{"id":"act_practice_pdf:pt1:math:008","source_id":"act_practice_pdf","source_item_id":"pt1-math-008","external_id":null,"program":"ACT","section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":"N","subcategory":"Number & Quantity","form_id":"act_practice_pdf:pt1","passage_id":null,"position":8,"scored":true,"layout_warning":"Stacked notation (fractions, radicals, matrices) does not survive text extraction. The image above is the question as printed; the text below it is approximate.","stem":"The initial speed, in miles per hour, of a certain car that skids to a stop can be estimated by multiplying the length of the skid, in feet, by 35 and then taking the square root of the product. According to this method, what is the estimated initial speed, in miles per hour, of the car when it makes a 108 -foot skid? _","stimulus":"","stimulus_html":"
\"Question
As printed in the official booklet.
","stem_html":"

The initial speed, in miles per hour, of a certain car that skids to a stop can be estimated by multiplying the length of the skid, in feet, by 35 and then taking the square root of the product. According to this method, what is the estimated initial speed, in miles per hour, of the car when it makes a 108 -foot skid? _

","rationale_html":null,"correct_answer":["H"],"equiv_key":"f24bc59e660c914dbf49a3f7","has_media":true,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"F","content_html":"

√ 143 _

","ord":0},{"label":"G","content_html":"

7 √ 105 _

","ord":1},{"label":"H","content_html":"

6 √ 105 _

","ord":2},{"label":"J","content_html":"

210 √ 3

","ord":3}],"passage":null,"attribution":{"source_id":"act_practice_pdf","source_name":"Official ACT full-length practice tests (PDF)","rights_holder":"ACT Education Corp.","canonical_url":"https://www.act.org/content/act/en/products-and-services/the-act/test-preparation.html","retrieved_from":"https://www.act.org/content/act/en/products-and-services/the-act/test-preparation.html","attribution":"Full-length ACT practice tests © ACT Education Corp., published free at act.org. Questions are retired items from previous ACT administrations.","disclaimer":"Extracted from a print-layout PDF: equations, figures and charts do not survive as text. Use the original PDF for anything that renders poorly. ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, does not sponsor, and does not endorse this project.","license":"ACT Education Corp. copyright. Published free for personal test preparation; not licensed for redistribution.","redistributable":false,"item_count":342},"equivalents":[{"id":"act_quizme:math:q2:01","source_id":"act_quizme","source_item_id":"math-q2-01","external_id":"1785a89d7bc4d779","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":1,"scored":true,"layout_warning":null,"stem":"The initial speed, in miles per hour, of a certain car that skids to a stop can be estimated by multiplying the length of the skid, in feet, by 35 and then taking the square root of the product. According to this method, what is the estimated initial speed, in miles per hour, of the car when it makes a 108-foot skid?","stimulus":"","stimulus_html":null,"stem_html":"

The initial speed, in miles per hour, of a certain car that skids to a stop can be estimated by multiplying the length of the skid, in feet, by 35 and then taking the square root of the product. According to this method, what is the estimated initial speed, in miles per hour, of the car when it makes a 108-foot skid?

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","rationale_html":"

A. Incorrect. Let s represent the initial speed of the car, in miles per hour, and l represent the length of the skid in feet. The equation that models the situation is then s≈35l. Remember to multiply, not add, the values underneath the square root.

B. Incorrect. Let s represent the initial speed of the car, in miles per hour, and l represent the length of the skid in feet. The equation that models the situation is then s≈35l. Remember that, when simplifying a radical such as ab2c, the constants outside of the radical will multiply, not add: a×bc, not a+bc.

C. Correct. Let s represent the initial speed of the car, in miles per hour, and l represent the length of the skid in feet. The equation that models the situation is then s≈35l. Substitute l=108 into the equation: s≈35108→s≈3,780. Simplify the radical by factoring 3,780=36105 and using the property ab=ab to yield 3,780=36105=6105.

D. Incorrect. Let s represent the initial speed of the car, in miles per hour, and l represent the length of the skid in feet. The equation that models the situation is then s≈35l. You may have used the equation s≈35l.

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