| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.90 |
| Score | 0% | 58% |
Which of the following statements about exponents is false?
b1 = b |
|
all of these are false |
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b0 = 1 |
|
b1 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
What is \( \frac{4}{7} \) x \( \frac{4}{6} \)?
| \(\frac{2}{5}\) | |
| 2\(\frac{2}{3}\) | |
| \(\frac{8}{21}\) | |
| \(\frac{8}{35}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{7} \) x \( \frac{4}{6} \) = \( \frac{4 x 4}{7 x 6} \) = \( \frac{16}{42} \) = \(\frac{8}{21}\)
A machine in a factory has an error rate of 9 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 182.2 | |
| 71.3 | |
| 182 | |
| 72.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{9}{100} \) x 10 = \( \frac{9 \times 10}{100} \) = \( \frac{90}{100} \) = 0.9 errors per hour
So, in an average hour, the machine will produce 10 - 0.9 = 9.1 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 9.1 = 182 error free parts were produced yesterday.
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?
| 5 | |
| 1 | |
| 12 | |
| 3 |
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.
Convert b-4 to remove the negative exponent.
| \( \frac{1}{b^4} \) | |
| \( \frac{4}{b} \) | |
| \( \frac{-1}{-4b} \) | |
| \( \frac{-4}{b} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.