A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

41,000 fans x \( \frac{5}{6} \) = \( \frac{205000}{6} \) = 34,167 fans.

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

2\( \sqrt{12} \) + 3\( \sqrt{3} \)
2\( \sqrt{4 \times 3} \) + 3\( \sqrt{3} \)
2\( \sqrt{2^2 \times 3} \) + 3\( \sqrt{3} \)
(2)(2)\( \sqrt{3} \) + 3\( \sqrt{3} \)
4\( \sqrt{3} \) + 3\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

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

vans = \( \frac{81}{12} \) = 6\(\frac{3}{4}\)

So, it will take 6 full vans and one partially full van to transport the entire team making a total of 7 vans.

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 15 workers at the company now and that's enough to staff 5 crews so there are \( \frac{15}{5} \) = 3 workers on a crew. 8 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 8 x 3 = 24 total workers to staff the crews during the busy season. The company already employs 15 workers so they need to add 24 - 15 = 9 new staff for the busy season.