a rope has a density and thickness such that a 3.25-centimeter-long segment of it weighs 61.40 grams. there are 28.3495 grams in an ounce and 2.54 centimeters in an inch. how many ounces would a 19.45 inch length of the same rope weigh?
a. 5.10 oz
b. 11.49 oz
c. 32.92 oz
d. 53.90 oz

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Unit Conversion" ], "new_concepts": [ "Dimensional Analysis", "Linear Density" ], "current_concepts": [ "Unit Conversion", "Dimensional Analysis", "Linear Density" ] } ## Convert the target length to centimeters Using the **Unit Conversion** knowledge point $$ \begin{aligned} L_{\text{cm}} &= 19.45\text{ in} \times 2.54\text{ cm/in} \ L_{\text{cm}} &= 49.403\text{ cm} \end{aligned} $$ ## Calculate the mass of the rope in grams Using the **Unit Conversion** knowledge point $$ \begin{aligned} \text{Linear Density} &= \frac{61.40\text{ g}}{3.25\text{ cm}} \ M_{\text{g}} &= 49.403\text{ cm} \times \frac{61.40\text{ g}}{3.25\text{ cm}} \ M_{\text{g}} &\approx 933.336\text{ g} \end{aligned} $$ ## Convert the mass from grams to ounces Using the **Unit Conversion** knowledge point $$ \begin{aligned} M_{\text{oz}} &= \frac{933.336\text{ g}}{28.3495\text{ g/oz}} \ M_{\text{oz}} &\approx 32.9225\text{ oz} \end{aligned} $$ ## Match the calculated value with the options The calculated mass is approximately $32.92\text{ oz}$, which corresponds to option (c).

a. 5.10 oz

b. 11.49 oz

c. 32.92 oz

d. 53.90 oz

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Unit Conversion" ] }

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Question

Explanation:

Convert the target length to centimeters

Calculate the mass of the rope in grams

Convert the mass from grams to ounces

Match the calculated value with the options

Answer: