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

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

Step-by-step explanation:

The given best fit curve for the collected data is

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

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

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 miles/hour

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

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

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