Question

the graph shows the winning times (in minutes) of a certain international track race, together with a linear approximation of the data. (a) an equation for a linear model, based on data from 1912–2016 (where x represents the year), is y = -0.01721x + 47.35. determine the slope. what does the slope represent? why is the slope negative? (b) what might be the reason there are no data points for the years 1916, 1940, and 1944? (c) the winning time for the 2000 race was 13.22 minutes. what does the model predict, and how far is the prediction from the actual value? (c) the winning time for the 2000 race was 13.22 minutes. what does the model predict, and how far is the prediction from the actual value? the model predicts a winning time of 12.93 minutes for the year 2000. (type an integer or decimal rounded to two decimal places as needed.) the prediction differs from the actual value of 13.22 minutes by □ minutes. (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Calculate the difference

The formula for the difference is \(| \text{Predicted value}-\text{Actual value}|\).
We know the predicted value \(y = 12.93\) and the actual value \(y_{actual}=13.22\).
So the difference \(d=|12.93 - 13.22|\).

Step2: Simplify the expression

\(d=| - 0.29|=0.29\)

Answer:

\(0.29\)