The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 have in common.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

The number of students taking German or Spanish is 13 + 7 = 20. Of that group of 20, 4 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 20 - 4 = 16 who are taking at least one language. 25 - 16 = 9 students who are not taking either language.

To multiply terms with radicals, multiply the coefficients and radicands separately:

9\( \sqrt{7} \) x 5\( \sqrt{8} \)
(9 x 5)\( \sqrt{7 \times 8} \)
45\( \sqrt{56} \)

Now we need to simplify the radical:

45\( \sqrt{56} \)
45\( \sqrt{14 \times 4} \)
45\( \sqrt{14 \times 2^2} \)
(45)(2)\( \sqrt{14} \)
90\( \sqrt{14} \)

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. 9 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 9 x 3 = 27 total workers to staff the crews during the busy season. The company already employs 15 workers so they need to add 27 - 15 = 12 new staff for the busy season.