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Answer :
To solve the problem, we need to determine what the value of [tex]\( f \)[/tex] (the femur length) is when the expected height [tex]\( h \)[/tex] is 170 centimeters, using the relationship [tex]\( h = 56.7 + 2.37 f \)[/tex].
Let's break it down step-by-step:
1. Understand the Formula: The formula given is [tex]\( h = 56.7 + 2.37 f \)[/tex], where:
- [tex]\( h \)[/tex] is the expected height in centimeters.
- [tex]\( f \)[/tex] is the length of the femur in centimeters.
2. Substitute the Given Height: We want to find [tex]\( f \)[/tex] when [tex]\( h = 170 \)[/tex] cm. So, substitute 170 for [tex]\( h \)[/tex] in the equation:
[tex]\[
170 = 56.7 + 2.37 f
\][/tex]
3. Solve for [tex]\( f \)[/tex]: To find [tex]\( f \)[/tex], we need to isolate it on one side of the equation.
- First, subtract 56.7 from both sides of the equation:
[tex]\[
170 - 56.7 = 2.37 f
\][/tex]
[tex]\[
113.3 = 2.37 f
\][/tex]
- Next, divide both sides by 2.37 to solve for [tex]\( f \)[/tex]:
[tex]\[
f = \frac{113.3}{2.37}
\][/tex]
4. Calculate the Femur Length: Perform the division:
[tex]\[
f \approx 47.81
\][/tex]
Thus, the femur length [tex]\( f \)[/tex] for someone with an expected height of 170 centimeters is approximately 47.81 centimeters. The correct interpretation of the [tex]\( f \)[/tex]-value in this context is: "The femur length for someone with an expected height of 170 centimeters."
Let's break it down step-by-step:
1. Understand the Formula: The formula given is [tex]\( h = 56.7 + 2.37 f \)[/tex], where:
- [tex]\( h \)[/tex] is the expected height in centimeters.
- [tex]\( f \)[/tex] is the length of the femur in centimeters.
2. Substitute the Given Height: We want to find [tex]\( f \)[/tex] when [tex]\( h = 170 \)[/tex] cm. So, substitute 170 for [tex]\( h \)[/tex] in the equation:
[tex]\[
170 = 56.7 + 2.37 f
\][/tex]
3. Solve for [tex]\( f \)[/tex]: To find [tex]\( f \)[/tex], we need to isolate it on one side of the equation.
- First, subtract 56.7 from both sides of the equation:
[tex]\[
170 - 56.7 = 2.37 f
\][/tex]
[tex]\[
113.3 = 2.37 f
\][/tex]
- Next, divide both sides by 2.37 to solve for [tex]\( f \)[/tex]:
[tex]\[
f = \frac{113.3}{2.37}
\][/tex]
4. Calculate the Femur Length: Perform the division:
[tex]\[
f \approx 47.81
\][/tex]
Thus, the femur length [tex]\( f \)[/tex] for someone with an expected height of 170 centimeters is approximately 47.81 centimeters. The correct interpretation of the [tex]\( f \)[/tex]-value in this context is: "The femur length for someone with an expected height of 170 centimeters."
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