| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.97 |
| Score | 0% | 59% |
What is the distance in miles of a trip that takes 2 hours at an average speed of 40 miles per hour?
| 450 miles | |
| 80 miles | |
| 375 miles | |
| 150 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 = \( 40mph \times 2h \)
80 miles
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 9 complete crews out on jobs?
| 16 | |
| 1 | |
| 20 | |
| 7 |
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. 9 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 9 x 4 = 36 total workers to staff the crews during the busy season. The company already employs 16 workers so they need to add 36 - 16 = 20 new staff for the busy season.
If a mayor is elected with 59% of the votes cast and 60% of a town's 29,000 voters cast a vote, how many votes did the mayor receive?
| 10,266 | |
| 10,614 | |
| 9,570 | |
| 14,964 |
If 60% of the town's 29,000 voters cast ballots the number of votes cast is:
(\( \frac{60}{100} \)) x 29,000 = \( \frac{1,740,000}{100} \) = 17,400
The mayor got 59% of the votes cast which is:
(\( \frac{59}{100} \)) x 17,400 = \( \frac{1,026,600}{100} \) = 10,266 votes.
Convert c-4 to remove the negative exponent.
| \( \frac{-1}{-4c^{4}} \) | |
| \( \frac{1}{c^4} \) | |
| \( \frac{-1}{c^{-4}} \) | |
| \( \frac{-1}{-4c} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( 7 \)\( \sqrt{27} \) - \( 8 \)\( \sqrt{3} \)
| 56\( \sqrt{9} \) | |
| -1\( \sqrt{81} \) | |
| -1\( \sqrt{9} \) | |
| 13\( \sqrt{3} \) |
To subtract these radicals together their radicands must be the same:
7\( \sqrt{27} \) - 8\( \sqrt{3} \)
7\( \sqrt{9 \times 3} \) - 8\( \sqrt{3} \)
7\( \sqrt{3^2 \times 3} \) - 8\( \sqrt{3} \)
(7)(3)\( \sqrt{3} \) - 8\( \sqrt{3} \)
21\( \sqrt{3} \) - 8\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
21\( \sqrt{3} \) - 8\( \sqrt{3} \)