Chapter 1.6, Problem 22PPS

(a)

To determine

To write: an inequality to represent the height of a woman given the length of her femur bone.

Answer to Problem 22PPS

The inequality is $2.6f+44.2<h<2.6f+50.2$

Explanation of Solution

Given information:

Forensic scientists use the equation $h=2.6f+47.2$ , where the height $h$ of a woman given the length in centimeters $f$ of her femur bone.

Suppose, the equation has a margin of error of $\pm 3$ centimeters.

Calculation:

If the error $\pm 3$ , then write it down likes:

  $\begin{array}{l}2.6f+47.2-3<h<2.6f+47.2+3\\ 2.6f+44.2<h<2.6f+50.2\end{array}$

(b)

To determine

To write: and solve an absolute value inequality that describes the woman’s height in centimeters.

Answer to Problem 22PPS

The inequality is $174.2<h<180.2$

Explanation of Solution

Given information:

Forensic scientists use the equation $h=2.6f+47.2$ , where the height $h$ of a woman given the length in centimeters $f$ of her femur bone.

The length of a female skeleton’s femur is 50 centimeters.

Calculation:

The length of a female skeleton’s femur is 50 centimeters means $f=50$ ,

Then, inequality is,

  $2.6\cdot 50+44.2<h<2.6\cdot 50+50.2$

Now, solve the inequality as shown,

  $\begin{array}{c}2.6\cdot 50+44.2<h<2.6\cdot 50+50.2\\ 130+44.2<h<130+50.2\\ 174.2<h<180.2\end{array}$