0T5wojvWd7Se8+ePfEdnOCjZJXDsrKyBLcaX3NO0Hr8+HEsW7YMixcvxmeffUa28XV1zKOcMA4CA3CSXmoN7Dl9r53EVUYt9bJIlBVVLEx8skhUOCCzIiryCDMblcIlZj5U2onXR3Nzs5B9X1FRYQAw0xtvO6F0zfyY7Zf+zLRayW2g8ejQmsh4zPSq9I+Zjdl+lXilTSK0qmhRicdMq652VLSY2ejQmsh4VPRKPVY8eNlCX9JKTw4gEHhbbd4d0wEdRokkQAK2JOCs1Ra2REhRTiGwfft2FBUVobm5GTNmzHCKbOokARIgAdsR4JkH23UJBVlBYNOmTUwcrABLnyRAAilJgMlDSnZ76gQtazjIxEGedeAZh9Tpd0ZKAiRgLQFetrCWL70PIYFLly5hy5Yt6OrqQm1tLcaNGzeEatg0CZAACSQPASYPydOXjCSAwLlz51BaWopTp06hsbGRiUMAG74kARIggcESYJ0H1nkY7BgKO36o10qfPXvWWP88YcIEo46D2S21h1pvGMAYG6g1BpxB7iLbQQKMcji5RgGjYbNkyzoPVixENfHJOg/hgMzWQcsjzGxU1h6b+VBpJ5KPw4cPi+zsbLFw4UJx8eJFU62yHTO9kdoJJafDRsWHmdZ4uVkRjw6tiYzHTK9K/5jZmO1XiVfaJEKrihaVeMy06mpHRYuZjQ6tiYxHRa/UY8WDEyY1ZH90YQ8CsobD1KlTeZ8Ke3QHVZAACSQxASYPSdy5qRSaXFGRk5ODmpoa3qcilTqesZIACQwJAU6YHBLsbFQXAbmi4rXXXsOKFSu4FFMXVPohARIgARMCTB5MAHG3fQlcuHABzz77LI4ePYr29nauqLBvV1EZCZBAkhHgZYsk69BUCaejowMrV640wt27dy8Th1TpeMZJAiRgCwJMHmzRDRQxEAJyYuT48eNx5513YuPGjRg1atRADqctCZAACZDAIAnwssUgAfLwxBLw3dyquroaN9xwA4YPH55YAWyNBEiABEgALBLFIlHaPwZWFIWR96h4++238fnnn6O4uBiTJk3SptsKvdrEhTii1hAgGt+SrUaYAa7INQCG5peSLYtEWVHFwsQni0SFAzIroiKPMLNRKVxi5iOwnfb2dvHwww8bf/K17zEQH75jIj2b6dXVjpkfs/1Su5lWaWPmx2y/ig8VGx1aVdrRFY+ZXh3t6PAhmSRCqy72Zlp1taODrQ6tiYxHRa/UY8WDcx40Z4J0p5eAnN9QUFCAzMxMvPPOO5wYqRcvvZEACZBAXAQ45yEubDwoEQQ++ugj466Ycn5DYWFhIppkGyRAAiRAAgoEmDwoQKJJYgn47oi5f/9+Fn5KLHq2RgIkQAJKBHjZQgkTjRJFoK2tDQ8++KDRXFlZGWbMmJGoptkOCZAACZCAIgEmD4qgaGY9gdraWmRlZWHu3LlG/YbRo0db3yhbIAESIAESGDABXrYYMDIeoJuAvD/FK6+8gvLyctTV1SEvL093E/RHAiRAAiSgkQCTB40w6WrgBORliscffxwZGRm8P8XA8fEIEiABEhgSAiwSxSJR2geealEYWdxkzZo1RvLw8MMPY9iwYdq1qDhU1aviy2obarWOMNlaw5ZcreEqvUq2LBJlRRULE58sEhUOKBGFVs6ePSseeOABkZ2dLerq6sJF9G8x02K2X7pRsTErtKLiQ4eNig8zrSoxq7Sjw0aH1kTGY6ZXBxMdPiSTRGjVxd5Mq652dLDVoTWR8ajolXqseHDCpHVJIT1HIHDkyBH/ago5QZLzGyJA4iYSIAESsDkBznmweQclizw5KbKyshLPPPMMZNGn6667jtUik6VzGQcJkEDKEWDykHJdnviA5aTIkpISeDweHD58GFOmTMEHH3yQeCFskQRIgARIQAsBXrbQgpFOohHw1W6Q96aQFSNl4sAHCZAACZCAswnwzIOz+8+26js6OrBy5UocPXqUtRts20sURgIkQALxEeCZh/i48agYBOS9KcaPH29Y7N27l5MiY7DiLhIgARJwIoGkrvNw9913O7FPHKv5b3/7mzGvQc5tkJcpRo0a5dhYKJwESIAEnECAdR6sWIhq4pN1HsIBxbtWWtZrkHUbFi5cKG6//fZwxyFb4m0n0I0OH9Kf2VppXe2Y+THbr6JV2pj5Mduv4kPFxoyrig8VG13xmOnV0Y4OH5JJIrTqYm+mVVc7Otjq0JrIeFT0Sj1WPHjZwgmppY01yksUciVFfn4+li1bhq1btw5ZpUgbY6I0EiABEkgqAkwekqo7ExuMXEkhb5/99ddfG/elKCgoSKwAtkYCJEACJDAkBLjaYkiwO7vRs2fPYtGiRXjzzTdRU1MDJg3O7k+qJwESIIGBEuCZh4ESS2F7WSVSnm1YsGABbrzxRp5tSOGxwNBJgARSmwDPPKR2/ytHH1gl8tVXX8Urr7yifCwNSYAESIAEkosAzzwkV39qj0aebdi0aROysrIwffp0yLoNU6dO1d4OHZIACZAACTiHAM88OKevEq60vr4eL730EjIyMvz3pEi4CDZIAiRAAiRgOwJJXSTKjHZaWhr27NljZmaL/atXr0ZZWVlCtMgJkR9++CHef/99LF26FDNmzBjQ8stEatUBxEl6qVVHj0f2QbaRuQx2K7kOlmD04yVbFomyooqFiU8WiQoGdPHiRbF06VIhubz44ouivb092KD/nVkxFpXCJWY+ZFNmNmb7VXxIGzO9utox82O2X0WrSswq7eiwMeOqolXFRodWFbY62tHhI1FadbHXMQ50cTPzo0OrLm5mWlXGgbSx6sHLFtGTupTac+DAATz33HPo6upCc3OzcbYhpQAwWBIgARIgAWUCTB6UUSWnobz75caNG1FeXo7q6mpcd911TBySs6sZFQmQAAloI8DVFtpQOsuRbxWF7+6X7e3tKCwsHNDcBmdFTLUkQAIkQAK6CPDMgy6SDvIjCz2tWbPGWEXBSxQO6jhKJQESIAGbEGDyYJOOSISML7/8EnPnzjVWmMiy0rNnz8bw4cMT0TTbIAESIAESSCICvGyRRJ0ZLRQ5r0He+VIuu5SFnuRSTHk/CiYO0YhxOwmQAAmQQCwCTB5i0XH4Pnm7bFkd0jevYfPmzVi+fDlGjRrl8MgonwRIgARIYCgJsEhUEhaJunLlClpbW407XspE4cc//jEmTZqUsHHmpKIwEoqT9FKrdcOYbK1hS67WcPV9d7FIlFWVLGL4TcYiUTU1NSI7O9v4k68DHypFR3TYJFuhFR1MZD+Y+THbL33oYKvSjg4bHVp1cVOJx0yvig8zG7P9KvGqjANd7Zj5MduvolUlZpV2dNiYjQEVrSo2OrSqspV2Vjw4YdK6pDChnmWRp1WrVuHgwYPGGQdOhkwofjZGAiRAAilFgHMeHN7d8lbZcgVFTk4ObrvtNk6GdHh/Uj4JkAAJOIEAkwcn9FIEjTJpkCsofLfKliso5syZw8mQEVhxEwmQAAmQgF4CTB708rTcW2DSIBtzu91cQWE5dTZAAiRAAiQQSIDJQyANG7/+5ptv/GcapEyZNKxbtw6ZmZk2Vk1pJEACJEACyUiAEyZt3qvyTMObb76JI0eO4IEHHjCSBiYMNu80yiMBEiCBJCfAOg82rfPg8XhQX1+P999/36jTIEtLr1y50hHD0UnruiVQJ+mlVus+AmRrDVtytYar77uLdR6sWIhq4tOOdR7cbrd48cUXhdQmn+V7+dCx/ljX2mIzPzq0ypjN2jHbr+JDha2udsz8mO1X0aoSs0o7Omw4DmRvBD90cJUezdjqasfMj9l+Fa3SxsyP2X4VHyo2ZlxVfKjY6IpHRa/UY8WDcx6sSwoH5DnSREjOaRgQQhqTAAmQAAkkiACThwSBjtaMnMuwbds2Y8mltOFEyGikuJ0ESIAESMAuBJg8DFFPyIqQsrjT1KlT8e1vf5tJwxD1A5slARIgARIYOAEmDwNnFvcRly5dMiZB+ipC3n///UZFyEceeYRLLuOmygNJgARIgAQSTYBLNRNAXN7lsra2FmvWrDFaKywsRFVVFatBJoA9myABEiABEtBPgMmDfqZ+j+fOncPbb7+NZ555BtnZ2Vi2bBl4wyo/Hr4gARIgARJwKAFetrCg4+TKCXmHy9GjR+Pjjz82zjjs378fBQUFGD58uAUt0iUJkAAJkAAJJI4Ai0RpLBJ1/PhxNDQ0YN++fUZhp3vvvRff/e53tfQmC61owRjRCdlGxDLojU7iKoN1kl5qHfTwjOjASVx9Y5ZFoqyoYmHiU0eRqF27domamhqRnZ1tFHaqqKgQ7e3tQS2bFQQx2y+dqRQDMfNjtl+2o8NGh1YVLTq0qrDV1Y6ZH7P9KloTyc1ML8eB7I3ghxkzaa1iY8ZWxYcOGxUfZlpVYlZpR4eNDq2JjEdFb/AI1PeOcx4i5p/mG+WlCVk+OnA+Q25uLidBmqOjBQmQAAmQgMMJcM7DADtQ1mdYtGiRUdTp6NGjxnyGQ4cOGfMZRo0aNUBvNCcBEiABEiCBxBDYtGmTsfJPR2tMHhQoylUT27dvx/Tp05GTk4PbbrvNKOq0detWTJo0ScEDTUiABEiABEhgaAmMHDkS8+bNM/4B7ujoGJQYJg8x8Mk7WfpWTcg6DXKp5dmzZ7FkyRIWdYrBjbtIgARIgATsR0DWGDp8+DC++uorjB8/3vinWBYvjOfB5CGEmjzLIBMFWQVy6dKl6OrqMmDv3r2blyZCWPEtCZAACZCAswhMmTIF77zzDqqrq1FUVIRHH30Ucg7fQB9MHvqJyRtU+c4yyEqQsibDW2+9BXlnSwmbDxIgARIgARJIBgKy3pA8CyFvxHjTTTcZc/jk799AzkKkfPLgO8sgb1AlzzI0NzdDToCUYK+//vpkGCeMgQRIgARIgATCCGRmZkLO3aupqcGKFSsgaxOpzoVI6iJRaWlpYbC4gQRIgARIgARIIDIBOSdC5Wx7Up95EEIg1p9EF2u/nfbddddd1GrSn/H2F9nG/pykAlcZI8cBx4GTxoCOMSsXAPzmN78xsoiFCxeivb1dKXGQB7BIVOTki1tJgARIgARIIGkJyCKHL730khFfXV0d8vLyBhRrUp95GBAJGpMACZAACZBAkhOQcxpKSkqQn58PWRV57969A04cJCKeeUjygcLwSIAESIAESEASkGcbZNKQnZ1tlCBQmdsQjRyTh2hkuJ0ESIAESIAEkojA7373O1RUVKC4uBhyueZgHo6+bOHtPITq0nzIVRUZRa/jUOeVwbDgsSRAAiRAAiSQtARksUNZIXmwiYME5NzkoecQNjz2S7jzq9ArLqO16K8ofex1tPZ4k7bjGRgJkAAJkAAJ2IGAQ5OHb9C2cz02TH8ey2aORTqGwTXzabw8/T0s39kGpg92GFrUQAIkQAIkkKwEnFkkynsCVbN/hHfn/zP+tODW/tMnXnQ3voRb105E058WINOhaVGyDjTGRQIkQAIkkDwEHPkT6z35r3i3/gZMmTAm/LpL/V40n/wmeXqIkZAACZAACZCAzQg4MHnwoqfjJI7hFmSNG2EznJRDAiRAAiRAAslPwIHJQ/J3CiMkARIgARIgATsTcGDykI4R4yZiMr6Au6PHzmypjQRIgARIgASSkoADkwcgfeI9mJ/3rZAOuYIzp06iM+9B5Ey8NmQf3w6MgJx8uhwZaWlGDQ1ZRyMtvwptQctYrqCzdQdK78tAWtpkFL12AJ1B+2WLKjZA8tXr8KKnrQm1761H0cTlaOwOA6PMJrjfVHiq2DiZeTfaGvfgvfVFmFjaiO5gQP3vVMZvyIHeTrRWl+I+OdYzivDaoc7wVVsqNopjPqT1oX/b04Z964v6P/MZuK90B1oj1M2J57OqcoyKDZT4Dz3KYAXdaNv3Gooy+r9L7ytFdWuEsSUP6m5Eqc/O+O79KaraYszfU+Kh8n2gYhMclfFOOPJxSbgrHxGukgZx3q//K9FQco/Iqzwuev3b+CIuAr2nRM2C7wt509G+P1cI115xoWWDyM19VTR4LgvR2yEayuaI3PKD4oK/QRUbIcSFg6I8d44oa+gQveKy8DS8KnJzN4iWC87txV53pZjzWKF4zAUBV5loOB8aiyIbP0v5QuUYFRsnM5ef+wXiscK5wgWEfP4DYJmO3wBb4+XXoqV8rsgtqxeeXiF6PfWiLHeuKG/5OsBQxUaRf4BXW7zsPSV2b9gs6t1936a9nmaxofD7AqGfw3g+qyrHqNgIFf62oBkg4rLo2L1JbKh3930v9nrEwQ2FwoU5IWNLHnJZdNQ8bYxr//duXqVwh351+L2r8FAZjyo2/kaDXsjbPDvzoTTgnBna0KruG0x5QYlZiKLe46Iy7x5R0vDV1R3nG0SJ6xFR6b7Ut03FRiRzEtgXW8TkQYnNVbTGK5VjVGySgbkRpytK8qAwfkPRuitFXlCS1yvON5QJV8CXt0wIzWyEEv+Qxm3wtvdks/ik43KQEiNeTAv4jMfzWVU5RsVGCCX+QRHY4E3vF+KTT/49+J/ZaGNX/p7lvRzhH43IcSjxUBmPKjaRJQhHXrYwTpmMmI7n3y7DTdUP4pq0CXis7hasf/tpTBvh3JAinBgagk3ncGjnH1C/bi1+U1WLxrbwE8N9S2XHBq92GfkD5D9xGu82nzJO96rYwHsKze9+islZGbi6bmYU7si/F8fe/VecjHS2fwiI6G5SiU1IoyrHqNgkP3Pz8RuM9hucbN6L+skTMc7/3ZGOkXfcjyeO+ZZ9q9gASvyDG7fFu/S/n4HcscOCtKTfPAFTXAGb4vmsqhyjYgM1/gFq7fEy/bvIzR0fXE4gfQwmTMkI0edF96Hd2FD/Jn71m0rUNrYh9mw+NR4q41HFJkSs/62jf2nTXTPwXPUxCOHBJ2ufwDRX8AfAHyVfKBPwtn2Ateta5f3XsK54HmZlPYLS2hMBg7l/4LomYsLNobwvo9740Vex8X3Zplq9DjU2wR2mcoyKTfIzNx+/wWT7kqlmuKZMwM1h34bNfcmw8QNnYuP7gYv5uQhp2+5vr7sLd2aNNFT2/cgM7LOqcoyKjVIf2Z1lkL7RmH3n31/9h8nbhvfWbkMnOtG0bjHmzcrFQ6W1aIt2qwVt41HtOyNIesCbsI9LwD6+TEEC6ZkLUCcEej0t2F1ZglyZRMx7AW+0dvXT6EGH+wsg6D+1UFAqNqlar0OFTTw8VfwmP3Pz8RvCtscD9zGEnP2KwwYq/EP82vatF90tTTjy80LkGWck4hk3Kseo2ABQ6SPbsgwR1v0Z6o48iP+VF3BGIv1WLKjzQPR60LJ7C0pygaZ1S/DUGy0B/7QF+FHioTIeVWwC2g15yeQhBAjf9hFId03DwwvWosFTj7LcT7Fh56dRZraTGAnYjwDH7yD6pKcFW6rHYNXP77j63/Eg3PFQH4EutG75ADet+h+RL6+nuzDt4UVY2/B/0VA2GU0bduNQxJVaPn9D+8zkYWj52771dNcsLHv5SWDHx2gxBvIIjMu6BTh2Eh3RTqtBxSZV63WosAkdFirHqNikHvPw8RvCdkQGsiYDx9yeyP/lSXMVG6UxH9K2Ld92oXXrnzCq7MmAH7h4xo3KMSo2qvxtCTNAlBc9rX/EzlEL8fNpNwRsj/AyfSxmLitFCepR13Iu3EDbeFT5zghv3reFyYOPBJ+jEOj/gPsvU1yLiTkPIi/U2vtXnDrShbz592BiuopNqtbrUGMTjFflGBWbVGQeOn6DySJ9AnLm54RsBLxnTuFIZw7m50xAuooN1PiHNWSrDVdwes8f8fns57Dg1r65Dj558dTWUTlGxUapj3xCbfrsPb0XWz/PwcsLvq92NsdIELKCJ6X7YtM2Hgc3Zpk8+DqEz1EIyOuS/4Fppf/df6dS4wM/eX9wVmxch7u978sW/T9SJjZ9XwpjsaPus4BLIvI63On+JCSKJIdvVuEXGqLKMSo2qcc8fPwGs+37Ap3sP7Mm9/Zfi/cXnFOxURzzwY3b6N0VdDZWYef1D+EJf+LQjRPVO9AkzzgaP1gD/KyqHKNi05+Yxe4jG6EMkeLtbMRvd16Lnz3hSxy86DnxHqqa/hpiGfC2x4OT04rxk8xIBQ/1jUel74wAWUEvoyzh5OaUJHBZeFo+ErtbPP1rky8Lz8HNouTlvuI5V5GoFBZRsXFywaKrNCK/ilHnQangU6hXFZ4qNknAPNpaeVlkTGn8hrJVKbijYqPIP7T5IX9/XrhrykSuvyicrzgcBAJqXcRV0E2lHo+KjSOLRPWKC+4aUZLrCii452N7tSZOr6dF7N7dYgPrKTcAAAqRSURBVBQok0PBKNJVUt5XgC/q2NA1HuMfs84tEhUVKnfET6C/wmP/l4irsFzsauivjhbmVCYWm0ShrKKIPFGy7aB/8F81VbHp/7DIinZwidyS7aJFVq108sMomOX7kpDPoRU6ZXBqbIIxqByjYuNU5v3Fm4J+5K5+CRtMZYVSpfEbTFb4q/9BILdEbPMn0AF2KjZx9WtAGwl/GaGyoZ9v+Lj1V58cwGdV5RgVG6U+Sji/6A32dtSIBcb3Y+B3Qf/rgKSsr6Jpf4LhKhTluz4RbpUKu9rGo9p3RmikaXJD0KkIviEBEiABEiABEiCBGAQ45yEGHO4iARIgARIgARIIJ8DkIZwJt5AACZAACZAACcQgwOQhBhzuIgESIAESIAESCCfA5CGcCbeQAAmQAAmQAAnEIMDkIQYc7iIBEiABEiABEggnwOQhnAm3kAAJkAAJkAAJxCDA5CEGHO4iARIgARIgARIIJ8DkIZwJt5AACZAACZAACcQgwOQhBhzuIgESIAESIAESCCfA5CGcCbeQAAmQAAmQAAnEIMDkIQYc7iIBEiABEiABEggnwOQhnAm3kAAJpDoBbyda97yN9UX5KG2McevkVOfE+FOWAJOHlO16Bp5yBLobUZqRhrS08L+MovV4r7ENPQFQvG1VyE+7YwA/nt1o27cRy6tPwBvgxzkvu9C6finWt55Dd1MFHpr7D3hx+1lr5Pccwvr8pag9fcUa//RKAhYTYPJgMWC6JwG7EXCVNOC8EJA31O37O4+mx6/Bh4/Pw9NVn/sTiPTMBagTLVg7c4xaCN0tqCxag9ZeNXN7WXnR3bgO84//EI9OHYWRM3+NEw1lcFklcsQdWFx6HUr+8Z9x2pmZllVk6NchBJg8OKSjKJMErCMwEpkPPI1Vm+7FvuJleKO1y7qm7Oq5pwVbfvUXLC/9bxibkG/FdIzMLcTyjv+DjU28LGLXYUFd0Qkk5GMSvXnuIQESsAeBYRg7dwl+nfcpNuz8FN0Awi5b9LShsaoU9/kve+SjtKoRbT1eQF4SuXUW1nV2or54Eq7JWI7Gbvkv9RV0ttZifdHkq5dL7itFlf8SifyPfzky0n6KrY1NqC7N77ebjKL1dX2+AwB5Ow/FtpFzFaoDNAa1FeAo6OUVnK7fjg3DZiFn4rVBeyx9k34L8p+aih1rP0Abzz5YiprO9RNg8qCfKT2SgDMJpI/BhCkZ6DxyCmfCfsy60PrG83h8//ew+UKvcbmj1/MCrtmxGM/sbIN35EysPdGAEpcLeZXH0etZhZkjgZ7W1/HYQ3twzdP16DUuk1yG5+XrsGPW8yFnOHZh8a/qcX3xrn7fGzD2o6fx1Bst/sso3tO1WDRtLrbhKbilhgvv4N5jLyD3F7v7Tv17/4LaRXl4qPHvsNZzGUL04sLm72H/4/Pwi9q/RJ+H4f0Cdb/fi8nz78HEqN+IviSnb75IRmkjutGNtsZ3+ydVnkbnoddRZMwpycfyxtPwBiYyGcWoOiFTssDHMLi+fzsm1+9F88lvAnfwNQnYnkDUj4rtlVMgCZCANQSOnUSHPJsQ+PCewdF9JzD53juROaLvayPd9QBWfXISdQtuReQvknM4tPMPcD9RhOLprn6bYXDlzscTeSew7+iZgB/0aSh5+XkUZI40Wk13TcX9029A077P4TGkfIOTdX9EFZ7Eyyvm9mkY8T38pOghoOqPqDt5Ed1Nv8eSqkn49YpiTHcNA5COEbc+gYq3HsKflvweTcaZkMCg+l/3eOA+dgOmTBgTJQ5pl44Rk+ZgWXklDnouw7M2F2hcg9xZP8OL2z048+lBeMYvQrXna7SU/yesfnw5NtS6cf281fiktwMNT3ag+BfvhZ1hSL95Aqa4mvFu86kAFhE0chMJ2IxA5M+8zURSDgmQwBATSL8Ztz1wK+pf+ifsPtSIWv9lh1i6xmDm2hZ41t6BM417UFtbi9rarSidNRPF9RdjHQhgBMZl3QL4EhnvKTS/2wxMnohx/cmL/EEfOXMVPGInFmReREtdPTpdEzHhZpk4+B7pGDFuIiZ31qOu5ZxvY9Cz98wpHOm8BVnjRgRtv/rGi54TO1BW8f/w4M+f9Ccmsu0OdyXy8C3cfPsPMc1IWEbiv97+A7g6L2HUD+7qS3LSR2PcxO9cjeWqY2BEBrImA8fcHv8ZlsDdfE0CdiXA5MGuPUNdJDBUBIJ+oH0ibsC0F96G+6070VWzFvNmZeH6tAzcV1qFxrbQ0/G+Y+SPbjWKMr6DrFm/w8EueQrhPyN/cy0q8yz6wexcjVnfuebq/Iq0NFyTVYx6n6SwZy96Ok7iWNh234bLOHNoM57+0XHkL+s/4+HbxWcSSGECTB5SuPMZOgkEEej+DHU7WuGaMgE3R/xmGInMmQVYsLYOQlyGp2UT5px5DbNy1/RPjgzyJmdcYucvyrBvdg06euuwdsFPUFDwMGZmXIT7WGeIsaa3eZVw9/qWoAY+R1ty2n9mwqz5i9vwqzUN6Ay5mmN2GPeTQLISiPgVkazBMi4SIIFoBK7g9Me12NH5CH5dfA/6Zh5Es5Xbh8E1bS4WFz0EV+dJnDoTodiRMZcAmDzje3AFfNN4L3RhwIsT0ycgZ35O2Kn/vhUhGciv+g9Mzc+D69in+LwzUIsXPa2v4b60n6KqLfKkxL55B1/A3RFYIssX+7dw8/T/idcbV+Pvtj2PZduu1sHwWQzq2ccoKwPRLpoMyj8PJgGLCAR8pC1qgW5JgARsTkBWhnwdy5fsxwOV/4ifZkZYrug9gar8ibivtPbq8smeNnxc1wos+Bny5RJH4/r9dX2xXuxBz4gfIP+JDNTveBdN/T/o3s4D+O3yV1A14BMP12Li7EUoy9p59QyA9zSatr2L+twXseqnt+LG3KewafZ+LFm+FYeM9rzoaduNX73wOlD+QuS4pFpDdxeOnPprlEmLcuLlo1jz1k/w78WPBhXSGmzH9s23yMH8nAkxJmsOthUeTwIWEBB8kAAJpAaB8w2ixAUBhP65RG7JFrG7xSN6A0j0uitFHqaJkoavjK29nhZRU14oXP7jvy8Ky2tEi+dy/1GXhafhVZFr7H9EVLoviV7PQbGtJM/fpquwXOxq+LOoKZkmXCUN4rzoFecbyoQroJ0+Z5eEu/IRAVeZaDh/VVWwP6l7e0D7QogLbtFQWdKvAQKuQlFe0yI8V10EROh72a8hr1K4Dbv+tv1xukRe5b+Jrw2d/excT4vy1Q/74wKkzafiuNTsP06y+zfRUDItZFsfTyH62/G369PDZxKwP4E0KdGCnIQuSYAESMA5BOS9Jh5aDaz/J7ww7YbE6JZnc2YXw126R70EeGKUsRUSMCXAyxamiGhAAiSQ9ATkvSZenoQ3fteYoHtNeNHdtB2rxv1vPJureO+QpO8EBugkAkwenNRb1EoCJGARAXmviaex5b804p3DCbi3h7yXxtqLWPfLHyXoXhoWYaPblCXAyxYp2/UMnARIgARIgATiI8AzD/Fx41EkQAIkQAIkkLIEmDykbNczcBIgARIgARKIjwCTh/i48SgSIAESIAESSFkCTB5StusZOAmQAAmQAAnER4DJQ3zceBQJkAAJkAAJpCyB/w+sgyE3GC1y/wAAAABJRU5ErkJggg=="></p>
</div>
<div class="specification">
<p>It is known that 8 buses travelled more than <em>m</em> kilometres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of buses that travelled a distance between 15000 and 20000 kilometres.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the cumulative frequency curve to find the median distance.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the cumulative frequency curve to find the lower quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the cumulative frequency curve to find the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence write down the interquartile range.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the percentage of buses that travelled a distance greater than the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of buses that travelled a distance less than or equal to 12 000 km.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>m</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The smallest distance travelled by one of the buses was 2500 km.<br>The longest distance travelled by one of the buses was 23 000 km.</p>
<p><strong>On graph paper</strong>, draw a box-and-whisker diagram for these data. Use a scale of 2 cm to represent 5000 km.</p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A discrete random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> has the following probability distribution.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.34.18.png" alt="N17/5/MATME/SP2/ENG/TZ0/04"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2|X > 0)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
<mrow>
<mo stretchy="false">|</mo>
</mrow>
<mi>X</mi>
<mo>></mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The scores of the eight highest scoring countries in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2019</mn></math> Eurovision song contest are shown in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>For this data, find</p>
</div>
<div class="specification">
<p>Chester is investigating the relationship between the highest-scoring countries’ Eurovision score and their population size to determine whether population size can reasonably be used to predict a country’s score.</p>
<p>The populations of the countries, to the nearest million, are shown in the table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Chester finds that, for this data, the Pearson’s product moment correlation coefficient is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>249</mn></math>.</p>
</div>
<div class="specification">
<p>Chester then decides to find the Spearman’s rank correlation coefficient for this data, and creates a table of ranks.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Write down the value of:</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the upper quartile.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the interquartile range.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine if the Netherlands’ score is an outlier for this data. Justify your answer.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether it would be appropriate for Chester to use the equation of a regression line for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> to predict a country’s Eurovision score. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of the Spearman’s rank correlation coefficient <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret the value obtained for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When calculating the ranks, Chester incorrectly read the Netherlands’ score as <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>478</mn></math>. Explain why the value of the Spearman’s rank correlation <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math> does not change despite this error.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All lengths in this question are in metres.</strong></p>
<p> </p>
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \sqrt {\frac{{4 - {x^2}}}{8}} ">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>8</mn>
</mfrac>
</msqrt>
</math></span>, for −2 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 2. In the following diagram, the shaded region is enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">A container can be modelled by rotating this region by 360˚ about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis.</p>
</div>
<div class="specification">
<p>Water can flow in and out of the container.</p>
<p>The volume of water in the container is given by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 4 , where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is measured in hours and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span> is measured in m<sup>3</sup>. The rate of change of the volume of water in the container is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'\left( t \right) = 0.9 - 2.5\,{\text{cos}}\left( {0.4{t^2}} \right)">
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.9</mn>
<mo>−<!-- − --></mo>
<mn>2.5</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.4</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The volume of water in the container is increasing only when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of the container.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During the interval <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>, he volume of water in the container increases by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> m<sup>3</sup>. Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> = 0, the volume of water in the container is 2.3 m<sup>3</sup>. It is known that the container is never completely full of water during the 4 hour period.</p>
<p> </p>
<p>Find the minimum volume of empty space in the container during the 4 hour period.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = - 0.5{x^4} + 3{x^2} + 2x">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>0.5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.09.00.png" alt="M17/5/MATME/SP2/ENG/TZ2/08"></p>
<p> </p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
<mi>x</mi>
<mo>=</mo>
<mi>p</mi>
</math></span>. There is a maximum at A where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
<mi>x</mi>
<mo>=</mo>
<mi>a</mi>
</math></span>, and a point of inflexion at B where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
<mi>x</mi>
<mo>=</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R">
<mi>R</mi>
</math></span> be the region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> , the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis, the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
<mi>x</mi>
<mo>=</mo>
<mi>b</mi>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
<mi>x</mi>
<mo>=</mo>
<mi>a</mi>
</math></span>. The region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R">
<mi>R</mi>
</math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The marks obtained by nine Mathematical Studies SL students in their projects (<em>x</em>) and their final IB examination scores (<em>y</em>) were recorded. These data were used to determine whether the project mark is a good predictor of the examination score. The results are shown in the table.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAnYAAABQCAYAAACUPjj7AAAgAElEQVR4Ae2dD3RU1b3vvzOhysUQuFy5cgI+WCQC2kSsyYq9yisD0YmIICWCSiWBZFlYglDzyKShYKtiIkwarha6sHZGEiotf2YeFmklmBh90F5yZyg2eYWkgRVqmMGHF8kfUf7M7Lf2OWcyZyZnkskkk8zh/rIWzPmzz96//dn77Pnt3++39+gYYwz0RwSIABEgAkSACBABIqB5AnrN14AqQASIABEgAkSACBABIiASIMWOOgIRIAJEgAgQASJABG4SAsPU6qHT6dQu0zUiQASIABEgAkSACBCBGCIQHFGnqtjxRFy5C04cQ/UgUYhAVAhovd9rWX4ty847I8kflVcyrEyJfViYopZIy/y1LDtvUC5/8B+5YoOJ0DkRIAJEgAgQASJABDRKgBQ7jTYciU0EiAARIAJEgAgQgWACpNgFE6FzIkAEiAARIAJEgAholAApdhptOBKbCBABIkAEiAARIALBBEixCyZC50SACBABIkAEiAAR0CgBUuw02nAkNhEgAkSACBABIkAEggmQYhdMhM6JABEgAkSACBABIqBRAqTYabThSGwiQASIABEgAkSACAQTIMUumAidEwEiQASIABEgAkRAowRIsdNow5HYRIAIEAEiQASIABEIJhCRYnfDWYZknU78KQv+cxbKf4m5ZbA73fAGlxTx+Q247SulMnLtcEecT6gHvehsqsX+siJsdXaGSjS019125IqcV8LuvtFHWbzodG7FLF0isqyn+9gu36DJuhg63eMoc17uY7n/nZO3o6nmPewvy0VyUQ3a1VB43XBWFGEWb9fEXGytG8h3Rq3APlzrbEKNfTfKcrNQVPOFyoPtaDqyFbmJ8rufmIuyI02IjbdHep/t+8uQm7weNe29jETec7Dnp0fwbqhgGZBLvfUdXr/DKMtNlcfdVOSWHUZTZy/1HBDZesskPPZedx0qirJE+RNzt6POfa23jAfpfm/sAXQ24UhZLhLl773E3K040qT6hg+SzOEUcw1u5x/E8YjLnRhqTAonq6ilCafvxPK4E0bfUbKL8rgTkWKnlC/42F1ZiOz051CuFUXgxl+w47FZWFRYB09wZW6Gc28T9q43o1ZYhqInp6BvDT4cU55cCZNwCIXr7WiKhe+OmG8Trgy/iJcrdmJNYSWuqMp7Gc7y57Gu8WHs9jB4nM/iYtHzsfHOeE/D+vQGVNhKUVj5XyrSX8N5+3oYchsws6ZN/D1pLv+lkuV4VVUJVMkiipe8TTvx9MvvwLamEJXq8BWlX8P5A2astroU14bysPe+4z1/AGsN61A/87foYAzM8wFyL5XD8Gqt+gRiEKsTFvvOOpQveQWNWVZ42FU4c79A0ZLtcA65Yto7e/Av47XZyK2fjZoOD5gofztKDK/3PoEYxHYIKMrrRt3W55A2bw9aJi1HbYcHrs2zkRCQaOhPeu87sTzuhNF3AhAPwrjDQvwBfMxW/7vuMLMkgCHHxlyKJB7XUVaek8L4s4KpmrUp7sXs4XUHMyeBAQZmdnTEppguG8vhvLGC2VzX+yCjh7VVFzOhX+1xkVWb0hiQxkzVF/tQtjaT9tTv+1QjzylmMQqq74Gn0cKMQjGrbvPIWcrtZLSwRt+lPhXmTzxQ8osyqrW5ar2+Zo2WRap19UvW+9FAyc6YJA8CGAeX72EdjjdYTkEByxEEZrScYv1EL457waVEdK7KmOekXq/u/SmiUgdIfnUZJYnU+gkfXx7sN/8B6zsh2TOm+k6I6R/s99g4YPIHNP2XzGGey4Scbey462rAnYE+GRj5e+g7qu2i1p/6XrOBkZ0xpipjsDyDM+70zYAToHV2P9ELD+DpJx4Sb7gvXMZX8LtRk1/fj8PrJfO7LssqW38k8yt3WflM27pZRbDWKN06/jx0Aa5Ybvq0omhWouySyEKRtaabS8LrdsKuzF/pNuIuzm+lo/AMF7kWhekjoUsug1PF29nlfk5+HTV/U7hCZq2HnZviA0z0WSiqqINbaeEKuM9dWNyFYoezyw3xGey5ydDpZuF1+36sF+sVyn16De6al2U3Xj6sp0O5Ai7BcbgKbiThkQfuinCWNhp3P5AOwIldh/865FaB7r1Oa1e+QfPRD1CVmowJ8b7XT4+E9IextP4DHG3+JrYrpL8dk+5LhLvuU/y9y8rSidbGK1iadW+EfWwIqtzpwI43gTUFj2LcEBQfWZG3YNykZAjuv+LE333vvBedrc04s/RhpCf4+lNkuUf9KW8Lju45gdSpiYjvKmwM0rNmon7Pn9CsHC+77sfOgX7cJNwnuFB34qw/7KDThcYzM5GVPiZ2BBUl4SE472Bd+SRsK3kOGcItMSZfH8WhcadPwAZ0JPC6j+N37x0TBUhKnYixClHOFC/Co6VV4hXhvkkYp/ei8/QurDJwN2ilP3audgvyMw2YV1bnf3kU+UiHslk2Mx9ban1Rd1XYkp8Jw6pdOO37whHN/vOQrczfXYlCYzbW2s/1Md5MFuJMMTK//SgKKxukC7WlyF6xHkWrsmHsKqcKW5Y9j3+vleOTZBO+/z5/tAGVhdmYt+F9nA8Y0GpRnL0IpWK9EnHfpNuD3KdcqSvFksyfoRZzYT74c+RNC2FYb/8rDu9yArgfM1OUrSHXhcd5vbcf1qLFyPfx8J5HjaiAL4a1iSsZw3BHSgaMANy7PoSjt5glOWv6CEFA/HI7CukdCE5zFHuOtkTWL4Ozitr5GGQs/gEMtQWYJ75r38BdsxOHxxXjR4bbo1bqwGZ8Gc4du4E1OUgbGTewWUc1Nz0SMhagwHAChfP+lzih87qrUXb4f2D3j2bEvFLtbf4T9lSNVhnTAFRpYFKTcD8WF9yP2sJ8rLI2oJOPlWUfYtzuF2CINaVaDMHZDiydDu9vn5MMJ0qjRlT7aTQyp3GnL1T7p9hVZvstbTod4hJnoIArPMIqbHkmFcMCJJkLs+NLMHYdTRsfRALveGuLUekGhJydOCXHLLiqfwYD3KgtfAU7QsXptR/Fm6u3wy3kwXJKivNhHfWw5KTAXfkLvFN3CcA3aNpbhkKuIBl+hmrXVTEmQsq/AdbVb6H2tgWouO6AOYkLaoDZ0QHWvA5pgYIH1AJIQY6lHh3Mgw5HOQz8bu127MI6qQ4dx2E2CKKFy3biHLjxz9tcjbesDYChHA65nq22VeCp3B+fxYUAxY6LIqfzfIKN31XOBK/jcsO7+PGzXKkzorj6LRSkjQ6Sz3/qvdCCk1zvFZIxaVzwjO0z2Jf/T6QvWIT8Lftg/YUdf+m8BGf5CmTKCrgvJ2mmyoVtRsuFWAl09kmnsU8+w69HkNVCS3XQIz5tFXYf34ZHjizD3SMnY1nL4yh98SEI/RtNBgkCt2RU4k0swcoe3p1BEqbvxcRnoGD3PpQ/Uof8u0chbtlneLZ0pQYsMpJlsR6TMXWC317XdwBD+cRopBW8jePl9+NIfipGxr2IlmdfwosZQtDkeyhllMqWlOgkZNwzHQ8VVMDF2nBq0zCUGwtCf68Ovdg9SEDjTg9wut0a4KFYgMFkQXVtCRaOD1IkjAsx/ztcCRmG+PjhkDoe1zoWYdNPnsI00S11C4TZq7DRlAbgEHZ8dEZUjIKlvvH3E7DxR91WcXATV+WOTEW+aEXzuQwvouHjEwCSkPNCHmaLpmie/0/xEQ86dpVgdiSzLGEecp+8B/HQI3769zBXVArTsDR3rlSH+Hswa+7UAJH1U/JwmDF4dn8PrVUHYLduxLPZ2yUr5ZVLaLui1OwEGJfOwXc4D/0IxI9QNpEV+cYfSspw3gqsMozvcUDxdlyC6GUeMQajAvLh4t2JhRVNCuXUivK1v8Cx770ND+fD9iJvynCpHiNGYewIfngRlzpU/NQBtaWTm5/AMIwcPQGpBaUwGYCq/LXYUHM+xi2Ncqt0OvC2bSJKCjIU7kBttZh+5L9gYmouzCYjULUBKzYcCQz70FZ1tCWt/jaMnpiGAnMBDNiH/BWbUdMVThMrVZGVaCENWd9PlydcCZi2rBCbjCc0vBCOxp1we5hSawj3GX+6HBtcohLAFQH+z4WPNudh9pTursFg11OX0pGUgemTZQVCzHk4Ro0dKR6dqT+Hi/7S5KMbuHiuWVJYut2TLojxfTf+H84eE9WaEKkivKyqJI3E2FHKOgTl3dkAa24q4hLTsSA7G9n5W1DrS9ItPzX3qy+x/9NtteK3f+lpC5LeOYErp2lLZUW6AcfvfhzPx+Ds01/rm+AoPhFTU4H6RlcPoQaxXE8phGJtuQfPFPwYm6v/E9XFQGnmithY1dsjustwvl2DiavmYHz/Rr4eS4nqTT6WrH0HeGYN1m0+CFf1CqA0F0vKewpdiapEYWauR/yEZKTiLBpbY2NjnDAFVyRrx2nrSyjHEyhY93NUu6pQjLeQGROrehVi4houtDT7w5t8t/STMOOpGUB9M1p94Uq+ezH/SeNOX5po0Ia3EWNHQTT6yNLpR46BaOw6U4dPzyoDxr9B28UOMVVwnJ70qB63jR4jujGRZIbjuk+pVHxWLIQw7F8x+SFewhVcuPzVEFoTuEv4FcmaaDDBYjsEh+sqrjvMUv27tVZPSqIAg/nPaK0uhoDetiAZhrETk0OUoSyUBy8bRZ5njnyKs0rjoTIZHQ8MAd/gGpSb5DafgadmTOrRChv02OCfiiEUr6I14x7JEqAfj9kle+AwI/YtAe0nsNdcjOwJt8oLrnTQjcrEFrcbVfl3I07niysdfKzhlSiPJa1TkdLlgdiIg45CoLAMe8WY2PByGopU+uQH8ZTx1qCiZSXE+ChmJPcwOQ56aihOvU37sTbfhYyUO8R3VC88gpKDB2DGdqzf2zSE3zHBNHyLbEKEzgQs3Ap+NkbPadzpU8MMmmIXLJX0kvMos33Y8NoeecEDXxiwHa9u4QH/c7FyVlJQnB7PRV5ByB89U4E3KxtEy4fXfUReSZoub6o6Fikz7+f+WlTt2oNa0VzOtf4KeWPVwRrE+YrBs2L1hckPIGvBY0i74yI+sR3p0eoYzEs6n48XfpCO8YYV2JaXAlRtxeYDoReBdCnP3dy9vtz5quSD+NWJBCzlcYGhApivtOGiuCfYWIwZ2WMAoi9j+gxJYDiSZzyK1ICFKLLrRANfbhBjBIM3iEvAXfffK022QtY7Bm4kzMZml2ICyL0MbdUwCQKMllPwKMMPYkDc7iL4xxL/PT3i75qODD4exvqfOKkZH7S6ntfpPIxPPYjkIfs2CgecL0YwKG38ZNyfcUfQxaE+9X1HnsKxhs8VCqdWWKvwo3FHBUroS0P3KumnYHFJobj4wF3Jg7DjoNPdikRxtSe3TL0UOrg5IR3LN+VB4CtLeRCruHDDKK4kFXJewPIMvuBgOKYsXictZKj9GTIT+Sw9DiPvXoZKtwBD8XOYw2eI+tswJomPij1vdxIaYW93EjD1ge9KCyWs2ZgQp4MubgIyP74GcY1FSKWrh3z1d8L4fB4MaJAXPaib2dQXPfh+iYJvuRKHKZu5S+1HyF86Q1KyLX9CO18tW+vfcqbnRRg9yEm3VAnopyxEScEpvPp6tRgbxVc2vv7qKRSULMSUoXsjVWXtdlFeGVi1wYydvm12Ov+G/RV/xpwVmTH+5dytNhq7IK8MrNqK13ZKE1qgHaf3vwvbnKeRFeMWL9+YXFBXjtfFmEx5Il/3JEoW93Xz9MFuOt+K5KMKQwQ3FBxChe07WJE1ObYs7QkzsGbbTPxx9Svye3oN7ro9qDipBdYqbUvjjgqUHi4Fb5/nO+9p075QGxT7nvV/Xmcu2wpx48sks4N131rXwzoaP2L7zDniJrq8TBhMzFLdyPxbBfvzCNwQuY01VluYySCI+QMpLMf8AWvsCNxm1ONyMJsyfyGHmW0O5upKdpW5jm9jOQLfAJiXX84cQXnw+nTVOcnMHL6KqG5u3MEcZkNgnT0u5thpYgZxk2GBGUyVzOFqZracJMXGv/+Qz1U2SlbdoFjafBLoaXNVtc2FfZsWczlsfl4d9cwibi5tZKadxxV8fOk1tOm0vwP2+ainfh9eZn5eYn8S23wRszR+Hfi4x8WOl8v93mBiOx2ufm+Qywvov/y+PiO/D1z+4I2TA/ozGPg7VaV8ZwOrGu5Z/2VnjLVVM5PvXZbftx43HxbT9/QOhSv9QLAPp+9cZS5HZa/jXvhS+1P2m3+Y7P0b2fvGwv5vnttv2Vk47BnzuI6znSaj/J0DJuSUs6rG/m/F33/5/e3oP2pjjVXl8nfbwLH25+8/6rf84fSdmB13wus7flq+cSp6446OF6am9/GVpiFuqSWP4rUvUFP0KDK5e5Yv1uDxc1Es7ebK2ov2mg2YllkKmKpxOqKfkvHx51l8gM2ztbJXWWQtGTv9/r+f/MQ+sjYfqKe0zF/LsvP2I/kHqhf3PZ+bkX1sO374L0PoxkpKHQQYZ96DWItm6Hs3GswnfO4DIfLNhX2bHBufR75mNqAdTMZUFhEgAkSACBCB2CEQ04rdDddZSL9jwffH24ySOTEWxxA77Rhakvh0/HDjMgjuKhx28I2b+/J3Dec/tGOXOw2movmxH//Vl6pRWiJABIgAESACNyEBDbhib0LqVKWYJXAzmuVjFnaQYMQ+CMggn2qZv5Zl581M8g9yZ1cUdzOyj2mLnYI9HRIBIkAEiAARIAJEgAj0QoAUu14A0W0iQASIABEgAkSACGiFACl2WmkpkpMIEAEiQASIABEgAr0QIMWuF0B0mwgQASJABIgAESACWiFAip1WWorkJAJEgAgQASJABIhALwRIsesFEN0mAkSACBABIkAEiIBWCKhud8KX/9IfESACRIAIEAEiQASIQGwTCP6VsGFq4vJEWt/bRa1edI0I9EZA6/1ey/JrWXber0j+3t6u6N0n9tFjG07OWuavZdl523D5g//IFRtMhM6JABEgAkSACBABIqBRAqTYabThSGwiQASIABEgAkSACAQTIMUumAidEwEiQASIABEgAkRAowRIsdNow5HYRIAIEAEiQASIABEIJkCKXTAROicCRIAIEAEiQASIgEYJkGKn0YYjsYkAESACRIAIEAEiEEyAFLtgInROBIgAESACRIAIEAGNEiDFTqMNR2ITASJABIgAESACRCCYACl2wUTonAgQASJABIgAESACGiVAip1GG47EJgJEgAgQASJABIhAMIGIFLsbzjIk63TiT1nwn7NQ+5dc5sSN4NKG7Pwz2HOTodMlI9f+WZSkaEdTzR6UrdwOZ1fFB6PcKFUnZrK9DGfZ49DpFsPa9E3YUnmbrMjSJWJWWR06w35q4BN6z9uRnxgke3sNihLV3ptEZFlPwzvwYkSUo9ftxHv7y5DLZU1cj5p2hWSdTaix70ZZbhaKar6IKP/oPnQNbucfsL8sF4k6HRKLatDeVaAXnU21sPO6JQfVqyvN0B9osu9069tBfT8A6zWct69GYpYVTYquFZBkKE68bjjf4307FTpdemD/7mzCEblP8e+9xNytONLk71lDIW73MkNw7dY2vjEoRsadbvJpsO8AUH1v8QVqitJVdSVdFPp/RIpd945EV244f4XHMp9G4YdfE4wBJOBtsmN94SEIppV4csrwsHPWT5mPIlMiagvLsLcPCmHYBYST0HsOB176KaxuZWIv2h0fYlfANd/9GXhqxiQM/Ut5De667Vietgz2ljuRW9sG5irB7ARZMu9pWJ/egApbKQor/8snfOx8et2o2/oc0ubtQcuk5ajt8MC1eTYSZAm9TTvx9MvvwLamEJVXYkfsAEk02Xeu4fyH9sC+bXwUM5LV31vv+ffx0urtUH0VAmAM3onXfQxblxsxz+7CpFwbOpgDm2ffLgngPQf72mzk1s9GTYcHjF2FM7cdJYbXAyc9gyeuaknqXGN93NF+3xEbQ/W9BdD+Vxze5VRpLwHGpx5E8gAP+sNUSgr/UpIZjtPrkNa/XMIvL+KUd2JhRTNYRcQZRPjgUJUbobgx99gXqLX8ElVIgynr3q4v5vDEHIP0LCOELaXYYFmJJxVf7OE9399Ul+EsN+PY7fdCwHVFZpfgODEWv3FdxWzhFv91Pltd0hLyS9CfMNpHXnQ6t2PJgpOYf6AKazOE7oqmfhry3t+LZU1WXNj9y2gL1Mf8OffnsKB+Dg44n0OGkrGck35KHt5/dwmarF9j94Y+Zj8oyTXadzpP4rdvjcFv2jz+SUAoXp11KF//CW5/JAW4ECrRIF/nMi1Zi/r5O+Bc+xCEoC9bb3M13rLeiqXVczEtnt+8BYLhKSxNzcdhxyXM9imAgyx2QHEhucb4uKP1viM2Qqj3livVDbj1N63wzB6vGE+5FW8DWqIwmQ/qugFdpP8nnXUom5Uomh/9rhCfa00H3aytcHbKNvggE7dOl4rcMjuc7muSHDecKEvmpuNZKKtxKszhWSiyn0Yn2tF0ZKvkNuIuuKJd/meh4hJ125ErupFXYr/zP2DvMq+nInfrMbgDXAPKvCXzdWJuGexON7y4Abd9Jb6VXogzXNIzhUj/lg6SK1qlXLE2sttWNPXz/Li8VtQEmPQVz+7/DzjtsktMNP9vR52Pi2or8fytKJLZi67yWUWw1jQFuSW5u8ouuxx89VJxLXC3m88lJzLLQpG1Bk2+tuMy+Hgmvwz74ZcxS0znM6Vz11cNrEVZsilarb4qFema5aTjgbtHqyTo6ZIeCXen4xEu2q4P4VC6EXt6bEDuceWoEm/iWRRkTQzM0evFhO/nByp1+AZN+y04uXDgZ26BhYdx1unAjnXvYvK2V9SVujCyGLoknPs7WFc+CdtK1JW6oZMt3JK12ne8aK87gPKqX+PV1yywdxtrlPW/DOeO3cCa55E17lbljSE85jK9gvLJ61GiotRxwfTjJuE+wYW6E2f942inC41nZiIrfcwQyu4rugeuMT3uaL3vcP49vLe4ga8mPAFTgFIHeJt+j80nM6IzmWch/gCEuMPYdYeZJQEMSWbmuB4yGWPMwzoc5czA02IRszR+zTyNFmYUz+cys+NL6WFPC7PlpTBeZvA/Ic/GWj2MF8rMSd3vS+mNrMC0hAlBzwumatYmlvAPZstJYkASy7H9QyrTZWM5Qen9ZQvMaDnFeLGMXWWttlXd8hbTCquYrfUr5rKt6CZ3ktnBrjOVclkbO2XJU88PCiZdz4aos9HCGiUBpfp0/a9kHvysMv8e0on1uirl2FHPLDnqbQNDOXN0yEKo8RSKWXWbh3labSxPCJYFDEIes5ySWqhL/K4DD2urLpY4qda1jTVW25jFtIjl2VrEtpLKEZjBfJx18Hw8p5jFKDAgjZmqL3bl3NMBb9d+/3UcZ+acN5ij47pcB6nvh8yXyzl3LbO1ysxDJuz9Rv/k/5o1WhYxGEzMss/McsQ2S2E55g9Yo6+dFSJI73L4bBWPqh72T3Zfeycxg+lXbJ85R+o7Qg4zVzVK/SGgVLmuch8NuBXhSb/l5+Vqte90vWu+91xgBpNNpd/wcecNliO+oxdZtSmNQfX97lsj9Je91JeNzGSpZGZ5vBNyyllVo3J8+pI5zHMZkMJyLPWsw9PKqjcWs/LjLvm7om8yK1P3V37pu7aPXGNl3NF43xHbsa/vLePjT17Xd5eyL/T1WK3v9M9iJ1unui+eWAm7m68g0CM+bTnKzHMB7MOGtyywbN6KKqQgx/I6VqZJVhjJxN0AGMrhkGMXWm2rIHBry8dncSHAegYIOTtxiqfrOA6zgaeqQvmu4dh0qg2MfQmHWB7gtp3A37sWMvhmNcGfAgwmGxp5fp4W2PJSeKmo+vhv+FxUxM/i8Ft2uDEXZseX/FsfnlYb8kTh/i/OXvBCWLgD1x1mJPH03D19naF5XRrUPNTepv1Ym2+FW2RQjw7GwDytqC42AjiEwnXv+K2YPlENxbA18rpdhY8LqurQ8Lla5a6g8aPfoxaAYKpGG8+/i8khFK63S4HK3ibsXW9GLQQYiqvg8ijkcG/H6jePop1bkva+gvzKBkDIg0Xky+BxVaGYc681Y90Oh3/2KsorwGA+LtbL07Qe3024hNo3S2B18zaX68vacMqSB8FtxYZ3HIqgdl+F+ec1XGhpFuNvhPsmYVxAT+VWUhOmZmYjf8s+WN9zSm2lH4k7pgK1Rxrg4n1Gfzsm3ZcIwIWTLV8M0qIE36w5B2miu0ZZJ/Vjb/OfYP/2fDw8XuGaVU8a3aveFhzdcwKGjBRMf2gNKlwedJxaB5Qvx4pu7RxdUSLJnXPcU5WEjHum46GCCrh4P9s0DOXGAuxwXo4ky0F+RsN9h7vnD7vAPC44DvwKJgNQu2V1937DLcJvAmtWpiN+kOmGLu4bNB/9AFWG+3DP9IdRUFEP1lGPTbDCuMKiGI9HI63gbRwvvx9H8lMxMu5FtDz7El5UC1cIXVh07kTANWbGHU33Hd6cfX9vwcda+3j84OE7Fa7ZgesaAV+XA5etMqfRSFv5kqiAuctX44fWBgh5L6NkWUrXi81jXg5zhWn399BadQB260Y8my0H1V65hLYrSs0uDUtz5RiH+Hswa+5UsTBh6Q/w5DQeHj0a02cZJCVLKUbI4xlYmv8YpvAvYf14/NvchwJTdnW6tzGrtQZ2+9sofna1HBDfgYtt4a/UBOQBhJdgfBE/8THQj8fsHxfBxJXF2t/jo0ZlRLcA49IcLJjC63YLxv/bbNG9GCik8uwWjJv8bUkp3pKJabll2G+vwbm7XpaUt8N5mMJb/fO/4eMqHrY8Hy+8MEuKJ+FylBwWlVcx2Fz8oj/KVUQYNxVimcgX0AuZ+PHGZRDgRu2OT9AYoF/OwNL594ptq4+Px4gb53DCxoNGG1DJB0PRRTsKd4vKbU9u0hvouHRRrNiIsaMwQllFDIOw8Jdoqy4W64kLl9Hh5XI9glfKCrGgKxh1OEaNHSkq6mcufTUIih03x/8OtskvokCetASIrXrC+0QdvlSLqcsAAAu5SURBVN3nGELVzPp3kbuV6kcjI2sO0sTYND3ipz2Fn2yaMbSLUMKqlRedrc2oF9KQ9f10OT4qAdOWFWKT8YR/QhNWXkORSON9x4dMLyDtieewufo/UV2citryA6jrCoO4DOfbNZhcsjLsSY8v2+h+dqK18SyEjCx8P02OKY1PwbKfvAhjrRnr9zb5xw79bRg9MQ0F5gIYsA/5KzajpsewmOhKLuUeCdcYGnd8iDTZdyJ5bwFJqTYg3bcgzcdggD77p9jJ1iluxQr8twMLBYW9Kv5ezF86QxY5BXPmpgUGpnY2wJqbirjEdCzIzkZ2/hbR4iQ+MGIMRo1QijkSY0d1X2XV/cs/XEJjMHqkT9ZhGDsxOUgpbMdpaz4S4xKRviAb2dk/xJZa3zoudVlCl+xXVpIemY7JymqNGIWxovbyGerPfanIYgTGjb7Nr9WPnYhU0TSoSBJweAvGL/gJDu40wcBVmspCLOJMF6QjMc4XjwjccJ3FsYDnVE68X+HSGV7XqXhk+gS/DNBjxKgxkrJ1phnnLio0OyEZk8YpLE8Xz6FeDD5UyZ9fcl/C5a+Uirsv3Zc4V9/T1jT+GDqcuSQqdnzm9Omnd2DD4ikKWX35DcJnpwNv2wSsWjAx/PLFmdu/xkSMjvdCC076unYXruFInvEojDiLxtah3DimS6AQB34Lb0AC/STMeGoGUN+MVmVMaECiGDjReN/pRtA3WUWVuLBAikH6HWwTn8GCobZMBwvr/QItJ13BV6FPfhBPGYH6RpfsleDfBS+hHE+gYN3PUc09F3gLmUu2K6x63bKJ8gVZsegr1xgad7oB0lLfieS9FQ080Z3MK1WLbnwH6oL3/B+wecM+ObsGWFebceC8vChC6e4zmGCxHYLDddXv2hwoISLMx+86NcJk2YcDDhc81x0w96hchSpsGEaOGSvePHPkU5xV6jNX2nBRNNTdidSJ/xwqg/Cu85lP7mZ8xDzoaPwINpsN+8w5EFCFLdkvidt/DEucDMk2eQmXOxSKmbIE/W0Yk8TNiI048mmrf9YKL660XYIoblIyJo71KcYAghXx20ZjHM8CBpgdHUETAD4hCJoEdJX/z5iYemfXWY8HolX3Bjqdf8Cn0x8bImuAFABsLl2ACXHSQhSdLg6jMkvh5jP7qf8Etf2Koj1z65Fb0E1fcLi623oypk6IHedZkOiiNXvcpGQI7ma0XPCNLYpUqcmYEKZrXPHUIB1qv++ogopPxNTUqXK/uYS6vb9GafYkxIlWe/6OjEXmFidQlY+pcUO4l5ocsuE+2dIt7AcYgdSpiaIHQvoucCEj5Q5x4sY9BCUHD8CM7YFWPVUY0boYGddYGndUyWii70T23kpu2OhO5qOv2HU2YOd6aS8vIednKM1JAXgM10vv47yo2EhmcN64wuQHkLXgMaTdcRGf2I5Iq0xVW32wLsruHVG4u/BA1nw8kfYv+PyT93GoJytUSPF81g8eFrgVr+1skGaC3vOoeX0ztnBriWE+Zk0NdDyGzE7tBt9rKZ9vrJmIWeur0ZFswMKFC7HwmScwR1Sw5IfuuAczjfzCUeza+X/kVcCydZIPvHzTRMjWDh5zuMGMnaeljTi97mq8/upOuHl83srvYapCr+smUsK9yFqaxn3MKH/ThtPcasLru15aIetfLR38pF8JvnKxTVIig5P4rJfc6nfBgb2fTsXiABfoN2i72CG6kpPGKKyewfkMyLkeCbNL4AqwXntkd/EiWBq/BvO5wbvKizF3iNhWiag/9jfFqnD5HehhP7Ku6gzpgR4J6Q9jqXAKxxo+V0xC+PhyPip7RQ1cdW+CvqMGo9OF5rR8ef/J2zF7syNoYncR1aY0wGhBo8eFw3nTwrd0q5UX8TV5a6T6E2hQulXF0IT75b0lFd8FynLiJ+P+jDuUVwb5OBKuMTbuqBHTRN+J5L2NvhuW4+yfYhdy8YQOuly+4IAHFf5YCr43lOPg9o0wlbwsLjxwW1fj2XL+qwAJmPrAd6WYMGu2ZO2Im4DMj69BXBfRLcZOrRdE65oe8VPTJYXIvR3ZE26FTncrEjMPAgZusvPH2OlHjpFcuAHbnXSXSz9lIUrExR2KmDNe39IqgC/QKFveP4uT/k4Yn8+Dgce/lRqRKFuP4iZki3GBQt7TyOIbhuqnYHFJYVA6X+ybEcVFWUjWD8eUxeukBSpuK/LvHiVuVxKXaEQpd0cbClHWaxD0GGQsfwE5AncLL8PdI+Og89VXyMOm5ekh9qe7BaIFhntrVWfSSraNeM/SiOmLv9MVtyne7XKxJOK+Sbf3s7Mryxug45hzh9wOw5r1mPPHn2K9POnwuv8MS8U5FJQslGIzB6jqUckmYQbWbJuJP65+RZ6E8I2W96Di5JMoGSr3fFQqyndX4MHX0Z3190V08VdK3nN2TQjEjX5fO4GHX5gR4v3uS+7RTqtHgmEFts35GKvX/1aefLpRZ3kXJwvWYbG4MboeCRkLUGA4ig2v7ZHS8C0uTh9Che07WJE1OfbGl1DYqO+EIjMI1wdHqe6fYtcjBg86+J5ShYcCFBb9+Mfxyja+4tWN2sJXsMN5JSAmjAfqG0yVcOz/NV54JAlw+2I0eiwsaje5vJsOVsIkapncombCTsf/xm9eeBiAE7sO/1Vc1alPnoNXy7m7k/8JuBMeqC+rGI20dbvRWP07mLn1Uk5vMFlQ3bgb6wIsTvLtPn3wlchrcbCxGhYTX2nr++Ou5GrUvrEA48VW5+lWYbfDppCDrzg2w+bYiU2+PXfiM7DuYC2q95lF5UzKTcqr8eDaMJRQHoC/FNtrA+URcspRVbsVefKCDJ+U/k+fBQZhxEfdhtTFT3SXRZxxuwHBGBMxbP66SUfe5uM4ZngcGVEKoA0uL5xz/fgFeKO2DKkfPyMudIlb8nuMWVMWtBhE+nmcuKn5qIITWzLHqrqZwylvYNPcgvELS1BbkYKPZ/NJyCQssSVgzc5VgX1D/Omif8LU/H2AuxSZoybE1E+5hcMk9vrOJRz/93nSRDIxF+XHrmPuxoKg/RrDqdkQpdFPxMI3bKhIrcFscfK5DLYxK7CzIMM/WYzPQMHuAygdt1uaoOriMKX0Ep79QwkWxlrcYA8Yqe/0ACfat7hSfeweLM6I7r6HOr5nilpd+BYmIW6pJadrRCAKBLgC8SgytwCm6g/8P+3jK4lvWj1tHg6tPICD6xQDsHjfi/aaDZiWWcofxukwf3lC6/1ey/JrWXbe5Uh+34s5+J/EfvCZK0vUMn8ty87bQE3+KFrslM1Ox0QgEgJjkLH4BzB0WUb5CrCtmCX/Yon37KeonbkNv1HOqruKuQTH4Sq4sQib8h/UgDuoS3A6IAJEgAgQASIQMQFS7CJGRw9GnwB3Fy/FRlOa/LNgndLmy7XvYm9dM/5ydDhe7nItB0rjPf8J3t3lhGBaKQdvB96nMyJABIgAESACNyMBcsXejK1609aJW+zewLx0M2Dahrc2LpA2lh7A+qqZtQcw+6hnpWX5tSw7b1iSP+rdO2QBxD4kmkG5oWX+WpadN66a/KTYDUq3p0K0QkDtJdGK7FxOLcuvZdm1zl7r8lPfGdpRSsv8tSx7qPeWXLFD+z5Q6USACBABIkAEiAARGDACpNgNGErKiAgQASJABIgAESACQ0uAFLuh5U+lEwEiQASIABEgAkRgwAiQYjdgKCkjIkAEiAARIAJEgAgMLQFS7IaWP5VOBIgAESACRIAIEIEBI0CK3YChpIyIABEgAkSACBABIjC0BFS3O+HLf+mPCBABIkAEiAARIAJEILYJBP/86zA1cYMTqaWha0SACBABIkAEiAARIAKxRYBcsbHVHiQNESACRIAIEAEiQAQiJkCKXcTo6EEiQASIABEgAkSACMQWAVLsYqs9SBoiQASIABEgAkSACERMgBS7iNHRg0SACBABIkAEiAARiC0CpNjFVnuQNESACBABIkAEiAARiJgAKXYRo6MHiQARIAJEgAgQASIQWwT+P0Y3om7XIQE2AAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>The equation of the regression line <em>y</em> on <em>x</em> is <em>y</em> = <em>mx</em> + <em>c</em>.</p>
</div>
<div class="specification">
<p>A tenth student, Jerome, obtained a project mark of 17.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
<mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean examination score.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <em>r </em>, Pearson’s product–moment correlation coefficient.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the exact value of <em>m</em> and of <em>c</em> for these data.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression line <em>y</em> on <em>x</em> to estimate Jerome’s examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Justify whether it is valid to use the regression line y on x to estimate Jerome’s examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1280</mn></math> students were asked which electronic device they preferred. The results per age group are given in the following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A student from the group is chosen at random. Calculate the probability that the student</p>
</div>
<div class="specification">
<p>A <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> test for independence was performed on the collected data at the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>%</mo></math> significance level. The critical value for the test is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>277</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>prefers a tablet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mtext>–</mtext><mn>13</mn></math> years old and prefers a mobile phone.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>prefers a laptop <strong>given that</strong> they are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mtext>–</mtext><mn>18</mn></math> years old.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>prefers a tablet or is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mtext>–</mtext><mn>16</mn></math> years old.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the null and alternative hypotheses.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> test statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>-value.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion for the test in context. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>160 students attend a dual language school in which the students are taught only in Spanish or taught only in English.</p>
<p>A survey was conducted in order to analyse the number of students studying Biology or Mathematics. The results are shown in the Venn diagram.</p>
<p> </p>
<p style="padding-left: 240px;">Set <em>S</em> represents those students who are <strong>taught</strong> in Spanish.</p>
<p style="padding-left: 240px;">Set <em>B</em> represents those students who <strong>study</strong> Biology.</p>
<p style="padding-left: 240px;">Set <em>M</em> represents those students who <strong>study</strong> Mathematics.</p>
<p style="padding-left: 210px;"> </p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A student from the school is chosen at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that are taught in Spanish.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that study Mathematics in English.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that study both Biology and Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {S \cap \left( {M \cup B} \right)} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mi>S</mi> <mo>∩</mo> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>∪</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {B \cap M \cap S'} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mi>B</mi> <mo>∩</mo> <mi>M</mi> <mo>∩</mo> <msup> <mi>S</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student studies Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student studies neither Biology nor Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student is taught in Spanish, given that the student studies Biology.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>On a school excursion, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> students visited an amusement park. The amusement park’s main attractions are rollercoasters (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">R</mtext></math>), water slides (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">W</mtext></math>), and virtual reality rides (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">V</mtext></math>).</p>
<p>The students were asked which main attractions they visited. The results are shown in the Venn diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A total of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> students visited the rollercoasters or the water slides.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students who visited at least two types of main attraction.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo> </mo><mi>R</mi><mo>∩</mo><mi>W</mi><mo>)</mo><mo> </mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly selected student visited the rollercoasters.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly selected student visited the virtual reality rides.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence determine whether the events in <strong>parts (d)(i)</strong> and <strong>(d)(ii)</strong> are independent. Justify your reasoning. </p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the hand lengths and the heights of five athletes on a sports team.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The relationship between <em>x</em> and <em>y</em> can be modelled by the regression line with equation <em>y</em> = <em>ax</em> + <em>b</em>.</p>
</div>
<div class="question">
<p>Another athlete on this sports team has a hand length of 21.5 cm. Use the regression equation to estimate the height of this athlete.</p>
</div>
<br><hr><br><div class="specification">
<p>The table below shows the distribution of test grades for 50 IB students at Greendale School.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.25.22.png" alt="M17/5/MATSD/SP2/ENG/TZ1/05"></p>
</div>
<div class="specification">
<p>A student is chosen at random from these 50 students.</p>
</div>
<div class="specification">
<p>A second student is chosen at random from these 50 students.</p>
</div>
<div class="specification">
<p>The number of minutes that the 50 students spent preparing for the test was normally distributed with a mean of 105 minutes and a standard deviation of 20 minutes.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the mean test grade of the students;</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the standard deviation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the median test grade of the students.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the interquartile range.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student scored a grade 5 or higher.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the first student chosen at random scored a grade 5 or higher, find the probability that both students scored a grade 6.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability that a student chosen at random spent at least 90 minutes preparing for the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected number of students that spent at least 90 minutes preparing for the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A dice manufacturer claims that for a novelty die he produces the probability of scoring the numbers <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> are all equal, and the probability of a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> is two times the probability of scoring any of the other numbers.</p>
</div>
<div class="specification">
<p>To test the manufacture’s claim one of the novelty dice is rolled <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>350</mn></math> times and the numbers scored on the die are shown in the table below.</p>
<p style="padding-left: 30px;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> goodness of fit test is to be used with a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> significance level.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of scoring a six when rolling the novelty die.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of scoring more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> sixes when this die is rolled <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> times.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected frequency for each of the numbers if the manufacturer’s claim is true.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null and alternative hypotheses.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the degrees of freedom for the test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the conclusion of the test, clearly justifying your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.iv.</div>
</div>
<br><hr><br><div class="specification">
<p>The stopping distances for bicycles travelling at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> are assumed to follow a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>76</mn><mo> </mo><mtext>m</mtext></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>12</mn><mo> </mo><mtext>m</mtext></math>.</p>
</div>
<div class="specification">
<p>Under this assumption, find, correct to four decimal places, the probability that a bicycle chosen at random travelling at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> manages to stop</p>
</div>
<div class="specification">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math> randomly selected bicycles are tested and their stopping distances when travelling at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> are measured.</p>
</div>
<div class="specification">
<p>Find, correct to four significant figures, the expected number of bicycles tested that stop between</p>
</div>
<div class="specification">
<p>The measured stopping distances of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math> bicycles are given in the table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>It is decided to perform a <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> goodness of fit test at the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> level of significance to decide whether the stopping distances of bicycles travelling at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> can be modelled by a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>76</mn><mo> </mo><mtext>m</mtext></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>12</mn><mo> </mo><mtext>m</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>in less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>in more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo> </mo><mtext>m</mtext></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>75</mn><mo> </mo><mtext>m</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>75</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo> </mo><mtext>m</mtext></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the null and alternative hypotheses.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>-value for the test.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion of the test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The maximum temperature <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
<mi>T</mi>
</math></span>, in degrees Celsius, in a park on six randomly selected days is shown in the following table. The table also shows the number of visitors, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, to the park on each of those six days.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_17.34.22.png" alt="M17/5/MATME/SP2/ENG/TZ2/02"></p>
<p>The relationship between the variables can be modelled by the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = aT + b">
<mi>N</mi>
<mo>=</mo>
<mi>a</mi>
<mi>T</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation to estimate the number of visitors on a day when the maximum temperature is 15 °C.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A water container is made in the shape of a cylinder with internal height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> cm and internal base radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p>The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>
<div class="specification">
<p>The volume of the water container is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5{\text{ }}{{\text{m}}^3}">
<mn>0.5</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The water container is designed so that the area to be coated is minimized.</p>
</div>
<div class="specification">
<p>One can of water-resistant material coats a surface area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2000{\text{ c}}{{\text{m}}^2}">
<mn>2000</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>, the surface area to be coated.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express this volume in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{c}}{{\text{m}}^3}"> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>, an equation for the volume of this water container.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}r}}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>A</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>r</mi> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (e), find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> which minimizes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of cans of water-resistant material that will coat the area in part (g).</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 66 people went on holiday to Hawaii. During their stay, three trips were arranged: a boat trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
<mi>B</mi>
</math></span>), a coach trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>) and a helicopter trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span>).</p>
<p>From this group of people:</p>
<table style="width: 691.333px;">
<tbody>
<tr>
<td style="width: 182px; text-align: right;">3 </td>
<td style="width: 526.333px;">went on all three trips;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">16 </td>
<td style="width: 526.333px;">went on the coach trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">13 </td>
<td style="width: 526.333px;">went on the boat trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">5 </td>
<td style="width: 526.333px;">went on the helicopter trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;"><em>x </em></td>
<td style="width: 526.333px;">went on the coach trip and the helicopter trip <strong>but not</strong> the boat trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">2<em>x </em>
</td>
<td style="width: 526.333px;">went on the boat trip and the helicopter trip <strong>but not</strong> the coach trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">4<em>x </em>
</td>
<td style="width: 526.333px;">went on the boat trip and the coach trip <strong>but not</strong> the helicopter trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">8 </td>
<td style="width: 526.333px;">did not go on any of the trips.</td>
</tr>
</tbody>
</table>
</div>
<div class="specification">
<p>One person in the group is selected at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a Venn diagram to represent the given information, using sets labelled <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B"> <mi>B</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C"> <mi>C</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H"> <mi>H</mi> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3"> <mi>x</mi> <mo>=</mo> <mn>3</mn> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n(B \cap C)"> <mi>n</mi> <mo stretchy="false">(</mo> <mi>B</mi> <mo>∩</mo> <mi>C</mi> <mo stretchy="false">)</mo> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this person</p>
<p>(i) went on at most one trip;</p>
<p>(ii) went on the coach trip, given that this person also went on both the helicopter trip and the boat trip.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>As part of his mathematics exploration about classic books, Jason investigated the time taken by students in his school to read the book <em>The Old Man and the Sea</em>. He collected his data by stopping and asking students in the school corridor, until he reached his target of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> students from <strong>each</strong> of the literature classes in his school.</p>
</div>
<div class="specification">
<p>Jason constructed the following box and whisker diagram to show the number of hours students in the sample took to read this book.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" width="458" height="149"></p>
<p style="text-align: center;"> </p>
</div>
<div class="specification">
<p>Mackenzie, a member of the sample, took <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math> hours to read the novel. Jason believes Mackenzie’s time is not an outlier.</p>
</div>
<div class="specification">
<p>For each student interviewed, Jason recorded the time taken to read <em>The Old Man and the Sea</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>x</mi></mfenced></math>, measured in hours, and paired this with their percentage score on the final exam <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>y</mi></mfenced></math>. These data are represented on the scatter diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Jason correctly calculates the equation of the regression line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for these students to be</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>54</mn><mi>x</mi><mo>+</mo><mn>98</mn><mo>.</mo><mn>8</mn></math>.</p>
<p style="text-align: left;">He uses the equation to estimate the percentage score on the final exam for a student who read the book in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> hours.</p>
</div>
<div class="specification">
<p>Jason found a website that rated the ‘top <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math>’ classic books. He randomly chose eight of these classic books and recorded the number of pages. For example, Book <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>H</mtext></math> is rated <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>44</mn><mtext>th</mtext></math> and has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>281</mn></math> pages. These data are shown in the table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Jason intends to analyse the data using Spearman’s rank correlation coefficient, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State which of the two sampling methods, systematic or quota, Jason has used.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the median time to read the book.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the interquartile range.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether Jason is correct. Support your reasoning.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the correlation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage score calculated by Jason.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether it is valid to use the regression line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for Jason’s estimate. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Copy and complete the information in the following table.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">i.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret your result.</p>
<div class="marks">[1]</div>
<div class="question_part_label">i.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Emlyn plays many games of basketball for his school team. The number of minutes he plays in each game follows a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> minutes.</p>
<p>In any game there is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><mo>%</mo></math> chance he will play less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>6</mn><mo> </mo><mtext>minutes</mtext></math>.</p>
</div>
<div class="specification">
<p>In any game there is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo> </mo><mo>%</mo></math> chance he will play less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>.</mo><mn>8</mn><mo> </mo><mtext>minutes</mtext></math>.</p>
</div>
<div class="specification">
<p>The standard deviation of the number of minutes Emlyn plays in any game is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math>.</p>
</div>
<div class="specification">
<p>There is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mo>%</mo></math> chance Emlyn plays less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> minutes in a game.</p>
</div>
<div class="specification">
<p>Emlyn will play in two basketball games today.</p>
</div>
<div class="specification">
<p>Emlyn and his teammate Johan each practise shooting the basketball multiple times from a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>. A record of their performance over the weekend is shown in the table below.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>On Monday, Emlyn and Johan will practise and each will shoot <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math> times from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a diagram to represent this information.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>7</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Emlyn plays between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mtext>minutes</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mtext>minutes</mtext></math> in a game.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Emlyn plays more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>minutes</mtext></math> in a game.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability he plays between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mtext>minutes</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mtext>minutes</mtext></math> in one game and more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>minutes</mtext></math> in the other game.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected number of successful shots Emlyn will make on Monday, based on the results from Saturday and Sunday.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Emlyn claims the results from Saturday and Sunday show that his expected number of successful shots will be more than Johan’s.</p>
<p>Determine if Emlyn’s claim is correct. Justify your reasoning.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> is normally distributed with mean, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
<mi>μ<!-- μ --></mi>
</math></span>. In the following diagram, the shaded region between 9 and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
<mi>μ<!-- μ --></mi>
</math></span> represents 30% of the distribution.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.15.49.png" alt="M17/5/MATME/SP2/ENG/TZ1/09"></p>
</div>
<div class="specification">
<p>The standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> is 2.1.</p>
</div>
<div class="specification">
<p>The random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y">
<mi>Y</mi>
</math></span> is normally distributed with mean <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ<!-- λ --></mi>
</math></span> and standard deviation 3.5. The events <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X > 9">
<mi>X</mi>
<mo>></mo>
<mn>9</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y > 9">
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
</math></span> are independent, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( {(X > 9) \cap (Y > 9)} \right) = 0.4">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
<mo>∩<!-- ∩ --></mo>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.4</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < 9)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
<mi>μ</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y > 9">
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
</math></span>, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(Y < 13)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo><</mo>
<mn>13</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>The heights of adult males in a country are normally distributed with a mean of 180 cm and a standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma {\text{ cm}}">
<mi>σ</mi>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span>. 17% of these men are shorter than 168 cm. 80% of them have heights between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(192 - h){\text{ cm}}">
<mo stretchy="false">(</mo>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span> and 192 cm.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>Arianne plays a game of darts.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The distance that her darts land from the centre, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>, of the board can be modelled by a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mtext>cm</mtext></math>.</p>
</div>
<div class="specification">
<p>Find the probability that</p>
</div>
<div class="specification">
<p>Each of Arianne’s throws is independent of her previous throws.</p>
</div>
<div class="specification">
<p>In a competition a player has three darts to throw on each turn. A point is scored if a player throws <strong>all</strong> three darts to land within a central area around <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>. When Arianne throws a dart the probability that it lands within this area is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>8143</mn></math>.</p>
</div>
<div class="specification">
<p>In the competition Arianne has ten turns, each with three darts.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>a dart lands less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mtext>cm</mtext></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>a dart lands more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mtext>cm</mtext></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Arianne throws two consecutive darts that land more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mtext>cm</mtext></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Arianne does <strong>not</strong> score a point on a turn of three darts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Arianne scores at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> points in the competition.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Arianne scores at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> points and less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> points.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that Arianne scores at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> points, find the probability that Arianne scores less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> points.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 7 adult men wanted to see if there was a relationship between their Body Mass Index (BMI) and their waist size. Their waist sizes, in centimetres, were recorded and their BMI calculated. The following table shows the results.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The relationship between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> can be modelled by the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = ax + b">
<mi>y</mi>
<mo>=</mo>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation to estimate the BMI of an adult man whose waist size is 95 cm.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{16}}{x}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>16</mn>
</mrow>
<mi>x</mi>
</mfrac>
</math></span>. The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> is tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8">
<mi>x</mi>
<mo>=</mo>
<mn>8</mn>
</math></span>.</p>
</div>
<div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> can be expressed in the form <em><strong>r</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}} 8 \\ 2 \end{array}} \right) + t">
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>8</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
</math></span><em><strong>u</strong></em>.</p>
</div>
<div class="specification">
<p>The direction vector of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x">
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 1 \\ 1 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em><strong>u</strong></em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acute angle between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f \circ f} \right)\left( x \right)"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mo>∘</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right)"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find the obtuse angle formed by the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8"> <mi>x</mi> <mo>=</mo> <mn>8</mn> </math></span> and the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2"> <mi>x</mi> <mo>=</mo> <mn>2</mn> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights, in grams, of oranges grown in an orchard, are normally distributed with a mean of 297 g. It is known that 79 % of the oranges weigh more than 289 g and 9.5 % of the oranges weigh more than 310 g.</p>
</div>
<div class="specification">
<p>The weights of the oranges have a standard deviation of σ.</p>
</div>
<div class="specification">
<p>The grocer at a local grocery store will buy the oranges whose weights exceed the 35th percentile.</p>
</div>
<div class="specification">
<p>The orchard packs oranges in boxes of 36.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that an orange weighs between 289 g and 310 g.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the standardized value for 289 g.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the value of σ.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>To the nearest gram, find the minimum weight of an orange that the grocer will buy.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the grocer buys more than half the oranges in a box selected at random.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The grocer selects two boxes at random.</p>
<p>Find the probability that the grocer buys more than half the oranges in each box.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows a probability distribution for the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}(X) = 1.2">
<mrow>
<mtext>E</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1.2</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.18.09.png" alt="M17/5/MATME/SP2/ENG/TZ2/10"></p>
</div>
<div class="specification">
<p>A bag contains white and blue marbles, with at least three of each colour. Three marbles are drawn from the bag, without replacement. The number of blue marbles drawn is given by the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>A game is played in which three marbles are drawn from the bag of ten marbles, without replacement. A player wins a prize if three white marbles are drawn.</p>
</div>
<div class="question">
<p>Jill plays the game nine times. Find the probability that she wins exactly two prizes.</p>
</div>
<br><hr><br><div class="specification">
<p>Ten students were surveyed about the number of hours, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, they spent browsing the Internet during week 1 of the school year. The results of the survey are given below.</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\sum\limits_{i = 1}^{10} {{x_i} = 252,{\text{ }}\sigma = 5{\text{ and median}} = 27.} ">
<munderover>
<mo movablelimits="false">∑<!-- ∑ --></mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</munderover>
<mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>252</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>σ<!-- σ --></mi>
<mo>=</mo>
<mn>5</mn>
<mrow>
<mtext> and median</mtext>
</mrow>
<mo>=</mo>
<mn>27.</mn>
</mrow>
</math></span></p>
</div>
<div class="specification">
<p>During week 4, the survey was extended to all 200 students in the school. The results are shown in the cumulative frequency graph:</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.35.16.png" alt="N16/5/MATME/SP2/ENG/TZ0/08.d"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the mean number of hours spent browsing the Internet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During week 2, the students worked on a major project and they each spent an additional five hours browsing the Internet. For week 2, write down</p>
<p>(i) the mean;</p>
<p>(ii) the standard deviation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During week 3 each student spent 5% less time browsing the Internet than during week 1. For week 3, find</p>
<p>(i) the median;</p>
<p>(ii) the variance.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Find the number of students who spent between 25 and 30 hours browsing the Internet.</p>
<p>(ii) Given that 10% of the students spent more than <em>k </em>hours browsing the Internet, find the maximum value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the mean weight, <em>y</em> kg , of children who are <em>x</em> years old.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The relationship between the variables is modelled by the regression line with equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = ax + b">
<mi>y</mi>
<mo>=</mo>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of<em> a</em> and of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your equation to estimate the mean weight of a child that is 1.95 years old.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A healthy human body temperature is 37.0 °C. Eight people were medically examined and the difference in their body temperature (°C), from 37.0 °C, was recorded. Their heartbeat (beats per minute) was also recorded.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean temperature difference from 37 °C, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean number of heartbeats per minute, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar y">
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot and label the point M(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar y">
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>) on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the Pearson’s product–moment correlation coefficient, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence describe the correlation between temperature difference from 37 °C and heartbeat.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A teacher is concerned about the amount of lesson time lost by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> students through arriving late at school. Over a period of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> weeks he records the total number of minutes they are late. He also asks them how far they live from school. The results are shown in the table below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question">
<p>Which of the correlation coefficients would you recommend is used to assess whether or not there is an association between total number of minutes late and distance from school? Fully justify your answer.</p>
</div>
<br><hr><br><div class="specification">
<p>Adam is a beekeeper who collected data about monthly honey production in his bee hives. The data for six of his hives is shown in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.46.13.png" alt="N17/5/MATME/SP2/ENG/TZ0/08"></p>
<p>The relationship between the variables is modelled by the regression line with equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = aN + b">
<mi>P</mi>
<mo>=</mo>
<mi>a</mi>
<mi>N</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>Adam has 200 hives in total. He collects data on the monthly honey production of all the hives. This data is shown in the following cumulative frequency graph.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.49.33.png" alt="N17/5/MATME/SP2/ENG/TZ0/08.c.d.e"></p>
<p>Adam’s hives are labelled as low, regular or high production, as defined in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.51.25.png" alt="N17/5/MATME/SP2/ENG/TZ0/08.c.d.e_02"></p>
</div>
<div class="specification">
<p>Adam knows that 128 of his hives have a regular production.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this regression line to estimate the monthly honey production from a hive that has 270 bees.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of low production hives.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>;</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of hives that have a high production.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Adam decides to increase the number of bees in each low production hive. Research suggests that there is a probability of 0.75 that a low production hive becomes a regular production hive. Calculate the probability that 30 low production hives become regular production hives.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The manager of a folder factory recorded the number of folders produced by the factory (in thousands) and the production costs (in thousand Euros), for six consecutive months.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.30.09.png" alt="M17/5/MATSD/SP2/ENG/TZ2/03"></p>
</div>
<div class="specification">
<p>Every month the factory sells all the folders produced. Each folder is sold for 2.99 Euros.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a scatter diagram for this data. Use a scale of 2 cm for 5000 folders on the horizontal axis and 2 cm for 10 000 Euros on the vertical axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean number of folders produced, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>;</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean production cost, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar C">
<mrow>
<mover>
<mi>C</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Label the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{M}}(\bar x,{\text{ }}\bar C)">
<mrow>
<mtext>M</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mover>
<mi>C</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo stretchy="false">)</mo>
</math></span> on the scatter diagram.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a reason why the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> is appropriate to model the relationship between these variables.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the equation of the regression line to estimate the least number of folders that the factory needs to sell in a month to exceed its production cost for that month.</p>
<div class="marks">[4]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>In a large university the probability that a student is left handed is 0.08. A sample of 150 students is randomly selected from the university. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> be the expected number of left-handed students in this sample.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the probability that exactly <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> students are left handed;</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the probability that fewer than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> students are left handed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Contestants in a TV gameshow try to get through three walls by passing through doors without falling into a trap. Contestants choose doors at random.<br>If they avoid a trap they progress to the next wall.<br>If a contestant falls into a trap they exit the game before the next contestant plays.<br>Contestants are not allowed to watch each other attempt the game.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The first wall has four doors with a trap behind one door.</p>
<p style="text-align: left;">Ayako is a contestant.</p>
</div>
<div class="specification">
<p>Natsuko is the second contestant.</p>
</div>
<div class="specification">
<p>The second wall has five doors with a trap behind two of the doors.</p>
<p>The third wall has six doors with a trap behind three of the doors.</p>
<p>The following diagram shows the branches of a probability tree diagram for a contestant in the game.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfwAAAFLCAYAAAAznT7eAAAgAElEQVR4Ae29D3CT15X//bW8Q5PUKHkJtEg4vzLUY5MMztLguv0VdjF2IuO3my1jCmyIHad2gewGQmFjCxzT5NcQNzYsDISQNMQuYJosEHugbBcsQDUtJMRr85Ka38bSeFh+bx3JXQgvKBpKmFp65zzSY8tCtmVbkvXn+8x4JD26z33u/Zxrneeec8+5SW632w0eJEACJEACJEACcU1AE9e9Y+dIgARIgARIgAQUAlT4HAgkQAIkQAIkkAAEqPATQMjsIgmQAAmQAAlQ4XMMkAAJkAAJkEACEKDCTwAhs4skQAIkQAIkQIXPMUACJEACJEACCUCACj8BhMwukgAJkAAJkAAVPscACZAACZAACSQAASr8BBAyu0gCJEACJEACVPgcAyRAAiRAAiSQAAQSQ+E7zDDqk5CUNNhfFozma4CrE/X5euiNZjjGJHwHrCd3onJfJ1wB67kGszELSfn1sPoX6GvrUtRbbw+8eoTtc1nrkZ+k1nMb1vqlge858C78FJCAC05rCz7YWgJ93zjSY4FxD5rMVjgDXhPNJ4cYg9JsZRzqkV/vP4ZdcJgrPQwCjF/PmPP+Pw3bfb8xqYzvtAD3HLaixC7Q95sx2O+b57zyuxbUb4hXLvpKmB3+P1DDoea4Go7QeH6fGArfS1hXcRo33W7I9gED/9pQkzsZ0MxEabMNtppcaMciFUcb6kpeR3vvYJVMQla+AbqOLnQ7B/5DuXqu4CK+h5zvfQZL90A14ur6EAdNehTnPzq29g3WLJ4flIDrsyNYm7MGx5JXor1XHT+d+MXjThwtWozn6y/FoNIftLuA9lHkF+vRYbH59esOeq50ATk5+N5d4/c2us6egElnQH7WpCEq51chJaDNRY1NHZNuuG+eRoUO8P+9C/537R6klx6C21aNXG2IVQTHVUhFP9LKQizNkd4+UctrkJKahky7Cc1t130geH4wO4qfw/PzvkRD8x98LA0uOLu70MEfUx9ekXp7DS07q1GfuQ4vrZ0LXd9/jRbpT/wjXtr8MPZXvYfWEc+GItX+0dwnBakZM2BvOIU23365ruDswc9Q/Hwp5sF//DrRbbkMXfHjyAq1ohhNF3hNFBLguBpPofT9dI1nI6Lm3gPMXarpMh/GPa+jRHEJeE2VTivM9UYs6DPt5sNYb4ZVZutiXpuZh1q7Haayh5E8iFlMk/Y9LDPcwMUr1/rN/uqPaX4+DPkGYMCP7XW0NZtgz0xDaoqI7Q7s7U3YWpLZ76pYYER9TJqXo2YEBG6I6xquXLQF/g6BZ0Mueyv2GfO9shHTfz3MVj9HkcuO9n3940hfsh0nB5RxwGquh3GB3luPzzhTWqOaT9+EubWhv5y+BFtPDnQzuOztaOpzR2SiZOuvcaHny0H6JKfvQdq8hTDYu3Cl505fOcXK1DEf+YZ85Bdj4EOp4w9obrAhM0OPFLlC+te01fu/I2blQTj01c43ESPQcwHH+8ZDEgaOPT+Tvte9s8C4s+/3RnV7clxFTGIhuREV/rAYTWg4q8NGay96bQexMluD9rfXo+jMI3jri17FNdBrexHJDSux5pAVLjGvdYpJTQdD3afoHcwsppmOecseg+ngh+jyWvU9JvtpyEjVQpv1OIrh82OrKJ0bMCz7HtI0Ljjb38TyJ48i+XkTehUXxZewbboPDXnr8Xb7jWF7xQIjIKCZgfxVhdCZypDzo634oKnF83A3SBWuz5qwYk4ZzFN/Cpti/u/EWxnnUJRTiabPvMrT9X/QtMKArL3JWGO5Cbf7JszzL6Gkr4wDnfXrkFN0BlNr2hUZ99p+iqln1iLjyR1o93UFmV7Dq41fRdmxbrjdX8J2YAZ+Y/AZB85WbFu+DG9c/QFalDF7Di/N6MJv9l8apAee056H0gs4ePaK96HUa7JXHjonK24pXLyCHnX8ijvKPg/L5k2HBjfQvm0Fnjx6L55v/9LjQuv9D2xKPoi8VXUD2z9kK/hlOAjY95/EhRkbYZXfjt5uHJh2AoYh5WJHS8MnmLTxHNy9f0LLyixoOa7CIZqw1plQCt9em4f7+2bl6gKX4RYYzUFxyfcxM0UDje6b+OZ9/41PTnYic/53kK7MtAGN7glU/7YLzaUzETzQCZg6Pc3Hj+812RsWYl7aPV4f6mf9P7ZOGywdj3l/TK+j9dCvYCkuQVm2znvPCdDlLEOxoRMnP+nptxqEdfgkSuUTMK2wGi2mbXjiZDmWLF6AjInJSEqSGXeT38w9kPlfi5mlNThQfB6rd55V3DSurtP4Rf1XULFpPQrTZcWIFjN/+DSK0YRfNF+Gy9GGX1a1omDXz7DWK2ONbi7WvbEDFZYtqJSHSxW/7llsemmRdzxOgC7rb5Ctu+AdBy44Wo9gm2WpTxkt0gvXY1PFHLWGwK+ayZg++wEfP76Y7D/zPnRqPA+lHSdwtksWl/qNX8cFHNrWg+KSZcjWTfDUr5mGnGeXwdDyET6x9VsNAt+cZ8NJQFdhxEuFMz2WmCDloit+Gj+cqQU0X0P6N1M4rsIpoDDVHbx+ClMDIlmt/yIWz8I974K9YBuimYq/fmImTFW/xJFW8xhWaHt/MPv8oGKyP4NMZQYvjRFf1zSvBcAFR9spNCAN06fKj+dk5Na0wVaThR7zUTQ1NaGpaQ+MebkoM90KticsNyIC4q9fh322L2Fr+w0aG3+FLc/YUFu2GHkZc1GiLtpTzNrt0M2ejqkD/rt8fZe3PIvbMAMZqYrx29MSZfGVDc2l6XCKvO0PY+6srw98iEzRIyMTPko4QCcGlPF3BanlPe1RPwV+9Swu7XMtKX2b5n3olCEqbVEtAJ77QO230pc21GRfh1kZn01oqjciL6MMpsA349lxJ3D5roXCgzeJ42pwNtH7zYCfpOhtZjS17AHMefE9WA58Bzcaa7A4LwMTR+ubVFasfsXjx/f/MVV9qMpK6NueldF9i6FccHbuQ4n+fmTk7cbHN2Su9zXkv9WEOsMwyiCaUMZkWyZAN+f/RmHhcry4rwPuLz5FY4Ue+8t+hkM+YZR3W5PuRUbZ4SB77FkJbx+itN3HlD5EMWDI9QdDXglAfSgV19Jtz0NnptcCJZd63VLKSn7lPl/xiSARl0QZ9BMzkPfGx1CcTA8U4K22d2DASBTLcG3k9+NCgONqXLCP9aZU+KMiqEV6biFKa5o9PtO2Xfh+z3bk5bw+wrjV/lm81XYFF31/TOX3VBb2ZZ5B88etnpXRajiey4pDazfiZEEjunubUVP6QxQW/gC5+luwdAylJkbV2YS/aMjY8pSZWFS2DAac7Xe/wLt+467wT3eQoU5ed88Q5O+2IAxSWDHL6wf5MojTfbN4C2xX/o+PBUqu9Szsy2w4hY/bfo+DspjPG47nsn6AtWWtKGi8gt7f1qC0sBCFhX8L/c3/QkcQt2WRKCfAcRXlAgrcPCr8wFxGcFZmfIuwsuRJ6PxWNA9fiXcldMcF/NuRY+hQzaHqhcoMajoutp/H/+6QxXxe86/izwcy5z7iEyIGuL64gWvqtXwNGQHP4jXbwBXpd9XuXaymxhmf+0/Y+5zsUvgG2rf+nTfxkVfu/jNdb5RIUv5e9HzrcRTrPsW5S3/q99VLNars1ZXwd7XD/8RgOR88IXT+pe/6rM7i/3czjhy8gtnTJw9wMXgeSrvQ/rtP0NEXQeL158PfJfEXfHHDL1LhrhvyRGwQ4LiKDTkNbCUV/kAew3/yZgNbYGzqX6nttOJUcztQ+g/IlwV3yqzoPk9dt5zwXVDtfwPPD2YTyjf+0cccqpaSmd430LFxI7b5zv69SsXUcBAtds/iJ5f9HHZUvox6TvBVeKF71aRj6Y6f44mGtViztQntXuae0MgGbFxVjTtbXsTS9HuU9RU5L1Si4PjLqNxxzqv0HbA21eLFcmBLdSHSNWK9yYdx44OoffVNmJX67sDechANpsc8Zf6vLPxoczaOr/4pdrTaPUrfeQn1a9aiNqMc1UvTByjewTurgTZnFXYVHEPRmgZ0KoNR2rMNr9a2D35Z3zfeWfy2jdjoM4Pv+1qZ6V3GxvImn9m/1xWgO4uGvb/3MrgDe+seVK5+ExyiffRi+A3HVSwKjwp/pFLTzMSzew9izZSjyFFWaichaeISHJ2yCsc2/x2mCVHNDBQYi3FH4vC/WopDyirmQW6kmsYCJtRRfzjhtwhsMnJ+sht7sz9Env4rSox26oaP8FDJbjQOt/J6kGbw9FAENEiZWYJftu9F4aSP8aKXeVLSVzBn55/w7U3/jmMvZntWPIv4py3CjpYdmN/zM+iTJRrkfuQcnYQ1bXuwfs4DnhtppiF38160PXsLryr1fQX6V2/h2b4ysrJ/O1oOzEePcQ6SJbpk4j/DMn8HLMfWYo43QmSoVvd9p/kGCnc0Yl+mGbnKmJ2JVR8/jDVbFvUVGeqNZup0zJbMbX1rSHxLe2d60A+c/Wvn4SfHapD9UYmXwRxs+N1klBw5rGSB862B72OUAMdVzAkuyS1L1XmQAAmQAAmQAAnENQHO8ONavOwcCZAACZAACXgIUOFzJJAACZAACZBAAhCgwk8AIbOLJEACJEACJECFzzFAAiRAAiRAAglAgAo/AYTMLpIACZAACZAAFT7HAAmQAAmQAAkkAAEq/AQQMrtIAiRAAiRAAlT4HAMkQAIkQAIkkAAEqPATQMjsIgmQAAmQAAlQ4XMMkAAJkAAJkEACEKDCTwAhs4skQAIkQAIkQIXPMUACJEACJEACCUCACj8BhMwukgAJkAAJkAAVPscACZAACZAACSQAASr8BBAyu0gCJEACJEACVPgcAyRAAiRAAiSQAASo8BNAyOwiCZAACZAACVDhcwyQAAmQAAmQQAIQoMJPACGziyRAAiRAAiRAhc8xQAIkQAIkQAIJQIAKPwGEzC6SAAmQAAmQABU+xwAJkAAJkAAJJAABKvwEEDK7SAIkQAIkQAJU+BwDJEACJEACJJAABKjwE0DI7CIJkAAJkAAJUOFzDJAACZAACZBAAhCgwk8AIbOLJEACJEACJECFzzFAAiRAAiRAAglAgAo/AYTMLpIACZAACZAAFT7HAAmQAAmQAAkkAAEq/AQQMrtIAiRAAiRAAlT4HAMkQAIkQAIkkAAEqPATQMjsIgmQAAmQAAlQ4XMMkAAJkAAJkEACEKDCTwAhs4skQAIkQAIkQIXPMUACJEACJEACCUCACj8BhMwukgAJkAAJkAAVPscACZAACZAACSQAASr8BBAyu0gCJEACJEACVPgcAyRAAiRAAiSQAASo8BNAyOwiCZAACZAACVDhcwyQAAmQAAmQQAIQoMKPWSG74DBXQp+UhKTB/vSVMDtcQfXQZa1HftJS1FtvK+X9PwdVyYBCt2GtX4qkEbRBudxpxcmtr2Gftx0DquQHEiABEiCBUROgwh81umi5cA4qTl+F2+2++89WjVzteIn4HqSXHoJ7RG1wwdG6FyXln6A3WvCyHSRAAiQQJwTGSxvECT52gwRIgARIgARigwAVfmzIaYytvAN7exO2lmT2m/8XGFFvtsIZbM1OK8z1Rizocx/kw1hvhtU5mMvAz6TvMMOo1yN/z0m07uuvR1+yHSetDgDioqjCzLyfw47DKMu4F3qjGfIN4IDVXA/jAr23/cPdO9hOsRwJkAAJJA4BKvy4l7ULzvY3sfzJo0h+3oRexfT/JWyb7kND3nq83X4jCAI30P72ehSdeQRvfdGruA56bS8iuWEl1hyyYjCVf3fFdphWbkXjxB/hmLSjtxsHpp2AYVUd2p2ANnczOk9vhA5LUGf5M2w1udDCgc76dcgpOoOpNe1K+3ttP8XUM2uR8eQOtA/6wHH33XmGBEiABBKZABV+zEu/HbV5U/pn7uoMvG+x3HW0HvoVLMUlKMvWwSPwCdDlLEOxoRMnP+kZXmG7evDJyU5kzv8O0lM8NWh0T6D6t11oLp3prTM4kLoKI14qnIkUKa7RIevxOdC1fIRPbHcCV+Bowy+rWlGw62dY622/RjcX697YgQrLFlSO6IEj8C14lgRIgAQSgcBfJUIn47uPsmjvBGpyJw/SzcnIrWmDTTGLH8WpG7Ic7nN8/MbLqG0BDMsGucz3tGYq/vqJmSir+iWOzMoHnKkw5KZ7lLZvuRG/1yAlNQ2ZMMHS7QTSJ/nV4IKj7RQa7A9j86yvD3ywSNEjIxNosNjgxExo/a7kRxIgARIggYEEOMMfyCMOP7ng7NyHEv39yMjbjY9viAH+a8h/qwl1BqBDUZjDdfsBzHnxPVgOfAc3GmuwOC8DE5P0WGCsh1nxvw93/Wi/v4OeK12wD3G5/eIV9ATvUxiiJn5FAiRAAvFNgAo/vuULuKw4tHYjThY0oru3GTWlP0Rh4Q+Qq78FS8dQqtQfjBbpuYUorWmG2/0lbG278P2e7cjLeT3oWH//Gof/PAFTp6dBN0RB3ezpmMpRPAQhfkUCJEACHgL8qYz3keC0wdIBZM59BDofabu+uIFro+77BOjmLMLKkiehs3fhSs8g/vdR169eqIE263EU6z7FuUt/GrjWQO1Xhj4ErgX1fnwlARIggfgl4KMC4reTCd0z7aPIL9bD1HAQLXaPYnbZz2FH5cuoD3aC7+pEfX4aFhib+sPwnFacam4HSv8B+Wn3hAix6tOX6ly45bwFlzYLP9qcjeOrf4odrXaP0ndeQv2atajNKEf10vSBvv0QtYTVkAAJkEC8EaDCj0KJ/vnPf0ZTUxNMJlMIWjcZOT/Zjb3ZHyJP/xVlNX/qho/wUMluNFbMCa5+zUw8u/cg1kw5ipyJyZ6IgIlLcHTKKhzb/HeYFsJRpEnLh3HjTZRlfBVfXfyv6HJpMbN0O1oOzEePcQ6SJQph4j/DMn8HLMfWYo43aiC4jrAUCZAACSQugSS35GTlETUEzp07h3Xr1iEnJwcbNmzApEn+K9ejpqlsCAmQAAmQQAwRYFhelAjLarViy5YtuHr1Kg4cOID09PQoaRmbQQIkQAIkEA8EqPDHWYrXr1/He++9h/379ysz+sLCwnFuEW9PAiRAAiQQjwRC6H2NRzzh7ZP46RcuXKjc5MyZM6CyDy9v1k4CJEACiUyAM/xxkP7FixfxyiuvKGZ7mu/HQQC8JQmQAAkkIAEq/AgKvbu7Gzt37oT468vLyzF37twI3p23IgESIAESSGQCUbNKPykpaVzlEM5gBQmzO3z4MEpKStDY2IiCggLce++949pf3pwESIAESCCxCESND18U7nj+hUvsEks/f/58yOz+888/V/z0VPbhos16SYAESIAEBiNAk/5gZMZ4PiJhdk4rTr59GLa//2eUpIcq290YO87LSYAESIAEopJA1Mzwo5LOKBolYXbV1dUoKirCkiVLcOTIkTDF1LvgaN2LkvJPIBve8iABEiABEiCBoQhQ4Q9FZwTfqelwJcwuNTUVEmZnMBhGUAOLkgAJkAAJkED4CFDhh4CtpMN96qmncP78eSUH/jPPPBPmRXkuOMxVmJn3c9hxGGUZ90JvNMPhMMOol33qd2JrSaaS8145jzuwtzf1nZMFkkkLjKg3W+FU+i/1VUKftBR7zCex3XttUlI+jPtaYed+8yEYJayCBEiABMaXABX+GPjLQryKigolJa7E1dfW1iqz+zFUGeSlGmhzN6Pz9EbosAR1lj/DVpMLrXK1HS0Nn2DSxnNw9/4JLSu/BU37m1j+5FEkP29Cr7I48kvYNt2Hhrz1eLv9hs89D2Nl0QFAKdeLLyyrgL3LsXxbq/fBwKco35IACZAACcQUASr8UYhLzPe7du1SVtx/97vfxfvvv4/Zs2ePoqbwXKIrfho/nKkFNF9D+jd70XroV7AUl6AsW+fdSnYCdDnLUGzoxMlPenz2mZ+F0l0/w1qlnAYp6Yvw0qalsGw7glYHp/nhkRZrJQESIIHIEKDCHyFnNcxOLjtx4kQMhNlNRm5NG2w1WegxH1VcDk1Ne2DMy0WZ6ZZf7x/G3Flf99lf3rs/vd2E5rbrfmX5kQRIgARIIJYIUOEHKS0Js1u0aJGSQEfS4a5evTpGtq51wdm5DyX6+5GRtxsf35CZ+teQ/1YT6gxAh8UWhLnehotXrvlYAoKExmIkQAIkQAJRQ4Bx+MOIQsLsXn/9dbS0tGD79u2xlw7XZcWhtRtxsqAR3XsKMU19xJMFfh12IChPhB6zp0/2mfkPA41fkwAJkAAJRB0B9ec/6ho23g1Sw+wefPBBzJo1Swmzi8nc904bLB1A5txHoPORtuuLG7h2F+TLsHR71u17vnLB2d2FDp0B+VmT7irNEyRAAiRAArFDwEcFxE6jw91SCbOTdLgSZifpcMMfZjeaHnn968qlLtxy3gpsctc+ivxiPUwNB9Fiv+MpbT+HHZUvo97uf9921L66DU1WBwBxBTRgTdExFOxahRwth4o/LX4mARIggVgiwF9xH2mJn14NsxM/vYTZTZoUvTNbTVo+jBtvoizjq/jq4n9FV8CUe5OR85Pd2Jv9IfL0X1Fi81M3fISHSnajsWKOT+/lrQEVxQ/j8mtzkZSUjIm5ZmTua8SOwm/QnO9Hih9JgARIINYIRM1ueeMJTvz07733Hvbv348NGzYoK+/Hsz2Rv7eayKcLmy37Ucq8/JEXAe9IAiRAAmEmkPAz/KamJkg6XDkkHW5hYWGYkbN6EiABEiABEog8gYRdpX/x4kVIdrz09HSI+V5eeZAACZAACZBAvBJIOJO+GmYn/vry8vLYC7OL15HIfpEACZAACYSVQMKY9CXMTnz0EmanpsONyTC7sA4HVk4CJEACJBCvBBJC4avpcGWzGwmzEz/9vffeG68yZb9IgARIgARI4C4Cce3DF7P9li1bcPXqVfrp7xI9T5AACZAACSQSgbhU+OKnf/vtt3HkyBFs3rwZBoMhkWTKvpIACZAACZDAXQTiyqSvpsOVMDutVquE2VHZ3yVzniABEiABEkhAAnEzw5d0uGK+l/A6ia1PTU1NQHGyyyRAAiRAAiQQmEDMK3xZiLdz506Iv17i6mfPDmr7t8A0eJYESIAESIAE4pRAzJr0xXy/a9cuZcW9GmZHZR+no5TdIgESIAESGDOBmFT4apidw+HAiRMnGGY35mHACkiABEiABOKdQEyZ9NXd7KZMmcIwu3gfmewfCZAACZBASAnEhMJX0+G2tLRg+/btTIcb0iHAykiABEiABBKBQFSb9NUwO0mHO2vWLCXMjulwE2FYso8kQAIkQAKhJhC1M3wJs1u3bh1ycnKUdLiTJk0Kdd9ZHwmQAAmQAAkkDIGoU/jip3/33XeVMLt33nmHYXYJMxTZURIgARIggXASiBqTvvjpJcyuqKhI2c1O0uIyzC6comfdJEACJEACiUQgKhS+ZMaTdLhynDlzRgmzSyQhsK8kQAIkQAIkEG4C42rSv3jxopIdT9LhHjhwQEmLG+4Os34SIAESIAESSEQC46LwGWaXiEONfSYBEiABEhhPAhE16UuY3f79+yFhdpIOV8z3DLMbT/Hz3iRAAiRAAolCIGIKX8Ls5s+fD9ns5vPPP2c63EQZYewnCZAACZBAVBAIu0lfwuxk29qrV6/STx8VImcjSIAESIAEEpFA2Gb44qevrq5WwuyWLFkCCbOTxXk8SIAEYpSAwwyjPglJSYP9ZcFovhZk527DWr8USfn1sLoAuDpRn5+G/PpOyMdRHUodeuiNZjiCrsAFp7UZWyvf87Qj6OtYkARij0DIFb6aDlfC7LRareKnNxgMsUeGLSYBEghIQFdxGjfdbrjv+mtDTe7kgNdE5KRmJkqbbbDV5EIb9A2vo7XuJZS33w76ChYkgVglEFKTvm+YncTWp6amxioXtpsESIAESIAE4opASGb4shCvoqJCial/5ZVXUFtbS2UfV8OEnSGBERJw2dHetBUlfS4APRYY62G2Bmtsd8Bqrodxgd7rQgji+gEmfRcc5krok5Zij7kF+4z53noyUbK1GVanOA6uwWxciLzadsBUhoxkH5eE0wpzvRELVPfFAiPqzVY4R4iBxUkgmgiMSeGL+V7S4RYWFiphdu+//z7T4UaTdNkWEhgXAjfQvm0Fnjx6L55v/9Jj+u/9D2xKPoi8VXVoV5TtUA1zwdleh1VF55DxVufA69d8MEJf+2GsfNWEiWWHlXp6bdsw7TfPY9XbbXBiMnJrTuB0xRzAUAdLr9cl4byE+ucXo+jM/0CNTdr/JWw1/wNninLw5NZWKv2hRMfvoprAqBW+LMqTMDuJqxfzvSj9e++9N6o7y8aRAAmMnYC9Ng/3qzPfvlef2bHjAg5t60FxyTJk6yZ4bqiZhpxnl8HQ8hE+sd0ZphF3YPvkI7RkzsW8dK83XjMNudXNcDeXIn1Ev1pzULFpPQq99Wh038Lj2Q+g5eQl2AKuDnTB0foeqk7Ox67qFd72T4Au+x/xxoFnYSnfikNW+vuHESC/jlICI/rX8e2DbFd74sQJZftaUfYSZ8+DBEgg/gkEXrTns2BPm4saWxtqsq/D3NSkTAia6o3IyyiDKSg8E6D/6/+JHNNu1B35PcxNLV4TfFAXD1MoBakZM4COLnQHtDRcR1uzCfbMxzBLfVhRatQgJTUNmbgMSzcN+8NA5tdRSmDUCl/6I0pf/PWyja3E2osfX+LueZAACSQyAQc668ugn5iBvDc+xg1B8UAB3mp7B4agFKYGKXPW4phlK75z49/w6uIFyJiYjKRI+NFd13Dlom0I4dlw8cq10YcODlEzvyKBcBMYk8JXGyfb2EqcvaTLle1txa8vJn8eJEACiUfAZf0Aa8taUdB4Bb2/rUFpYSEKC/8W+pv/hY6gcWiQkp6DwtIa/NbtRq+tDY3f70FV3nK8GnSsf9A36y+omYzps/X9n+96p8fs6ZMRkh/Ou+rmCRIIL4GQjlsx7Ut+fDkkDl98+7KwjwcJkECiEHDB2d2FDovblocAACAASURBVDyMubO+7qMY/4IvbgS7Qv9uVhrdHBSuLEGxLtwz7EnIyjdA13EBl+y+aw3Ufs1ARmrK3Q3kGRKIAQIhVfjSX1m4t3r1akXZnz9/Hk899RQkPp8HCZBAIhDQQJv1OIp1Z9Gw9/ewKwvj7sDeugeVq9+EPSgE3ix8CyrR1BfG54D11Cm0ohCr8mf4PEgEVeEQhbw+faXEbTidLmizl2PzE2ewunIPWhWl74KzswFrivYiY8uLWJp+zxD18SsSiF4CIVf4alcl6Y7498vLy5X4fPHvS7w+DxIggegjYDKZkJ2dHRqLnHYefnKsBtkflUCfLGl452DD7yaj5MhhVOiC6fs9SH92B9rWTMLRnPu98fP3I+foJKw59hIWTfOu/A+mqmHL3IO0ghXYeKcKGckzsPhQF1wps1D6ZiMOzP9/YdR/BUlJyZj4j/+J+QdacOzFbHB+PyxUFohSAkluyY8Z5kPM+sePH8frr7+OZ555BmVlZQzhCzNzVk8CwRCQRbbyMD5lyhTl4Zz7XQRDjWVIIDYJREThq2hkId97772nxO5v2LBBid1Xv+MrCZBA5AjI/6I8gLe0tGD79u2YO3du5G7OO5EACYwLgbCZ9AP1RsL4xL9/4MABZca/aNEihvEFAsVzJBAmAurmVg8++CBmzZqlLLKlsg8TbFZLAlFGIKIzfP++S7KedevWKcl7ZMYvDwQ8SIAEwkOA/2/h4cpaSSBWCIyrwhdIqn9/8eLF2LdvH5YsWUL/fqyMHrYzJgiIn/7dd99VrGmykJZ++pgQGxtJAiEnEFGTfqDWSxifxO9//vnnyip+yc8vK4Z5kEC4CST15YGXleSR/wt3/8RPL0mwJBmWJMWS5FhU9uGmzvpJIHoJjPsM3x+NzEYkTe/Vq1eVsD7+QPkT4mcSGJ6AJL1iVMzwnFiCBBKJQNQpfBW+zPKrqqogC/uee+45+vdVMHwlgSEISJKrV155RZnJ//jHP+aMfghW/IoEEo3AuJv0BwNuMBiUFcSSwEdWFDNN72CkeJ4EoOxdIfH0K1euVOLpw+Ord8B6cicq93Vy8xgOOhKIQQJRq/CFpfj3JVGP+PclTa/497kNbwyOMjY5bARk0ev+/fuVh2Lx08teFmELs3O0oa7kdbT3hq07rJgESCCMBKJa4av9Vrfhlfh98e+vWLGC8fsqHL4mLAFxe8lDsKSslodiWfwqD8k8SIAESCAQgZhQ+GrDZQGfrDQuKCjgNrwqFL4mHAFZ2CoPvbt371aSWFVWVoZ/jYvDDOPMPNTa7TCVPYxkfSXMjv+G2Zil7FO/Z2sJ9BLpoJx3AS472pu2okSvRj/oscBYD3PfZjjXPNfmvwnz+Tf7yy0wYl+7nS6DhBvV7HAkCMSUwleBcBtelQRfE4mAhNlVV1crD7uSryKiYXbaXNR0nkaFTgdD3afotVUjV+v9+Wj5d5ydVA6r+0vYWlYhW+tA+7YVePLovXi+/UvIdh3u3v/ApuSDyFtVh3ansoWeR3Sm1Sh6C95yN2FZk4y9WSuwrf1GIomWfSWBiBCISYUvZAJtw0v/fkTGDG8SYQJqOtyFCxdCq9UqfnpZ1Bo1h+5JlPzwEaRgAnTp30CK4wIObetBcckyZOu8O9tppiHn2WUwtHyET2w++8zrnseu6hXeclqkF67HpooebDt0AY6o6SAbQgLxQeCvYr0b6ja8ajjS0aNHwXCkWJcq268SkIdYWbci7iyJVJHxHvWHWANsbYDTCnPT76DM1W98jDfKatGCJVjm24HMxzBLfShQznv2p7dXnULbSzn9VgTfa/ieBEhgVARidobv39vZs2fj/fffVzKKSWYxyTAmMyMeJBCLBGQhnoTZibKXuHoJs4sJZa/AdqCzvgz6iRnIe+Njj8J/oABvtb0DAy7D0u0cXiT2Llzp8bEEDH8FS5AACQxDIG4UvvRTTdN74sQJpduygllmRTxIIFYIyEOqPKzKOhUJs5OHWHmYjaXDZf0Aa8taUdB4Bb2/rUFpYSEKC/8W+pv/hY5gO6JLw/SpXndAsNewHAmQwJAE4krhqz313YZX4vclW5+Y/HmQQDQTUMPsHA4H5KE1NsPsXHB2d6EDD2PurK+j/wfmL/jiRgCvfEcXun0X8cGJbstl6IofR5a6KDCahca2kUAMEej/f4yhRgfbVPF7iim0vLxcMYuKiVRMpTxIIJoISJidPJQePnw4cmF2owGQokdG5n2eK285MUBP99WngTbrcRTrzqJh7+9hVxbk34G9dQ8qV78Je1857xv7Xrz62hFYlcrEFWBEUcN3seuFedD6l+VnEiCBMRGIa4WvkpHMY6p//6GHHlIyk9G/r9Lh63gRkDA7eQiVNSfyULpnz57ozn2vmYECYzHuSBz+V0txqGuQNTLaefjJsRpkf1QCfbLE4c/Bht9NRsmRw6jQ+dHOKUbxty/jtfRkJCXdj9wzs7CvpRqF02jO9yPFjyQwZgJRu3nOmHs2SAXyI/v2228rMcybN29GVIU3DdJmno4vAvKwefz4cSxevBj79u2DxNQnXoY8SbyzEHkX/wmW46VIT4ipR3yNY/Ym9ggk3L+Z+PclM5mk6RUTqphSxaTKgwQiQUDC7GQxqawtkXS4sldE4in7SJDmPUiABPwJxHwcvn+Hgv0s/n0xocoPsJhUc3JysGHDhvCnKA22gSwXVwTkofLdd99VHi7feeedmFt5H1fCYGdIIEEJJJxJP5CcxcQqs/2SkhI0NjYqufo56wpEiudGSkDGVl1dnbJuRB4oZeU9DxIgARIYDwIJZ9IPBFmUO7fhDUSG58ZCQHJAiPleDtm2lsp+LDR5LQmQwFgJcIYfgKCYX2X19JQpU5TV02L+50ECwRJQ0zzLuGGa52CpsRwJkEC4CVDhD0FYEqFUVVUpC/uee+45+veHYMWvAIkAef3119HS0oLt27dDwkF5kAAJkEC0EKBJfwhJSMiemGIlh/mDDz6opOll/P4QwBL0KxkT+/fvV8aIpMOVMUNln6CDgd0mgSgmQIU/jHBU//4f//hHJZTqqaeeUlb2D3MZv04QAmqYnWRwlDC72EyHmyDCYjdJIMEJ0KQ/wgFA/+wIgcVpcVnnITvZXb16VUnfzHUecSpodosE4ogAFf4ohSkrsMVfK6v7ly9fTv/+KDnG2mXM1BhrEmN7SYAEVAI06askRvgqplvx1cqxcOFCbsM7Qn6xVlz89PKQJ7LWarWK7JmWOdakyPaSQGIT4Aw/BPL3zaL2yiuvMItaCJhGUxW+bpwXXnhBWcQZTe1jW0iABEggGAJU+MFQCrKMLOASv674c6kYgoQWxcVkId7OnTuVdLh8kItiQbFpJEACQRGgST8oTMEV8t2GV0z+u3btAsP4gmMXTaVEZiI7kaGE2cnWyrNnz46mJrItJEACJDBiAlGj8JOSZN/s8fsbMblBLpAwPlEUJ06cgMPhUFKrSgIfHrFBQGQl6XBFdiJDkSX3VYgN2bGVJEACQxOgSX9oPmP+luFbY0YYkQqYTjkimHkTEiCBcSQQNTP8cWQQ1luLP1+24S0vL1e24ZUc/RLaFerDZa1HvlhI9JUwO1yhrt5Tn6sT9fl66I1mOAa9wzWYjVlIyq+HNUzNGPTWo/hCZFFdXa3IRmQksmJM/ShA8hISIIGoJ0CFHyERiX9fwvjEJyxpeiUVa+j8+7fRdfYEOtb/HD/PPIPmttA/UCiYNDNR2myDrSYX2ghxC9dt1DA7kYWkTmY63HCRZr0kQALRQoAKP4KSUP37koJVVoCLrzgk/n3Hh6iruozi7z+NwmXTUFvz65iYXUcQ/YBbqelwz58/r6TDleRJ9NMPQMQPJEACcUiACn8chDpp0iRUVlbiwIED2L17N1asWKGEfo2uKS442k6hAQbkZ01D2ryFMJhO4GzXbW91t2GtXxrAxO6Cw1wJfZ8LwAWn1Yx6Y7538aQeC4z1MFt9jPcBTPouezuatpZAryy4zETJ1l/jQs+XPl3xrzcJSQuMqDdb4fQpFYm3qp9eQiffeecdJSWuyIIHCZAACSQCASr8cZSy+IqPHDmCJUuWKD5k8SWP3L9/HW3NJqD4cWRpNdCkfQ/LDBdw8OwVeFzo9wR4CJBO+14HODsb8HzOWpyZ+lPYet1w97ajZuoZFGUsx9b2G4EpOVuxbfkyvHH1B2j5ohdu9zm8NKMLv9l/qb+8sw1vr6rAmYx/wRduN9zuL2HbdB8a8qpwyKo+lPQXD8c7NcyuqKhIcakIc4bZhYM06yQBEohmAlT4USCdsWzD67L+GjW1QHH+ox6/umY65i17DKaq/WjxLt5THwIafv2H/lm14w9oblCvu47WX76BkwX/C9Vr50Ino0KjQ/a6f8GBih6UVzYFcBG44Gg9gm2Wpdj00iKkp8hFWqQXrsemijl9VF22SzjZMgPz56UhRTk7Abrcl/Fb9yGUpt/TVy5cbyQdrrhO5FDD7MJ1L9ZLAiRAAtFMgAo/SqQjPmTxJYt/X3zLoqQkpevQh2exnkkn5nzVNO2d0dtN/Yv3NDOQv2ohLNuOoFV5CLiDz041oSHjaSzNngQoyt+GzLmPeJR9301TkJoxA+joQrfTf8m9x0Jgz0xDqqLs1Yu813g/avSz8ETOWVTV/Rtazf820EWgXhKGV2G3aNEihaW4TlavXs0NjsLAmVWSAAnEDgEq/CiTlfiUa2trFR/zfffdN3TrXFdw9uBZwP5z5N2f3Je4KDmjDCa0o6H5D97wuQmY9nghiuF9CHBdRvMvTiCzuADfStHA1XMFF+1D3MrehSs9dwYWcF3DlYu2gecCfUrJxovHWnDgO/8fGl9dibyM+5GUlA9jvRnWux4iAlUwsnPiEpHQx5UrVyqhkMKSYXYjY8jSJBB9BLzhvkMkZxs6XHhgjzxhzEtRr7gVB1vnNPCaIT8FWN80ZHn1S6cVJ7e+hn0Rcm9S4avgo+xVfMxDKyoXHC37UWWahzrLn+FW/OPiI5e/Xtw8vRGofRsfqANJ+yjyi6E8BNzo+hAHTY9h2bzpkAGgmTods3VDANClYfrUCQMLaCZj+mz9wHODfUpJR27hCtT81gZ3rw1tjU+gpyoPOa+2DBHPP1hlgc+Ln15CHSXMTkIfGWYXmBPPkkBME9BtxOmbsl5I/a3rfx3XcOFRhSyLW3QvSso/QW+EhEKFHyHQob+Nd9Fd6T8gP83fF66BNutxFOvO+izem4SsfAPQ0IR3m47BZFiIeep1ysOAHh3n/hP2AZZ7J7otl4G7zPbSG099urvM/d5rBuuwRoc5hc+ipHgO7BevoGfA/Qa7aOjzapjdpUuXFJcI0+EOzYvfkgAJJCYBKvxYlbu66O7pv8W0QFLUPoal6x+D6eCH6FKUqgba7EVYn9GE8o0fw7Dse0jru24Ssn+0Bk8cfxmVO855lb4DnfVGFNVOxZbqQqT3lVWBaaDNWYVdBcdQtKYBnYp53gFr0za8WtuuFoLHdJYPY1Ond8GghOn9Ds2tQOmqPJ829F0S9BsJs5OQRgmzEz+9mO8ZZhc0PhYkgTglcAf29iZsLcnsc3OOLBR4FKHE/iZ9hxlGvR75e06idZ8RC7yuCH3JdpxUQp0lLLoKM/N+DjsOoyzjXp8Mpg5YzfUwLtB72x86F+hdP+NxOgLirFu3Yf3gbdSqi+4C9u4BfOvvC2Ew7UZdyzVPiZRH8ffF8wBdIVblz1DM+Z4vNEiZWYw3W3Zgfs/PoE+WTYxm4h8tc3HA8h5enPNAwDtA8w0U7mjEvkwzcifKGoKZWPXxw1izZVFfeU16Efa2rcKUo0swURn0yZiYcxRT1vwCmxd9w6cNfZcM+8Y3Ha6ENEqY3dDuj2GrZAESIIG4IOCCs/1NLH/yKJKfN6F3QCjwerw9WIixb99DFkpsh2nlVjRO/BGOSTt6u3Fg2gkYVtWh3Qloczej8/RG6LBEcct6XBIy0VqHnKIzmFrTrrS/1/ZTTD2zFhlP7kD7WNc9uXmQQIwQuHXrlruxsdH97W9/2/3GG2+45TMPEiCBRCBw1X26Yo4bQMA/XcVp900Fg6dc/2cvm95P3XWGb7oNdZ+6e91ud6+lzm3AEned5c9ut/vPbkvdEjcMdW5Lr/93QbJV6te5++5787S7Qof+z0o1ve6bpze6dX339f/sdruV62a5SxuvKO3su7tyXtfX/r7zI3zzV74PNnxPAtFM4Pjx41i8eDH27dunhDBGc1vZNhIggTAQkEV7nZuRqx3MOD0ZuTVtsEHM4kdx6oYsh/scH7/xMmpbAMOy4dvkCSWuUkKJZ+XfA2fq3yI3PRS7h2iQkpqGTJhg6XYC6Wootdomb9ZU+8PYPOvrA62fKXpkZAINFhucmDnqvUwGo6a2gK8kEDUEZDGexWLB73//eyXGXnz4PEiABEign4ALzs59KNHfj4y83fj4hixg+hry32pCnQHoUBRmf+mA7yIcStzfhjvoudKFISOkx7jQmQq/nzbfxQAB8dVHYrvhGEDBJpIACfgTcFlxaO1GnCxoRHdvM2pKf4jCwh8gV38Llo6hVKlfRREIJfa7I4AJmDo9DUNGSM+ejqlj0NpjuPTu5vIMCUSKgLrd8KxZs5TYe0mhG7rthiPVC96HBEggpAScNlg6cFfWUNcXN+Bdujzy24UhlDhwI9Rw6k9x7tKfvHuheEuq/crQe1OUB65huLNU+MMR4vdRSyBQOmKJyedBAiSQoAS8OUVMDQfRYvdkB3XZz2FH5cuoD3KCH85Q4oFSUX36ctaFW85bcGmz8KPN2Ti++qfY0Wr3KH3nJdSvWYvajHJUL00f6NsfWOGwn6jwh0XEAtFOQE1HLLH4EpM/tu2Go723bB8JxBcBdTfL0KzJmYycn+zG3uwPkaf/ihLHnrrhIzxUshuNPpt6DUUwHKHEg91Pk5YP48abKMv4Kr66+F/R5dJiZul2tByYjx7jHCRLKPPEf4Zl/g5Yjq3FnAH7lgxW6+Dnk2RV/+Bf8xsSiD0CJpMJVVVVysK+5557jsl4Yk+EbHGCEFD/V2XjsOXLl/N/Ncxy5ww/zIDDWn2EN14Ia19CWLm63bBWq8XChQtB/34I4bIqEggBAZnNy26Whw8fVrJkcjfLEEANogrO8IOAFJ1F1NSMXdhs2R+RveWjk8PQreru7sbOnTshPzDl5eWQxX48SIAExoeAZMl8/fXX0dLSgu3bt/P/McJi4Aw/wsB5u8gSSE1NVXLsv/LKK4p/X7bODY2vMLL94N1IIJYJiJ9eLG2ym6VE1nA3y/GRJhX++HAf413V2b3fxgveDRsWGHf2bRzh2SN6uM0kpL5K6JOWYo/5JLb3bTqRD+O+Vr8d9MbY9HG6XLYblpz7snVuUVERdu3aBZlt8CABEggvAXU3y/Pnzyu7WYq/XiJseESeABV+5JmH4I6aQTZekKrtaGn4BJM2noO7909oWfktaILeTOIwVhYdAJRNJ3rxhWUVsHc5lm9r9e50F4Kmj3MVkq3vxIkTSitU//44N4m3J4G4JCCWNLGocTfL6BEvFX70yCJkLdEVP40fztQCmq8h/Zu9aD30K1iKS1CWrfPGcE6ALmcZig2dOPlJj0+Ch1ko3fUzrFXKaZCSvggvbVoKy7YjaHWEYOP6kPVwbBVJGJ8sEpIwPpl1yOKhixcvjq1SXk0CIyCQ5N0udbxeR9DUERcVy5lY0MSSJhY17mY5YoRhu4Cb54QNbbRUPJLNJB7G3AGbNngTQ9h3o7ltPXJzJ0dLp0LSDknTW1tbCzE5io9fPr/wwgsQvz8PEggngXiNhhY/vSzKE7O9+Olpug/nKBp53Zzhj5xZjF0Rgs0kYMPFK9d8LAExhmCY5srK/ffff1+ZjYjJX2YnTNM7DDR+TQI+BMRCJpYysZiJ5UwsaKFV9i44rc3YWvkerPFjbPQhGJm3VPiR4Tx+dwnJZhJ6zJ4+eUwpHccPQHB3lh8n1b/vcDgwf/58SFIQHiRAAoMTEPO9+OlXrlyphL2KxUwsZaE/rqO17iWUt98OfdUJVCMVfrwLW910Ye4j0PlIO/BmEpc9+zT3MXHB2d2FDp0B+Vn+ezf3FYqrN+Lfr6ysVGYpkhREZi0M44srEbMzISAgFrD9+/crYXbip2eYXQigRqAKHxUQgbvxFiEkEGDjhUC1j2gziXbUvroNTVaHspmDs7MBa4qOoWDXKuRoE2uocBveQIOJ50gAiuVLLGCS1Orzzz9XLGOhNd/7U74Gs3Eh8mrbAVMZMpKzYDT/tzeUOB/GPa+jRJ+EpCQ5L3viMQzZn6D6ObF+xdVex8nrXRsv9Abq2Eg2kzCgovhhXH5tLpKSkjEx14zMfY3YUfiNuDbnB6KmnlO34ZVZjCQNkVkN/fsqHb4mEgGxdMnGVLt371YsYGIJE4tY+A9ZeHwCp2XzG0MdLL1tqOlbQGxCw1kdNlp70Ws7iJXZD8DJMOTBRSKb5/BIdAK97punN7p1WOKus/w50WEM2v/PP//cXV5e7v72t7/tPnv27KDl+AUJxBMBGfevvfaaMu6bm5vHqWtX3acr5rhhqHNbeqUJ6m/WHHfF6as+bfKU01Wcdt/0Oevu/dRdZ/im21D3qbu379pZ7tLGK26lOqWst07dRvfpm/1nfauJ9fec4Q/+LMRvSGAAAW7DOwAHP8Q5ATUdriSoko2oxE8vG1NF9+ENQ67JQo/5qJLOt6lpD4x5uSgz3fJr+mBhyCY0t8VnFk4qfL8hwI8kMBwB8e9LMpElS5YoyUWqq6uZpnc4aPw+pghIboqnnnpKCbOT2PrQh9mFCwfDkIciy8Q7Q9FJmO8kVW81bO6E6XBIOiqznb/5m79RtvgU/35jYyMKCgpCHH8ckqayEhIIioDv7pKSjEr2oIipwzcMeU8hpqlTWtlnpMMOBNWd+A1DVnHElEzZWBKIFgKyOlmyislqZUk6IquXZXbEgwRiiYCY7yXhlOSikAWqkogq5pS9AGcY8pDDjgp/SDz8kgSCI6D699955x1uwxscMpaKEgKSYEoeVCXhlGwsJUo/vGF2o+l4ClIzZngvvA2n8y+BK2EYcmAu3rNU+EPi4ZckMDIC3IZ3ZLxYevwISJidJJaSBFOSDjdyYXaj6fM9SCtYgY13qpCRPAOLD3UhYBQyGIY8FN0kCTMYqgC/IwESGB0BMZPW1dUpsfsbNmygf390GHlViAlIOlzZ4KalpQXbt2+H5JpIrMMFh7kKM/O6sNmyH6Xp9yRM9znDTxhRs6ORJiBmUVndLKucxb8vq565DW+kpcD7qQTUMDtZYDpr1iymw1XBJNArV+knkLDZ1fEhINvtchve8WHPu3oIyELSdevWIScnR1lgGpkMeaQfbQRo0o82ibA9cU1AZlnHjx/v2zO8rKwsChdIxbUIEqpz4qd/9913lQ2gYjLMLqGkFf7O0qQffsa8Awn0ERAzv7oNr5yU1dFi8udBAqEkIH56CbMrKipSwuwkUVRMhtmFEgrrStg9USh6EhhXAmJSFf++rI6WGT+34R1XccTVzeUBUtLhyiHpcOUBkwcJCAGa9DkOSCAKCPj6WGVFP32sUSCUGGuCLAgVs72kfv7xj3+svMZYF9jcMBOgwg8zYFZPAsESUP37ixcvxr59+5Rc/dGXACXY3rBcpAgwzC5SpGP/PvThx74M2YM4IaD69yVNr+Q0F/++ZEHjQQKBCMgD4v79+yFhdpIOV8z3iRdTH4gMzw1GgAp/MDI8TwLjREDM+ZL1TPz7kgWN/v1xEkQU31ZcQPJAKA+G8oAYnelwoxhggjaNJv0EFTy7HTsEZJZfVVWlKP7nnnuO/v3YEV3IWyphdlu2bMHVq1eV3A7ir+dBAsES4Aw/WFIsRwLjREC24RVzrSTwEfOtrMIWcy6PxCEgfvrq6molzG7JkiWQMDsq+8SRf6h6SoUfKpKshwTCSED8+9yGN4yAo7RqebBTw+y0Wq3y4CcPgDxIYDQEaNIfDTVeQwLjTEBMuxUVFZgyZQrKy8s52xtneYTj9r5hdi+88IJi4QnHfVhn4hCgwk8cWbOncUhAZn+y85nM/pcvX07/fhzIWBbi7dy5k+lw40CW0dYFmvSjTSJsDwmMgICszhb/vhySXY3+/RHAi7KiYr6XdLgiUwmze//995kON8pkFOvNocKPdQmy/aMmkJSUhPH8G3XD/S4U/77/NrwStsUjdghIJIaE2TkcDpw4cYJhdrEjuphqKU36MSUuNpYEhifg6/tlitXheY1nCa7FGE/6iXdvzvATT+bscZwTkF3RxBwsZmHZLU3MxCEP43N1oj5fj6SkLBjN18JE9Das9UuRpK+E2eEa5B4uOMyV0CctRb319iBlou+0b5idLLrcs2cPF15Gn5jirkVU+HEnUnaIBAA1Ta+Yh+UI9Ta8rq4PcbCjEFt+/hAamv8AR1ig34P00kNw26qRq42Pnyo1zE7yKUheBabDDcvAYaWDEIiP/6JBOsfTJJDoBHy34T1//rySrU9M/mM7rqGlbjc6igvx48InkVn7Nj6Iodn12Po++qvVdLgiB0mHK5EV8mDGgwQiRYAKP1KkeR8SGEcCkpWttrZWidmXLVQlhl/Cv0Z1OP6A5gagOP9RPJD2PSwzXMDBs1fQZ3RXzP1pyK/v7D+n3OgazMYs6I1mr0XAAau5HsYF4hqQBZT5MNabYXWqNQUw6bvsaG/aihK9Z8GlvmQbjl/4bGA3nFaY641Y0Lco07/egcXD/Un100tK3HfeeUeRA7c/Djd11h+IABV+ICo8RwJxSkB2U1P9+w899JCy29rI/PsuONpOoQEG5GdNAjTTMW/ZYzAd/BBdqp4OdE54+jwoaOFAZ/065BSdwdSadvS63ei1/RRTz6xFxpM70N6n9H0FcQPt21Yg643r+EHLTbjdvbC+NAMXfnMS9r5iN9D+9noUnXkEb33RctykFQAAFc1JREFUC7dS74tIbliJNYesfg8gfReF5Y0aZifrKGQ9haTDlfUVPEhgvAhQ4Y8Xed6XBMaJgOrfH9U2vC4rPqjZCxQ/jizFr34P0uYthMG0G3Ut6uI99VwTfv3/3PD20u9BwdGGX1a1omDXz7A2Wwf5IdLo5mLdGztQYdmCykDK2XEBh7b1oGLTehSma+UKpKQvwkubnoVOZenqwScnO5E5/ztIT/H8vGl0T6D6t11oLp2p3EctGs5XyYcg6ybkUMPswnk/1k0CwRCgwg+GEsuQQBwSCLQNr6weH+pQFuuZ9Io5X1SuHBrFrG8bsHhPk5aHVaX/B9sOXfCY711/xKlfmZCxfhGytfBYCewPY+6srw9Uwil6ZGQCHRYbnN76PS/eBwb7DGSkpvh8o0FKahoy1TOaqfjrJ2bCVPVLHGk1o8ls9atHLRieV1kfIdsZi59etjeW/Ag034eHNWsdOQEq/JEz4xUkEFcExL8vYWHi2x9aOd1G19kTMKEdtXlT+pMWJT+MMpMd9oZTaFPD5zQP4fGnnwS851xdp/GL+hko/vtHkYI76LnS5WOGvxun/eIV9KguAuXr4a/x1PIA5rz4HiwHvoMbjTVYnJeBiUl6LDDWw2wNTyyB3FcelGRdxMqVK5V1ErJegrvZ3S1XnhlfAlT448ufdyeBqCEwrH/Z8SHqqs7CUPep4nMX/3jf383TqMBe1Hyg+sk10GY9jmKY0Nz2medBwbAQ89LuATABU6en9ZvhAxDQzZ6OqQN+nYa/pr8aLdJzC1Fa0wy3+0vY2nbh+z3bkZfz+hDx/P1Xj+Sd+On379+vbFssfnqG2Y2EHstGmsCAf6lI35z3IwESiBUCqg++EKvyZww0w0sXtI8iv1g/cPGecg5o+M2v0HTwAgzLvoc05RfH+zCg+xTnLv1p4EI6pw2WDiAzQw9fw73465UHCN1lWLp9jf0uOLu70DEoxgnQzVmElSVPQmfvwpWeO4OWHOkXapjdpUuXlDA7yYHPMLuRUmT5SBKgwo8kbd6LBGKWwHW0NZuA4kI8Pm1CgF5MQvbSp5FjOoGzXWrGO8+5jG0bsdH0GJbNm97/oKDNwo82Z+P46p9iR6vdo/Sdl1C/Zi1qM8pRvTS9v6x6N+08vLDru2goMqK+U8zzLjitR/Daq3v73QPekMAFxqb+8D6nFaea24HSf0C+YmFQKxzdq4TZrVixAhJmJ356Md8P7QoZ3X14FQmEmgAVfqiJsj4SiEMCLuuvUVM7FeuXPgZ1sd7AbmqQ8q0CFBvOoqruQ2+cvXpOB91dylaLmaXb0XJgPnqMc5AsMfMT/xmW+TtgObYWc7wr7AfeYwKmFVajZd8snMm9H0lJyZi4qg3fXvMCDGpBzUw8u/cg1kw5ipyJyZ51BhOX4OiUVTi2+e8wbQy/eL7pcJcsWaKE2dFPr4LnaywQ4OY5sSAltpEESGBcCcisXuLp9Xq9kseApvtxFQdvPkoCY3jeHeUdeRkJkAAJxBgBmclLljw5Xn755dFnKYyxfrO58UWACj++5MnekAAJhImA7y6EskAvLLsQhqntrJYEhAAVPscBCZAACQRJQM1SGK5dCINsBouRwKgI0Ic/Kmy8iARIgAQA8e2/++67yqskLho2lwGhkcA4EqDCH0f4vDUJkEB8EJCY/HXr1iEnJwcbNmxgmF58iDXuekGTftyJlB0iARKINAHZhVCy7Em2vQcffHAUuxBGusW8XyISoMJPRKmzzyRAAiEnoPr3R7ULYchbwwpJ4G4CNOnfzYRnSIAEAhJwwHpyL/baDNhcErmtZgM2JQZOin9fsvFdvXpVycbHJD0xILQ4byJn+HEuYHaPBEJGwNGGupLX0d4bshrjuiJR8LIL4T/90z8pSXtkN73hth+OayDs3LgToMIfdxGwASRAAvFMwGAwKP79WbNmKf79pqYmyC57PEgg0gSo8CNNnPcjgVgk4DDDODMPtXY7TGUPI1lfCbPjv2E2ZiFpgRF7tpZAL/nwlfMuwGVHe9NWlOiTPPns79qT/prn2vw3YT7/Zn+5BUbsa/duphOLnAZps/j3n3nmGWVXvfPnz2P+/PmQlf08SCCSBKjwI0mb9yKBWCWgzUVN52lU6HQw1H2KXls1crXen4+Wf8fZSeWwyt7zLauQrXWgfdsKPHn0Xjzf/iXcbjfcvf+BTckHkbeqDu1OVz8F02oUvQVvuZuwrEnG3qwV2NZ+o79MHL2TXfVkdz3ZZU/8+7Lrnvj6eZBAJAhQ4UeCMu9BAvFMQPckSn74CFIwAbr0byDFcQGHtvWguGQZsnXerXQ105Dz7DIYWj7CJzafPel1z2NX9QpvOS3SC9djU0UPth264N1xLz7BiX//yJEjkF33ZFOe6upq+vfjU9RR1Ssq/KgSBxtDAnFAQKwBtjbUZF+HuakJ4rNuqjciL6MMJv/uZT6GWepDgfJdClIzZsDecAptDh9LgP91cfJZ9e9rtVosXLhQYUX/fpwINwq7QYUfhUJhk0ggtgk40FlfBv3EDOS98TEU4/wDBXir7R0YcBmWbufw3bN34UqPjyVg+CtitoT491evXq0oe/HvP/XUU/Tvx6w0o7vhfxXdzWPrSIAEYo2Ay/oB1pa1oqDxCvYUfsO7Q5cLDrMJHQBmB9MhXRqmT/W6A4IpHwdlUlNTFf/+xYsXIXn5jx49ih//+Mdg/H4cCDdKusAZfpQIgs0ggfgg4IKzuwsdeBhzZ33dZzvOv+CLG467u9jRhW7fRXxwottyGbrix5GlLgq8+6q4PiMb8Ih/X9L0in+f2/DGtbgj2jkq/Iji5s1IIIYJpOiRkXmfpwO3nBigp/u6pYE263EU686iYe/vYVfc8Hdgb92DytVvwt5XzvvGvhevvnYEVqUycQUYUdTwXex6YR60/mUT7HNhYSG4DW+CCT3M3aXCDzNgVk8CcUNAMwMFxmLckTj8r5biUNcgyWO08/CTYzXI/qgE+mSJw5+DDb+bjJIjh1Gh86ORU4zib1/Ga+nJSEq6H7lnZmFfSzUKpyWWOd+PSt9HCeMT/76E8Yl/f9GiRRCTPw8SGA0B5tIfDTVeQwIkMEYCknhnIfIu/hMsx0uRzqlHUDwlWY/E74tf/4UXXoD4/XmQQLAE+G8WLCmWIwESIIFxJiDb8L7//vuKf19M/vTvj7NAYuz2VPgxJjA2lwRIILEJqNvwin/f4XAoaXpNprsyHCQ2JPY+IAGa9ANi4UkSIAESiA0C3IY3NuQUDa2kwo8GKbANJEACJDBGAuLfX7duHXJycrBhwwbIgj8eJOBLgCZ9Xxp8TwIkQAIxSkD8+2fOnFH8+w8++CD279/PbXhjVJbhajYVfrjIsl4SIAESiDAB1b//+eef49KlS9yGN8L8o/12NOlHu4TYPhIgARIYJQHx71dUVGDKlCkoLy9nmt5RcoyXy6jw40WS7AcJkAAJDEJAVvFXVVUpiXuee+45+vcH4RTvp2nSj3cJs38kQAIJT0DdhlcS9Yh/X7Ys5ja8iTcsqPATT+bsMQmQQAISEP/+M888gz/+8Y9Kml5uw5t4g4Am/cSTOXtMAiRAAkpOftmGV9L0chvexBgQnOEnhpzZSxIgARIYQCDQNrzXr18fUIYf4osAFX58yZO9IQESIIEREZCc/BK/L8fChQvp3x8RvdgqTJN+bMmLrSUBEiCBsBHo7u7Gzp07IeF8Yu4XKwCP+CFAhR8/smRPSIAESCAkBLgNb0gwRl0lNOlHnUjYIBIgARIYXwLchnd8+Yfr7lT44SLLekmABEgghgmoaXplG1455s+fr/j3Y7hLCd90mvQTfggQAAmQAAkMT4Db8A7PKNpLUOFHu4TYPhIgARKIIgLchjeKhDHCptCkP0JgLE4CJEACiUyA2/DGrvSp8GNXdmw5CZAACYwLAdW/L9vwSiif+Pdlgx4e0U2AJv3olg9bRwIkEIcEkpKSxrVXbrc7pPdXt+GVSmtra7kNb0jphq4yKvzQsWRNJEACJJDQBLgNb3SLnyb96JYPW0cCJEACMUMgMtvw3oa1finESqI3muEIEx2XtR75SVkwmq8NfgeHGUa9Hvn1nXANXipqvqHCjxpRsCEkQAIkEPsE1G14xb9//vx5xb8vK/tDdriu4OzBz7B+yyZkNpxCmyM8qlaTXopmdxtqcieHrOnjXREV/nhLgPcnARIggTgkMGnSJMWff+DAAWzZsgUrVqxQcvSPrasuOFr2o6pjPr7/43/AssxDqPnAGhOz67H1OzRXU+GHhiNrIQESIAESCEAgPT0dR44cQUFBAYqKirBr1y6Mfhve62hrNgHFjyPrgRmYt+wxmA5+iK6+Sb7X3J9fD2vfOWmUCw5zJfT6SpgVi4ALTqsZ9cZ8xTWQlKTHAmM9zNZ+B8HdJv07sLc3YWtJpucafQm2Hr+AngF9dsBqrodxgX7QegcUj/AHKvwIA+ftSIAESCARCYRkG17HH9DcABTnPwot7kHavIUwmE7gbNdtL9JA5+QrnwcFLeDsbMDzOWtxZupPYet1w93bjpqpZ1CUsRxb228EEI8LzvY3sTzrF7j6g8P4wu2G27oRMy6cxH67WlzK1GFV0TlkvNUJiYRw9/4HNiUfRN6aD/weQNRrIvtKhR9Z3rwbCZAACSQsAfHvr169WsnJL/79p556CsH792/D+sHbqIUB+VmTFIaatO9hmeEsquo+7Fu85zl3AQ2//gOcKukBDwrX0frLN3Cy4H+heu1c6EQLanTIXvcvOFDRg/LKpgDK+TpaD/0KlgojXiqciRSpN2UmCl8yokKn3uQObJ98hJbMuZiXrvWc1ExDbnUz3M2lSI8CbRsFTVBh8ZUESIAESCARCKSmpir+/VdeeUXx71dUVCgJfIbsu7JY7yx0Ys7XelWXZjrmLZsHu+/iPc0M5K9aCMu2I2hVzPd38NmpJjRkPI2l2ZMARfnbkDn3EY+y77tpClIzZgAdXeh2DvAH9F+Tofcoe/WaFD0yMu/zfpoA/V//T+SYdqPuyO9hbmqB1b8e9bpxeqXCHyfwvC0JkAAJJDqB2bNn4/3338d3v/td3Lp1a0gcrq4PcdBkh702D/cnJXl95Pcio+wwYDehue269/oJmPZ4IYrhPee6jOZfnEBmcQG+laKBq+cKLvaZ4QPc0t6FKz13Bnwx7DVKaQ1S5qzFMctWfOfGv+HVxQuQMTEZSQuMqDdb+60NA2qO7Acq/Mjy5t1IgARIgAR8CKhpemVx3+DHNbTU7YbJUAeL+NzFP973dxWnK4Daml/3m+K1jyK/GGho/gNuKA8Kj2HZvOkQhaeZOh2z+8zwAe6oS8P0qRMGfDHsNX2lNUhJz0FhaQ1+63aj19aGxu/3oCpvOV4dKp6/7/rwvqHCDy9f1k4CJEACJDBWAooZ/kuUrspD2l1aaxKy8g3QDVi85zmHhia823QMJsNCzEu7x9MK5WFAj45z/wn7AMu9E92Wy0BmGlJT/G6iXmOxDZypO22wdAxumdDo5qBwZQmKdTZcvHJt3MMH/Xo1VqnwehIgARIgARIIJQEXHG2n0IAn8fTjDymz9IG1a6DNXoT1ORdw8OwVr1L1nstoQvnGj2FY9j2fB4VJyP7RGjxx/GVU7jjnVfoOdNYbUVQ7FVuqCwMssJuMnBcqUdCwFmvqL3mUvrMTTa/VoLbPPeANCVxQiaa+8D4HrKdOoRWFWJU/I0DbB/Yk3J+o8MNNmPWTAAmQAAmMnoDLig9qDiFj/SJkq4v1/GtLeRR/X/wYTFX70aJm3lPOzQN0/spWg5SZxXizZQfm9/wM+mRZDzAT/2iZiwOW9/DinAf8a1c+a6Ytwo6Wrcg88xQmyhqCiWvx8bdLscWgLtq7B+nP7kDbmkk4mnO/d43B/cg5Oglrjr2ERdMGugkC3iTMJ7l5TpgBs3oSIAESIAESiAYCnOFHgxTYBhIgARIgARIIMwEq/DADZvUkQAIkQAIkEA0EqPCjQQpsAwmQAAmQAAmEmQAVfpgBs3oSIAESIAESiAYCVPjRIAW2gQRIgARIgATCTIAKP8yAWT0JkAAJkAAJRAMBKvxokALbQAIkQAIkQAJhJkCFH2bArJ4ESIAESGCsBFxwWpuxtfK9/nz5Y60yAa+nwk9AobPLJEACJBBbBK6jte4llLffjq1mR1lrqfCjTCBsDgmQAAmQAAmEgwAVfjiosk4SIAESIIEQEbgGs3Eh8mrbAVMZMpKzYDT/NxzmSuiT8mHc8zpK9JIPX85fA3AH9vYmbC3J9OazT/Lbk97lvXYp9phPYntfuXwY97X67aAXoi5ESTVU+FEiCDaDBEiABEggEIHJyK05gdMVcwBDHSy9bajJnewtaELDWR02WnvRazuIldkPwNn+JpY/eRTJz5vQ63bD7f4Stk33oSFvPd5uv+Fzg8NYWXQAUMr14gvLKmDvcizf1jpwC1yfK2L9LRV+rEuQ7ScBEiCBhCUwB8Ul38fMFA00um/imyk30HroV7AUl6AsW+fdjnYCdDnLUGzoxMlPenz2pJ+F0l0/w1qlnAYp6Yvw0qalsGw7glZ1x7044/pXcdYfdocESIAESCBhCYg1oA02OGA1H8WpG70APsfHb7yM2hbAsMwXzMOYO+vrPnvUa5CSmoZM+240t61Hbp8Vwfea2H7PGX5sy4+tJwESIAES6CPggrNzH0r09yMjbzc+vuEC8DXkv9WEOgPQYbEFYa634eKVaz6WgL7KY/4NZ/gxL0J2gARIgARIQCHgsuLQ2o04WdCI7j2FmKZOaR1mGDvswOxgOOkxe/pkn5l/MNfERhkVR2y0lq0kARIgARIggcEIOG2wdACZcx+Bzke7ub64AVm/P/C4DEu30+eUC87uLnToDMjPmuRzPn7e+iCJn06xJyRAAiRAAvFEIAWpGTO8HboNp/MvgTunfRT5xXqYGg6ixX5HKeOyn8OOypdRb/e/pB21r25Dk9UBQFwBDVhTdAwFu1YhRxufqjE+e+UvV34mARIgARKIYQL3IK1gBTbeqUJG8gwsPtQFWY539zEZOT/Zjb3ZHyJP/xUlDj91w0d4qGQ3GiWsb8BhQEXxw7j82lwkJSVjYq4ZmfsasaPwG3FpzpeuJ7ndbvcABvxAAiRAAiRAAnFLQBLvVGFmXhc2W/ajNP2euO2pf8c4w/cnws8kQAIkQAIkEIcEqPDjUKjsEgmQAAmQAAn4E6BJ358IP5MACZAACZBAHBLgDD8OhcoukQAJkAAJkIA/ASp8fyL8TAIkQAIkQAJxSIAKPw6Fyi6RAAmQAAmQgD8BKnx/IvxMAiRAAiRAAnFIgAo/DoXKLpEACZAACZCAPwEqfH8i/EwCJEACJEACcUiACj8OhcoukQAJkAAJkIA/ASp8fyL8TAIkQAIkQAJxSIAKPw6Fyi6RAAmQAAmQgD8BKnx/IvxMAiRAAiRAAnFI4P8HADPL2ZZEExwAAAAASUVORK5CYII="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that Ayako avoids the trap in this wall.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that only one of Ayako and Natsuko falls into a trap while attempting to pass through a door <strong>in the first wall</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy</strong> the probability tree diagram and write down the relevant probabilities along the branches.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A contestant is chosen at random. Find the probability that this contestant fell into a trap while attempting to pass through a door in the second wall.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A contestant is chosen at random. Find the probability that this contestant fell into a trap.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>120 contestants attempted this game.</p>
<p>Find the expected number of contestants who fell into a trap while attempting to pass through a door in the third wall.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A manufacturer produces 1500 boxes of breakfast cereal every day.</p>
<p>The weights of these boxes are normally distributed with a mean of 502 grams and a standard deviation of 2 grams.</p>
</div>
<div class="specification">
<p>All boxes of cereal with a weight between 497.5 grams and 505 grams are sold. The manufacturer’s income from the sale of each box of cereal is $2.00.</p>
</div>
<div class="specification">
<p>The manufacturer recycles any box of cereal with a weight <strong>not </strong>between 497.5 grams and 505 grams. The manufacturer’s recycling cost is $0.16 per box.</p>
</div>
<div class="specification">
<p>A <strong>different </strong>manufacturer produces boxes of cereal with weights that are normally distributed with a mean of 350 grams and a standard deviation of 1.8 grams.</p>
<p>This manufacturer sells all boxes of cereal that are above a minimum weight, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
<p>They sell 97% of the cereal boxes produced.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a diagram that shows this information.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Find the probability that a box of cereal, chosen at random, is sold.</p>
<p>(ii) Calculate the manufacturer’s expected daily income from these sales.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the manufacturer’s expected daily recycling cost.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Jim writes a computer program to generate 500 values of a variable <em>Z</em>. He obtains the following table from his results.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>In this situation, state briefly what is meant by</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="indent2" style="margin-top:12.0pt;">Use a chi-squared goodness of fit test to investigate whether or not, at the 5 % level of significance, the N(0, 1) distribution can be used to model these results.</p>
<div class="marks">[12]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="indent2" style="margin-top:12.0pt;">a Type I error.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="indent2" style="margin-top:12.0pt;">a Type II error.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Casanova restaurant offers a set menu where a customer chooses <strong>one</strong> of the following meals: pasta, fish or shrimp.</p>
<p>The manager surveyed <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>150</mn></math> customers and recorded the customer’s age and chosen meal. The data is shown in the following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> test was performed at the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>%</mo></math> significance level. The critical value for this test is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>605</mn></math>.</p>
</div>
<div class="specification">
<p>Write down</p>
</div>
<div class="specification">
<p>A customer is selected at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>0</mn></msub></math>, the null hypothesis for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the expected number of children who chose shrimp is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>31</mn></math>, correct to two significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mn>2</mn></msub></math> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>-value.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion for this test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability that the customer is an adult.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability that the customer is an adult or that the customer chose shrimp.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the customer is a child, calculate the probability that they chose pasta or fish.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A nationwide study on reaction time is conducted on participants in two age groups. The participants in Group X are less than 40 years old. Their reaction times are normally distributed with mean 0.489 seconds and standard deviation 0.07 seconds.</p>
</div>
<div class="specification">
<p>The participants in Group Y are 40 years or older. Their reaction times are normally distributed with mean 0.592 seconds and standard deviation <em>σ</em> seconds.</p>
</div>
<div class="specification">
<p>In the study, 38 % of the participants are in Group X.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A randomly selected participant has a reaction time greater than 0.65 seconds. Find the probability that the participant is in Group X.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Ten of the participants with reaction times greater than 0.65 are selected at random. Find the probability that at least two of them are in Group X.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>At Penna Airport the probability, P(<em>A</em>), that all passengers arrive on time for a flight is 0.70. The probability, P(<em>D</em>), that a flight departs on time is 0.85. The probability that all passengers arrive on time for a flight and it departs on time is 0.65.</p>
</div>
<div class="specification">
<p>The number of hours that pilots fly per week is normally distributed with a mean of 25 hours and a standard deviation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
<mi>σ<!-- σ --></mi>
</math></span>. 90 % of pilots fly less than 28 hours in a week.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that event <em>A</em> and event <em>D</em> are <strong>not</strong> independent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {A \cap D'} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<msup>
<mi>D</mi>
<mo>′</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p> Given that all passengers for a flight arrive on time, find the probability that the flight does <strong>not</strong> depart on time.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
<mi>σ</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>All flights have two pilots. Find the percentage of flights where <strong>both</strong> pilots flew more than 30 hours last week.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the average body weight, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, and the average weight of the brain, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>, of seven species of mammal. Both measured in kilograms (kg).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_10.57.27.png" alt="M17/5/MATSD/SP2/ENG/TZ1/01"></p>
</div>
<div class="specification">
<p>The average body weight of grey wolves is 36 kg.</p>
</div>
<div class="specification">
<p>In fact, the average weight of the brain of grey wolves is 0.120 kg.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of the average body weights for these seven species of mammal.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the data from these seven species calculate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, the Pearson’s product–moment correlation coefficient;</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the data from these seven species describe the correlation between the average body weight and the average weight of the brain.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
<mi>y</mi>
<mo>=</mo>
<mi>m</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your regression line to estimate the average weight of the brain of grey wolves.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error in your estimate in part (d).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A biased four-sided die is rolled. The following table gives the probability of each score.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of<em> k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected value of the score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The die is rolled 80 times. On how many rolls would you expect to obtain a three?</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The Malvern Aquatic Center hosted a 3 metre spring board diving event. The judges, Stan and Minsun awarded 8 competitors a score out of 10. The raw data is collated in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The Commissioner for the event would like to find the Spearman’s rank correlation coefficient.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of the Pearson’s product–moment correlation coefficient, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, interpret the relationship between Stan’s score and Minsun’s score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your regression equation from part (b) to estimate Minsun’s score when Stan awards a perfect 10.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether this estimate is reliable. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy</strong> and complete the information in the following table.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of the Spearman’s rank correlation coefficient, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r_s}">
<mrow>
<msub>
<mi>r</mi>
<mi>s</mi>
</msub>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Comment on the result obtained for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r_s}">
<mrow>
<msub>
<mi>r</mi>
<mi>s</mi>
</msub>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Commissioner believes Minsun’s score for competitor G is too high and so decreases the score from 9.5 to 9.1.</p>
<p>Explain why the value of the Spearman’s rank correlation coefficient <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r_s}">
<mrow>
<msub>
<mi>r</mi>
<mi>s</mi>
</msub>
</mrow>
</math></span> does not change.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Lucy sells hot chocolate drinks at her snack bar and has noticed that she sells more hot chocolates on cooler days. On six different days, she records the maximum daily temperature, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>, measured in degrees centigrade, and the number of hot chocolates sold, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math>. The results are shown in the following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAmoAAABOCAYAAACQcDp2AAAgAElEQVR4Ae1dz2scSbLe/0QGnSQQ2Pjik09mkX0QxsxhwBcPssCG9eLDwAxIyOwwh8cYWowYWBhYJMYMLA/sFl6WBeOhmctgtDS8hWEQ/ZjDYESzmIcRzWKMaeIRWRlZUVlRv7qzW9VVIRBdXZWVGd8XUZFfZWZV/w70TxlQBpQBZUAZUAaUAWWglgz8rpZWqVHKgDKgDCgDyoAyoAwoA6BCTYNAGVAGlAFlQBlQBpSBmjKgQq2mjlGzlAFlQBlQBpQBZUAZSAi15aULoP/KgcaAxoDGgMaAxoDGgMbA+cUAl6cpocYP6rYyoAy0mwFM1G34U5zN87L6tFk+bbM/Vag1K5YVjTIQlIE2J8egRNaksrb4E+luC1bFWZOLK5AZkj9VqAUiV6tRBprIgJQ0FOfiMtAWf6KH2oJVcS7u9ShZLvlThZrElO5TBpQBw4CUNJpIjeJsnlfVp83yaZv9qUKtWbGsaJSBoAy0OTkGJbImlbXFn0h3W7AqzppcXIHMkPypQi0QuVqNMtBEBqSkoTgXl4G2+BM91BasinNxr0fJcsmfKtQkpnSfMqAMGAakpNFEahRn87yqPm2WT9vsTxVqzYplRaMMBGWgzckxKJE1qawt/kS624JVcdbk4gpkhuRPFWqByNVqlIEmMiAlDcW5uAy0xZ/oobZgVZyLez1Klkv+VKEmMaX7lAFlwDAgJY0mUqM4m+dV9WmzfNpmf6pQa1YsKxplICgDbU6OQYmsSWVt8SfS3RasirMmF1cgMyR/TifUhl3Ycr8Pegm2uq+Tpp71YGcl/q2sy50+fEiWmPLbBxh2H5gLcnmzC8Mpazu/08cwGvwIzzrbsN8fnZ8Z593yaAC9px3449eh42QaYG+h37kFy0u34XDwzlU0HhzATRf7cYzjRRb/X4Wd3huIyq7Cjc4xLJp3paThSAiycQaD3nN41rkLl7d7cFZQ5/i0C/dXkr4oOKXU4dnjLGVGXGg0gB86d2HNxtPa5j78MChiJz49a6t2OLmh49/g6N5VuHlwAmO+f8Lt2WKNcvbR0w5sXdyF3plk8RkMXu7DFvWBK3dh7+UgeA6YLU4AwLzc/SvsbW6YfCa5Yzz8CfY3r0S5b30XjgLEqt/OzHH6DRbirpa7/Oqzvks4Awq1C7DmJdoP/Q5cZh2XCrUM13zow95F7OCvw15rhdoI+p3r5kIPHycZvJfYTYIsGdtjOOt9ATe3v4f+8L0VYug/EhB4AR/AzsYXNoG/gd72VXa8RMM1KSIljXCmvYPBwT34ZPNjI0iSHAutmI4cOwPiWSgz4a7Z4qxolMW5tvkETkYoAN7DsPcl3FjJEgTl668VzoTZ7+G0+xDWllYXQqhhXvjozl34BEWY6BeLZ+UeHJ5EAns8fAmP1q9lip0EHRW+zNSn4xM4vHUbtu7gdRfdeKZMG/0Ljr57BUMM1fEQ/vn1XVgTOUmdWWnHTHH6lhTirpi7/Ppzvks4gwq1ZMAikNtsdOEC1KkDzuFp/odUqOFtWw2FGgksP0G9gR+/ewGn5iaaxXkiOb2DwfMXMDBlUNjtlhMj84++3BalpJF7wiQHMSlurKZu9JJV4cjmQ/h8+w6sNVyoRTcHXswZjqbv5Ofiz6TjSnwbw6j/DWx99hlsrSyGUItA2Ws/cd1buGJMR+ULb0hKMMaLzMOnYkwaI97Brz++srnQWmVm0rz45QZPuD0PnL5p2bhtSdHPfi3Vvks4Awm127CzjdNDzDkWwPLKPdj57Fp6pMQb2l9eugJbna4ZoQDAC3cfbpjROFbn6Bj21ldheYmmkYSpTy56en02fbABO90TGAEfjl6FG3ZUxFDppnIfwNEwnqR1I4M0vTpNG77PXJtsyuxiB/qmeRxe78Hh9oYVvGjvAfTYsLKz7eJj6P3yAvb84ecEzxuw891xdOeDdri278Fh7+/xuUteOWOzHSUy/KOtG7Bz0IOBuePHArEvLn/1FF7sWps3DiKxkrADz+f+fg1Hm5cSot6NLjobC3wCVMd1eNx9Co9snETTKMU8+m6JINPUfbLtZFkSc+kR5UQ5wiEl9UTBen2RkkZwCwuTne3IO6/g1Ajeho+omY6OcpxlG/dlTrGV98hc/FnenKgk5vXNb6B/+hJ2miLUwOaF9X3ouxyJ+24t1oia9WWhYGE+N2UTuNnBKTbPI3YLcRfmruqAJZyBhNoDeNb71qzZoVGzCCB2Xl34wZ/SclMYTJzQWox7XavOaW3QBVg2nT0buXBBEIsDt0bNiah03Sguojvy5DF3h0Od6VKyY3ZiKCXUkvUgwYVt+H5zbbK6rFCL1uOw/TSNzIbTnW10jH+uP4QdEm5uPxO+UtuuHO8oaFoibUs8PcN84eqw4qXQ3ySyeP12GtjZWOATJ9R4HRHWMjz6bsGbBRoFi+IvXcLsceswhTWa/BS6ceE3M/x4TbelpBHc1KJkRx356IP1ScOFGlDuuwJbBz/DaHwKvT/twv7xcOq1W3PxZ6UAQayfwl7/LYAVqIuxRg1B5oyoscGGKEe+g2GvAztf/xTfKFfiKbvwPHxaKFiMefZmfvO/oDd8n23whEfmgdM3rRB3Ue7yKyzxXcIZTKgdvX4VrbMyooo6Oey8fklNaZGIW3aCiwkBN5qEs2E0gnYVPv/LN3DfrAeI5/z5KI4k1JyIcPXgegI6n5LhBVimNsuKAiYGK7chOcrVx9eo0UiNTdbmvDM4ObiXmEKLhRqV46ORF0Cyj8R0PKK2Cjd2XybXGKDYotEfEiOOO/TNz3BoRCAJPy7UbkWJFz7AaPQuXsOV6++Mqc+yPuFCjdoZ/wdG//m3XR9G/CCRaR7TbolvDJyQTxeKsRVOx5E/w03tCOYE3yUljeCN5CY71pE78dx0ocbW+pibnnB45+LP0gFCI6X2IZtGCTUk4T0Mj/9sHyaY3XU/D58WChbqI0y80uxV6UAoVXAeOH1DCnHn5i6/tnLfJZzhhNpwyBZMv2bbb1JCjcwdD/vwt24Xjg627TQnEwemUFJ04HTZ/e5v7K6SiYPUaBcJCKwoFgG803UiZ2KhNkEbBJ5/SkLN7eMjRGzbiiiHgUQV1uvOle1LC7XkaFV0Z4ttRcLRtcFGyjCY6D/ilPmCpjs5RtP35Pk79pGzD8+vLNS8hOi4iO0lu80n5y1hb4Y9iTKxmMsddTPnlKkvUXktviBHM//LTHZ4/X8Lj9w1TzeA4YQLYZsLTmqs1OcZDLrfwF7nsyg3rn8ZZJSiVjhHx7C/+zxe39Q4oYZLLp7DXucx7JilGBvwqHfK+q9SgVBYaB4+LRQs1srx8BiemKU6fl9dCKOwwDxw+kYU4s7MXX5N5b9LOAMKtfd2WmIVbn71GD7H0S/TYQsdlBuNETpPEk2EyxKBxi+vPISjUz6kysRBSqjx0SnBBqNn7FOp1KYoCgK3Qbj4pxMTzGZni8CREUmRuHIiijBgvVJ9TKw6IURt8HNT57+NX4HCxJnxB3033Mc8cTFsYJbyt+wjWajFbbmRVDeixsUpF3r5PHJ3RNvxdKzjK1WIRskK1qdFJGTesKSqrdEOKWkENy8r2fkdeWtG1HDE91P4oxWo0dOCqxDPQEzugbn4s5R5b6H/9eNkPm+UUBvD6OQJ3P+DXcqD09dm3S7NNpQiqVShefi0ULBwS7OuZ15mgu154PTNKsQ9A6wSzoBC7QMb/cBOkUY2/A6YjUKsb8Nh9x/mAQJRcACbErWiYM2tYUNKhQ67rEipu1BzQ8lMvPlRJGEwtEiv+/D9wEWMN0KRaPssXqvlC7qEPbEvksKmrL8F+7B+EpOJdYNxW2mh5vGVwFLlLWYZ9nDMrm5PHPIybrtEfa5sfTakpBHcOjHZ0ehZlsCmG8Ew1swFZ0lTo87BuybN8o1LU7+6ojY43bWT5V8Pf0nueLHZY7W5TRqVNzHt+8sut8mYceC2V9mePU6wSzzK5Dm0POIldcNeBZRQdh44/WabKdRswkVC4ydA/Q6KjUKQ6HJ3G2y9GC7GPHli5/evwNZXX7rtePpT6LCnEWouecTDtu5uFjGFGLXzIwG/izYznuh9SownughEgSvW5/uBiyB8mrQbPcFJ78FBvJSAGC9mcbOZxsR3AuETuHTxxr5ICjWGI9ffgn3IDWub/C76xI2oeUKNnr5aYuv1BB7TbokFJnHtl4kuYox1b+rYL2i+Ew90AyMWqt3OuSRHUahJVJB4m74T92ufC06/UfF7FkaMn2vNEWoSdnOth7s+Zu/THKEmYrG+bbxQw1jd8JYpSQ6vtm/2/kzb00yhRk/B8E4+NeWWHiVDByxfuw43+MsD3QMA9PQhP4+Gj2NxEEREiU8nrsLv169FbwiflVBLCFwSq1yoenedbFF/GKHm1Y/+SKwHjBffG1+Z49E57mEFNrqZFGrcb6wd3988dkz9VnCV9UmmUCvHo3CJxiOJUmLldpGgTVcS73E+JmEbH6rz1lySowq1ZAjY3BdfWzaGL/pLP5Knlfk2F3+WMUQqI4obqWC5fbPHmiPU6MldlqujB7CuL6SAyRQsJg9eZa+5il7OfJMGF8q5qlSp2fszbUYmbipaOnfRCcWfEs6wU5840mJ/WicehRBGSsZD6H9HDxDQu8x+te/Swo7sf+3P9lxIrsvgnaN5su99vH4qkIiKF0OiqIjeFfZL73H0CwuB2ki7ij8dxDH77//CUaHkT8mEEWoP4Fn/J7sIFEfSpJ868d+jhu9BeyG/R83/qbBCf78xlCR+hmSJxDi+7JoWqOb4JFOoYdXFPKZ9wkbzEkKM3RwwwUoPXoj14E4aGUzUlVm6NgekpBHOOBo9YgI+9+lZKt/kEbWI3WTMp6/7SX0wW39OapU9b5GEGl3PLgcII4GJvJeVV6fkbOa/aUozAewaTdy4ejfx2Hd0+8FfQYIszTd2i3BTLmK85Oau8n6WcE4n1Mq3rSXryIC4/quOhp6XTXSxTjsKFl/U8Q3MeWGq1q6UNKrVsBilFedi+KmKlerTKmzVv2yb/alCrf7xOTsLVagVcBu/HmY6gUWCL/xIUAGAqQ+3OTlOTV4NK2iLP5H6tmBVnDW80KYwSfKnCrUpCF34U1WolXChFVlTTFnSLyNMJ/ZKmDqDIlLSmEEz516l4jx3FwQ3QH0anNJzrbDN/lShdq6hp40rA/VmoM3Jsd6emcy6tvgT2WkLVsU52bVQ17Mkf6pQq6u31C5loAYMSEmjBmYFN0FxBqf03CtUn567C4Ia0GZ/qlALGkpamTLQLAbanByb5ckITVv8iWjbglVxNutKlfypQq1ZPlY0ykBQBqSkEbSBmlSmOGviiIBmqE8DklmDqtrsTxVqNQhANUEZqCsDbU6OdfXJNHa1xZ/IUVuwKs5proj6nSv5U4Va/fykFikDtWFAShq1MS6gIYozIJk1qUp9WhNHBDKjzf5UoRYoiLQaZaCJDLQ5Oao/F5sBjd3F9p9vfZv9qULNjwb9rgwoA46BNidHR0KDNtriT3RZW7AqzgZdoBlxmxJq6HT9Vw40BjQGNAY0BjQGNAY0Bs4nBrj8TAk1flC3lQFloN0MYJJuw5/ibJ6X1afN8mmb/alCrVmxrGiUgaAMtDk5BiWyJpW1xZ9Id1uwKs6aXFyBzJD8qUItELlajTLQRAakpKE4F5eBtvgTPdQWrIpzca9HyXLJnyrUJKZ0nzKgDBgGpKTRRGoUZ/O8qj5tlk/b7E8Vas2KZUWjDARloM3JMSiRNamsLf5EutuCVXHW5OIKZIbkTxVqgcjVapSBJjIgJQ3FubgMtMWf6KG2YFWci3s9SpZL/lShJjGl+5QBZcAwICWNJlKjOJvnVfVps3zaZn+qUGtWLCsaZSAoA21OjkGJrEllbfEn0t0WrIqzJhdXIDMkf6pQC0SuVqMMNJEBKWkozsVloC3+RA+1BaviXNzrUbJc8qcKNYkp3acMKAOGASlpNJEaxdk8r6pPm+XTNvtThVqzYlnRKANBGWhzcgxKZE0qa4s/ke62YFWcNbm4Apkh+XM6oTbswpb5bdBVuNE5hlHC0NdwtHnJXCyXO334kDg2wy8f+rB3EX+b6xJsdV/PsKEpqx4N4IfOXVij31bdOIDB2K/zAwy7DwyHy5tdGPqHJ/o+htHgR3jW2Yb9ftJj1aubhX3Vrcg9w8XoAzgaVonCkDzlWugdfAv9zi1YXroNh4N39tgI+p3rURxQvJhPxDSCwcFt4dh12OuPYDw4gJtL0vXpNZvxVUoaGUWr7z7rwc6K9Dt6q3Dz4ATochgPj+HJ9kaEceUu7L0ceLmmetP+GeFwnsGg9xyede7C5e0enPkNed/Hp124v8J9bQuMh/DPryk/bMBO9yQI5rniHA+h/9023DCxegW2Oi9gMCKvEhHRdXb0tANbF3ehd+Yfp3LVP8NhzWg7Fb++H89g8HIftijGax+7Es7qGDJjWqq+wr5g/hwNoNf9K+xtbsBO741sAY/dlbuwfzx0+Sg+YQxnvd24D8c4F/vx+IwyWxLOQEINk+0t2Ou/ZXaoUGNkeJuCgy92oJ/SETMQQk7IRh25Z1jFrzOwr6IFhcUnFWpBeSq00hWIhNUFWEt18jxmrsDWwc+JjpvOW0ZRtvsShq6/ewO97aue8HPNFW5ISaPwpFIFOB5frLEOb3QMexv3bKIcw+jkCWytXIH73d+ExFmqYbFQGJzvYHBwDz7Z/Ngk77QPvabHv8HRvSuCb97C/3Sfwj+H7wHgPQyP/wxbK1ezOxWv2ryv88OJNxx3YOvrn6JYHP0Mh5tXYO1eF05dbIK5kfjozl34BMXMyiIJtfdw2n2Y00nb4yv34PAkkuvj4Ut4tH4tiB+5j8P4lNdI2xNgyIxpqnPyzyA4xydweOs2bN3B6y7rmsLY/djl0chvH3v6BgAcVspfyRvMSZFKOAMKNV9NqlDLdhQTOLkKnJULNaIWVIDMwL5s0iY7slBCjUSVlECYsEl1aOWOFQoHgWEpaQjFJtj1BnqdfegZMcJOx1GKWzS6jMLntidaqfOocaeOncHGqmc3w2g2sTN4CJ9v34G1xOgpwPjXn+DHUxRp9BfFxST+oxroM6g/c3CaGwcvTqORFim2Iz8vlFAzNxBfZI8AitxI8UyemfwzqE+5GZUxZMc0r3bS7ZA4oxtbKRajm4ebidi1+TXRV49h1N+Hm6kb6knRxedJOMMKtSV+pysItYxO80O/A5dx2JDECBcTvT6bIqQpAD4cuwo3tr+HPiV8d+4l2Hr6ik0fSEPvOE1xADvrq3bqaAN2DnpseD4WIpe/egovdu30S8JhMcHRFtb537C3iYodlTbadwC9AU2CxLxEx7FM1jRt3D5yc8qngNa34UnfG47FIV2cQqCh9iUPj+Of7gAuwLI4kkeY3sOw32VYLsDa5j784LBUtA+KuCnbri1XhBeLOcx86hOnW14kcC3jtES3H939u3MknopiBgDQrgOa8pFigHB6n24qhdtKZUjESaNt8TFx6J3wJJIP1Zv/KSWN/DNKHh3/Gwa/0jVB52BHdiee9jQdxaX4uy2Wl2SppqqfQXGKHRy3CJP8N7DVeQWnZuqEjSDyYrRt6hPu6Ol4hc/54LTCy8+TmbwsmlCjGyPM7X+Bo540FW+vyfV96LvpXtx3a4FG1KpgqBjTFWKWioaM3ewckhG7Jjfz65RyLvaxXda/k7WTf0o4Awm1K264f3nlIRyZu8FYkLg1atRhLCU7omyhxjpKI3rw+4a9C00ec3ebTqgljyN4/F/bfAIn5sIRhq5TZZgQce1LHSU55QxODu4lh8PdeTQ1HPNCNpUSaut3YMsJSsLGAsdOLcR1UpkLsEzJwvHPjmUKteiOIVpfwsojHudjxk+RfVCGG+SxTLsohqKplFy8WJ3DHMdcdGfvYTJ+sjca7hxWxvBUJmbwrhLXmLFzaZv8QOGS+KTk749M20K2k0Phz9dvmaMu5oVjWMCdK99BJszwviCOuf2hnbc+tfkDAExyFDBl7Z/C0KA4MwWJNRBHYza/gf7og13jwq7jBAa8oejB4fYDeNQ7DTLVOx+cthPzhRpk7V8woeauJ7rGUbB12Q0+OjHOY1Gf8w6GvQ7s0FRwws/TfQnq04QpFTCUjulEA5W+hMSZKdSyrl0v50Tnk//xkwaRKkESC0s4Awm167DXewl7VkhE6xBiQTKNUHPCCgOBhIqb92edIgkO12mhQPnSTq28h2HvS7uo1XZWhngUHfEagrjzpw6NCRG3Bu8DjEa0yDvJc+w8toZofAo9GolzHTWrl0YRk1XZb6wcC4RozhxHAWkkziY6I6JiPHE5tpjc8VOwRs0lI7bmiWGJhHFZ++xwshVDbn0Vq8+JyVLtVsDrRBcJNTqXccLWGrhYlXgqEzPuPIohFJUUu4LocH4nu+QbgTi2eHLwt7M6fLr7y2vfGZLYkJJGokDAL4jxIz6VQLHgd/jGD4zfADYExZmV7I2dmLM+tetdSJxLfiOfoY8lITAZ6PngpFj2cUWY3E21g2DLTzDi66oQNoJiFeoHXHD+/C92RoblE1eW1hdGPkzdYLly023MFmcZDGVjuj44o3wq5BBPkDmLM/aPh334m5s9ocEYd9ZEG5I/wwm1/pmZs41GYNDgf6Wf+kx1mhGO7BE1TmT85Bu/0N25KaFGIoa4ihMfdsbvaLqVRju8z5QQ8TsLqtZ9UnISRkSog18iccQETlmhlmifsFiM1KGlRluoI2BTnE5IkC0OQHIjw1fJQgxHnn1QgZsy7VbBm1kfTuv+A466T+GQnijEEVcSCgJPLta8WMELC//NuUz0LS/hdPtf4ajbhb/509RJIlHNuSc7nVh0ZRh/qc6M+SB1jCrIq5vKyJ9S0pBLTrsXMT7wpoUofvmNDz1J6IuA6doPijNTqOEIxbfwyD0IQfhysLCnz/yF+JMgng9OGg1NzmAM+9/Dznp6KhsoP2TG7yRI5/h6DrrhTNmPI6LPYa/z2Iq5jWAjo5yRoD7lFZvtIgwTxHSqjXI7QuIMJdTIchoUcf0HHZjgU8IZUKjhqx7YCBebCnMdj9hpso6GRIvQSWZ1ZK7zTAk1X4jwzuoVvKbXXmR0utF6udi2Ygfw+r3XkTg8JB7jet26PNGhWeWoLVufq9/HDOD4oenmnLLchNR5/KDbLmlfnghx9kRYSrXrzimBNxVz9OSgPxoVfXexmmqDYc2NGYDE6yR42fVdOHLr+xyJdkMYgXZFSJgzIVnqGBWieLkADh8dKviUkkbBKZMdRnFzS1qczdejovD9PhLWiRuDyZrkZwXFmSXURsewv/ucPfVYQqgZI61QTwkBjqDc9lxwGlOS60DXNjvwzIw8SKI0HD7OQlCsvGJpOzXKG+WZ+3+wT7mSmHMzM1Ilk+2bHc4SGCaO6epYQ+LMFGpZ127GiFqMwl7LM7pGAwu1+E4KSaV/1zmkOk2EyTrAoELNn+aJO7vLnWP4P3r/CQm8mHG2FdvmMLCjyU026uF3IiFG1Igb0yh1vPMYUZMSKyGP+UkKTs8+umPGmCjixsVITrv2Ykqv16KOj40guvrs1Cc71ywEfo4PEJC9TMikhJpQN9GQ+YkPHjyHI/POHvtwiY/fnSvYQMdc/PARZnvQHaObADqJf+bUzYsJ2yGTo1C925Wa9nRHvA3jv5q/4kBM9ix+WG6kHGk+M2NDehLN46Xk16D+FHFmGRLlR/mGtwFCzXBxJ373ofnujx7agYwcP2exl7c/qE95Q4UYpotp3lSZ7ZA4M4Wa7av8OI3K5/RJuCoR31kZwLcSzvBCDdILrp3IcZ1K/HQoDRmica6zT3WS6Ea5s3EjMCS43Lm4Ro1GMHLWqOH0lH0nVWwLdYixEHEYciIqciYK1LhOcHdSbFG/JE7FeuP2HTemHHFBnTMTiWzNXYyHrZ9w/KRHoxIm2CRs1se493KxBwJMQJa1b8o1avxBBNNuBby+UCuIQedniSd2blbMxA8q8GkOdk1kXsgxJj9JuBgX7tbimMtLInST4t+8JDwufpGShlhwqp2I3Z/2FCo019It4eXaQtmKu4LitNeO78e0SdTR5fkOz4rKXfbeQZaur3jP+eC0+det0fXttLEvxLdfssr3oFiLGj7rwaNd9oJjkyv86836OzMHFDUiH58ZzokwlI1pGUve3pA4o7xJ/XyyVXMsEYtl/IZlHsOjrBfoJpvI/SbhnIFQw7xCL3L0ppO8/WgQCoHfr1+LnpSkUSOpk5xEqAl3rvE6DyY6vHLuAQYmqFwHnksxm/r16ky+EDhL4PiVZ5XzhRpfsB6PZEb8coGIvone8eSOkcD1m2ZPLbmyDhOJkAr28WlxVw/Zyhdhxk8aZbdbAa8v1Api0HWuIk9lYiYvBuIblBTdtjM2v1TBEzl/ujWRPNCX7EEV9yRuuubY53JiEs5wu9AHM/9DrsVpT2qZXutyPX6BKh0K9BkU51RCzYp69vodc8O18cC9OHUayPPFidOf+Csod+Hy5p/tC3wl6xdLqJkF5GYkPsIyHv4E+9sd752ANg+wG+foYbXrNX1Zs+SXSTAsvlCLlnDlvfA2Wt8crzvGBy6+hZ0/8ReNS3yW2yddo7MRaqYPwZ9G8YQa7ufvArPv+fql9zj7PWruZ45InLDpKZw4pYcCSHA4kRe9Ry3/J0z8d2L571qLhUg5oYaOoE4l6z1qWCauNzlS5jsyqxxxQSNq9rwy7xVzbzq3IinzLhfrlN6j1oEjtzC+on2luCnTbgW8vlCTYvC7Yxie2p9Dc2KIP+3ExW5RzKBtfhk8fxsOxfctWSzmNPuTSsYGenUDiVn6xJHQs/RPlxjxmzFKSiOBDhtrs2BTShoFp1Q+PB48gfupn6DDauKRwOS7CCs3UXhCGJzUSZGv8DNvtIzK8zL+GkrMSd34PZGFSPILzAcn4SoR9xSb7ubNH4XKx5N3NAzWdAvxTLdgK6IAAAJBSURBVAW+NeAu7D390Xs1hz2HPQiCtpiytf75szRW82Sr+xmwMhjI9zymhXon2BXGn5RT2DXKb4zJLv4TbuymKTrMZ+jwgZkOPCvK7VRviU8J53RCrUSjWkQZUAbKMkBJpPrIV3YLlDilBxGyz6IjUtKgY036VJxN8maERX3aLJ+22Z8q1JoVy4pmoRmIp33dFOzUeEj8TXaH2+bkODX1NaygLf5E6tuCVXHW8EKbwiTJnyrUpiBUT1UGwjNghdUE05SSLfRww6TCT0oaUjuLvk9xLroH0/arT9OcLPKeNvtThdoiR67argzMmIE2J8cZU3su1bfFn0huW7AqznO5lGbWqORPFWozo1srVgYWnwEpaSw+qjQCxZnmZNH3qE8X3YNJ+9vsTxVqyVjQb8qAMsAYaHNyZDQ0ZrMt/kSHtQWr4mzM5WmASP5UodYsHysaZSAoA1LSCNpATSpTnDVxREAz1KcByaxBVW32pwq1GgSgmqAM1JWBNifHuvpkGrva4k/kqC1YFec0V0T9zpX8qUKtfn5Si5SB2jAgJY3aGBfQEMUZkMyaVKU+rYkjApnRZn+qUAsURFqNMtBEBtqcHNWfi82Axu5i+8+3vs3+TAk1JEP/lQONAY0BjQGNAY0BjQGNgfOJAS5UE0KNH9BtZUAZUAaUAWVAGVAGlIHzZUCF2vnyr60rA8qAMqAMKAPKgDKQyYAKtUxq9IAyoAwoA8qAMqAMKAPny4AKtfPlX1tXBpQBZUAZUAaUAWUgk4H/B65ag3kSr4ZQAAAAAElFTkSuQmCC"></p>
<p>The relationship between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> can be modelled by the regression line with equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>a</mi><mi>T</mi><mo>+</mo><mi>b</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the regression equation, estimate the number of hot chocolates that Lucy will sell on a day when the maximum temperature is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>°</mo><mtext>C</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The aircraft for a particular flight has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math> seats. The airline’s records show that historically for this flight only <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>%</mo></math> of the people who purchase a ticket arrive to board the flight. They assume this trend will continue and decide to sell extra tickets and hope that no more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math> passengers will arrive.</p>
<p>The number of passengers that arrive to board this flight is assumed to follow a binomial distribution with a probability of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>9</mn></math>.</p>
</div>
<div class="specification">
<p>Each passenger pays <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>150</mn></math> for a ticket. If too many passengers arrive, then the airline will give <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>300</mn></math> in compensation to each passenger that cannot board.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The airline sells <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> tickets for this flight. Find the probability that more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math> passengers arrive to board the flight.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the expected number of passengers who will arrive to board the flight if <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math> tickets are sold.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum number of tickets that could be sold if the expected number of passengers who arrive to board the flight must be less than or equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find, to the nearest integer, the expected increase or decrease in the money made by the airline if they decide to sell <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> tickets rather than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math>.</p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The mass <em>M</em> of apples in grams is normally distributed with mean <em>μ</em>. The following table shows probabilities for values of <em>M</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The apples are packed in bags of ten.</p>
<p>Any apples with a mass less than 95 g are classified as small.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <em>μ</em> = 106.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>P</em>(M < 95) .</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a bag of apples selected at random contains at most one small apple.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected number of bags in this crate that contain at most one small apple.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least 48 bags in this crate contain at most one small apple.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^2}{{\text{e}}^{3x}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mn>3</mn>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right)"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> has a horizontal tangent line at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0"> <mi>x</mi> <mo>=</mo> <mn>0</mn> </math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W">
<mi>W</mi>
</math></span>, of newborn babies in Australia are normally distributed with a mean 3.41 kg and standard deviation 0.57 kg. A newborn baby has a low birth weight if it weighs less than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> kg.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that 5.3% of newborn babies have a low birth weight, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A newborn baby has a low birth weight.</p>
<p>Find the probability that the baby weighs at least 2.15 kg.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A discrete random variable <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> has the following probability distribution.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAc8AAABNCAYAAADAd+9MAAAR8klEQVR4Ae2dz2scyRXH9z+RYU4jENj4opNPe9DqIIzJYcEXgyywIQ4+LDgwQkuWPYQERngwGAyJhIVhWUhGeAm52Ay++CAzLAEfxMAGjBmG4IMRczDCNC9UT9eo+nVP15S6qqZK/hqMe7pfvVf9ea/r1a9uf0X4AwIgAAIgAAIgYETgKyNpCIMACIAACIAACBCSJ4IABEAABEAABAwJIHkaAoM4CIAACIAACCB5IgZAAARAAARAwJBALnk2li4R/oIBYgAxgBhADCAGijGg5tdc8hQXBDD88UMArP1wFlbAGqz9EfBnCXG9ONZInv7YFywh8AtInJ0Aa2doC4rBuoDE2Qmwdoa2oJizRvIsIPJ3gjvDn+UvzxJY+/M5WIO1PwL+LPG4RvL0x75giTujIIAT1giAtTWUWkVgrUVkTQCsraHUKuKskTy1yNwJcGe4swTNYO0vBsAarP0R8GeJxzWSpz/2BUvcGQUBnLBGAKytodQqAmstImsCYG0NpVYRZ43kqUXmToA7w50laAZrfzEA1mDtj4A/SzyukTz9sS9Y4s4oCOCENQJgbQ2lVhFYaxFZEwBrayi1ijhrJE8tMncC3BnuLEEzWPuLAbAGa38E/FnicY3k6Y99wRJ3RkEAJ6wRAGtrKLWKwFqLyJoAWFtDqVXEWSN5apG5E+DOcGcJmsHaXwyANVj7I+DPEo9rJE9/7AuWuDMKAiGdSEbUf9qidfH94+Zt6hyNKAmpfpq6RMV6PKBe9yfa3dyg7d4HzZ2Fdzka1uMBvWzfppX0m97LtN56Rv3RaXhAK2oUDWs6pdHRY9pqiu/FCtZdGoxjakGKn/hE8qwITNeX4gn8j9Rvf0vrOy9olBAloxf0/dq3tNv/6BqRNf3RsE6Oaf/GTdq6tUqNpWtIntYigClK3tEvD5/Qy8FJeiEZvabO5io11jrUj6hRjyOuExr/+pwOsg63ZL3S6tGEPvNNoD85ayTPBTqKO2OBVak0nQz26Hpzh3onsqeY0Elvh1Y29mggT1VqWPzFWFhLUilzJE+Jw/q/yW+v6dUwP8qMkXkUcZ38l169eq/MVGXtR65Nse5i6wo5ayRP64jnV8idMX9Jn5KfaLB3kxo8UZ70aLt5k/YHn3xW5ty24mB9dnsxNuSy9rGxlvWmNKbjGu3HyVq0KbdovX1E4yn88A8460iT53s63Lwy+b9Hm/fpUPQgkxG9eThZv7ja7tPn8H0Rx3+TJaYRN5apMMWSNjTLdH3vWOlRhgudB364NZ3UDMlzAR4SMX05a08WYP48JmOLaxLr+Xs7tJUtAZ3nnhdVhrOONHlO8CXDLt1tXqKV1s/08uGPtH8c0wx6cQF6UUFRaXdWkpx1vlLZ4i7ywF9cTeazjOQ5Hyd7UmIq8Qe6HvloyB4P25qyqdp0c9Ylaqzt0GG23mzbkit9vA2JOnkSfaBe6xo1llbpbvddFCMg1bHcGeq1YI5nJclZ54OpeL4iUbBWqozkqcDwcTg+ot3NR1FtFhJYYotrErtu+89oe22ZGnLW0Id/LdjgrCNPnrI3E8/am+pD7gz1WjDHmLZdiCuQPH1i/0j9CGeuBKEo2pASV8YY35z1BUme8ay9qXHEnaFeC+d4smGIr3lOgj+eTkscrM+8HmPjImsfF+tTGj5/QgeRLfnEyVrWmojSTvnXUb2KxeM66uQp3jf8odWiP66VbGhR/BTqIXdGqPVMG/LctvJsxM934IZ6AxH20JE8fQTTKY16T6jTGypLPid0/PQZvZq+luWjHue3EUsbUrhDsewT+easeJNn8o4Of9+iw+HJ5FUK0bgP/0MHD/9NQ7x7WIjVeifwkYR6/MxLI3maMzMrcUKD7s7ki1lyE4v8F51CM5Qa6cnGzg3afnqUfmSFkiH1dm7S1t5bvKqiYWf3crYGd7ZbK6Fxv0PrEX7yKapeo/IqUGOtRQd9fJ7PbmBLbXITnPiMWfY3osZc3EX4cX1Kw+797LN8CueUd1xLQOGzJqLxW9oXX2/K4nlls02HkbUfZXEd78hTtjUR/xtF4EfMV606WKs03B6DtVu+qnawVmm4PeaskTzd8q7Uzp1RKYyLtQiAdS18RoXB2ghXLWGwroXPqDBnjeRphM+uMHeGXe3QphIAa5WG22OwdstX1Q7WKg23x5w1kqdb3pXauTMqhXGxFgGwroXPqDBYG+GqJQzWtfAZFeaskTyN8NkV5s6wqx3aVAJgrdJwewzWbvmq2sFapeH2mLNG8nTLu1I7d0alMC7WIgDWtfAZFQZrI1y1hMG6Fj6jwpw1kqcRPrvC3Bl2tUObSgCsVRpuj8HaLV9VO1irNNwec9ZInm55V2rnzqgUxsVaBMC6Fj6jwmBthKuWMFjXwmdUmLNG8jTCZ1eYO8OudmhTCYC1SsPtMVi75atqB2uVhttjzhrJ0y3vSu3cGZXCuFiLAFjXwmdUGKyNcNUSButa+IwKc9a55Cku4i8YIAYQA4gBxABioBgDarbNJU9xQQDDHz8EwNoPZ2EFrMHaHwF/lhDXi2ON5OmPfcESAr+AxNkJsHaGtqAYrAtInJ0Aa2doC4o5ayTPAiJ/J7gz/Fn+8iyBtT+fgzVY+yPgzxKPayRPf+wLlrgzCgI4YY0AWFtDqVUE1lpE1gTA2hpKrSLOGslTi8ydAHeGO0vQDNb+YgCswdofAX+WeFwjefpjX7DEnVEQwAlrBMDaGkqtIrDWIrImANbWUGoVcdZInlpk7gS4M9xZgmaw9hcDYA3W/gj4s8TjGsnTH/uCJe6MggBOWCNwIVknI3rz8DatiPezm3do//jEGq86ii4k6zpAHJYF6znhWnhWOGskzznZuxDjznBhAzonBC4i62TwE32/95bG9JH67RvU2NijQbJ4j19E1ounWl4DsC7nws/aeFY4ayRPTtnjb+4Mj6a/OFMXnXUy2KPrzR3qnSw+e1501iE9PGBt7o3zPiucNZKnOXtrJbgzrCmGogKBi85aNAi/u9Ol4eJzJ77mVIg+dycuely7IHfeZ4Wztpc8k2Pa31gu/Tbuymab/tkb0HgmiYTGg+e0235Og3H29I+6tJX71u4V2uq+J6LPNOrey9vZ7NJopm5bF07o+GmHOi+q7sPMFneGWWlImxAIknXyjg7vXKPre8dUL+eJadvvaLf/0QSJM9kgWTu728UqPh/rUxr1n9H2mmivV2nr4Wsa6QLwpEfbzeK3XhtLyxbidw6GATwrnLW95JndfzokXrpJ+4NPkzPjYzpsbUyclK7PcFCnNOr9mbbaR8XkOn5L+5ur1FD1ieLjI9pdu0LrrT3qDXxuksjquvNCH2z8Nkt+c2eUiOCUJQLhsT6lYfc+rdRufERMPqFOb1gzAVsCje8I2wM5hybzuE5o3O/Q+tqP1BudEiVD6u3coPWy9ndqP6GT3s5kY1puQCOSqdLWT+VtH4TxrHDW7pOn4ChHpYU1GenIDvXliDPHXTpN6d2kzr5JW6WJOFfY0Q/Ry/9WE2zzmebOmK8UpM5DICzWIu4f0daDB7TVVGLb+MYSGh//TJ3n79LEmYx+pVdeO5PlFQ6LdXkdL8pZY9ZpW/w1bfc+nCFIR5VVSfAD9dqdSbI9K0Ukyt1wvUktnGeFs/aTPOkD9VrXir2UbARZOW0lpwvE1OzCE+ckcgqjazWgDI65MwyKQtSQQFCsRdxvPqL+8AVtnzt5ntLo6DFt5abSqhpAQ2A1xINiXeM+Yihqyrq87RLt89ezp1+T/9HgNz7D94kGe7dml7EFL6BnhbP2kzxLR55yVKl74LPE27xF2w9cjjjVtdRVutsVvXmlgbrcpv7nLCI+92n38iVaafWIh5RJzHBnmJT1L5tfJ7n7j3/R3zeWazPwdR/hsFbWJ9OO4YyRZxZjot6Ny2168/6IDtLlD/FO523qHI2CmablPgyHNa/Z2e/P/TZdzaYgr7Zf0/vpGuAlWtl8TG/ElGYEf8xYi4R3kxqFGcCsjTV51Um06Te+o8OhS07zPSu+fMlZO0qeq2fTqtOXU5fZVKdMirrt9ZnDl3j5sshWE2DZ4nZ2Tk2EXE26ML1KjWaLDl88pu3S6eH3dLh5pSQIubLq39wZ1dKLvHpCx3t3aEVsLlDfK1ySm7gWWbf5bIfBOpuCkutLVckzva0sztZu0d3Wk0mDns7WLAfzTmcZ/TBYl9WMnUs3JS7T+uY92k43zWTLSLXXoZkdhz/NWM9KkrPOz654umO15uBhtnZxxfBZ8eBLztpR8mSJq3mbdrv9/CYb2bOuSmQpQ7GgLTYcXaKr7T7JwV81+DpX5Yj4Eq3M3Po/pn77m+I0tKFZ7gzD4p7EzxqUs00FspOimzXwVMU5zATBenxEnZ3nZ6+T6JKnXLJYU/cEZA2d7rmZg4krkSBYa29OPuesU54x99PWaCupFTBjPStJzjo/y7wY0NzLr5vOEj3veaNnxY8vOWtHyXOORnWe5CnXOP/2jHbFazAm0wrndZoop2vUSCbPb2i3P/sFHF0VuDN08gu5Lkc6kTXgnNXiWX+k/sO/5qe5NHE2mY66lm+k5BKIr2eBg5zj9+JZz1FJ+QyzKczJmuCMqfR51HqWMWNtado2nbL9QfNBjmzWpLA7Nz+wKu+kmD4rWXvs2JecdbjJUybOdJow6xlpt0XLEVHeQeKmc391vXbZ45/ZQH05yXPSgLPGJONTd83XZzvDA9+n7dSWjCkei9PfvMNZ1tDJWQC5Ju/9LuYyuHDW89Qy64TkY1issd2gRvN+vpMzj74FyZiyTjsHLMlM3oa4MvfmH+dTtqbPiidfctZhJs9c4hRRKYflHtbYhO0/tWj7wUbFmqZMnrzBM3uCuDPMSvuQlp0RdYSdNTARrXcKUkGyThsJ1jGZunXSc8817tl7z7OXE6aFF3oQJGtOJF0jU0f14rWfA9pqht0x4bdhzDpNNKavqqhWPUzZqubkcdWz4smXnLXl5Cl7xjfm+NpJNprM9YLkjs5r2W5XSY6IUkBiJ9wBHZe+E6rInvtQvIzboj9039Fn8a3QJfFw/UbHT5/QL7ldZWV1NzfKnWGuwXUJ2WnJGhSx+etRm3b/Iv4nj3odB9c15/qDZF3VIGS9b5kok9Fr6ogPhsiX2/kNBvQ7SNY5Piyup7vql2nd0gdQcuYc/jBnnbXRMo7SgQr7SEL2NZ+zPQ7KDcw1ZavI2zqc+az48yVnbS95ZkNnYWD6d+a0pyAqbzprhOUa6LS8HO1IOUWv9d1w2RTZ0gZtd48nXzqarvXt0CF/8bx0msA8SrgzzDV4KDH9ypPouHTo5WA42SxV6VsP9TI0ESTrmQ0Ckbr9fvI8bdD2Xu/s85WG9+9TPEjWOQBy5khpU9ZatF/5CdGcgmB+nI+18gqeaPOeHuU3c1Ykz2RwQHflbnGfFGY+K/58yVnbS57nAZkmofnn2s9jwkWZyaaC+iMv7gwXdbWu01LHwXq9NArjYl223qm5wYAuB8860hguc3HwrMsqbfOcR19y1otNnum7POI7i+pWfJtkXegSa35f8Of5CusLLhjb18kD374FmxonywK59U6b6h3rCp51OopR1zsdA3GoPnjWDu89Ve3Rl5z1gpOnuH27H1t36yu7deXOcFt3C9rT9RHxzu09Ohy5f+PWQo2nKmJinQy7dLfpYXPclI7dg7BZy4+MxxfDZV4Km3VZjW2e8+tLzjqA5ClglvyXZDYZW9F1QoPuI9qVa6IWdHJnWFDpSEXZunNcjU8crIvrNzGOPoNlXdhXEf/oM1jWjlqiqdoF+JKzDiR5TpF8UQfcGV/UzXu+WbD2BxyswdofAX+WeFwjefpjX7DEnVEQwAlrBMDaGkqtIrDWIrImANbWUGoVcdZInlpk7gS4M9xZgmaw9hcDYA3W/gj4s8TjGsnTH/uCJe6MggBOWCMA1tZQahWBtRaRNQGwtoZSq4izRvLUInMnwJ3hzhI0g7W/GABrsPZHwJ8lHtdInv7YFyxxZxQEcMIaAbC2hlKrCKy1iKwJgLU1lFpFnDWSpxaZOwHuDHeWoBms/cUAWIO1PwL+LPG4ziVPcRF/wQAxgBhADCAGEAPFGFBTdS55qhdwDAIgAAIgAAIgUE4AybOcC86CAAiAAAiAwEwC/wegegZWEGZiNQAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> which gives the largest value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the largest value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = a\sin bx + c">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mi>sin</mi>
<mo><!-- --></mo>
<mi>b</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 12">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>12</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.53.31.png" alt="N16/5/MATME/SP2/ENG/TZ0/10"></p>
<p style="text-align: center;">The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> has a minimum point at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(3,{\text{ }}5)">
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5</mn>
<mo stretchy="false">)</mo>
</math></span> and a maximum point at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(9,{\text{ }}17)">
<mo stretchy="false">(</mo>
<mn>9</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>17</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> is obtained from the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> by a translation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} k \\ 0 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mi>k</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>. The maximum point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> has coordinates <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(11.5,{\text{ }}17)">
<mo stretchy="false">(</mo>
<mn>11.5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>17</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> changes from concave-up to concave-down when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = w">
<mi>x</mi>
<mo>=</mo>
<mi>w</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>.</p>
<p>(ii) Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = \frac{\pi }{6}">
<mi>b</mi>
<mo>=</mo>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
</math></span>.</p>
<p>(iii) Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<p>(ii) Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x)">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
<p>(ii) Hence or otherwise, find the maximum positive rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A jar contains 5 red discs, 10 blue discs and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> green discs. A disc is selected at random and replaced. This process is performed four times.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that the first disc selected is red.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> be the number of red discs selected. Find the smallest value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> for which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{Var}}(X{\text{ }}) < 0.6">
<mrow>
<mtext>Var</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">)</mo>
<mo><</mo>
<mn>0.6</mn>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>