| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.87 |
| Score | 0% | 57% |
Simplify \( \sqrt{50} \)
| 5\( \sqrt{2} \) | |
| 6\( \sqrt{4} \) | |
| 3\( \sqrt{2} \) | |
| 4\( \sqrt{2} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{50} \)
\( \sqrt{25 \times 2} \)
\( \sqrt{5^2 \times 2} \)
5\( \sqrt{2} \)
Convert c-3 to remove the negative exponent.
| \( \frac{1}{c^3} \) | |
| \( \frac{1}{c^{-3}} \) | |
| \( \frac{-1}{-3c^{3}} \) | |
| \( \frac{3}{c} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 91.2 | |
| 81.9 | |
| 117.6 | |
| 110.7 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{4}{100} \) x 5 = \( \frac{4 \times 5}{100} \) = \( \frac{20}{100} \) = 0.2 errors per hour
So, in an average hour, the machine will produce 5 - 0.2 = 4.8 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 4.8 = 91.2 error free parts were produced yesterday.
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 9 to 2 and the ratio of baseball to basketball cards is 9 to 1, what is the ratio of football to basketball cards?
| 1:4 | |
| 3:1 | |
| 1:8 | |
| 81:2 |
The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.
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 8 complete crews out on jobs?
| 12 | |
| 7 | |
| 17 | |
| 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 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. 8 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 8 x 4 = 32 total workers to staff the crews during the busy season. The company already employs 20 workers so they need to add 32 - 20 = 12 new staff for the busy season.