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.

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

3\( \sqrt{32} \) + 8\( \sqrt{2} \)
3\( \sqrt{16 \times 2} \) + 8\( \sqrt{2} \)
3\( \sqrt{4^2 \times 2} \) + 8\( \sqrt{2} \)
(3)(4)\( \sqrt{2} \) + 8\( \sqrt{2} \)
12\( \sqrt{2} \) + 8\( \sqrt{2} \)

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

If 51% of the town's 10,000 voters cast ballots the number of votes cast is:

(\( \frac{51}{100} \)) x 10,000 = \( \frac{510,000}{100} \) = 5,100

The mayor got 73% of the votes cast which is:

(\( \frac{73}{100} \)) x 5,100 = \( \frac{372,300}{100} \) = 3,723 votes.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{10 + 4 + 8 + 6}{4} \) = \( \frac{28}{4} \) = 7

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

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{455mi}{65mph} \)
7 hours