| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
How many hours does it take a car to travel 65 miles at an average speed of 65 miles per hour?
| 1 hour | |
| 3 hours | |
| 4 hours | |
| 9 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{65mi}{65mph} \)
1 hour
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 9 to 2 and the ratio of baseball to basketball cards is 9 to 1, what is the ratio of football to basketball cards?
| 81:2 | |
| 9:4 | |
| 1:1 | |
| 1:8 |
The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. 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 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.
What is \( \frac{2}{6} \) x \( \frac{1}{8} \)?
| \(\frac{1}{56}\) | |
| \(\frac{1}{24}\) | |
| \(\frac{1}{20}\) | |
| \(\frac{1}{3}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{6} \) x \( \frac{1}{8} \) = \( \frac{2 x 1}{6 x 8} \) = \( \frac{2}{48} \) = \(\frac{1}{24}\)
Simplify \( \sqrt{80} \)
| 2\( \sqrt{10} \) | |
| 6\( \sqrt{10} \) | |
| 4\( \sqrt{5} \) | |
| 5\( \sqrt{5} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{80} \)
\( \sqrt{16 \times 5} \)
\( \sqrt{4^2 \times 5} \)
4\( \sqrt{5} \)
What is \( 8 \)\( \sqrt{20} \) - \( 9 \)\( \sqrt{5} \)
| 72\( \sqrt{20} \) | |
| -1\( \sqrt{5} \) | |
| -1\( \sqrt{20} \) | |
| 7\( \sqrt{5} \) |
To subtract these radicals together their radicands must be the same:
8\( \sqrt{20} \) - 9\( \sqrt{5} \)
8\( \sqrt{4 \times 5} \) - 9\( \sqrt{5} \)
8\( \sqrt{2^2 \times 5} \) - 9\( \sqrt{5} \)
(8)(2)\( \sqrt{5} \) - 9\( \sqrt{5} \)
16\( \sqrt{5} \) - 9\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
16\( \sqrt{5} \) - 9\( \sqrt{5} \)