{"id":"cb_question_bank:00e83679-c3d7-4a99-a021-2eb49c3891b2","source_id":"cb_question_bank","source_item_id":"00e83679-c3d7-4a99-a021-2eb49c3891b2","external_id":"abfd9618-c65d-4fd8-9f89-254e3dfa9529","ibn":null,"question_id":"beca03de","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A rectangle has a length that is 15 times its width. The function y equals left parenthesis 15 w right parenthesis left parenthesis w right parenthesis represents this situation, where y is the area, in square feet, of the rectangle and y greater than 0 . Which of the following is the best interpretation of 15 w in this context?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A rectangle has a length that is <math alttext=\"15\"><mn>15</mn>\n</math> times its width. The function <math alttext=\"y equals left parenthesis 15 w right parenthesis left parenthesis w right parenthesis\"><mi>y</mi><mo>=</mo><mfenced><mrow><mrow><mn>15</mn></mrow><mi>w</mi></mrow></mfenced><mfenced><mi>w</mi></mfenced></math> represents this situation, where <math alttext=\"y\"><mi>y</mi>\n</math> is the area, in square feet, of the rectangle and <math alttext=\"y greater than 0\"><mi>y</mi><mo>&gt;</mo><mn>0</mn></math>. Which of the following is the best interpretation of <math alttext=\"15 w\"><mrow><mn>15</mn></mrow><mi>w</mi></math> in this context?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It's given that a rectangle has a length that is <math alttext=\"15\"><mn>15</mn>\n</math> times its width. It's also given that the function <math alttext=\"y equals left parenthesis 15 w right parenthesis left parenthesis w right parenthesis\"><mi>y</mi><mo>=</mo><mfenced><mrow><mn>15</mn><mi>w</mi></mrow></mfenced><mfenced><mi>w</mi></mfenced></math> represents this situation, where <math alttext=\"y\"><mi>y</mi>\n</math> is the area, in square feet, of the rectangle and <math alttext=\"y greater than 0\"><mi>y</mi><mo>&gt;</mo><mn>0</mn></math>. The area of a rectangle can be calculated by multiplying the rectangle's length by its width. Since the rectangle has a length that is <math alttext=\"15\"><mn>15</mn>\n</math> times its width, it follows that <math alttext=\"w\"><mi>w</mi>\n</math> represents the width of the rectangle, in feet, and <math alttext=\"15 w\"><mrow>\n\t<mn>15</mn>\n\t<mi>w</mi>\n</mrow>\n</math> represents the length of the rectangle, in feet. Therefore, the best interpretation of <math alttext=\"15 w\"><mrow>\n\t<mn>15</mn>\n\t<mi>w</mi>\n</mrow>\n</math> in this context is that it's the length of the rectangle, in feet.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is the best interpretation of <math alttext=\"y\"><mi>y</mi>\n</math>, not <math alttext=\"15 w\"><mrow>\n\t<mn>15</mn>\n\t<mi>w</mi>\n</mrow>\n</math>, in the given function.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is the best interpretation of <math alttext=\"w\"><mi>w</mi>\n</math>, not <math alttext=\"15 w\"><mrow>\n\t<mn>15</mn>\n\t<mi>w</mi>\n</mrow>\n</math>, in the given function.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.826000+00:00","source_updated_at":"2023-08-02T20:25:59.826000+00:00","options":[{"label":"A","content_html":"<p style=\"text-align: left;\">The length of the rectangle, in feet</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">The area of the rectangle, in square feet</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">The difference between the length and the width of the rectangle, in feet</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">&nbsp;The width of the rectangle, in feet</p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}