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

2\( \sqrt{9} \) x 3\( \sqrt{5} \)
(2 x 3)\( \sqrt{9 \times 5} \)
6\( \sqrt{45} \)

Now we need to simplify the radical:

6\( \sqrt{45} \)
6\( \sqrt{5 \times 9} \)
6\( \sqrt{5 \times 3^2} \)
(6)(3)\( \sqrt{5} \)
18\( \sqrt{5} \)

There are 4 5-passenger taxis available so that's 4 x 5 = 20 total seats. There are 24 people needing transportation leaving 24 - 20 = 4 who will have to find other transportation.

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 9 workers at the company now and that's enough to staff 3 crews so there are \( \frac{9}{3} \) = 3 workers on a crew. 7 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 7 x 3 = 21 total workers to staff the crews during the busy season. The company already employs 9 workers so they need to add 21 - 9 = 12 new staff for the busy season.

If 89% of the town's 22,000 voters cast ballots the number of votes cast is:

(\( \frac{89}{100} \)) x 22,000 = \( \frac{1,958,000}{100} \) = 19,580

The mayor got 90% of the votes cast which is:

(\( \frac{90}{100} \)) x 19,580 = \( \frac{1,762,200}{100} \) = 17,622 votes.

The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.