A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

48,000 fans x \( \frac{3}{4} \) = \( \frac{144000}{4} \) = 36,000 fans.

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

3\( \sqrt{50} \) + 8\( \sqrt{2} \)
3\( \sqrt{25 \times 2} \) + 8\( \sqrt{2} \)
3\( \sqrt{5^2 \times 2} \) + 8\( \sqrt{2} \)
(3)(5)\( \sqrt{2} \) + 8\( \sqrt{2} \)
15\( \sqrt{2} \) + 8\( \sqrt{2} \)

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

If 52% of the town's 13,000 voters cast ballots the number of votes cast is:

(\( \frac{52}{100} \)) x 13,000 = \( \frac{676,000}{100} \) = 6,760

The mayor got 65% of the votes cast which is:

(\( \frac{65}{100} \)) x 6,760 = \( \frac{439,400}{100} \) = 4,394 votes.

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

Diane scored 95% on the test meaning she earned 95% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.95 = 114 points. Each question is worth 3 points so she got \( \frac{114}{3} \) = 38 questions right.