A truck driver travels from a distributor to a retailer every week. The driver records the distance that he is from the retailer at different times during his trip. After several weeks of collecting data, the driver creates a scatter plot of the data. The best-fit line is Y=73.6 - 67.8x where x is the number of hours spent driving and y is the distance, in miles, from the retailer. Which of the following statements are true? Select all that apply. A. The distance from the retailer increases with time. B. The distance from the retailer decreases with time. C. The distributor is 67.8 miles away from the retailer. D. The distributor is 73.6 miles away from the retailer. E. The truck is traveling at a rate of 67,8 miles per hour. 1 1 1 ED 1 1 1 1

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Ritz01 Ritz01 · Answer 1 · 2020-11-25T10:35:47+01:00

Answer:

Options (B), (D), and (E) are correct.

Step-by-step explanation:

The given best fit curve for the collected data is

[tex]y=73.6 - 67.8x\cdots(i)[/tex]

Where x is the number of hours spent driving and y is the distance of distributer, in miles, from the retailer.

As the driver starts recording the time when he starts from the retailer, so at the starting time, x=0, the driver is at the retailer.

So, putting x=0 in the given equation (i) to get the distance between the distributor and retailer, we have

[tex]y =73.6 - 67.8\times 0[/tex]

[tex]\Rightarrow y= 73.6[/tex] miles.

So, the distributor is 73.6 miles away from the retailer.

From equation (i), as x (time) increases the value of y (distance) decreases.

So, The distance from the retailer decreases with time.

Now, obtaining the rate of change the distance,y, from quation (i), with respect to time,x, to get the speed of the truck, we have

[tex]\frac {dy}{dx}=-67.8[/tex] mile/hour

Negative sign shows that the distance is decreasing, taking the magnitude of the rate of change of distance with respect to time to get the speed,

speed [tex]= | dy/dx |= | -67.8 | = 67.8[/tex] miles/hour

So, the speed of the truck is 67.8 miles per hour.

Hence, options (B), (D), and (E) are correct.

joaobezerra joaobezerra · Answer 2 · 2021-11-19T12:47:49+01:00

Using linear function concepts, it is found that the correct options are:

B. The distance from the retailer decreases with time.

D. The distributor is 73.6 miles away from the retailer.

E. The truck is traveling at a rate of 67,8 miles per hour

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

In this problem, the distance, in miles, after x hours driving is modeled by:

[tex]y = 73.6 - 67.8x[/tex]

The slope is [tex]m = -67.8[/tex], which means that the distance decreases with time, and the truck is traveling at a rate of 67.8 miles per hour, hence options B and E are correct.
The y-intercept is of [tex]b = 73.6[/tex], which means that the initial distance is of 73.6 miles, hence option D is correct.

A similar problem is given at https://brainly.com/question/24808124