Question

22.) Forensic scientists use the equation h=2.6f+47.2 to estimate the height h of a woman given the length in centimeters of her femur bone.a.) Suppose the equation has a margin of error +/- 3 centimeters. Write an inequality to represent the height of a woman given the length of her femur bone.b.) If the length of a female skeleton's femur is 50 centimeters, write and solve an absolute value inequality that describes the woman's height in centimeters.

Answer 1

a) We have to calculate the interval within which the height is predicted by this formula.

The real height is between +/- 3 cm of the predicted height, so we can write:

[tex]h_{}-3Being "hr" the real height and "h" the predicted height.

We can replace h with the formula in order to have the inequality in function of "f":

[tex]\begin{gathered} h_{}-3Then, the inequality that represents the height of a woman given the length of her femur bone is:[tex]2.6f+44.2

b) If the length of the femur is 50 cm (f=50), we can write the inequality as an "absolute value inequality" as:

[tex]\begin{gathered} |h_r-h|<3 \\ |h_r-(2.6f+47.2)|<3_{} \\ |h_r-(2.6\cdot50+47.2)|<3 \\ |h_r-(130+47.2)|<3 \\ |h_r-177.2|<3 \\ -3The woman's height should be between 174.2 and 180.2 centimeters.