Question

there is a roughly linear relationship between the length of someones femur (the long leg - bone in your thigh) and their expected height. within a certain population, this relationship can be expressed using the formula $h = 2.39f + 57.2$, where $h$ represents the expected height in centimeters and $f$ represents the length of the femur in centimeters. what is the meaning of the $h$-value when $f = 54$?

answer

the change in expected height for every one additional centimeter of femur length.
the expected height for someone with a femur length of 54 centimeters.
the expected height for someone with a femur length of 186.26 centimeters.
the femur length for someone with an expected height of 54 centimeters.

Explanation:

Step1: Understand the formula

The formula is \( h = 2.39f + 57.2 \), where \( h \) is expected height (cm) and \( f \) is femur length (cm). We need to find the meaning of \( h \) when \( f = 54 \).

Step2: Interpret the variables

In the formula, \( f = 54 \) means the femur length is 54 cm. Substituting \( f = 54 \) into the formula gives the \( h \)-value, which represents the expected height for a person with a femur length of 54 cm.

Step3: Analyze the options

• The first option refers to the slope (change per cm of femur), not the \( h \)-value at \( f = 54 \).
• The second option (correct) describes \( h \) as the expected height for someone with \( f = 54 \) cm.
• The third option misinterprets the relationship (swaps femur and height).
• The fourth option also swaps femur and height.

Answer:

The expected height for someone with a femur length of 54 centimeters.