| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
What is c2 x 3c4?
| 3c6 | |
| 3c2 | |
| 3c8 | |
| 4c8 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
c2 x 3c4
(1 x 3)c(2 + 4)
3c6
| 0.6 | |
| 1 | |
| 1.2 | |
| 9.0 |
1
If all of a roofing company's 15 workers are required to staff 5 roofing crews, how many workers need to be added during the busy season in order to send 8 complete crews out on jobs?
| 12 | |
| 2 | |
| 9 | |
| 8 |
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 15 workers at the company now and that's enough to staff 5 crews so there are \( \frac{15}{5} \) = 3 workers on a crew. 8 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 8 x 3 = 24 total workers to staff the crews during the busy season. The company already employs 15 workers so they need to add 24 - 15 = 9 new staff for the busy season.
A triathlon course includes a 200m swim, a 50.1km bike ride, and a 5.2km run. What is the total length of the race course?
| 46.6km | |
| 55.5km | |
| 57.5km | |
| 62.7km |
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 200 meters to kilometers, divide the distance by 1000 to get 0.2km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.2km + 50.1km + 5.2km
total distance = 55.5km
Convert x-3 to remove the negative exponent.
| \( \frac{1}{x^{-3}} \) | |
| \( \frac{1}{x^3} \) | |
| \( \frac{-1}{x^{-3}} \) | |
| \( \frac{3}{x} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.