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There's a roughly linear relationship between the length of someone's femur (the long leg-bone in your thigh) and their expected height. Within a certain population, this relationship can be expressed using the formula [tex]h = 2.41f + 60[/tex], where [tex]h[/tex] represents the expected height in centimeters and [tex]f[/tex] represents the length of the femur in centimeters.

What is the meaning of the [tex]f[/tex]-value when [tex]h = 160[/tex]?

A. The change in expected height for every one additional centimeter of femur length.
B. The femur length for someone with an expected height of 160 centimeters.
C. The expected height for someone with a femur length of 16 centimeters.

Answer :

To find the meaning of the femur length [tex]\( f \)[/tex] when the expected height [tex]\( h = 160 \)[/tex] centimeters, we need to solve the equation of the linear relationship:

[tex]\[ h = 2.41f + 60 \][/tex]

Given that [tex]\( h = 160 \)[/tex], we substitute this value into the equation:

[tex]\[ 160 = 2.41f + 60 \][/tex]

Now, we want to isolate [tex]\( f \)[/tex]. First, subtract 60 from both sides of the equation:

[tex]\[ 160 - 60 = 2.41f \][/tex]

[tex]\[ 100 = 2.41f \][/tex]

Next, solve for [tex]\( f \)[/tex] by dividing both sides by 2.41:

[tex]\[ f = \frac{100}{2.41} \][/tex]

This calculation gives an approximate result of:

[tex]\[ f \approx 41.49 \][/tex]

Therefore, the femur length [tex]\( f \)[/tex] for someone with an expected height of 160 centimeters is approximately 41.49 centimeters.

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