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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 h, equals, 62, point, 6, plus, 2, point, 3, 5, fh=62.6+2.35f, where hh represents the expected height in centimeters and ff represents the length of the femur in centimeters. What is the meaning of the hh-value when f, equals, 49f=49?

Answer
Multiple Choice Answers
The expected height for someone with a femur length of 177.75 centimeters.
The change in expected height for every one additional centimeter of femur length.
The femur length for someone with an expected height of 49 centimeters.
The expected height for someone with a femur length of 49 centimeters.

1 answer

To solve for the expected height \( h \) when the femur length \( f \) is 49 centimeters using the formula \( h = 62.6 + 2.35f \), we substitute \( f \) with 49:

\[ h = 62.6 + 2.35 \times 49 \]

Calculating \( 2.35 \times 49 \):

\[ 2.35 \times 49 = 115.15 \]

Now add that to 62.6:

\[ h = 62.6 + 115.15 = 177.75 \]

So, when \( f = 49 \), the expected height \( h \) is 177.75 centimeters.

Now, let's analyze what this value means in relation to the provided choices:

  1. The expected height for someone with a femur length of 177.75 centimeters. - This is incorrect as we just calculated the expected height for a femur length of 49 centimeters.

  2. The change in expected height for every one additional centimeter of femur length. - This is incorrect; this value (2.35) represents the slope in the equation, not the specific height.

  3. The femur length for someone with an expected height of 49 centimeters. - This is incorrect because we're evaluating a femur length of 49 centimeters, not the other way around.

  4. The expected height for someone with a femur length of 49 centimeters. - This is correct as we just calculated that the expected height \( h \) is 177.75 centimeters when \( f \) is 49.

Thus, the correct answer is:

The expected height for someone with a femur length of 49 centimeters.