| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.52 |
| Score | 0% | 70% |
What is \( \frac{45\sqrt{32}}{9\sqrt{8}} \)?
| 4 \( \sqrt{\frac{1}{5}} \) | |
| 5 \( \sqrt{4} \) | |
| \(\frac{1}{4}\) \( \sqrt{\frac{1}{5}} \) | |
| 5 \( \sqrt{\frac{1}{4}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{45\sqrt{32}}{9\sqrt{8}} \)
\( \frac{45}{9} \) \( \sqrt{\frac{32}{8}} \)
5 \( \sqrt{4} \)
Find the average of the following numbers: 13, 11, 15, 9.
| 9 | |
| 7 | |
| 12 | |
| 17 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{13 + 11 + 15 + 9}{4} \) = \( \frac{48}{4} \) = 12
What is the distance in miles of a trip that takes 3 hours at an average speed of 60 miles per hour?
| 60 miles | |
| 350 miles | |
| 100 miles | |
| 180 miles |
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 distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 60mph \times 3h \)
180 miles
Solve for \( \frac{5!}{2!} \)
| \( \frac{1}{9} \) | |
| 336 | |
| 56 | |
| 60 |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60
If all of a roofing company's 16 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 8 complete crews out on jobs?
| 6 | |
| 15 | |
| 14 | |
| 16 |
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 16 workers at the company now and that's enough to staff 4 crews so there are \( \frac{16}{4} \) = 4 workers on a crew. 8 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 8 x 4 = 32 total workers to staff the crews during the busy season. The company already employs 16 workers so they need to add 32 - 16 = 16 new staff for the busy season.