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. due to many countries being at war, there were no race events in those years. d. bicycling was more popular in 1916, 1940, and 1944 than running. (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 \\(\square\\) minutes for the year 2000. (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Identify the linear model equation

The linear model equation is given as \( y = -0.01721x + 47.35 \), where \( x \) represents the year and \( y \) represents the winning time in minutes.

Step2: Substitute \( x = 2000 \) into the equation

To find the predicted winning time for the year 2000, we substitute \( x = 2000 \) into the equation:

$$
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$$

Answer:

The model predicts a winning time of \( \boxed{12.93} \) minutes for the year 2000.