| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.49 |
| Score | 0% | 70% |
What is \( \frac{9\sqrt{24}}{3\sqrt{8}} \)?
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{3}} \) | |
| 3 \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{3} \) | |
| 3 \( \sqrt{\frac{1}{3}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{9\sqrt{24}}{3\sqrt{8}} \)
\( \frac{9}{3} \) \( \sqrt{\frac{24}{8}} \)
3 \( \sqrt{3} \)
How many hours does it take a car to travel 40 miles at an average speed of 20 miles per hour?
| 7 hours | |
| 1 hour | |
| 2 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 = \( \frac{40mi}{20mph} \)
2 hours
The __________ is the greatest factor that divides two integers.
greatest common factor |
|
greatest common multiple |
|
least common multiple |
|
absolute value |
The greatest common factor (GCF) is the greatest factor that divides two integers.
If all of a roofing company's 6 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 5 complete crews out on jobs?
| 4 | |
| 3 | |
| 9 | |
| 12 |
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 6 workers at the company now and that's enough to staff 3 crews so there are \( \frac{6}{3} \) = 2 workers on a crew. 5 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 5 x 2 = 10 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 10 - 6 = 4 new staff for the busy season.
What is \( \frac{4}{9} \) x \( \frac{4}{9} \)?
| \(\frac{16}{81}\) | |
| \(\frac{2}{27}\) | |
| \(\frac{1}{48}\) | |
| \(\frac{4}{45}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{9} \) x \( \frac{4}{9} \) = \( \frac{4 x 4}{9 x 9} \) = \( \frac{16}{81} \) = \(\frac{16}{81}\)