The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%

To subtract these radicals together their radicands must be the same:

3\( \sqrt{8} \) - 6\( \sqrt{2} \)
3\( \sqrt{4 \times 2} \) - 6\( \sqrt{2} \)
3\( \sqrt{2^2 \times 2} \) - 6\( \sqrt{2} \)
(3)(2)\( \sqrt{2} \) - 6\( \sqrt{2} \)
6\( \sqrt{2} \) - 6\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{13 + 9 + 12 + 10}{4} \) = \( \frac{44}{4} \) = 11

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 20 workers at the company now and that's enough to staff 5 crews so there are \( \frac{20}{5} \) = 4 workers on a crew. 8 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 8 x 4 = 32 total workers to staff the crews during the busy season. The company already employs 20 workers so they need to add 32 - 20 = 12 new staff for the busy season.