adook101

To determine the area of the photograph with the border combined, you need to account for the width of the border on all sides. The width x will be added to both the length and the width of the photograph. Let's break it down:

The original dimensions of the photograph are 8 inches by 10 inches. With the border added, the total dimensions will become:

Width: 8+2x8 + 2x

Height: 10+2x10 + 2x

The area aa of the photograph and the border combined can be represented by the following function:

a=(8+2x)(10+2x)a = (8 + 2x)(10 + 2x)

This function will allow Anna to determine the area in square inches for any given width of the border x

Since the balls are indistinguishable, we must only count the number of balls in the different boxes.

There are  ways to arrange the balls as  (specifically, box 1 can have 5, box 2 can have 5, box 3 can have 5).

There are  to arrange  and  ways to arrange ; in each case, we must choose one of the 3 boxes to have the largest number of balls, and also one of the remaining two boxes to be left empty.

However, there are only  ways to arrange , and  ways to arrange ; in each case, we must choose one box to have the `different' number of balls (3 in the  case and 1 in the  case).

This gives a total of  arrangements.

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