Chapter 8.9, Problem 17STP

(a)

To determine

To calculate: To make a scatter plot of the data

Answer to Problem 17STP

Scatter plot of data is created

Explanation of Solution

Given information: Table showing the heat index at different humidity levels for a temperature of ${90}^{\circ }F$

Heat Index at ${90}^{\circ }F$
Humidity (%)	0	10	30	50	70
Heat Index (${}^{\circ }F$ )	83	85	90	96	106

Calculation:

Data is given as

Heat Index at ${90}^{\circ }F$
Humidity (%)	0	10	30	50	70
Heat Index ( ${}^{\circ }F$ )	83	85	90	96	106

Scatter plot is created by graphing the above points:

  

Conclusion:

Hence, scatter plot is drawn

(b)

To determine

To calculate: To make an equation in slope-intercept form of line of fit

Answer to Problem 17STP

Theequation in slope intercept form of line is $y=\frac{23}{70}x+83$

Explanation of Solution

Given information: Table showing the heat index at different humidity levels for a temperature of ${90}^{\circ }F$

Heat Index at ${90}^{\circ }F$
Humidity (%)	0	10	30	50	70
Heat Index ( ${}^{\circ }F$ )	83	85	90	96	106

Formula Used:

Equation of line passing through two points is given as

  $y-y_2=\frac{y_2-y_1}{x_2-x_1}\left(x-x_2\right)$

Slope intercept form of line is given as

  $y=mx+c$

Where,

  $m=$ Slope

  $c=$ y-intercept

Calculation:

Data is given as

Heat Index at ${90}^{\circ }F$
Humidity (%)	0	10	30	50	70
Heat Index ( ${}^{\circ }F$ )	83	85	90	96	106

Consider the points on graph as follows:

  $\left(0,83\right)$ and $\left(70,106\right)$

Equation of line passing through above points is

  $\begin{array}{l}y-83=\frac{106-83}{70-0}\left(x-0\right)\\ y-83=\frac{23}{70}\left(x\right)\\ y=\frac{23}{70}x+83\end{array}$

Conclusion:

Hence, equation in slope intercept form of line is $y=\frac{23}{70}x+83$

(c)

To determine

To calculate: To predict the heat index when the humidity is $100\%$

Answer to Problem 17STP

Theheat index when the humidity is $100\%$ is ${116}^{\circ }F$

Explanation of Solution

Given information: Table showing the heat index at different humidity levels for a temperature of ${90}^{\circ }F$

Heat Index at ${90}^{\circ }F$
Humidity (%)	0	10	30	50	70
Heat Index ( ${}^{\circ }F$ )	83	85	90	96	106

Formula Used:

Equation of line passing through two points is given as

  $y-y_2=\frac{y_2-y_1}{x_2-x_1}\left(x-x_2\right)$

Slope intercept form of line is given as

  $y=mx+c$

Where,

  $m=$ Slope

  $c=$ y-intercept

Calculation:

Equation in slope intercept form of line is

  $y=\frac{23}{70}x+83$

Heat index when the humidity is $100\%$ is calculated by substituting $x=100$

  $\begin{array}{l}y=\frac{23}{70}\left(100\right)+83\\ y=\frac{23}{7}\left(10\right)+83\\ y=32.85+83\\ y=115.85\\ y\approx {116}^{\circ }F\end{array}$

Conclusion:

Hence, the heat index when the humidity is $100\%$ is ${116}^{\circ }F$