Question

The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.

Based on the table, which value represents the rate of change for this situation?
−3
− 1/3
3
1/3

Answer 1

[AI-generated answer — Bot GPT 3.5]

1/3

Answer 2

A worker is packing items in boxes. The table shows the linear relationship between the number of items the worker has packed in boxes after different amounts of time.

#7.
Which statement describes the rate of change of the number of items the worker packed in boxes with respect to the number of minutes the worker has been packing items in boxes?
The worker packed 8 items in boxes per minute. The worker packed 37 items in boxes per minute. The worker packed 4 items in boxes per minute. The worker packed 15 items in boxes per minute.
Number of Minutes
Number of Items Packed
5
20
7
28
11
44
14
56

Answer 3

[AI-generated answer — Bot GPT 3.5]

The worker packed 4 items in boxes per minute.

To find the rate of change, we can divide the change in the number of items packed by the change in the number of minutes.

For example, between minutes 5 and 7, the worker packed 8 items in boxes in 2 minutes.
Rate of change = (28 - 20) / (7 - 5) = 8 / 2 = 4 items per minute

This rate of change is consistent throughout the table, so the worker packed 4 items in boxes per minute.

Answer 4

What is the rate of change of y with respect to x for this line?

5/2
− 6/5
2/3
− 5/6

Answer 5

[AI-generated answer — Bot GPT 3.5]

The rate of change of y with respect to x for a line can be determined by finding the slope of the line.

Given the equation of the line is in the form y = mx + b, where m is the slope, we need to identify the coefficient of x to find the rate of change of y with respect to x.

For example, if we have the equation y = (5/2)x, the coefficient of x is 5/2, which represents the rate of change of y with respect to x.

Therefore, the rate of change of y with respect to x for this line is 5/2.

Answer 6

What is the rate of change of the balance with respect to the number of deposits?

$100 per deposit
$50 per deposit
$0.50 per deposit
$2 per deposit

Answer 7

[AI-generated answer — Bot GPT 3.5]

To determine the rate of change of the balance with respect to the number of deposits, we need to calculate the slope of the line or relationship between the balance and the number of deposits.

If the rate of change is constant and linear, divide the change in balance by the change in the number of deposits.

For example, if after 5 deposits the balance increased by $500 and after 10 deposits the balance increased by $1000, the rate of change of the balance with respect to the number of deposits would be:

Rate of change = ($1000 - $500) / (10 - 5) = $500 / 5 deposits = $100 per deposit

Therefore, the rate of change of the balance with respect to the number of deposits is $100 per deposit.

Answer 8

The function y = 3.75 + 1.5(x − 1) can be used to determine the cost in dollars for a taxi ride of x miles. What is the rate of change of the cost in dollars with respect to the number of miles?

$1.50 per mile
$3.75 per mile
$4.25 per mile
$5.25 per mile

Answer 9

[AI-generated answer — Bot GPT 3.5]

The rate of change of the cost in dollars with respect to the number of miles can be found by identifying the coefficient of x in the function y = 3.75 + 1.5(x - 1), as the coefficient represents the rate of change.

In this case, the coefficient of x is 1.5, which means the rate of change of cost in dollars with respect to the number of miles is $1.50 per mile.

Therefore, the rate of change of the cost in dollars with respect to the number of miles is $1.50 per mile.