The commerce department reported receiving the following applications for the malcolm

D.Total cost and the number of hats purchased

Step-by-step explanation:

When two variables are directly proportional, they increase or decrease at the same rate. This can be represented by the formula

Y = KX

where Y and X are the variables and K represents a constant.

If the pairs can be written in this form then they are directly proportional. In other words, if you can identify the constant K for each pair then they are directly proportional.

Lets take each pair.

A.Hours worked and money earned

This most likely would have a constant K which is equal to the amount of money paid per hour. This amount is usually a fixed amount.

B.Distance and time when speed is constant

Already the constant K is indicated as speed

C.Area and side length of a square

This could be a bit tricky as some people might see the relationship as

Area = The square of the side length

However, for this case the constant K is also taken to be equal to the side length.

Therefore, this can be written as

Area = K × Side length          (where K is the length of the square)

D.Total cost and the number of hats purchased

This is a case of replicating option B without indicating a constant. If the option included "all hats are the same price" then we have a constant for the pairs, unfortunately it didn't and that makes it least likely to be directly proportional.