To determine the vertical height of the stairway given the height of each stair and the number of stairs, follow these steps:
1. Identify the number of stairs:
The stairway consists of 10 stairs.
2. Determine the height of each stair in fractional inches:
Each stair is [tex]\(7 \frac{3}{8}\)[/tex] inches high.
3. Convert the fractional height to a decimal:
[tex]\(7 \frac{3}{8}\)[/tex] inches can be converted to a decimal by recognizing that [tex]\(\frac{3}{8}\)[/tex] is [tex]\(0.375\)[/tex]. Therefore,
[tex]\[
7 \frac{3}{8} = 7 + 0.375 = 7.375 \text{ inches}
\][/tex]
4. Calculate the total height of the stairway:
Multiply the height of each stair by the number of stairs:
[tex]\[
\text{Total height} = \text{Number of stairs} \times \text{Height of each stair} \\
\text{Total height} = 10 \times 7.375 = 73.75 \text{ inches}
\][/tex]
Therefore, the vertical height of the stairway is [tex]\(\boxed{73.75}\)[/tex] inches.
