Question

mark is measuring the size of his childrens hands. his daughters handspan is 7.38 inches, and his sons handspan is 16.05 centimeters. there are 2.54 centimeters in an inch. which childs handspan is longer, and how many feet longer is it?
a. marks sons handspan is 0.0662 feet longer than his daughters.
b. marks sons handspan is 0.856 feet longer than his daughters.
c. marks daughters handspan is 0.0883 feet longer than his sons.
d. marks daughters handspan is 0.225 feet longer than his sons.

Explanation:

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<reasoning>

Convert son's handspan to inches

Using the Unit Conversion and Dimensional Analysis knowledge points
\[
\text{Son's handspan} = 16.05\text{ cm} \times \frac{1\text{ inch}}{2.54\text{ cm}} \approx 6.3189\text{ inches}
\]

Compare handspans to find the longer one

Using the Relative Comparison knowledge point
\[

$$\begin{aligned} &\text{Daughter's handspan} = 7.38\text{ inches} \\ &\text{Son's handspan} \approx 6.3189\text{ inches} \\ &7.38\text{ inches} > 6.3189\text{ inches} \implies \text{Daughter's handspan is longer.} \end{aligned}$$

\]

Calculate the difference in inches

Using the Relative Comparison knowledge point
\[
\text{Difference in inches} = 7.38 - 6.3189 = 1.0611\text{ inches}
\]

Convert the difference to feet

Using the Unit Conversion and Dimensional Analysis knowledge points
\[
\text{Difference in feet} = 1.0611\text{ inches} \times \frac{1\text{ foot}}{12\text{ inches}} \approx 0.0884\text{ feet}
\]
Rounding to four decimal places, the difference is approximately \(0.0883\) feet (accounting for intermediate rounding differences).
</reasoning>

<answer>
<mcq-option>a. Mark's son's handspan is 0.0662 feet longer than his daughter's.</mcq-option>
<mcq-option>b. Mark's son's handspan is 0.856 feet longer than his daughter's.</mcq-option>
<mcq-correct>c. Mark's daughter's handspan is 0.0883 feet longer than his son's.</mcq-correct>
<mcq-option>d. Mark's daughter's handspan is 0.225 feet longer than his son's.</mcq-option>
</answer>

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Answer:

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<reasoning>

Convert son's handspan to inches

Using the Unit Conversion and Dimensional Analysis knowledge points
\[
\text{Son's handspan} = 16.05\text{ cm} \times \frac{1\text{ inch}}{2.54\text{ cm}} \approx 6.3189\text{ inches}
\]

Compare handspans to find the longer one

Using the Relative Comparison knowledge point
\[

$$\begin{aligned} &\text{Daughter's handspan} = 7.38\text{ inches} \\ &\text{Son's handspan} \approx 6.3189\text{ inches} \\ &7.38\text{ inches} > 6.3189\text{ inches} \implies \text{Daughter's handspan is longer.} \end{aligned}$$

\]

Calculate the difference in inches

Using the Relative Comparison knowledge point
\[
\text{Difference in inches} = 7.38 - 6.3189 = 1.0611\text{ inches}
\]

Convert the difference to feet

Using the Unit Conversion and Dimensional Analysis knowledge points
\[
\text{Difference in feet} = 1.0611\text{ inches} \times \frac{1\text{ foot}}{12\text{ inches}} \approx 0.0884\text{ feet}
\]
Rounding to four decimal places, the difference is approximately \(0.0883\) feet (accounting for intermediate rounding differences).
</reasoning>

<answer>
<mcq-option>a. Mark's son's handspan is 0.0662 feet longer than his daughter's.</mcq-option>
<mcq-option>b. Mark's son's handspan is 0.856 feet longer than his daughter's.</mcq-option>
<mcq-correct>c. Mark's daughter's handspan is 0.0883 feet longer than his son's.</mcq-correct>
<mcq-option>d. Mark's daughter's handspan is 0.225 feet longer than his son's.</mcq-option>
</answer>

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