Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{83}{8} \) = 10\(\frac{3}{8}\)

So, it will take 10 full vans and one partially full van to transport the entire team making a total of 11 vans.

If 56% of the town's 37,000 voters cast ballots the number of votes cast is:

(\( \frac{56}{100} \)) x 37,000 = \( \frac{2,072,000}{100} \) = 20,720

The mayor got 58% of the votes cast which is:

(\( \frac{58}{100} \)) x 20,720 = \( \frac{1,201,760}{100} \) = 12,018 votes.

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 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 3 workers on a crew. 5 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 5 x 3 = 15 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 15 - 6 = 9 new staff for the busy season.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To simplify a radical, factor out the perfect squares:

\( \sqrt{75} \)
\( \sqrt{25 \times 3} \)
\( \sqrt{5^2 \times 3} \)
5\( \sqrt{3} \)