The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. 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 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

If 84% of the town's 37,000 voters cast ballots the number of votes cast is:

(\( \frac{84}{100} \)) x 37,000 = \( \frac{3,108,000}{100} \) = 31,080

The mayor got 86% of the votes cast which is:

(\( \frac{86}{100} \)) x 31,080 = \( \frac{2,672,880}{100} \) = 26,729 votes.

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

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

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

The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] 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 [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 have in common.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{9}{49}} \)
\( \frac{\sqrt{9}}{\sqrt{49}} \)
\( \frac{\sqrt{3^2}}{\sqrt{7^2}} \)
\(\frac{3}{7}\)