The organizers of a 5k race surveyed runners about their finishing times (f) and the number of previous races they had run (n). The organizers found a negative linear relationship between f and n that is best modeled by the equation f=-1.2n+38.1. What statement is true? The model predicts that for each additional race a runner has run, the finishing time decreases by about 1.2 minutes. The model predicts that the finishing time for a runner in a 5k race is about 38.1 minutes. The model predicts that the finishing time for a runner who has run 1.2 previous 5k races is about 38.1 minutes. The model predicts that the finishing time for a runner who has run 1.2 previous 5k races is about 1.2 minutes.

Question

Mathematics

Tamara Bentley

18 February, 20:56

The organizers of a 5k race surveyed runners about their finishing times (f) and the number of previous races they had run (n). The organizers found a negative linear relationship between f and n that is best modeled by the equation f=-1.2n+38.1. What statement is true? The model predicts that for each additional race a runner has run, the finishing time decreases by about 1.2 minutes. The model predicts that the finishing time for a runner in a 5k race is about 38.1 minutes. The model predicts that the finishing time for a runner who has run 1.2 previous 5k races is about 38.1 minutes. The model predicts that the finishing time for a runner who has run 1.2 previous 5k races is about 1.2 minutes.

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Answers (2)

Know the Answer?

Ariel Huerta · Answer 1

The first thing we must do for this case is to define variables.

n = number of 5k races covered

f = end time.

We have the following equation:

f = - 1.2n + 38.1

We note that the slope of the line is:

m = - 1.2 minutes per race

Therefore, the time decreases 1.2 minutes when the number of races increases n.

Answer:

The model predicts that for each additional race to runner has run, the finishing time decreases by about 1.2 minutes

Ellie Ferguson · Answer 2

Let's interpret this equation. If we have that a runner has 0 races under his belt, he completes the race in 38.1 min. We have that the slope is - 1.2 min/race and the intercept at n=0 is 38.1 min. Hence, for every race, the duration of the run decreases by 1.2 min (or increases by - 1.2 min).

Lets derive that. Suppose a runner that has run n races, runs once more.

The difference of times is:

(-1.2 (n+1) + 38.1) - (-1.2n+38.1) = - 1.2 (n+1) - (-1.2n) = - 1.2n-1.2+1.2n=1.2 minutes.

Hence, the correct answer is the first.