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

8\( \sqrt{175} \) + 2\( \sqrt{7} \)
8\( \sqrt{25 \times 7} \) + 2\( \sqrt{7} \)
8\( \sqrt{5^2 \times 7} \) + 2\( \sqrt{7} \)
(8)(5)\( \sqrt{7} \) + 2\( \sqrt{7} \)
40\( \sqrt{7} \) + 2\( \sqrt{7} \)

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

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $700
i = 0.02 x $700
i = $14

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{3 x 2}{2 x 2} \) + \( \frac{3 x 1}{4 x 1} \)

\( \frac{6}{4} \) + \( \frac{3}{4} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{6 + 3}{4} \) = \( \frac{9}{4} \) = 2\(\frac{1}{4}\)

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:

32,000 fans x \( \frac{5}{6} \) = \( \frac{160000}{6} \) = 26,667 fans.

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.