| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.79 |
| Score | 0% | 56% |
If a mayor is elected with 69% of the votes cast and 34% of a town's 25,000 voters cast a vote, how many votes did the mayor receive?
| 6,205 | |
| 6,545 | |
| 6,120 | |
| 5,865 |
If 34% of the town's 25,000 voters cast ballots the number of votes cast is:
(\( \frac{34}{100} \)) x 25,000 = \( \frac{850,000}{100} \) = 8,500
The mayor got 69% of the votes cast which is:
(\( \frac{69}{100} \)) x 8,500 = \( \frac{586,500}{100} \) = 5,865 votes.
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?
| 9 | |
| 12 | |
| 7 | |
| 2 |
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.
Convert b-5 to remove the negative exponent.
| \( \frac{5}{b} \) | |
| \( \frac{1}{b^{-5}} \) | |
| \( \frac{-1}{b^{-5}} \) | |
| \( \frac{1}{b^5} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{3}{2} \) + \( \frac{8}{6} \)?
| 2\(\frac{5}{6}\) | |
| 2 \( \frac{1}{5} \) | |
| 1 \( \frac{8}{6} \) | |
| 1 \( \frac{9}{6} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 3}{2 x 3} \) + \( \frac{8 x 1}{6 x 1} \)
\( \frac{9}{6} \) + \( \frac{8}{6} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{9 + 8}{6} \) = \( \frac{17}{6} \) = 2\(\frac{5}{6}\)
If a rectangle is twice as long as it is wide and has a perimeter of 30 meters, what is the area of the rectangle?
| 72 m2 | |
| 128 m2 | |
| 50 m2 | |
| 2 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 30 meters so the equation becomes: 2w + 2h = 30.
Putting these two equations together and solving for width (w):
2w + 2h = 30
w + h = \( \frac{30}{2} \)
w + h = 15
w = 15 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 15 - 2w
3w = 15
w = \( \frac{15}{3} \)
w = 5
Since h = 2w that makes h = (2 x 5) = 10 and the area = h x w = 5 x 10 = 50 m2