the graph shows the distance in miles of a runner over x hours. what is the average rate of speed over the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of speed (average rate of change of distance with respect to time) over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$, where $a = 9$, $b = 11$, $f(9)=6$ and $f(11)=11$.

Step2: Substitute values into formula

$\frac{f(11)-f(9)}{11 - 9}=\frac{11 - 6}{2}$.

Step3: Calculate the result

$\frac{11 - 6}{2}=\frac{5}{2}=2.5$ miles per hour.

Answer:

$2.5$ miles per hour