Question

a donut shop is open from 6 am to 2 pm each day. they make all of their donuts for each day before they open. the graph represents the number of donuts they have left at the end of each hour on tuesday. on sunday, they started with 500 donuts and sold out after being open for 6 hours. they opened with approximately 300 fewer donuts on tuesday than on sunday. true false the line of best fit for sunday would be steeper than the line of best fit for tuesday. true false the slope represents the number of donuts they sell each hour. true false

Explanation:

Step1: Analyze Tuesday's starting donuts

From the graph, at 0 hours (opening), the remaining donuts on Tuesday are around 350 (since the first point at x=0 is near 350).

Step2: Calculate the difference for the first statement

Sunday started with 500 donuts. The difference between 500 and 350 is 150, not 300. So the first statement is False.

Step3: Analyze the slope for Sunday and Tuesday

For Sunday: They sold 500 donuts in 6 hours, so the slope (rate of selling) is $\frac{500}{6} \approx 83.33$ donuts per hour. For Tuesday: From x=0 (350 donuts) to x=8 (100 donuts), the change in donuts is 350 - 100 = 250, over 8 hours, so slope is $\frac{250}{8} = 31.25$ donuts per hour. Since 83.33 > 31.25, Sunday's line of best fit is steeper. So the second statement is True.

Step4: Interpret the slope meaning

The slope of the line (change in donuts over change in hours) represents the number of donuts sold per hour (since remaining donuts decrease as hours pass, the slope's magnitude is the rate of selling). So the third statement is True.

Answer:

1. They opened with approximately 300 fewer donuts on Tuesday than on Sunday: False
2. The line of best fit for Sunday would be steeper than the line of best fit for Tuesday: True
3. The slope represents the number of donuts they sell each hour: True