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Algebra')\n## AuthorText1('Blitzer')\n## EditionText1('1')\n## Section1('5.1')\n## Problem1('')\n## KEYWORDS('polynomials')\n## Date: 2007/10\n\nDOCUMENT(); # This should be the first executable line in the problem.\n\nloadMacros(\n  \"PGstandard.pl\",\n  \"PGchoicemacros.pl\",\n  \"MathObjects.pl\",\n  \"PGcourse.pl\"\n);\n\nTEXT(beginproblem());\n\n######################################\n#  Setup\n\n\n\n$a = random(1,3,1);  \n\n$b = random(-1,1,2);  \n\n\n$p = Formula(\"$a x^2 + $b x\"); #Use this to build the polynomial\n\n\n$input1 = list_random(-3,-2,2,3);    \n\n$input2 = -1*$input1 + non_zero_random(-1,1,2);\n\n\n\n$c= $p-\u003eeval(x=\u003e$input2);    #Input2 is a zero of the polynomial.\n$f = Compute($p - $c)-\u003ereduce;    \n$poly = $f-\u003eTeX;\n\n\n#----Scramble the input\n@input = ($input1, $input2, 0);\n@slice = NchooseK(3,3);\n@x = @input[@slice];      #Want one positive, negative and zero\n                         \n\n######################################\n\n#  Main text\n\n\n\nBEGIN_TEXT\n\nFind the indicated functional values.  \n\n\n\n \\[ g(x) =   $poly   \\]\n\n\n\n$BR\n\n$BR\n\na) \\( g($x[0]) \\) = \\{ans_rule(15)\\}\n\n$BR\n\n$BR\n\nb) \\( g($x[1]) \\) = \\{ans_rule(15)\\}\n\n$BR\n\n$BR\n\nc) \\( g($x[2]) \\) = \\{ans_rule(15)\\}\n\n$BR\n\nEND_TEXT\n\n\n\n######################################\n\n#  Answer\n\n\n\n$ans_a = $f-\u003eeval(x=\u003e$x[0]);\nANS($ans_a-\u003ecmp);\n\n$ans_b = $f-\u003eeval(x=\u003e$x[1]);\nANS($ans_b-\u003ecmp);\n\n$ans_c = $f-\u003eeval(x=\u003e$x[2]);\nANS($ans_c-\u003ecmp);\n\n\n$showPartialCorrectAnswers = 1;\n\n######################################\n\n\n\n;\nENDDOCUMENT();\n","use_equation_editor":null,"webwork_features":[],"part_attributes":[{"id":"5a1dbefc387b30000416735d","part_id":"5a1353e5c0421000041487f5","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"-10","format":"ws","answer_name":"AnSwEr0001","extra":false,"applet_state":false,"multipart":false,"manually_gradable":false,"answer_text":"\\(-10\\)"},{"id":"5a1dbefc387b30000416735e","part_id":"5a1353e5c0421000041487f6","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"-24","format":"ws","answer_name":"AnSwEr0002","extra":false,"applet_state":false,"multipart":false,"manually_gradable":false,"answer_text":"\\(-24\\)"},{"id":"5a1dbefc387b30000416735f","part_id":"5a1353e5c0421000041487f7","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"0","format":"ws","answer_name":"AnSwEr0003","extra":false,"applet_state":false,"multipart":false,"manually_gradable":false,"answer_text":"\\(0\\)"}],"interactive_html":"\u003cp\u003e\nFind the indicated functional values.  \n\n\n\n \\[g(x) =   3x^{2}-x-24\\]\u003cbr\u003e\u003cbr\u003e\n\na) \\(g(-2)\\) = \u003cinput type=\"text\" class=\"codeshard\" size=\"15\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" value=\"\"\u003e\u003cinput type=\"hidden\" name=\"previous_AnSwEr0001\" value=\"\"\u003e\u003cbr\u003e\u003cbr\u003e\n\nb) \\(g(0)\\) = \u003cinput type=\"text\" class=\"codeshard\" size=\"15\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 \" value=\"\"\u003e\u003cinput type=\"hidden\" name=\"previous_AnSwEr0002\" value=\"\"\u003e\u003cbr\u003e\u003cbr\u003e\n\nc) \\(g(3)\\) = \u003cinput type=\"text\" class=\"codeshard\" size=\"15\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 \" value=\"\"\u003e\u003cinput type=\"hidden\" name=\"previous_AnSwEr0003\" value=\"\"\u003e\u003cbr\u003e\u003c/p\u003e","static_html":"\u003cp\u003e\nFind the indicated functional values.  \n\n\n\n \\[g(x) =   3x^{2}-x-24\\]\u003cbr\u003e\u003cbr\u003e\n\na) \\(g(-2)\\) = \u003cspan class=\"ww-blank\" name=\"AnSwEr0001\"\u003e \u003c/span\u003e\u003cbr\u003e\u003cbr\u003e\n\nb) \\(g(0)\\) = \u003cspan class=\"ww-blank\" name=\"AnSwEr0002\"\u003e \u003c/span\u003e\u003cbr\u003e\u003cbr\u003e\n\nc) \\(g(3)\\) = \u003cspan class=\"ww-blank\" name=\"AnSwEr0003\"\u003e \u003c/span\u003e\u003cbr\u003e\u003c/p\u003e","timeout":false,"header_text":null}],"instructional":false,"sketchable":true,"print_num_spacing_lines":3,"print_page_break":false,"corrected":false,"blacklisted":false,"readonly":{"created_at":"2023-10-01T17:19:30.148-04:00","updated_at":"2023-10-01T17:19:30.148-04:00","version":21,"user_id":"58ecdcd48ccf1800120c8ac3","name":"Algorithmic 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Student must simplify.\nContext()-\u003eoperators-\u003eundefine(\"+\",\"-\",\"*\",\"/\");\n\nBEGIN_TEXT \n\nSimplify the expression:\n$PAR\n$BCENTER\n \\($a+$b \\times 2\\)\n\n$ECENTER\n$PAR\n\n\\{ans_rule(20)\\}\nEND_TEXT\nContext()-\u003enormalStrings;\n\n##############################################################\n#\n#  Answers\n#\n#\n\nANS($ans-\u003ecmp);\n\n\nENDDOCUMENT();        ","use_equation_editor":null,"webwork_features":[],"part_attributes":[{"id":"6140143fe83ef70004abc874","part_id":"5aed04bf606633a77096392d","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"16+4*2","format":"ws","answer_name":"AnSwEr0001","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"\\(16+4\\cdot 2\\)"}],"interactive_html":"\n\nSimplify the expression:\n\u003cdiv align=\"center\"\u003e\n \\(16+4 \\times 2\\)\n\n\u003c/div\u003e\n\u003cp\u003e\n\n\u003cinput type=\"text\" class=\"codeshard\" size=\"20\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0001\" value=\"\"\u003e\n\n\n\u003c/p\u003e","static_html":"\u003cp\u003e\n\nSimplify the expression:\n\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \\(16+4 \\times 2\\)\n\n\u003c/div\u003e\n\u003cp\u003e\n\n\u003cspan class=\"ww-blank\" name=\"AnSwEr0001\"\u003e \u003c/span\u003e\n\n\n\n\u003c/p\u003e","timeout":false,"header_text":{"css":[],"js":[],"inlinejs":[]}}],"instructional":false,"sketchable":true,"print_num_spacing_lines":3,"print_page_break":false,"corrected":false,"blacklisted":false,"readonly":{"created_at":"2024-09-01T15:01:23.196-04:00","updated_at":"2024-09-01T15:01:23.196-04:00","version":27,"user_id":"58ecdcd48ccf1800120c8ac3","name":"Algorithmic (WebWorK)","skill_ids":["5a135ec1c04210000415682c","5a1420fdac370c0004c7801e","5a135ec1c04210000415682c","5a1420fdac370c0004c7801e","5a135ec1c04210000415682c","5a1420fdac370c0004c7801e"],"current_digest":"PE29voU0tYKySf4RtUGln8O57I33bdx/Yvjqoma8x3Q=","tags":"common core,prealgebra","points":1.0,"type":"webwork","multipart":false,"shallow":true,"static":true,"sources":[{"source":"problem","id":"66d4ba03511ae000025648c5"},{"Subject":"Arithmetic","Title":"Pre-Algebra","ChapterTitle":"Integers","ChapterSection":"Multiple operations","ChapterNumber":".","CodeInstitution":"Mississippi College","CodeAuthor":"John Travis","Level":"2","source":"part","id":"66d4ba03511ae000025648c5"}],"owned":false,"url":"/problems/66d4ba03511ae000025648c5","searchable_text":"Simplify the expression PAR BCENTER a b times 2 ECENTER PAR ans rule 20","abilities":["read","create","add","remove","open"]},"content_license":{"license_type":"OPL","source_url":"https://github.com/Edfinity/webwork-open-problem-library/blob/0914437ac334603bf1f15257757073ac63121956/OpenProblemLibrary/MC/PreAlgebra/setPreAlgebraC01S02/OrderOps03.pg"}},"readonly":{"shallow":true}}},"readonly":{"level_range":"13","created_at":"2019-02-12T12:03:43.860-05:00","updated_at":"2026-03-15T15:38:19.399-04:00","tags":"openstax,math,oer,college_algebra,algebra","author_ids":[],"licensed":true,"thumbnail":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c62fc6fed52946e68d8d2b0/thumb_college-algebra-2.jpg","free":false,"user_price":40.0,"term_price":40.0,"displayed_price":40.0,"levels":"13"},"image":{"identifier":"college-algebra-2.jpg","size":100735,"url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c62fc6fed52946e68d8d2b0/college-algebra-2.jpg","thumb_url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c62fc6fed52946e68d8d2b0/thumb_college-algebra-2.jpg"}},{"id":"5cd472ba59824b6a0a67e3ea","name":"OpenStax Introductory Statistics","summary":"Edfinity is supported by the National Science Foundation","description":"\u003cp dir=\"ltr\" id=\"isPasted\"\u003eThis online user-contributed homework course comprises of algorithmic problems carefully organized into problem sets mapped to textbook sections. Use this course as-is, or customize at any level. You can mix-and-match problems from other user-contributed courses, add problems from the user-contributed problem repository, or write your own problems.\u003c/p\u003e\u003cp dir=\"ltr\"\u003e\u003cstrong\u003eHow to use this course\u003c/strong\u003e\u003c/p\u003e\u003col\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eHomework\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Assign high quality problems with hints and personalized feedback to develop problem-solving skills.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eTesting\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Create summative secure online quizzes and tests in minutes.\u0026nbsp;\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eSupplementary resources:\u003c/strong\u003e Embed videos, class notes, and applets alongside assignments.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eIntervention:\u003c/strong\u003e Use rich analytics to identify and monitor at-risk students for timely intervention.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eAnalytics:\u003c/strong\u003e Drill down into student performance and identify problematic or difficult topics.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eFlipped classroom:\u003c/strong\u003e Assign pre-class assignments. 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All rights reserved. \n# Unauthorized use including modification, sharing, copying is not permitted. \n# For additional information and/or permission to use write to:\n# support@edfinity.com\n\n## DESCRIPTION\n##\n## ENDDESCRIPTION\n\n## DBsubject('Quantitative Reasoning')\n## DBchapter('Statistical Reasoning')\n## DBsection('Fundamentals of Statistics')\n## Date('5/07/2022')\n## Author('Anna Lurie')\n## Institution('Palm Beach State College')\n## TitleText1('')\n## EditionText1('1')\n## AuthorText1('')\n## Section1('')\n## Problem1('')\n## KEYWORDS('population', 'sample','parameter','statistic')\n\n\n##############################################################\n#  Initialization\n##############################################################\n\nDOCUMENT();      \n\nloadMacros(\n    \"PGstandard.pl\",\n    \"MathObjects.pl\",\n    \"PGML.pl\",\n    \"parserRadioButtons.pl\",\n    \"randomizers.pl\"\n);\n\nTEXT(beginproblem());\n\n##############################################################\n#  Problem Setup\n##############################################################\n\nContext(\"Numeric\");\n#randomization of the sample size\n$ssize = random(200,250,1);\n#randomization of sample statistic\n$pct = random(40,50,1);\n#interviewers\n@people = (\n    \" hiring managers\",\n    \" human resource professionals\",\n    \" interviewers\",\n    \" hiring committee managers\",\n    );\n@mistake = (\n    \" not to know enough about the company they are applying to.\",\n    \" using their cell phone during an interview.\",\n    \" to dress inappropriately.\",\n    \" talking too much or not enough.\",\n    );\n\n#randomization of question\n$k = random(0,3,1);\n\n\n#Making a radio button choice for identifying the population or the sample\n@population_choices = (\n    \" all $people[$k].\",\n    \" \\($pct\\)% of all $people[$k].\",\n    \" \\($pct\\)% of the \\($ssize\\) $people[$k].\",\n    \" The \\($ssize\\) of $people[$k] selected for this survey.\"\n);\n         \n$radio1 = RadioButtons([[@population_choices]], 0);\n$radio2 = RadioButtons([[@population_choices]], 3);\n\n#making a radio button choice for identifying the parameter\n@parameter_choices = (\n    \" \\($ssize\\) $people[$k].\",\n    \" All $people[$k].\",\n    \" The percent of $people[$k] in this study who said one of the most common \n    mistakes job candidates make is $mistake[$k]\",\n    \" The percent of all $people[$k] who said one of the most common \n    mistakes job candidates make is $mistake[$k]\",\n);\n\n$radio3 = RadioButtons([[@parameter_choices]], 3);\n\n#making a radio button choice for identifying the statistic\n@statistic_choices = (\n    \" \\($ssize\\) $people[$k].\",\n    \" All $people[$k].\",\n    \" The percent of $people[$k] in this study, \\($pct\\)%, who said one of the most common \n    mistakes job candidates make is $mistake[$k]\",\n    \" The percent of all $people[$k] who said one of the most common \n    mistakes job candidates make is $mistake[$k]\",\n);\n\n$radio4 = RadioButtons([[@statistic_choices]], 2);\n\n##############################################################\n#  Text\n##############################################################\n\nBEGIN_PGML\n\nIn a survey of [`[$ssize]`] [$people[$k]], [`[$pct]`]% said one of the most\ncommon mistakes job candidates make is [$mistake[$k]] \n    \n    A. Describe the population in this study. \n    \n        [____]{$radio1}\n        \n    B. What is the sample in this study?\n    \n        [____]{$radio2}\n        \n    C. Identify the population parameter in this study.\n    \n        [____]{$radio3}\n        \n    D.  Identify the sample statistic in this study.\n    \n        [____]{$radio4}\n\nEND_PGML\n\n##############################################################\n#  Answers and Solutions\n##############################################################\n\n\nBEGIN_PGML_SOLUTION\n\n    A. The population is all individuals, so it is all [$people[$k]].\n    \n    B.  The sample is the individuals selected from the population, so it is the\n    [`[$ssize]`] of [$people[$k]] selected for this survey.\n    \n    C. The population parameter is a numerical summary of a population, so it is the percent of all [$people[$k]] \n       who said one of the most common mistakes job candidates make is [$mistake[$k]]\n       \n    D.  The sample statistic is a numerical summary of a sample, so it is the percent of [$people[$k]] in this\n    study, [`[$pct]`]%, who said one of the most common mistakes job candidates make is [$mistake[$k]]\n\nEND_PGML_SOLUTION\n\nENDDOCUMENT();\n","use_equation_editor":null,"webwork_features":[],"part_attributes":[{"id":"627717330073e100046a4e04","part_id":"627717330073e100046a4e00","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"Choice 2","format":"ws","answer_name":"AnSwEr0001","extra":false,"applet_state":false,"multipart":false,"manually_gradable":false,"answer_text":"Choice 2"},{"id":"627717330073e100046a4e05","part_id":"627717330073e100046a4e01","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"Choice 3","format":"ws","answer_name":"AnSwEr0002","extra":false,"applet_state":false,"multipart":false,"manually_gradable":false,"answer_text":"Choice 3"},{"id":"627717330073e100046a4e06","part_id":"627717330073e100046a4e02","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"Choice 2","format":"ws","answer_name":"AnSwEr0003","extra":false,"applet_state":false,"multipart":false,"manually_gradable":false,"answer_text":"Choice 2"},{"id":"627717330073e100046a4e07","part_id":"627717330073e100046a4e03","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"Choice 2","format":"ws","answer_name":"AnSwEr0004","extra":false,"applet_state":false,"multipart":false,"manually_gradable":false,"answer_text":"Choice 2"}],"interactive_html":"\n\u003cdiv class=\"PGML\"\u003e\nIn a survey of \\(250\\)  human resource professionals, \\(40\\)% said one of the most\ncommon mistakes job candidates make is  using their cell phone during an interview. \n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"margin:0 0 0 2.25em\"\u003e\n\u003col type=\"A\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003eDescribe the population in this study. \n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 1 \" value=\"B0\"\u003e \\(40\\)% of all  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 1 \" value=\"B1\"\u003e all  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 2 \" value=\"B2\"\u003e The \\(250\\) of  human resource professionals selected for this survey.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 3 \" value=\"B3\"\u003e \\(40\\)% of the \\(250\\)  human resource professionals.\u003c/label\u003e\n\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhat is the sample in this study?\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 option 1 \" value=\"B0\"\u003e \\(40\\)% of all  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 option 1 \" value=\"B1\"\u003e \\(40\\)% of the \\(250\\)  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 option 2 \" value=\"B2\"\u003e The \\(250\\) of  human resource professionals selected for this survey.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 option 3 \" value=\"B3\"\u003e all  human resource professionals.\u003c/label\u003e\n\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eIdentify the population parameter in this study.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 option 1 \" value=\"B0\"\u003e \\(250\\)  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 option 1 \" value=\"B1\"\u003e The percent of all  human resource professionals who said one of the most common \n    mistakes job candidates make is  using their cell phone during an interview.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 option 2 \" value=\"B2\"\u003e All  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 option 3 \" value=\"B3\"\u003e The percent of  human resource professionals in this study who said one of the most common \n    mistakes job candidates make is  using their cell phone during an interview.\u003c/label\u003e\n\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eIdentify the sample statistic in this study.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 option 1 \" value=\"B0\"\u003e The percent of all  human resource professionals who said one of the most common \n    mistakes job candidates make is  using their cell phone during an interview.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 option 1 \" value=\"B1\"\u003e The percent of  human resource professionals in this study, \\(40\\)%, who said one of the most common \n    mistakes job candidates make is  using their cell phone during an interview.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 option 2 \" value=\"B2\"\u003e All  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 option 3 \" value=\"B3\"\u003e \\(250\\)  human resource professionals.\u003c/label\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class=\"solution\"\u003e\n\u003cp\u003e\u003cb\u003eSolution:\u003c/b\u003e \u003cbr\u003e\u003c/p\u003e\n\u003cdiv class=\"PGML\"\u003e\n\u003cdiv style=\"margin:0 0 0 2.25em\"\u003e\n\u003col type=\"A\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003eThe population is all individuals, so it is all  human resource professionals.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eThe sample is the individuals selected from the population, so it is the\n\\(250\\) of  human resource professionals selected for this survey.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eThe population parameter is a numerical summary of a population, so it is the percent of all  human resource professionals \n   who said one of the most common mistakes job candidates make is  using their cell phone during an interview.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eThe sample statistic is a numerical summary of a sample, so it is the percent of  human resource professionals in this\nstudy, \\(40\\)%, who said one of the most common mistakes job candidates make is  using their cell phone during an interview.\u003c/li\u003e\n\u003c/ol\u003e\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e","static_html":"\u003cdiv class=\"PGML\"\u003e\nIn a survey of \\(250\\)  human resource professionals, \\(40\\)% said one of the most\ncommon mistakes job candidates make is  using their cell phone during an interview. \n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"margin:0 0 0 2.25em\"\u003e\n\u003col type=\"A\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003eDescribe the population in this study. \n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 1 \" value=\"B0\"\u003e \\(40\\)% of all  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 1 \" value=\"B1\"\u003e all  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 2 \" value=\"B2\"\u003e The \\(250\\) of  human resource professionals selected for this survey.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 3 \" value=\"B3\"\u003e \\(40\\)% of the \\(250\\)  human resource professionals.\u003c/label\u003e\n\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhat is the sample in this study?\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 option 1 \" value=\"B0\"\u003e \\(40\\)% of all  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 option 1 \" value=\"B1\"\u003e \\(40\\)% of the \\(250\\)  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 option 2 \" value=\"B2\"\u003e The \\(250\\) of  human resource professionals selected for this survey.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 option 3 \" value=\"B3\"\u003e all  human resource professionals.\u003c/label\u003e\n\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eIdentify the population parameter in this study.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 option 1 \" value=\"B0\"\u003e \\(250\\)  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 option 1 \" value=\"B1\"\u003e The percent of all  human resource professionals who said one of the most common \n    mistakes job candidates make is  using their cell phone during an interview.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 option 2 \" value=\"B2\"\u003e All  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 option 3 \" value=\"B3\"\u003e The percent of  human resource professionals in this study who said one of the most common \n    mistakes job candidates make is  using their cell phone during an interview.\u003c/label\u003e\n\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eIdentify the sample statistic in this study.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 option 1 \" value=\"B0\"\u003e The percent of all  human resource professionals who said one of the most common \n    mistakes job candidates make is  using their cell phone during an interview.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 option 1 \" value=\"B1\"\u003e The percent of  human resource professionals in this study, \\(40\\)%, who said one of the most common \n    mistakes job candidates make is  using their cell phone during an interview.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 option 2 \" value=\"B2\"\u003e All  human resource professionals.\u003c/label\u003e\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"radio\" name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 option 3 \" value=\"B3\"\u003e \\(250\\)  human resource professionals.\u003c/label\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class=\"solution\"\u003e\n\u003cp\u003e\u003cb\u003eSolution:\u003c/b\u003e \u003cbr\u003e\u003c/p\u003e\n\u003cdiv class=\"PGML\"\u003e\n\u003cdiv style=\"margin:0 0 0 2.25em\"\u003e\n\u003col type=\"A\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003eThe population is all individuals, so it is all  human resource professionals.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eThe sample is the individuals selected from the population, so it is the\n\\(250\\) of  human resource professionals selected for this survey.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eThe population parameter is a numerical summary of a population, so it is the percent of all  human resource professionals \n   who said one of the most common mistakes job candidates make is  using their cell phone during an interview.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eThe sample statistic is a numerical summary of a sample, so it is the percent of  human resource professionals in this\nstudy, \\(40\\)%, who said one of the most common mistakes job candidates make is  using their cell phone during an interview.\u003c/li\u003e\n\u003c/ol\u003e\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e","timeout":false,"header_text":{"css":[],"js":[],"inlinejs":[]}}],"instructional":false,"sketchable":true,"print_num_spacing_lines":3,"print_page_break":false,"corrected":false,"blacklisted":false,"readonly":{"created_at":"2022-11-02T16:57:15.080-04:00","updated_at":"2022-11-02T16:57:15.080-04:00","version":44,"user_id":"58ecdcd48ccf1800120c8ac3","name":"Algorithmic (WebWorK)","skill_ids":[],"current_digest":"XtByKvQiU/NjVL2auAmVU/BOBxI90GyGjXQZVH4wHKw=","tags":"parameter,population,sample,statistic","points":4.0,"type":"webwork","multipart":true,"shallow":true,"static":true,"sources":[{"source":"problem","id":"6362d9ab7a688b0003f1ba64"},{"Subject":"Quantitative Reasoning","ChapterTitle":"Statistical Reasoning","ChapterSection":"Fundamentals of Statistics","Edition":"1","CodeInstitution":"Palm Beach State College","CodeAuthor":"Anna Lurie","source":"part","id":"6362d9ab7a688b0003f1ba64"}],"owned":false,"url":"/problems/6362d9ab7a688b0003f1ba64","searchable_text":"In a survey of ssize people k pct said one of the mostcommon mistakes job candidates make is mistake k A Describe the population in this study radio1 B What is the sample in this study radio2 C Identify the population parameter in this study radio3 D Identify the sample statistic in this study radio4 SOLUTION A The population is all individuals so it is all people k B The sample is the individuals selected from the population so it is the ssize of people k selected for this survey C The population parameter is a numerical summary of a population so it is the percent of all people k who said one of the most common mistakes job candidates make is mistake k D The sample statistic is a numerical summary of a sample so it is the percent of people k in this study pct who said one of the most common mistakes job candidates make is mistake k","abilities":["read","create","add","remove","open"]}},"readonly":{"shallow":true}}},"readonly":{"level_range":"13","created_at":"2019-05-09T14:34:34.704-04:00","updated_at":"2026-03-15T15:38:19.425-04:00","tags":"oer,statistics,openstax","author_ids":[],"licensed":true,"thumbnail":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5cd472ba59824b6a0a67e3ea/thumb_intro-statistics-2.jpg","free":false,"user_price":40.0,"term_price":40.0,"displayed_price":40.0,"levels":"13"},"image":{"identifier":"intro-statistics-2.jpg","size":88793,"url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5cd472ba59824b6a0a67e3ea/intro-statistics-2.jpg","thumb_url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5cd472ba59824b6a0a67e3ea/thumb_intro-statistics-2.jpg"}},{"id":"5c3411750a0bb313d41f3d27","name":"OpenStax College Physics","summary":"Edfinity is supported by the National Science Foundation","description":"\u003cp dir=\"ltr\" id=\"isPasted\"\u003eThis online user-contributed homework course comprises of algorithmic problems carefully organized into problem sets mapped to textbook sections. 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randomized variants, hints, and tips\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-hand-holding-heart fa-fw mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eAdaptive learning and personalization\u003cbr\u003e\u003c/strong\u003eEach student receives personalized support\u003cbr\u003eto fill learning gaps.\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-fw fa-code-branch mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eCorequisite course structures\u003cbr\u003e\u003c/strong\u003eUse pre-built corequisite content,\u003cbr\u003eor create your own.\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-hands-helping fa-fw mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eLMS integration and accessibility\u003cbr\u003e\u003c/strong\u003eConnect to your LMS in minutes. \u003ca class=\"”underline”\" href=\"http://edfinity.com/vpat\" target=\"_blank\"\u003eVPAT here\u003c/a\u003e.\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-plug fa-fw mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eWeBWorK-compatible\u003cbr\u003e\u003c/strong\u003eImport and author WeBWorK problems.\u003c/div\u003e","preview_assignment":{"id":"60148172f48b9300048ba1ad","name":"1.1 Functions and Function Notation","product":{"id":"5c776a38346d603ed82ec67a","name":"OpenStax Precalculus"},"master_set":{"id":"68a727fc41e05682ec2bdbdf","problems":{"id":"68a727fc41e05682ec2bdbe8","proof":false,"graphical_geometric":false,"tags_array":[],"skill_ids":[],"contest_event_ids":[],"header":"","solution":"","part_attributes":[{"id":"5c641e34eb855f0004eb0e23","part_id":"5c641e34eb855f0004eb0e22","description":null,"points":2.0,"automatic_manual_credit":true,"accessible":false,"format":"ww","pg":"\n## DBsubject(Algebra)\n## DBchapter()\n## DBsection()\n## KEYWORDS('algebra')\n\n\n#  Initialization\n\nDOCUMENT();\n\nloadMacros(\n\"PGstandard.pl\",\n\"MathObjects.pl\",\n\"AnswerFormatHelp.pl\",\n\"parserPopUp.pl\",\n\"parserImplicitEquation.pl\",\n\"PGML.pl\",\n\"PGcourse.pl\",\n);\n\nTEXT(beginproblem());\n\ninstall_problem_grader(~~\u0026std_problem_grader);\n\n$showPartialCorrectAnswers = 0;\n\n\n$video = MODES(\nHTML=\u003e \n'\u003ciframe width=\"420\" height=\"315\" src=\"//www.youtube.com/embed/zT69oxcMhPw\"frameborder=\"0\" allowfullscreen\u003e\u003c/iframe\u003e', \nTeX =\u003e\n\"An embedded YouTube video.\"\n);\n\n\n#  Setup\n\nContext(\"Numeric\");\n\n$i1=random(1,2);\n$i2=random(3,4);\n$i3=random(5,6);\n$d1=$i2;\n$d2=$i3;\n$d3=random(1,4);\n\n$popup1 = PopUp(\n  [\"?\",\"Yes\",\"No\"],\n  \"Yes\",\n);\n\n$k1=random(1,2);\n$k2=random(3,4);\n$k3=random(5,6);\n$f1=$k2;\n$f2=$k3;\n$f3=random(1,4);\n\n$ck1=chr($k1+96);\n$ck2=chr($k2+96);\n$ck3=chr($k3+96);\n$cf1=chr($f1+96);\n$cf2=chr($f2+96);\n$cf3=$ck3;\n\n$popup2 = PopUp(\n  [\"?\",\"Yes\",\"No\"],\n  \"Yes\",\n);\n\n#  Main text\n\nBEGIN_PGML\n\nDetermine if each of the following relations represents a function.\n\n+ [` \\{([$i1],[$d1]),([$i2],[$d2]),([$i3],[$d3])\\} `]     [___________]{$popup1} \n\n+ [` \\{([$ck1],[$cf1]),([$ck2],[$cf2]),([$ck3],[$cf3])\\} `]     [___________]{$popup1} \n\n\n[$video]*\nEND_PGML\n\n\nBEGIN_TEXT\n$BR\n\nIf the video does not work, \\{ htmlLink (\"https://www.youtube.com/watch?v=zT69oxcMhPw\", \"click here to watch on YouTube.\", \"TARGET='_blank'\")\\}\n$BR\nEND_TEXT\n\n#  Solution\n\n#BEGIN_PGML_SOLUTION\n#Solution explanation goes here.\n#END_PGML_SOLUTION\n\nCOMMENT('MathObject version. Uses PGML.');\n\nENDDOCUMENT();","use_equation_editor":null,"webwork_features":["hide_partial_correctness"],"part_attributes":[{"id":"5c641e34eb855f0004eb0e27","part_id":"5c641e34eb855f0004eb0e25","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"Yes","format":"ws","answer_name":"AnSwEr0001","extra":false,"applet_state":false,"multipart":false,"manually_gradable":false,"answer_text":"Yes"},{"id":"5c641e34eb855f0004eb0e28","part_id":"5c641e34eb855f0004eb0e26","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"Yes","format":"ws","answer_name":"AnSwEr0002","extra":false,"applet_state":false,"multipart":false,"manually_gradable":false,"answer_text":"Yes"}],"interactive_html":"\n\u003cdiv class=\"PGML\"\u003e\nDetermine if each of the following relations represents a function.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cul type=\"square\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003e\\(\\{(2,3),(3,5),(5,3)\\}\\)     \u003cselect name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" size=\"1\" class=\"base-select\"\u003e\n\u003coption value=\"?\" class=\"tex2jax_ignore\"\u003e?\u003c/option\u003e\n\u003coption value=\"Yes\" class=\"tex2jax_ignore\"\u003eYes\u003c/option\u003e\n\u003coption value=\"No\" class=\"tex2jax_ignore\"\u003eNo\u003c/option\u003e\n\u003c/select\u003e \u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003e\\(\\{(a,d),(d,f),(f,f)\\}\\)     \u003cselect name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 \" size=\"1\" class=\"base-select\"\u003e\n\u003coption value=\"?\" class=\"tex2jax_ignore\"\u003e?\u003c/option\u003e\n\u003coption value=\"Yes\" class=\"tex2jax_ignore\"\u003eYes\u003c/option\u003e\n\u003coption value=\"No\" class=\"tex2jax_ignore\"\u003eNo\u003c/option\u003e\n\u003c/select\u003e \u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003ciframe width=\"420\" height=\"315\" src=\"//www.youtube.com/embed/zT69oxcMhPw\" frameborder=\"0\" allowfullscreen\u003e\u003c/iframe\u003e\n\u003c/div\u003e\n\u003cbr\u003e\n\nIf the video does not work, \u003ca href=\"https://www.youtube.com/watch?v=zT69oxcMhPw\" target=\"_blank\"\u003eclick here to watch on YouTube.\u003c/a\u003e\n\u003cbr\u003e","static_html":"\u003cdiv class=\"PGML\"\u003e\nDetermine if each of the following relations represents a function.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cul type=\"square\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003e\\(\\{(2,3),(3,5),(5,3)\\}\\)     \u003cselect class=\"pg-select\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" size=\"1\"\u003e\n\u003coption value=\"?\" class=\"tex2jax_ignore\"\u003e?\u003c/option\u003e\n\u003coption value=\"Yes\" class=\"tex2jax_ignore\"\u003eYes\u003c/option\u003e\n\u003coption value=\"No\" class=\"tex2jax_ignore\"\u003eNo\u003c/option\u003e\n\u003c/select\u003e \u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003e\\(\\{(a,d),(d,f),(f,f)\\}\\)     \u003cselect class=\"pg-select\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 \" size=\"1\"\u003e\n\u003coption value=\"?\" class=\"tex2jax_ignore\"\u003e?\u003c/option\u003e\n\u003coption value=\"Yes\" class=\"tex2jax_ignore\"\u003eYes\u003c/option\u003e\n\u003coption value=\"No\" class=\"tex2jax_ignore\"\u003eNo\u003c/option\u003e\n\u003c/select\u003e \u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003ciframe width=\"420\" height=\"315\" src=\"//www.youtube.com/embed/zT69oxcMhPw\" frameborder=\"0\" allowfullscreen\u003e\u003c/iframe\u003e\n\u003c/div\u003e\n\u003cbr\u003e\n\nIf the video does not work, \u003ca href=\"https://www.youtube.com/watch?v=zT69oxcMhPw\" target=\"_blank\"\u003eclick here to watch on YouTube.\u003c/a\u003e\n\u003cbr\u003e","timeout":false,"header_text":{"css":[],"js":[],"inlinejs":[]}}],"instructional":false,"sketchable":true,"print_num_spacing_lines":3,"print_page_break":false,"corrected":false,"blacklisted":false,"readonly":{"created_at":"2025-08-21T10:06:52.737-04:00","updated_at":"2025-08-21T10:06:52.737-04:00","version":21,"user_id":"58ecdcd48ccf1800120c8ac3","name":"Algorithmic (WebWorK)","skill_ids":[],"current_digest":"a+XhqoobF8VjtDyB9AEDZdag3+wyQTm7383OMMWQnDs=","tags":"algebra","points":2.0,"type":"webwork","multipart":true,"shallow":true,"static":true,"sources":[{"source":"problem","id":"68a727fc41e05682ec2bdbe8"},{"Subject":"Algebra","Comment":"MathObject version. Uses PGML.","source":"part","id":"68a727fc41e05682ec2bdbe8"}],"owned":false,"url":"/problems/68a727fc41e05682ec2bdbe8","searchable_text":"If the video does not work htmlLink https www youtube com watch v zT69oxcMhPw click here to watch on YouTube TARGET blank Determine if each of the following relations represents a function i1 d1 i2 d2 i3 d3 popup1 ck1 cf1 ck2 cf2 ck3 cf3 popup1 video SOLUTION Solution explanation goes here","abilities":["read","create","add","remove","open"]}},"readonly":{"shallow":true}}},"readonly":{"level_range":"13","created_at":"2019-02-27T23:57:28.048-05:00","updated_at":"2026-03-15T15:38:19.610-04:00","tags":"math,oer,openstax,precalculus,college_algebra,trigonometry","author_ids":[],"licensed":true,"thumbnail":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c776a38346d603ed82ec67a/thumb_precalculus-2.jpg","free":false,"user_price":40.0,"term_price":40.0,"displayed_price":40.0,"levels":"13"},"image":{"identifier":"precalculus-2.jpg","size":111998,"url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c776a38346d603ed82ec67a/precalculus-2.jpg","thumb_url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c776a38346d603ed82ec67a/thumb_precalculus-2.jpg"}},{"id":"5c6c7c0e7758b300165b7b6e","name":"OpenStax Calculus Volume 2","summary":"Edfinity is supported by the National Science Foundation","description":"\u003cp dir=\"ltr\" id=\"isPasted\"\u003eThis online user-contributed homework course comprises of algorithmic problems carefully organized into problem sets mapped to textbook sections. 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Save precious class time for discussions.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eEmporium classes:\u003c/strong\u003e Use Edfinity for individual/group work for large enrollment sections in labs.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eEdfinity is a full-featured homework system that supports mathematically-aware problems with algebraic input, evaluation of mathematical expressions, randomized variants, prerequisite pathways for personalized learning, collaboration, coordinated courses, flexible configuration of students\u0026rsquo; experience, and complete customization of assignments.\u003c/p\u003e","description_more":"","price":40.0,"sort_order":0,"active":true,"individual_license":false,"section_id":"60247f638fd7e6000488f801","permissive_license":false,"type":"course","section_license":true,"taxable":false,"purchasable":true,"related_product_ids":["5c533d7d78811e0e5904234d","5c58eabf4a8e21002b802892","5c6cb0717758b325775b77fe","5c735527c6e851001a2555ad","5f16ff9e4a1e8d1366b8f2b1"],"audience":"educator_audience","site_ids":["55843bd46435650003000000"],"show_toc":true,"author_roles":[],"author_role_title":"Contributors (Alphabetical)","tags_array":["math","openstax","oer","calculus"],"hidden_tags":["adaptive"],"term_pricing":true,"highlights":"\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-subscript fa-fw mr-2\"\u003e\u003c/span\u003e \u003cstrong\u003eInteractive, algorithmic problems\u003cbr\u003e\u003c/strong\u003eAlgebraic, graphing, open response; randomized variants, hints, and tips\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-hand-holding-heart fa-fw mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eAdaptive learning and personalization\u003cbr\u003e\u003c/strong\u003eEach student receives personalized support\u003cbr\u003eto fill learning gaps.\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-fw fa-code-branch mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eCorequisite course structures\u003cbr\u003e\u003c/strong\u003eUse pre-built corequisite content,\u003cbr\u003eor create your own.\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-hands-helping fa-fw mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eLMS integration and accessibility\u003cbr\u003e\u003c/strong\u003eConnect to your LMS in minutes. \u003ca class=\"”underline”\" href=\"http://edfinity.com/vpat\" target=\"_blank\"\u003eVPAT here\u003c/a\u003e.\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-plug fa-fw mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eWeBWorK-compatible\u003cbr\u003e\u003c/strong\u003eImport and author WeBWorK problems.\u003c/div\u003e","preview_assignment":{"id":"60247f658fd7e6000488f80a","name":"1.1 Approximating Areas","product":{"id":"5c6c7c0e7758b300165b7b6e","name":"OpenStax Calculus Volume 2"},"master_set":{"id":"68b859a7d3947be6145cca10","problems":{"id":"65db57cebab61d0002d2d100","proof":false,"graphical_geometric":false,"tags_array":[],"skill_ids":["5a137e40c04210000417afb5","5a141b92ac370c0004c74d71","5e052d852c8f6700034fbc95"],"contest_event_ids":[],"header":"","solution":"","part_attributes":[{"id":"5a137e3fc04210000417afa9","part_id":"5a137e3fc04210000417afa8","description":null,"points":4.0,"automatic_manual_credit":true,"accessible":false,"format":"ww","pg":"#DESCRIPTION\n#  Interpreting Riemann sums in terms of area\n#ENDDESCRIPTION\n\n## Updated by the Edfinity Team in 2022\n\n## DBsubject(Calculus - single variable)\n## DBchapter(Integrals)\n## DBsection(Riemann sums)\n## Date(5/10/2008)\n## Institution(University of Rochester)\n## Author(Paul Pearson)\n## MLT(graphs)\n## Level(2)\n## MO(1)\n## TitleText1('Calculus: Early Transcendentals')\n## AuthorText1('James Stewart')\n## EditionText1('6')\n## Section1('5.1')\n## Problem1('2 3 4')\n## KEYWORDS('Integrals', 'Area and Distance','Riemann sums','area')\n\nDOCUMENT();\nloadMacros(\n  \"PGstandard.pl\",\n  \"MathObjects.pl\",\n  \"parserPopUp.pl\",\n  \"PGgraphmacros.pl\",\n  \"weightedGrader.pl\",\n  \"PGcourse.pl\",\n  \"PGML.pl\",\n  \"niceTables.pl\",\n);\n\nContext(\"Numeric\");\n\ninstall_weighted_grader();\n\n$showPartialCorrectAnswers = 1;\n\n# Construct a graph for the left endpoint Riemann sum,\n# define the function to be graphed, and add it to the graph\n$graphL = init_graph(-1,-1,9,9,ticks=\u003e[10,10],axes=\u003e[0,0],pixels=\u003e[400,400]);\n$c = random(4,6,1); # a constant for scaling the function\n$f = FEQ(\"- x**2 / $c + 2 * x for x in \u003c-1,9\u003e using color:blue and weight:2\");\n#$ftex = \"-\\frac{x^2}{$c} + 2 x\";\n$ftex = Compute(\"-x^2/$c + 2x\");\n# the parentheses around $fRefL are necessary\n($fRefL) = plot_functions( $graphL, $f );\n\n\n# Generate arrays of x and y values for the Riemann sum.\n# There are n+1 entries in each array so that we can use\n# only one pair of arrays for both the left and the right \n# endpoint Riemann sums.\n#$a = random(2,4,1); # left endpoint of interval\nif ($c == 4) { $a = random(2,3,1); }\nif ($c == 5) { $a = random(2,4,1); }\nif ($c == 6) { $a = random(3,4,1); }\n$b = $a+4; # right endpoint of interval\n$n = 8; # number of rectangles\n$deltax = ($b - $a)/$n;\nforeach $k (0..$n) { $x[$k] = $a + $k * $deltax; }\nforeach $k (0..$n) { $y[$k] = \u0026{$fRefL-\u003erule}($x[$k]); }\n\n\n# Graph the left endpoint Riemann sum\n$lightblue = $graphL-\u003eim-\u003ecolorAllocate(148,201,255);\n$darkblue = $graphL-\u003eim-\u003ecolorAllocate(100,100,255);\n# Create arrays of pixel references for x and y values\nforeach $k (0..8) {\n   $xpixL[$k] = $graphL-\u003eii($x[$k]);\n   $ypixL[$k] = $graphL-\u003ejj($y[$k]);\n}\n$xaxisL = $graphL-\u003ejj(0);\n# Plot the rectangles in the Riemann sum\nforeach $k (0..$n-1) {\n   $graphL-\u003eim-\u003efilledRectangle($xpixL[$k],$ypixL[$k],$xpixL[$k+1],$xaxisL,$lightblue);\n   $graphL-\u003eim-\u003erectangle($xpixL[$k],$ypixL[$k],$xpixL[$k+1],$xaxisL,$darkblue);\n}\n$graphL-\u003elb(new Label ( 8.5,0,'x','black','right','top'));\n$graphL-\u003elb(new Label ( -0.25,8.5,'y','black','right','top'));\n\n\n# Construct a graph for the right endpoint Riemann sum\n$graphR = init_graph(-1,-1,9,9,ticks=\u003e[10,10],axes=\u003e[0,0],pixels=\u003e[400,400]);\n# the parentheses around $fRefR are necessary\n($fRefR) = plot_functions( $graphR, $f );\n\n\n# Graph the right endpoint Riemann sum\n$lightblue = $graphR-\u003eim-\u003ecolorAllocate(148,201,255);\n$darkblue = $graphR-\u003eim-\u003ecolorAllocate(100,100,255);\n# Create arrays of pixel references for x and y values\nforeach $k (0..8) {\n   $xpixR[$k] = $graphR-\u003eii($x[$k]);\n   $ypixR[$k] = $graphR-\u003ejj($y[$k]);\n}\n$xaxisR = $graphR-\u003ejj(0);\n# Plot the rectangles in the Riemann sum\nforeach $k (1..$n) {\n   $graphR-\u003eim-\u003efilledRectangle($xpixR[$k-1],$ypixR[$k],$xpixR[$k],$xaxisR,$lightblue);\n   $graphR-\u003eim-\u003erectangle($xpixR[$k-1],$ypixR[$k],$xpixR[$k],$xaxisR,$darkblue);\n}\n$graphR-\u003elb(new Label ( 8.5,0,'x','black','right','top'));\n$graphR-\u003elb(new Label ( -0.25,8.5,'y','black','right','top'));\n\n# answers\n\n$LeftRiemannSum = 0;\nforeach $k (0..$n-1) { $LeftRiemannSum = $LeftRiemannSum + $y[$k]; }\n$LeftRiemannSum = Real($deltax * $LeftRiemannSum);\n\n$LeftCompare = PopUp(['[select an answer]','an overestimate of','equal to','an underestimate of','there is ambiguity'],'there is ambiguity');\n\n$RightRiemannSum = 0;\nforeach $k (1..$n) { $RightRiemannSum = $RightRiemannSum + $y[$k]; }\n$RightRiemannSum = Real($deltax * $RightRiemannSum);\n\n$RightCompare = PopUp(['[select an answer]','an overestimate of','equal to','an underestimate of','there is ambiguity'],'there is ambiguity');\n\n# answer checker for LeftCompare and RightCompare.  Original version required 'there is ambiguity' in every case.\n\n$integrate_f = Compute(\"-x^3/(3*$c) + x^2\");\n$area = ($integrate_f-\u003eeval(x=\u003e$b))-($integrate_f-\u003eeval(x=\u003e$a));\n\n$compareCheck = sub {\n  my ($correct,$student,$ansHash)=@_;\n  my $truearea = $ansHash-\u003e{truearea};\n  my $riemannsum = $ansHash-\u003e{riemannsum}; \n  my $alt;\n  if ($riemannsum \u003c $truearea){\n    $alt = 'an underestimate of';\n  }\n  elsif ($riemannsum \u003e $truearea){\n    $alt = 'an overestimate of';\n  }\n  else {\n    $alt = 'equal to';\n  }\n  if ( ($student eq $alt) or ($student eq 'there is ambiguity') ){\n    return 1;\n  }\n  else {\n    return 0;\n  }\n};\n\n\nTEXT(beginproblem());\nContext()-\u003etexStrings;\nBEGIN_PGML\n\na. The rectangles in the graph below illustrate a left endpoint Riemann sum for [` \\displaystyle f(x) = [$ftex] `] \non the interval [` \\lbrack [$a], [$b] \\rbrack `].  \n\n    The value of this left endpoint Riemann sum is [__], \n    and this Riemann sum is [@ $LeftCompare-\u003emenu() @]*** the area\n    of the region enclosed by [`\\displaystyle y = f(x) `], the x-axis, and\n    the vertical lines [`x = [$a]`] and [`x = [$b]`].\n    \n    [@\n    DataTable([\n        [image( insertGraph($graphL), width=\u003e400, tex_size=\u003e800 ) ],\n        [\"Left endpoint Riemann sum for \\\\(y = $ftex \\\\) on \\\\( \\\\lbrack $a, $b \\\\rbrack \\\\)\"]\n    ],\n    midrules=\u003e1,\n    align=\u003e'|c|')\n    @]***\n\n\nb. The rectangles in the graph below illustrate a right endpoint Riemann sum for [` \\displaystyle f(x) = [$ftex] `] \non the interval [` \\lbrack [$a], [$b] \\rbrack `].\n\n    The value of this right endpoint Riemann sum is [__], \n    and this Riemann sum is [@ $RightCompare-\u003emenu() @]*** the area \n    of the region enclosed by [`\\displaystyle y = f(x) `], the x-axis, \n    the vertical lines [`x = [$a]`] and [`x = [$b]`].\n    \n    [@\n    DataTable([\n        [image( insertGraph($graphR), width=\u003e400, tex_size=\u003e800 ) ],\n        [\"Right endpoint Riemann sum for \\\\(y = $ftex \\\\) on \\\\( \\\\lbrack $a, $b \\\\rbrack \\\\)\"]\n    ],\n    midrules=\u003e1,\n    align=\u003e'|c|')\n    @]***\n\nEND_PGML\nContext()-\u003enormalStrings;\n\nWEIGHTED_ANS( $LeftRiemannSum-\u003ecmp(),45);\nWEIGHTED_ANS( $LeftCompare-\u003ecmp( checker =\u003e $compareCheck, truearea =\u003e $area, riemannsum =\u003e $LeftRiemannSum ),5);\nWEIGHTED_ANS( $RightRiemannSum-\u003ecmp(),45);\nWEIGHTED_ANS( $RightCompare-\u003ecmp(checker =\u003e $compareCheck, truearea =\u003e $area, riemannsum =\u003e $RightRiemannSum ),5);\n\n#NAMED_WEIGHTED_ANS('optional2',str_cmp(\"there is ambiguity\"),5);\n\n#NAMED_WEIGHTED_ANS('optional3',num_cmp($RightRiemannSum),45);\n\n#NAMED_WEIGHTED_ANS('optional4',str_cmp(\"there is ambiguity\"),5);\n\nContext()-\u003etexStrings;\nSOLUTION(EV3(\u003c\u003c'END_SOLUTION'));\n\na. The left endpoint Riemann sum is \n\\( f($x[0]) \\cdot 0.5 + f($x[1]) \\cdot 0.5 + \\cdots + f($x[$n-1]) \\cdot 0.5\n= ( $y[0] + $y[1] + \\cdots + $y[7] ) \\cdot 0.5 = $LeftRiemannSum.\\)\n$BR\n$BR\n\nb. The right endpoint Riemann sum is \n\\( f($x[1]) \\cdot 0.5 + f($x[2]) \\cdot 0.5 + \\cdots + f($x[$n]) \\cdot 0.5\n= ( $y[1] + $y[2] + \\cdots + $y[$n] ) \\cdot 0.5  = $RightRiemannSum.\\)\n\nEND_SOLUTION\nContext()-\u003enormalStrings;\n\nENDDOCUMENT();\n","use_equation_editor":null,"webwork_features":[],"part_attributes":[{"id":"630503d75844e2000459d6ed","part_id":"5a137e40c04210000417afab","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"22.0833","format":"ws","answer_name":"AnSwEr0001","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"\\(22.0833\\)"},{"id":"630503d75844e2000459d6ee","part_id":"5a137e40c04210000417afac","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"there is ambiguity","format":"ws","answer_name":"AnSwEr0002","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"there is ambiguity"},{"id":"630503d75844e2000459d6ef","part_id":"5a137e40c04210000417afad","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"22.75","format":"ws","answer_name":"AnSwEr0003","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"\\(22.75\\)"},{"id":"630503d75844e2000459d6f0","part_id":"5a137e40c04210000417afae","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"there is ambiguity","format":"ws","answer_name":"AnSwEr0004","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"there is ambiguity"}],"interactive_html":"\n\u003cdiv class=\"PGML\"\u003e\n\u003col type=\"a\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003eThe rectangles in the graph below illustrate a left endpoint Riemann sum for \\(\\displaystyle f(x) = {\\frac{-x^{2}}{6}+2x}\\) \non the interval \\(\\lbrack 3, 7 \\rbrack\\).\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nThe value of this left endpoint Riemann sum is \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0001\" value=\"\"\u003e\n, \nand this Riemann sum is \u003cselect name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 \" size=\"1\" class=\"base-select\"\u003e\n\u003coption value=\"[select an answer]\" class=\"tex2jax_ignore\"\u003e[select an answer]\u003c/option\u003e\n\u003coption value=\"an overestimate of\" class=\"tex2jax_ignore\"\u003ean overestimate of\u003c/option\u003e\n\u003coption value=\"equal to\" class=\"tex2jax_ignore\"\u003eequal to\u003c/option\u003e\n\u003coption value=\"an underestimate of\" class=\"tex2jax_ignore\"\u003ean underestimate of\u003c/option\u003e\n\u003coption value=\"there is ambiguity\" class=\"tex2jax_ignore\"\u003ethere is ambiguity\u003c/option\u003e\n\u003c/select\u003e the area\nof the region enclosed by \\(\\displaystyle y = f(x)\\), the x-axis, and\nthe vertical lines \\(x = 3\\) and \\(x = 7\\).\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003ctable style=\"border-collapse:collapse; text-align:center; margin:0 auto; \"\u003e\n\u003ccolgroup\u003e\u003ccol style=\"border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; \"\u003e\u003c/colgroup\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\u003ctd style=\"padding-left:6pt; padding-right:6pt; border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; border-top:solid 1px; \"\u003e\n\u003ca href=\"https://webwork.edfinity.com/webwork2_files/tmp/quick/2022/08-23//gif/d8fb65ac-fea0-3d27-aa4d-2480ca8d6616___60bebb46-6ea6-3df3-8c43-11d9de3e8f5b.png\" target=\"_blank\" onclick=\"window.open(this.href,this.target, 'width=430,height=430,scrollbars=yes,resizable=on'); return false;\"\u003e\n\t\t\t         \u003cimg src=\"https://webwork.edfinity.com/webwork2_files/tmp/quick/2022/08-23//gif/d8fb65ac-fea0-3d27-aa4d-2480ca8d6616___60bebb46-6ea6-3df3-8c43-11d9de3e8f5b.png\" width=\"400\" alt=\"generated image\"\u003e\n\t\t\t         \u003c/a\u003e\n\t\t\t\u003c/td\u003e\u003c/tr\u003e\n\u003ctr\u003e\u003ctd style=\"padding-left:6pt; padding-right:6pt; border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; border-top:solid 1px; border-bottom:solid 1px; \"\u003eLeft endpoint Riemann sum for \\(y = \\frac{-x^{2}}{6}+2x\\) on \\(\\lbrack 3, 7 \\rbrack\\)\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eThe rectangles in the graph below illustrate a right endpoint Riemann sum for \\(\\displaystyle f(x) = {\\frac{-x^{2}}{6}+2x}\\) \non the interval \\(\\lbrack 3, 7 \\rbrack\\).\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nThe value of this right endpoint Riemann sum is \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0003\" value=\"\"\u003e\n, \nand this Riemann sum is \u003cselect name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 \" size=\"1\" class=\"base-select\"\u003e\n\u003coption value=\"[select an answer]\" class=\"tex2jax_ignore\"\u003e[select an answer]\u003c/option\u003e\n\u003coption value=\"an overestimate of\" class=\"tex2jax_ignore\"\u003ean overestimate of\u003c/option\u003e\n\u003coption value=\"equal to\" class=\"tex2jax_ignore\"\u003eequal to\u003c/option\u003e\n\u003coption value=\"an underestimate of\" class=\"tex2jax_ignore\"\u003ean underestimate of\u003c/option\u003e\n\u003coption value=\"there is ambiguity\" class=\"tex2jax_ignore\"\u003ethere is ambiguity\u003c/option\u003e\n\u003c/select\u003e the area \nof the region enclosed by \\(\\displaystyle y = f(x)\\), the x-axis, \nthe vertical lines \\(x = 3\\) and \\(x = 7\\).\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003ctable style=\"border-collapse:collapse; text-align:center; margin:0 auto; \"\u003e\n\u003ccolgroup\u003e\u003ccol style=\"border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; \"\u003e\u003c/colgroup\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\u003ctd style=\"padding-left:6pt; padding-right:6pt; border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; border-top:solid 1px; \"\u003e\n\u003ca href=\"https://webwork.edfinity.com/webwork2_files/tmp/quick/2022/08-23//gif/d8fb65ac-fea0-3d27-aa4d-2480ca8d6616___616c684b-f660-38d4-b603-7b9c3cdc0b00.png\" target=\"_blank\" onclick=\"window.open(this.href,this.target, 'width=430,height=430,scrollbars=yes,resizable=on'); return false;\"\u003e\n\t\t\t         \u003cimg src=\"https://webwork.edfinity.com/webwork2_files/tmp/quick/2022/08-23//gif/d8fb65ac-fea0-3d27-aa4d-2480ca8d6616___616c684b-f660-38d4-b603-7b9c3cdc0b00.png\" width=\"400\" alt=\"generated image\"\u003e\n\t\t\t         \u003c/a\u003e\n\t\t\t\u003c/td\u003e\u003c/tr\u003e\n\u003ctr\u003e\u003ctd style=\"padding-left:6pt; padding-right:6pt; border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; border-top:solid 1px; border-bottom:solid 1px; \"\u003eRight endpoint Riemann sum for \\(y = \\frac{-x^{2}}{6}+2x\\) on \\(\\lbrack 3, 7 \\rbrack\\)\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class=\"solution\"\u003e\u003cp\u003e\u003cb\u003eSolution:\u003c/b\u003e \u003cbr\u003e\na. The left endpoint Riemann sum is \n\\(f(3) \\cdot 0.5 + f(3.5) \\cdot 0.5 + \\cdots + f(6.5) \\cdot 0.5\n= ( 4.5 + 4.95833333333333 + \\cdots + 5.95833333333333 ) \\cdot 0.5 = 22.0833.\\)\n\u003cbr\u003e\n\u003cbr\u003e\n\nb. The right endpoint Riemann sum is \n\\(f(3.5) \\cdot 0.5 + f(4) \\cdot 0.5 + \\cdots + f(7) \\cdot 0.5\n= ( 4.95833333333333 + 5.33333333333333 + \\cdots + 5.83333333333333 ) \\cdot 0.5  = 22.75.\\)\n\n\n\u003c/p\u003e\u003c/div\u003e","static_html":"\u003cdiv class=\"PGML\"\u003e\n\u003col type=\"a\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003eThe rectangles in the graph below illustrate a left endpoint Riemann sum for \\(\\displaystyle f(x) = {\\frac{-x^{2}}{6}+2x}\\) \non the interval \\(\\lbrack 3, 7 \\rbrack\\).\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nThe value of this left endpoint Riemann sum is \u003cspan class=\"ww-blank\" name=\"AnSwEr0001\"\u003e \u003c/span\u003e\n\n, \nand this Riemann sum is \u003cselect class=\"pg-select\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 \" size=\"1\"\u003e\n\u003coption value=\"[select an answer]\" class=\"tex2jax_ignore\"\u003e[select an answer]\u003c/option\u003e\n\u003coption value=\"an overestimate of\" class=\"tex2jax_ignore\"\u003ean overestimate of\u003c/option\u003e\n\u003coption value=\"equal to\" class=\"tex2jax_ignore\"\u003eequal to\u003c/option\u003e\n\u003coption value=\"an underestimate of\" class=\"tex2jax_ignore\"\u003ean underestimate of\u003c/option\u003e\n\u003coption value=\"there is ambiguity\" class=\"tex2jax_ignore\"\u003ethere is ambiguity\u003c/option\u003e\n\u003c/select\u003e the area\nof the region enclosed by \\(\\displaystyle y = f(x)\\), the x-axis, and\nthe vertical lines \\(x = 3\\) and \\(x = 7\\).\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003ctable style=\"border-collapse:collapse; text-align:center; margin:0 auto; \"\u003e\n\u003ccolgroup\u003e\u003ccol style=\"border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; \"\u003e\u003c/colgroup\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\u003ctd style=\"padding-left:6pt; padding-right:6pt; border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; border-top:solid 1px; \"\u003e\n\u003cimg src=\"https://webwork.edfinity.com/webwork2_files/tmp/quick/2022/08-23//gif/d8fb65ac-fea0-3d27-aa4d-2480ca8d6616___60bebb46-6ea6-3df3-8c43-11d9de3e8f5b.png\" width=\"400\" alt=\"generated image\"\u003e\n\t\t\t\u003c/td\u003e\u003c/tr\u003e\n\u003ctr\u003e\u003ctd style=\"padding-left:6pt; padding-right:6pt; border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; border-top:solid 1px; border-bottom:solid 1px; \"\u003eLeft endpoint Riemann sum for \\(y = \\frac{-x^{2}}{6}+2x\\) on \\(\\lbrack 3, 7 \\rbrack\\)\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eThe rectangles in the graph below illustrate a right endpoint Riemann sum for \\(\\displaystyle f(x) = {\\frac{-x^{2}}{6}+2x}\\) \non the interval \\(\\lbrack 3, 7 \\rbrack\\).\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nThe value of this right endpoint Riemann sum is \u003cspan class=\"ww-blank\" name=\"AnSwEr0003\"\u003e \u003c/span\u003e\n\n, \nand this Riemann sum is \u003cselect class=\"pg-select\" name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 \" size=\"1\"\u003e\n\u003coption value=\"[select an answer]\" class=\"tex2jax_ignore\"\u003e[select an answer]\u003c/option\u003e\n\u003coption value=\"an overestimate of\" class=\"tex2jax_ignore\"\u003ean overestimate of\u003c/option\u003e\n\u003coption value=\"equal to\" class=\"tex2jax_ignore\"\u003eequal to\u003c/option\u003e\n\u003coption value=\"an underestimate of\" class=\"tex2jax_ignore\"\u003ean underestimate of\u003c/option\u003e\n\u003coption value=\"there is ambiguity\" class=\"tex2jax_ignore\"\u003ethere is ambiguity\u003c/option\u003e\n\u003c/select\u003e the area \nof the region enclosed by \\(\\displaystyle y = f(x)\\), the x-axis, \nthe vertical lines \\(x = 3\\) and \\(x = 7\\).\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003ctable style=\"border-collapse:collapse; text-align:center; margin:0 auto; \"\u003e\n\u003ccolgroup\u003e\u003ccol style=\"border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; \"\u003e\u003c/colgroup\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\u003ctd style=\"padding-left:6pt; padding-right:6pt; border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; border-top:solid 1px; \"\u003e\n\u003cimg src=\"https://webwork.edfinity.com/webwork2_files/tmp/quick/2022/08-23//gif/d8fb65ac-fea0-3d27-aa4d-2480ca8d6616___616c684b-f660-38d4-b603-7b9c3cdc0b00.png\" width=\"400\" alt=\"generated image\"\u003e\n\t\t\t\u003c/td\u003e\u003c/tr\u003e\n\u003ctr\u003e\u003ctd style=\"padding-left:6pt; padding-right:6pt; border-right:solid 1px; border-left:solid 1px; text-align:center; white-space:nowrap; border-top:solid 1px; border-bottom:solid 1px; \"\u003eRight endpoint Riemann sum for \\(y = \\frac{-x^{2}}{6}+2x\\) on \\(\\lbrack 3, 7 \\rbrack\\)\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class=\"solution\"\u003e\u003cp\u003e\u003cb\u003eSolution:\u003c/b\u003e \u003cbr\u003e\na. The left endpoint Riemann sum is \n\\(f(3) \\cdot 0.5 + f(3.5) \\cdot 0.5 + \\cdots + f(6.5) \\cdot 0.5\n= ( 4.5 + 4.95833333333333 + \\cdots + 5.95833333333333 ) \\cdot 0.5 = 22.0833.\\)\n\u003cbr\u003e\n\u003cbr\u003e\n\nb. The right endpoint Riemann sum is \n\\(f(3.5) \\cdot 0.5 + f(4) \\cdot 0.5 + \\cdots + f(7) \\cdot 0.5\n= ( 4.95833333333333 + 5.33333333333333 + \\cdots + 5.83333333333333 ) \\cdot 0.5  = 22.75.\\)\n\n\n\u003c/p\u003e\u003c/div\u003e","timeout":false,"header_text":{"css":[],"js":[],"inlinejs":[]}}],"instructional":false,"sketchable":true,"print_num_spacing_lines":3,"print_page_break":false,"corrected":false,"blacklisted":false,"readonly":{"created_at":"2024-02-25T10:07:58.685-05:00","updated_at":"2024-02-25T10:07:58.685-05:00","version":118,"user_id":"58ecdcd48ccf1800120c8ac3","name":"Algorithmic (WebWorK)","skill_ids":["5a137e40c04210000417afb5","5a141b92ac370c0004c74d71","5e052d852c8f6700034fbc95"],"current_digest":"cGZM9x4dnQMG+akXT3MA0zrZbGpnSNNVkheJTYOlULQ=","tags":"area,area and distance,integrals,riemann sums","points":4.0,"type":"webwork","multipart":true,"shallow":true,"static":true,"sources":[{"source":"problem","id":"65db57cebab61d0002d2d100"},{"Subject":"Calculus - single variable","Title":"Calculus: Early Transcendentals","ChapterTitle":"Integrals","ChapterSection":["Riemann Sums"],"ChapterNumber":"5.1","Edition":"6","Author":"James Stewart","CodeInstitution":"University of Rochester","CodeAuthor":"Paul Pearson","Level":"2","ProblemNumber":"2 3 4","source":"part","id":"65db57cebab61d0002d2d100"}],"owned":false,"url":"/problems/65db57cebab61d0002d2d100","searchable_text":"a The left endpoint Riemann sum is f x 0 cdot 0 5 f x 1 cdot 0 5 cdots f x n 1 cdot 0 5 y 0 y 1 cdots y 7 cdot 0 5 LeftRiemannSum b The right endpoint Riemann sum is f x 1 cdot 0 5 f x 2 cdot 0 5 cdots f x n cdot 0 5 y 1 y 2 cdots y n cdot 0 5 RightRiemannSum a The rectangles in the graph below illustrate a left endpoint Riemann sum for displaystyle f x ftex on the interval lbrack a b rbrack The value of this left endpoint Riemann sum is and this Riemann sum is LeftCompare menu the area of the region enclosed by displaystyle y f x the x axis and the vertical lines x a and x b DataTable image insertGraph graphL width 400 tex size 800 Left endpoint Riemann sum for y ftex on lbrack a b rbrack midrules 1 align c b The rectangles in the graph below illustrate a right endpoint Riemann sum for displaystyle f x ftex on the interval lbrack a b rbrack The value of this right endpoint Riemann sum is and this Riemann sum is RightCompare menu the area of the region enclosed by displaystyle y f x the x axis the vertical lines x a and x b DataTable image insertGraph graphR width 400 tex size 800 Right endpoint Riemann sum for y ftex on lbrack a b rbrack midrules 1 align c","abilities":["read","create","add","remove","open"]},"content_license":{"license_type":"OPL","source_url":"https://github.com/Edfinity/webwork-open-problem-library/blob/97db7f4511788610ad3f32581f54d426835f5cc1/OpenProblemLibrary/Rochester/setIntegrals0Theory/S05.01.AreaDistance.PTP00.pg"}},"readonly":{"shallow":true}}},"readonly":{"level_range":"13","created_at":"2019-02-19T16:58:38.697-05:00","updated_at":"2026-03-15T15:38:19.293-04:00","tags":"math,openstax,oer,calculus","author_ids":[],"licensed":true,"thumbnail":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c6c7c0e7758b300165b7b6e/thumb_calculus-4.jpg","free":false,"user_price":40.0,"term_price":40.0,"displayed_price":40.0,"levels":"13"},"image":{"identifier":"calculus-4.jpg","size":92521,"url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c6c7c0e7758b300165b7b6e/calculus-4.jpg","thumb_url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c6c7c0e7758b300165b7b6e/thumb_calculus-4.jpg"}},{"id":"5c6cb0717758b325775b77fe","name":"OpenStax Calculus Volume 3","summary":"Edfinity is supported by the National Science Foundation","description":"\u003cp dir=\"ltr\" id=\"isPasted\"\u003eThis online user-contributed homework course comprises of algorithmic problems carefully organized into problem sets mapped to textbook sections. Use this course as-is, or customize at any level. You can mix-and-match problems from other user-contributed courses, add problems from the user-contributed problem repository, or write your own problems.\u003c/p\u003e\u003cp dir=\"ltr\"\u003e\u003cstrong\u003eHow to use this course\u003c/strong\u003e\u003c/p\u003e\u003col\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eHomework\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Assign high quality problems with hints and personalized feedback to develop problem-solving skills.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eTesting\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Create summative secure online quizzes and tests in minutes.\u0026nbsp;\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eSupplementary resources:\u003c/strong\u003e Embed videos, class notes, and applets alongside assignments.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eIntervention:\u003c/strong\u003e Use rich analytics to identify and monitor at-risk students for timely intervention.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eAnalytics:\u003c/strong\u003e Drill down into student performance and identify problematic or difficult topics.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eFlipped classroom:\u003c/strong\u003e Assign pre-class assignments. 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       # This should be the first executable line in the problem.\n\nloadMacros(\n    \"PGstandard.pl\",\n    \"MathObjects.pl\",\n    \"PGML.pl\",\n);\n\nTEXT(beginproblem());\n\nContext(\"Numeric\")-\u003evariables-\u003eadd(y=\u003e\"Real\",t=\u003e\"Real\");\n$a = random(2,9);\ndo {$b = random(1,9);} until ($b != $a);\n$r = random(2,5);\n$rr = $r**2;\n$y = Formula(\"$b-$r*sin(t)\");\n\nBEGIN_PGML\nThe circle\n\n\u003e\u003e [``(x - [$a])^2 + (y - [$b])^2 = [$rr]``] \u003c\u003c\n\ncan be drawn with parametric equations.\nAssuming the circle is traced clockwise as the parameter increases and\n\n\u003e\u003e [``x(t) = [$a] + [$r] \\cos t``], \u003c\u003c\n\nthen \n\n\u003e\u003e [``y(t) = ``] [__]{$y}. \u003c\u003c\n\nEND_PGML\n\nENDDOCUMENT();\n","use_equation_editor":null,"webwork_features":[],"part_attributes":[{"id":"637fc5c158ed1a0004e9bde0","part_id":"5a134a64c04210000413c91a","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"1-3*sin(t)","format":"ws","answer_name":"AnSwEr0001","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"\\(1-3\\sin\\!\\left(t\\right)\\)"}],"interactive_html":"\n\u003cdiv class=\"PGML\"\u003e\nThe circle\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{(x - 9)^2 + (y - 1)^2 = 9}\\)\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\ncan be drawn with parametric equations.\nAssuming the circle is traced clockwise as the parameter increases and\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{x(t) = 9 + 3 \\cos t}\\),\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nthen \n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{y(t) = }\\) \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0001\" value=\"\"\u003e\n.\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e","static_html":"\u003cdiv class=\"PGML\"\u003e\nThe circle\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{(x - 9)^2 + (y - 1)^2 = 9}\\)\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\ncan be drawn with parametric equations.\nAssuming the circle is traced clockwise as the parameter increases and\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{x(t) = 9 + 3 \\cos t}\\),\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nthen \n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{y(t) = }\\) \u003cspan class=\"ww-blank\" name=\"AnSwEr0001\"\u003e \u003c/span\u003e\n\n.\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e","timeout":false,"header_text":{"css":[],"js":[],"inlinejs":[]}}],"instructional":false,"sketchable":true,"print_num_spacing_lines":3,"print_page_break":false,"corrected":false,"blacklisted":false,"readonly":{"created_at":"2023-12-13T16:41:36.946-05:00","updated_at":"2023-12-13T16:41:36.946-05:00","version":41,"user_id":"58ecdcd48ccf1800120c8ac3","name":"Algorithmic (WebWorK)","skill_ids":["5a134a55c04210000413c84e","5a141ca6ac370c0004c7579f","5a134a55c04210000413c84e","5a141ca6ac370c0004c7579f","5a1ec4d9dbc33f0004162df5","5a134a55c04210000413c84e","5a141ca6ac370c0004c7579f","5a1ec4d9dbc33f0004162df5","5a134a55c04210000413c84e","5a141ca6ac370c0004c7579f","5a1ec4d9dbc33f0004162df5"],"current_digest":"Zzq6cfwviOHSpmMB3tWWnhCEWxoZpEKcsHhA2Ay9nXk=","tags":"polar coordinates","points":1.0,"type":"webwork","multipart":false,"shallow":true,"static":true,"sources":[{"source":"problem","id":"657a2510ca75f9000262a4d7"},{"Subject":"Calculus - single variable","Title":"Calculus: Early Transcendentals","ChapterTitle":"Parametric","ChapterSection":["Curves"],"ChapterNumber":"11.1","Edition":"1","Author":"Rogawski","Level":"2","ProblemNumber":"30","source":"part","id":"657a2510ca75f9000262a4d7"}],"owned":false,"url":"/problems/657a2510ca75f9000262a4d7","searchable_text":"The circle x a 2 y b 2 rr can be drawn with parametric equations Assuming the circle is traced clockwise as the parameter increases and x t a r cos t then y t y","abilities":["read","create","add","remove","open"]}},"readonly":{"shallow":true}}},"readonly":{"level_range":"13","created_at":"2019-02-19T20:42:09.786-05:00","updated_at":"2026-03-15T15:38:19.276-04:00","tags":"math,openstax,oer,calculus","author_ids":[],"licensed":true,"thumbnail":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c6cb0717758b325775b77fe/thumb_calculus-4.jpg","free":false,"user_price":40.0,"term_price":40.0,"displayed_price":40.0,"levels":"13"},"image":{"identifier":"calculus-4.jpg","size":92521,"url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c6cb0717758b325775b77fe/calculus-4.jpg","thumb_url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c6cb0717758b325775b77fe/thumb_calculus-4.jpg"}},{"id":"5ceac311339ffb605929190f","name":"OpenStax University Physics Vol. 1 - Mechanics","summary":"Edfinity is supported by the National Science Foundation","description":"\u003cp dir=\"ltr\" id=\"isPasted\"\u003eThis online user-contributed homework course comprises of algorithmic problems carefully organized into problem sets mapped to textbook sections. 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Student must simplify.\nContext()-\u003eoperators-\u003eundefine(\"+\",\"-\",\"*\",\"/\");\n\nBEGIN_TEXT \n\nSimplify the expression:\n$PAR\n$BCENTER\n \\($a+$b \\times 2\\)\n\n$ECENTER\n$PAR\n\n\\{ans_rule(20)\\}\nEND_TEXT\nContext()-\u003enormalStrings;\n\n##############################################################\n#\n#  Answers\n#\n#\n\nANS($ans-\u003ecmp);\n\n\nENDDOCUMENT();        ","use_equation_editor":null,"webwork_features":[],"part_attributes":[{"id":"6140143fe83ef70004abc874","part_id":"5aed04bf606633a77096392d","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"16+4*2","format":"ws","answer_name":"AnSwEr0001","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"\\(16+4\\cdot 2\\)"}],"interactive_html":"\n\nSimplify the expression:\n\u003cdiv align=\"center\"\u003e\n \\(16+4 \\times 2\\)\n\n\u003c/div\u003e\n\u003cp\u003e\n\n\u003cinput type=\"text\" class=\"codeshard\" size=\"20\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0001\" value=\"\"\u003e\n\n\n\u003c/p\u003e","static_html":"\u003cp\u003e\n\nSimplify the expression:\n\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \\(16+4 \\times 2\\)\n\n\u003c/div\u003e\n\u003cp\u003e\n\n\u003cspan class=\"ww-blank\" name=\"AnSwEr0001\"\u003e \u003c/span\u003e\n\n\n\n\u003c/p\u003e","timeout":false,"header_text":{"css":[],"js":[],"inlinejs":[]}}],"instructional":false,"sketchable":true,"print_num_spacing_lines":3,"print_page_break":false,"corrected":false,"blacklisted":false,"readonly":{"created_at":"2024-09-01T15:01:23.196-04:00","updated_at":"2024-09-01T15:01:23.196-04:00","version":27,"user_id":"58ecdcd48ccf1800120c8ac3","name":"Algorithmic (WebWorK)","skill_ids":["5a135ec1c04210000415682c","5a1420fdac370c0004c7801e","5a135ec1c04210000415682c","5a1420fdac370c0004c7801e","5a135ec1c04210000415682c","5a1420fdac370c0004c7801e"],"current_digest":"PE29voU0tYKySf4RtUGln8O57I33bdx/Yvjqoma8x3Q=","tags":"common core,prealgebra","points":1.0,"type":"webwork","multipart":false,"shallow":true,"static":true,"sources":[{"source":"problem","id":"66d4ba03511ae000025648c5"},{"Subject":"Arithmetic","Title":"Pre-Algebra","ChapterTitle":"Integers","ChapterSection":"Multiple operations","ChapterNumber":".","CodeInstitution":"Mississippi College","CodeAuthor":"John Travis","Level":"2","source":"part","id":"66d4ba03511ae000025648c5"}],"owned":false,"url":"/problems/66d4ba03511ae000025648c5","searchable_text":"Simplify the expression PAR BCENTER a b times 2 ECENTER PAR ans rule 20","abilities":["read","create","add","remove","open"]},"content_license":{"license_type":"OPL","source_url":"https://github.com/Edfinity/webwork-open-problem-library/blob/0914437ac334603bf1f15257757073ac63121956/OpenProblemLibrary/MC/PreAlgebra/setPreAlgebraC01S02/OrderOps03.pg"}},"readonly":{"shallow":true}}},"readonly":{"level_range":"13","created_at":"2019-09-06T11:54:46.695-04:00","updated_at":"2026-03-15T15:38:19.410-04:00","tags":"openstax,trigonometry,algebra,college_algebra","author_ids":[],"licensed":true,"thumbnail":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5d7281469184305031d25d1a/thumb_algebra-and-trigonometry-2.jpg","free":false,"user_price":40.0,"term_price":40.0,"displayed_price":40.0,"levels":"13"},"image":{"identifier":"algebra-and-trigonometry-2.jpg","size":85044,"url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5d7281469184305031d25d1a/algebra-and-trigonometry-2.jpg","thumb_url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5d7281469184305031d25d1a/thumb_algebra-and-trigonometry-2.jpg"}}]}