Question

question 11 of 23 · multiple choice

the walls of a house are finished with 1\ x 8\ lap siding. if each course has 6-7/8\ exposed to the weather and there are 33 courses from the bottom to the top, what is the height of the sided wall?

a 264\
b 226-7/8\
c 226-5/8\
d 173-1/4\

Explanation:

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"new_concepts": [
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<reasoning>

Identify the given values

Identify the key parameters.

• Number of courses: \(33\)
• Exposed height per course: \(6\frac{7}{8}''\)

Set up the calculation

Using the Fraction Word Problems knowledge point
\[
\text{Total Height} = \text{Number of courses} \times \text{Exposed height per course}
\]
\[
\text{Total Height} = 33 \times 6\frac{7}{8}''
\]

Convert mixed number to improper fraction

Using the Fraction Arithmetic knowledge point
\[
6\frac{7}{8} = \frac{6 \times 8 + 7}{8} = \frac{55}{8}
\]

Multiply the values

Using the Fraction Arithmetic knowledge point
\[
\text{Total Height} = 33 \times \frac{55}{8} = \frac{1815}{8}
\]

Convert back to a mixed number

Using the Fraction Arithmetic knowledge point
\[
\frac{1815}{8} = 226\frac{7}{8}''
\]
</reasoning>

<answer>
<mcq-option>A 264"</mcq-option>
<mcq-correct>B 226-7/8"</mcq-correct>
<mcq-option>C 226-5/8"</mcq-option>
<mcq-option>D 173-1/4"</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given values

Identify the key parameters.

• Number of courses: \(33\)
• Exposed height per course: \(6\frac{7}{8}''\)

Set up the calculation

Using the Fraction Word Problems knowledge point
\[
\text{Total Height} = \text{Number of courses} \times \text{Exposed height per course}
\]
\[
\text{Total Height} = 33 \times 6\frac{7}{8}''
\]

Convert mixed number to improper fraction

Using the Fraction Arithmetic knowledge point
\[
6\frac{7}{8} = \frac{6 \times 8 + 7}{8} = \frac{55}{8}
\]

Multiply the values

Using the Fraction Arithmetic knowledge point
\[
\text{Total Height} = 33 \times \frac{55}{8} = \frac{1815}{8}
\]

Convert back to a mixed number

Using the Fraction Arithmetic knowledge point
\[
\frac{1815}{8} = 226\frac{7}{8}''
\]
</reasoning>

<answer>
<mcq-option>A 264"</mcq-option>
<mcq-correct>B 226-7/8"</mcq-correct>
<mcq-option>C 226-5/8"</mcq-option>
<mcq-option>D 173-1/4"</mcq-option>
</answer>

<post_analysis>
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