| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
4! = ?
3 x 2 x 1 |
|
5 x 4 x 3 x 2 x 1 |
|
4 x 3 |
|
4 x 3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
What is \( 7 \)\( \sqrt{32} \) - \( 9 \)\( \sqrt{2} \)
| -2\( \sqrt{2} \) | |
| 63\( \sqrt{64} \) | |
| 19\( \sqrt{2} \) | |
| 63\( \sqrt{2} \) |
To subtract these radicals together their radicands must be the same:
7\( \sqrt{32} \) - 9\( \sqrt{2} \)
7\( \sqrt{16 \times 2} \) - 9\( \sqrt{2} \)
7\( \sqrt{4^2 \times 2} \) - 9\( \sqrt{2} \)
(7)(4)\( \sqrt{2} \) - 9\( \sqrt{2} \)
28\( \sqrt{2} \) - 9\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
28\( \sqrt{2} \) - 9\( \sqrt{2} \)9 members of a bridal party need transported to a wedding reception but there are only 2 2-passenger taxis available to take them. How many will need to find other transportation?
| 9 | |
| 5 | |
| 2 | |
| 7 |
There are 2 2-passenger taxis available so that's 2 x 2 = 4 total seats. There are 9 people needing transportation leaving 9 - 4 = 5 who will have to find other transportation.
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 8 complete crews out on jobs?
| 5 | |
| 10 | |
| 9 | |
| 4 |
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. 8 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 8 x 2 = 16 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 16 - 6 = 10 new staff for the busy season.
A triathlon course includes a 500m swim, a 40.6km bike ride, and a 9.5km run. What is the total length of the race course?
| 44.9km | |
| 39.4km | |
| 50.6km | |
| 42.8km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.5km + 40.6km + 9.5km
total distance = 50.6km