File "SL-paper2.html"
Path: /IB QUESTIONBANKS/4 Fourth Edition - PAPER/HTML/Mathematical Studies/Topic 2/SL-paper2html
File size: 589.31 KB
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-746ec5d03ead8d9e8b3bb7d32173f2b4e2e22a05f0c5278e086ab55b3c9c238e.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-3c91afd8a2942c18d21ed2700e1bdec14ada97f1d3788ae229315e1276d81453.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>
<li class="active dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Questionbanks
<b class="caret"></b>
</a><ul class="dropdown-menu">
<li>
<a href="../../geography.html" target="_blank">DP Geography</a>
</li>
<li>
<a href="../../physics.html" target="_blank">DP Physics</a>
</li>
<li>
<a href="../../chemistry.html" target="_blank">DP Chemistry</a>
</li>
<li>
<a href="../../biology.html" target="_blank">DP Biology</a>
</li>
<li>
<a href="../../furtherMath.html" target="_blank">DP Further Mathematics HL</a>
</li>
<li>
<a href="../../mathHL.html" target="_blank">DP Mathematics HL</a>
</li>
<li>
<a href="../../mathSL.html" target="_blank">DP Mathematics SL</a>
</li>
<li>
<a href="../../mathStudies.html" target="_blank">DP Mathematical Studies</a>
</li>
</ul></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>
<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>
</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="images/logo.jpg" alt="Ib qb 46 logo">
</div>
</div>
</div><h2>SL Paper 2</h2><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">As part of his IB Biology field work, Barry was asked to measure the circumference of trees, in centimetres, that were growing at different distances, in metres, from a river bank. His results are summarized in the following table.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/Schermafbeelding_2014-09-20_om_14.50.23.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether <em>distance from the river bank </em>is a continuous <strong>or </strong>discrete variable.</span></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><span><strong>On graph paper, </strong>draw a scatter diagram to show Barry’s results. Use a scale of 1 cm to represent 5 m on the <em>x</em>-axis and 1 cm to represent 10 cm on the <em>y</em>-axis.</span></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><span>Write down</span></p>
<p><span>(i) the mean distance, \(\bar x\), of the trees from the river bank;</span></p>
<p><span>(ii) the mean circumference, \(\bar y\), of the trees.</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><span>Plot and label the point \({\text{M}}(\bar x,{\text{ }}\bar y)\) on your graph.</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><span>Write down</span></p>
<p><span>(i) the Pearson’s product–moment correlation coefficient, \(r\), for Barry’s results;</span></p>
<p><span>(ii) the equation of the regression line \(y\) on \(x\), for Barry’s results.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw the regression line \(y\) on \(x\) on your graph.</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><span><strong>Use the equation of the regression line</strong> \(y\) on \(x\) to estimate the circumference of a tree that is 40 m from the river bank.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</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 class="p1">In the month before their IB Diploma examinations, eight male students recorded the number of hours they spent on social media.</p>
<p class="p2">For each student, the number of hours spent on social media <span class="s1">(\(x\)) </span>and the number of IB Diploma points obtained <span class="s1">(\(y\)) </span>are shown in the following table.</p>
<p class="p2" 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 class="p1">Use your graphic display calculator to find</p>
</div>
<div class="specification">
<p class="p1">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 <span class="s1">3 </span>and <span class="s1">30 </span>hours on social media.</p>
<p class="p1">The equation of the regression line <span class="s1"><em>y </em></span>on <span class="s1"><em>x </em></span>for these ten female students is</p>
<p class="p1">\[y = - \frac{2}{3}x + \frac{{125}}{3}.\]</p>
<p class="p1">An eleventh girl spent <span class="s1">34 </span>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 class="p1"><span class="s1">On graph paper, draw a scatter diagram for these data. Use a scale of </span><span class="s2">2 cm </span>to represent <span class="s2">5 </span>hours on the \(x\)-axis and <span class="s2">2 cm </span>to represent <span class="s2">10 </span>points on the \(y\)-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 class="p1"><span class="s1">(i) <span class="Apple-converted-space"> \({\bar x}\)</span>, </span>the mean number of hours spent on social media;</p>
<p class="p2">(ii) <span class="Apple-converted-space"> \({\bar y}\)</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 class="p1"><span class="s1">Plot the point \((\bar x,{\text{ }}\bar y)\) </span>on your scatter diagram and label this point <span class="s2">M</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 class="p1"><span class="s1">Write down the value of \(r\), </span>the Pearson’s product–moment correlation coefficient, for these data.</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 class="p1">Write down the equation of the regression line \(y\) <span class="s1">on \(x\) for these eight male students.</span></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 class="p1">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 class="p1">Use the given equation of the regression line to estimate the number of IB Diploma <span class="s1">points that this girl obtained.</span></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 class="p1">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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A survey was conducted to determine the length of time, \(t\), in minutes, people took to drink their coffee in a café. The information is shown in the following grouped frequency table.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/Schermafbeelding_2014-09-02_om_11.43.00.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the total number of people who were surveyed.</span></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><span>Write down the mid-interval value for the \(10 < t \leqslant 15\) group.</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><span>Find an estimate of the mean time people took to drink their coffee.</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><span>The information above has been rewritten as a cumulative frequency table.</span></p>
<p><span><img src="images/Schermafbeelding_2014-09-02_om_11.46.53.png" alt><br></span></p>
<p><span>Write down the value of \(a\) and the value of \(b\).</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><span>This information is shown in the following cumulative frequency graph.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.50.20.png" alt><br></span></p>
<p><span>For the people who were surveyed, use the graph to estimate</span></p>
<p><span>(i) the time taken for the first \(40\) people to drink their coffee;</span></p>
<p><span>(ii) the number of people who take less than \(8\) minutes to drink their coffee;</span></p>
<p><span>(iii) the number of people who take more than \(23\) minutes to drink their coffee.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</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, \(N\), 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 \({\chi ^2}\) 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 \(N\) 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 \(N\), 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 \(N\), 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 \(N\);</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 \(N\).</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 \(p\)-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 \({\chi ^2}\) 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 class="p1">The cumulative frequency graph shows the speed, \(s\)<span class="s1">, in \({\text{km}}\,{{\text{h}}^{ - 1}}\), of \(120\) </span>vehicles passing a hospital gate.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-21_om_07.03.09.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Estimate the minimum possible speed of one of these vehicles passing the hospital gate.</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 class="p1">Find the median speed of the vehicles.</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 class="p1">Write down the <span class="s1">\({75^{{\text{th}}}}\) </span>percentile.</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 class="p1">Calculate the interquartile range.</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 class="p1">The speed limit past the hospital gate is \(50{\text{ km}}\,{{\text{h}}^{ - 1}}\).</p>
<p class="p1">Find the number of these vehicles that exceed the speed limit.</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 class="p1">The table shows the speeds of these vehicles travelling past the hospital gate.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-21_om_07.07.41.png" alt></p>
<p class="p1">Find the value of \(p\) and of \(q\).</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 class="p1">The table shows the speeds of these vehicles travelling past the hospital gate.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-21_om_07.07.41.png" alt></p>
<p class="p1">(i) Write down the modal class.</p>
<p class="p1">(ii) Write down the mid-interval value for this class.</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 class="p1">The table shows the speeds of these vehicles travelling past the hospital gate.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-21_om_07.07.41.png" alt></p>
<p class="p1">Use your graphic display calculator to calculate an estimate of</p>
<p class="p1">(i) the mean speed of these vehicles;</p>
<p class="p1">(ii) the standard deviation.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">It is proposed that the speed limit past the hospital gate is reduced to \(40{\text{ km}}\,{{\text{h}}^{ - 1}}\) from the current \(50{\text{ km}}\,{{\text{h}}^{ - 1}}\)<span class="s1">.</span></p>
<p class="p2">Find the percentage of these vehicles passing the hospital gate that <strong>do not </strong>exceed the current speed limit but <strong>would </strong>exceed the new speed limit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">i.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The table below shows the scores for 12 golfers for their first two rounds in a local golf tournament.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Write down the mean score in Round 1.</span></p>
<p><span>(ii) Write down the standard deviation in Round 1.</span></p>
<p><span>(iii) Find the number of these golfers that had a score of more than one standard deviation above the mean in Round 1.</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><span>Write down the correlation coefficient, <em>r</em>.</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><span><span>Write down the equation of the regression line of</span><span> <em>y</em> on <em>x</em>.</span></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><span>Another golfer scored 70 in Round 1.</span></p>
<p><span>Calculate an estimate of his score in Round 2.</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><span>Another golfer scored 89 in Round 1.</span></p>
<p><span>Determine whether you can use the equation of the regression line to estimate his score in Round 2. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The figure below shows the lengths in centimetres of fish found in the net of a small trawler.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the total number of fish in the net.</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><span>Find (i) the modal length interval,</span></p>
<p><span>(ii) the interval containing the median length,</span></p>
<p><span>(iii) an estimate of the mean length.</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><span>(i) Write down an estimate for the standard deviation of the lengths.</span></p>
<p><span>(ii) How many fish (if any) have length <strong>greater than</strong> three standard deviations <strong>above</strong> the mean?</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><span>The fishing company must pay a fine if more than 10% of the catch have lengths less than 40cm.</span></p>
<p><span>Do a calculation to decide whether the company is fined.</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><span>A sample of 15 of the fish was weighed. The weight, <em>W</em> was plotted against length, <em>L</em> as shown below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Exactly <strong>two</strong> of the following statements about the plot could be correct. Identify the two correct statements. </span></p>
<p><span><strong>Note:</strong> You do <strong>not</strong> need to enter data in a GDC <strong>or</strong> to calculate <em>r</em> exactly.</span></p>
<p><span>(i) The value of <em>r</em>, the correlation coefficient, is approximately 0.871.</span></p>
<p><span>(ii) There is an exact linear relation between <em>W</em> and <em>L</em>.</span></p>
<p><span>(iii) The line of regression of <em>W</em> on <em>L</em> has equation <em>W</em> = 0.012<em>L</em> + 0.008 .</span></p>
<p><span>(iv) There is negative correlation between the length and weight.</span></p>
<p><span>(v) The value of <em>r</em>, the correlation coefficient, is approximately 0.998.</span></p>
<p><span>(vi) The line of regression of <em>W</em> on <em>L</em> has equation <em>W</em> = 63.5<em>L</em> + 16.5.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Daniel grows apples and chooses at random a sample of <span class="s1">100 </span>apples from his harvest.</p>
<p class="p1">He measures the diameters of the apples to the nearest <span class="s1">cm</span>. The following table shows the distribution of the diameters.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-22_om_08.48.03.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using your graphic display calculator, write down the value of</p>
<p class="p1">(i) the mean of the diameters in this sample;</p>
<p class="p1">(ii) the standard deviation of the diameters in this sample.</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 class="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">Calculate the percentage of <strong>small </strong>apples in Daniel’s harvest.</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 class="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">Of the apples harvested, <span class="s1">5</span>% are <strong>large </strong>apples.</p>
<p class="p1">Find the value of \(a\).</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 class="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">Find the percentage of <strong>medium </strong>apples.</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 class="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">This year, Daniel estimates that he will grow <span class="s1">\({\text{100}}\,{\text{000}}\) </span>apples.</p>
<p class="p1">Estimate the number of <strong>large </strong>apples that Daniel will grow this year.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The table shows the distance, in km, of eight regional railway stations from a city centre terminus and the price, in \($\), of a return ticket from each regional station to the terminus.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-03_om_09.54.14.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram for the above data. Use a scale of \(1\) cm to represent \(10\) km on the \(x\)-axis and \(1\) cm to represent \(\$10\) on the \(y\)-axis.</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><span>Use your graphic display calculator to find</span></p>
<p><span>(i) \(\bar x\), the mean of the distances;</span></p>
<p><span>(ii) \(\bar y\), the mean of the prices.</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><span>Plot and label the point \({\text{M }}(\bar x,{\text{ }}\bar y)\) on your scatter diagram.</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><span>Use your graphic display calculator to find</span></p>
<p><span>(i) the product–moment correlation coefficient, \(r\,;\)</span></p>
<p><span>(ii) the equation of the regression line \(y\) on \(x\).</span></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><span>Draw the regression line \(y\) on \(x\) on your scatter diagram.</span></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><span>A ninth regional station is \(76\) km from the city centre terminus.</span></p>
<p><span><span><span>Use the equation of the regression line to estimate the price of a return ticket to the city centre terminus from this regional station. </span></span><span><span><strong>Give your answer correct to the nearest </strong></span><span><span>\({\mathbf{\$ }}\).</span></span></span></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><span>Give a reason why it is valid to use your regression line to estimate the price of this return ticket.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The actual price of the return ticket is \(\$80\).</span></p>
<p><span><strong>Using your answer to part (f)</strong>, calculate the percentage error in the estimated price of the ticket.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The lengths (\(l\)) in centimetres of \(100\) copper pipes at a local building supplier were measured. The results are listed in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the mode.</span></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><span>Using your graphic display calculator, write down the value of</span><br><span>(i) the mean;</span><br><span>(ii) the standard deviation;</span><br><span>(iii) the median.</span></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><span>Find the interquartile range.</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><span>Draw a box and whisker diagram for this data, on graph paper, using a scale of \(1{\text{ cm}}\) to represent \(5{\text{ cm}}\).</span></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><span>Sam estimated the value of the mean of the measured lengths to be \(43{\text{ cm}}\).</span></p>
<p><span>Find the percentage error of Sam’s estimated mean.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Alex and Kris are riding their bicycles together along a bicycle trail and note the following distance markers at the given times.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram of the data. Use 1 cm to represent 1 hour and 1 cm to represent 10 km.</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><span>Write down for this set of data </span><span>the mean time, \(\bar t\).</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><span>Write down for this set of data the mean distance, \(\bar d\).</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><span>Mark and label the point \(M(\bar t,{\text{ }}\bar d)\) on your scatter diagram.</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><span>Draw the line of best fit on your scatter diagram.</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><span><strong>Using your graph</strong>, estimate the time when Alex and Kris pass the 85 km distance marker. Give your answer correct to <strong>one decimal place</strong>.</span></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><span>Write down the equation of the regression line for the data given.</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><span><strong>Using your equation</strong> calculate the distance marker passed by the cyclists at 10.3 hours.<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Is this estimate of the distance reliable? Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In a mountain region there appears to be a relationship between the number of trees growing in the region and the depth of snow in winter. A set of 10 areas was chosen, and in each area the number of trees was counted and the depth of snow measured. The results are given in the table below.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In a study on \(100\) students there seemed to be a difference between males and females in their choice of favourite car colour. The results are given in the table below. A \(\chi^2\) test was conducted.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find </span><span><span>the mean number of trees</span><span>.</span></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, a, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the mean depth of snow.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, a, iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the standard deviation of the depth of snow.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, a, iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The covariance, <em>S<sub>xy</sub></em> = 188.5.</span></p>
<p><span>Write down the product-moment correlation coefficient, <em>r</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the regression line of <em>y</em> on <em>x</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If the number of trees in an area is 55, estimate the depth of snow.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the equation of the regression line to estimate the depth of snow in an area with 100 trees.<br></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, e, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Decide whether the answer in (e)(i) is a valid estimate of the depth of snow in the area. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, e, ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the total number of male students.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the expected frequency for males, whose favourite car colour is blue, is 12.6.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is \(5.99\) at the \(5\%\) significance level.</span></p>
<p><span>Write down the null hypothesis for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B, c, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is \(5.99\) at the \(5\%\) significance level.</span></p>
<p><span>Write down the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B, c, ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is \(5.99\) at the \(5\%\) significance level.</span></p>
<p><span>Determine whether the null hypothesis should be accepted at the \(5\%\) significance level. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B, c, iv.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The number of bottles of water sold at a railway station on each day is given in the following table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down</span></p>
<p><span>(i) the mean temperature;</span></p>
<p><span>(ii) the standard deviation of the temperatures.</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><span>Write down the correlation coefficient, \(r\), for the variables \(n\) and \(T\).</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><span>Comment on your value for \(r\).</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><span>The equation of the line of regression for \(n\) on \(T\) is \(n = dT - 100\).</span></p>
<p><span>(i) Write down the value of \(d\).</span></p>
<p><span>(ii) Estimate how many bottles of water will be sold when the temperature is \({19.6^ \circ }\).</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><span>On a day when the temperature was \({36^ \circ }\) Peter calculates that \(314\) bottles would be sold. Give one reason why his answer might be unreliable.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram shows the cumulative frequency graph for the time <em>t</em> taken to perform a certain task by 2000 men.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the diagram to estimate </span><span>the median time.</span></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><span>Use the diagram to estimate the upper quartile and the lower quartile.</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><span>Use the diagram to estimate the interquartile range.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a, iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of men who take <strong>more than</strong> 11 seconds to perform the task.</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><span>55 % of the men took less than<em> p</em> seconds to perform the task. Find <em>p</em>.</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><span>The times taken for the 2000 men were grouped as shown in the table below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down the value of </span><span><em>a</em>.</span></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><span>The times taken for the 2000 men were grouped as shown in the table below.</span></p>
<p><span><img alt="onbekend.png"></span></p>
<p><span>Write down the value of <em>b</em>.</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><span>Use your graphic display calculator to find an estimate of</span><span> the mean time</span><span>.</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><span>Use your graphic display calculator to find an estimate of the standard deviation of the time.</span></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><span>Everyone who performs the task in <strong>less than</strong> one standard deviation <strong>below</strong> the mean will receive a bonus. Pedro takes 9.5 seconds to perform the task.</span></p>
<p><span>Does Pedro receive the bonus? Justify your answer.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</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,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"></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><span style="font-size: medium; font-family: times new roman,times;">A random sample of 167 people who own mobile phones was used to collect data on the amount of time they spent per day using their phones. The results are displayed in the table below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Manuel conducts a survey on a random sample of 751 people to see which television programme type they watch most from the following: Drama, Comedy, Film, News. The results are as follows.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Manuel decides to ignore the ages and to test at the 5 % level of significance whether the most watched programme type is independent of <strong>gender.</strong></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State the modal group.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to calculate approximate values of the mean and standard deviation of the time spent per day on these mobile phones.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On graph paper, draw a fully labelled histogram to represent the data.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a table with 2 rows and 4 columns of data so that Manuel can perform a chi-squared test.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State Manuel’s null hypothesis and alternative hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the expected frequency for the number of females who had ‘Comedy’ as their most-watched programme type. Give your answer to the nearest whole number.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using your graphic display calculator, or otherwise, find the chi-squared statistic for Manuel’s data.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) State the number of degrees of freedom available for this calculation.</span></p>
<p><span>(ii) State his conclusion.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The speed, \(s\) , in \({\text{km }}{{\text{h}}^{ - 1}}\), of \(120\) vehicles passing a point on the road was measured. </span><span style="font-size: medium; font-family: times new roman,times;">The results are given below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the midpoint of the \(60 < s \leqslant 70\) interval.</span></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><span>Use your graphic display calculator to find an estimate for</span></p>
<p><span>(i) the mean speed of the vehicles;</span></p>
<p><span>(ii) the standard deviation of the speeds of the vehicles.</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><span>Write down the number of vehicles whose speed is less than or equal to \({\text{60 km }}{{\text{h}}^{ - 1}}\).</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><span>Consider the cumulative frequency table below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down the value of \(a\) , of \(b\) and of \(c\) .</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><span>Consider the cumulative frequency table below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Draw a cumulative frequency graph for the information from the table. Use \(1\) cm to represent \({\text{10 km }}{{\text{h}}^{ - 1}}\) on the horizontal axis and \(1\) cm to represent \(10\) vehicles on the vertical axis.</span></p>
<p> </p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your cumulative frequency graph to estimate</span></p>
<p><span>(i) the median speed of the vehicles;</span></p>
<p><span>(ii) the number of vehicles that are travelling at a speed less than or equal to \({\text{65 km }}{{\text{h}}^{ - 1}}\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>All drivers whose vehicle’s speed is greater than one standard deviation above the speed limit of \({\text{50 km }}{{\text{h}}^{ - 1}}\) will be fined. </span></p>
<p><span>Use your graph to estimate the number of drivers who will be fined.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Francesca is a chef in a restaurant. She cooks eight chickens and records their masses and cooking times. The mass <em>m</em> of each chicken, in kg, and its cooking time <em>t</em>, in minutes, are shown in the following table.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram to show the relationship between the mass of a chicken and its cooking time. Use 2 cm to represent 0.5 kg on the horizontal axis and 1 cm to represent 10 minutes on the vertical axis.</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><span>Write down for this set of data</span></p>
<p><span>(i) the mean mass, \(\bar m\) ;</span></p>
<p><span>(ii) the mean cooking time, </span><span><span>\(\bar t\)</span> .</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><span>Label the point \({\text{M}}(\bar m,\bar t)\) on the scatter diagram.</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><span>Draw the line of best fit on the scatter diagram.</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><span>Using your line of best fit, estimate the cooking time, in minutes, for a 1.7 kg chicken.</span></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><span>Write down the Pearson’s product–moment correlation coefficient, <em>r</em> .</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><span>Using your value for <em>r</em> , comment on the correlation.</span></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><span>The cooking time of an additional 2.0 kg chicken is recorded. If the mass and cooking time of this chicken is included in the data, the correlation is weak.</span></p>
<p><span>(i) Explain how the cooking time of this additional chicken might differ from that of the other eight chickens.</span></p>
<p><span>(ii) Explain how a new line of best fit might differ from that drawn in part (d).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part A</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">A university required all Science students to study one language for one year. A survey was carried out at the university amongst the 150 Science students. These students all studied one of either French, Spanish or Russian. The results of the survey are shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Ludmila decides to use the \({\chi ^2}\) test at the \(5\% \) level of significance to determine whether the choice of language is independent of gender.</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">At the end of the year, only seven of the female Science students sat examinations in Science and French. The marks for these seven students are shown in the following table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State Ludmila’s null hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the expected frequency for the females studying Spanish.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the \({\chi ^2}\) test statistic for this data.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether Ludmila accepts the null hypothesis. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a labelled scatter diagram for this data. Use a scale of \(2{\text{ cm}}\) to represent \(10{\text{ marks}}\) on the \(x\)-axis (\(S\)) and \(10{\text{ marks}}\) on the \(y\)-axis (\(F\)).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic calculator to find</span></p>
<p><span></span></p>
<p><span>(i) \({\bar S}\), the mean of \(S\) ;</span></p>
<p><span>(ii) \({\bar F}\), the mean of \(F\) .</span></p>
<p><span> </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Plot the point \({\text{M}}(\bar S{\text{, }}\bar F)\) on your scatter diagram.</span></p>
<p><span></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the equation of the regression line of \(F\) on \(S\) .</span></p>
<p><span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw the regression line on your scatter diagram.</span></p>
<p><span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Carletta’s mark on the Science examination was \(44\). She did not sit the French examination. </span></p>
<p><span>Estimate Carletta’s mark for the French examination.</span></p>
<p><span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span></span><span>Monique’s mark on the Science examination was 85. She did not sit the French examination. Her French teacher wants to use the regression line to estimate Monique’s mark.</span></p>
<p><span> State whether the mark obtained from the regression line for Monique’s French examination is reliable. Justify your answer.</span></p>
<p><span></span></p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">B.g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram below shows a square based right pyramid. ABCD is a square of side 10 cm. VX is the perpendicular height of 8 cm. M is the midpoint of BC.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p> </p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In a mountain region there appears to be a relationship between the number of trees growing in the region and the depth of snow in winter. A set of 10 areas was chosen, and in each area the number of trees was counted and the depth of snow measured. The results are given in the table below.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A path goes around a forest so that it forms the three sides of a triangle. The lengths of two sides are 550 m and 290 m. These two sides meet at an angle of 115°. A diagram is shown below.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the length of XM.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the standard deviation of the number of trees.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, a, ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of VM.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the angle between VM and ABCD.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of the third side of the triangle. Give your answer correct to the nearest 10 m.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">B, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the area enclosed by the path that goes around the forest.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">B, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Inside the forest a second path forms the three sides of another triangle named ABC. Angle BAC is 53°, AC is 180 m and BC is 230 m.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Calculate the size of angle ACB.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">B, c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For an ecological study, Ernesto measured the average concentration \((y)\) of the fine dust, \({\text{PM}}10\), in the air at different distances \((x)\) from a power plant. His data are represented on the following scatter diagram. The concentration of \({\text{PM}}10\) is measured in micrograms per cubic metre and the distance is measured in kilometres.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>His data are also listed in the following table.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>Use the scatter diagram to find the value of \(a\) and of \(b\) in the table.</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</p>
<p>i) \({\bar x}\) , the mean distance from the power plant;</p>
<p>ii) \({\bar y}\) , the mean concentration of \({\text{PM}}10\) ;</p>
<p>iii) \(r\) , the Pearson’s product–moment correlation coefficient.</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>Write down the equation of the regression line \(y\) on \(x\) .</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>Ernesto’s school is located \(14\,{\text{km}}\) from the power plant. He uses the equation of the regression line to estimate the concentration of \({\text{PM}}10\) in the air at his school.</p>
<p>i) Calculate the value of Ernesto’s estimate.</p>
<p>ii) State whether Ernesto’s estimate is reliable. Justify your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</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><span style="font-family: times new roman,times; font-size: medium;">The heat output in thermal units from burning \(1{\text{ kg}}\) of wood changes according to the wood’s percentage moisture content. The moisture content and heat output of \(10\) blocks of the same type of wood each weighing </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(1{\text{ kg}}\)</span> were measured. These are shown in the table.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram to show the above data. Use a scale of \(2{\text{ cm}}\) to represent \(10\% \) on the <em>x</em>-axis and a scale of \(2{\text{ cm}}\) to represent \(10\) thermal units on the <em>y</em>-axis.</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><span>Write down</span><br><span>(i) the mean percentage moisture content, \(\bar x\) ;</span><br><span>(ii) the mean heat output, \(\bar y\) .</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><span>Plot the point \((\bar x{\text{, }}\bar y)\) on your scatter diagram and label this point M .</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><span>Write down the product-moment correlation coefficient, \(r\) .</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><span>The equation of the regression line \(y\) on \(x\) is \(y = - 0.470x + 83.7\) . Draw the regression line \(y\) on \(x\) on your scatter diagram.</span></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><span>The equation of the regression line \(y\) on \(x\) is \(y = - 0.470x + 83.7\) . Estimate the heat output in thermal units of a \(1{\text{ kg}}\) block of wood that has \(25\% \) moisture content.</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><span>The equation of the regression line \(y\) on \(x\) is \(y = - 0.470x + 83.7\) . State, with a reason, whether it is appropriate to use the regression line \(y\) on \(x\) to estimate the heat output in part (f).<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In an environmental study of plant diversity around a lake, a biologist collected</span> <span style="font-family: times new roman,times; font-size: medium;">data about the number of different plant species (<em>y</em>) that were growing at different </span><span style="font-family: times new roman,times; font-size: medium;">distances (<em>x</em>) in metres from the lake shore.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram to show the data. Use a scale of 2 cm to represent 10 metres on the <em>x</em>-axis and 2 cm to represent 10 plant species on the<em> y</em>-axis.</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><span>Using your scatter diagram, describe the correlation between the number of different plant species and the distance from the lake shore.</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><span>Use your graphic display calculator to write down</span><span> \(\bar x\), the mean of the distances from the lake shore.</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><span>Use your graphic display calculator to write down \(\bar y\), the mean number of plant species.</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><span>Plot the point (\(\bar x\), \(\bar y\)) on your scatter diagram. <strong>Label this point M.</strong></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><span>Write down the equation of the regression line <em>y</em> on <em>x</em> for the above data.</span></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><span>Draw the regression line <em>y</em> on <em>x</em> on your scatter diagram.</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><span>Estimate the number of plant species growing 30 metres from the lake shore.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">200 people were asked the amount of time <em>T</em> (minutes) they had spent in the supermarket. The results are represented in the table below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State if the data is discrete or continuous.</span></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><span>State the modal group.</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><span>Write down the midpoint of the interval 10 < <em>T</em> ≤ 20 .</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><span>Use your graphic display calculator to find an estimate for</span></p>
<p><span>(i) the mean;</span></p>
<p><span>(ii) the standard deviation.</span></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><span>The results are represented in the cumulative frequency table below, with upper class boundaries of 10, 20, 30, 40, 50.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down the value of</span></p>
<p><span>(i) <em>q</em>;</span></p>
<p><span>(ii)<em> r</em>.</span></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><span>The results are represented in the cumulative frequency table below, with upper class boundaries of 10, 20, 30, 40, 50.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>On graph paper, draw a cumulative frequency graph, using a scale of 2 cm to represent 10 minutes (<em>T</em>) on the horizontal axis and 1 cm to represent 10 people on the vertical axis.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><strong>Use your graph</strong> from part (f) to estimate</span></p>
<p><span>(i) the median;</span></p>
<p><span>(ii) the 90<sup>th</sup> percentile of the results;</span></p>
<p><span>(iii) the number of people who shopped at the supermarket for more than </span><span>15 minutes.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br>