| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.00 |
| Score | 0% | 60% |
Convert a-3 to remove the negative exponent.
| \( \frac{1}{a^{-3}} \) | |
| \( \frac{1}{a^3} \) | |
| \( \frac{-1}{-3a} \) | |
| \( \frac{3}{a} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
If a mayor is elected with 57% of the votes cast and 31% of a town's 44,000 voters cast a vote, how many votes did the mayor receive?
| 7,775 | |
| 9,002 | |
| 8,184 | |
| 12,276 |
If 31% of the town's 44,000 voters cast ballots the number of votes cast is:
(\( \frac{31}{100} \)) x 44,000 = \( \frac{1,364,000}{100} \) = 13,640
The mayor got 57% of the votes cast which is:
(\( \frac{57}{100} \)) x 13,640 = \( \frac{777,480}{100} \) = 7,775 votes.
If all of a roofing company's 20 workers are required to staff 5 roofing crews, how many workers need to be added during the busy season in order to send 10 complete crews out on jobs?
| 20 | |
| 15 | |
| 19 | |
| 6 |
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 20 workers at the company now and that's enough to staff 5 crews so there are \( \frac{20}{5} \) = 4 workers on a crew. 10 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 10 x 4 = 40 total workers to staff the crews during the busy season. The company already employs 20 workers so they need to add 40 - 20 = 20 new staff for the busy season.
What is \( \frac{5}{6} \) + \( \frac{6}{14} \)?
| \( \frac{2}{42} \) | |
| 2 \( \frac{9}{14} \) | |
| 1\(\frac{11}{42}\) | |
| 2 \( \frac{8}{16} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 7}{6 x 7} \) + \( \frac{6 x 3}{14 x 3} \)
\( \frac{35}{42} \) + \( \frac{18}{42} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{35 + 18}{42} \) = \( \frac{53}{42} \) = 1\(\frac{11}{42}\)
A triathlon course includes a 100m swim, a 40.9km bike ride, and a 8.5km run. What is the total length of the race course?
| 40km | |
| 44.8km | |
| 41.2km | |
| 49.5km |
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 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.1km + 40.9km + 8.5km
total distance = 49.5km