| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.99 |
| Score | 0% | 60% |
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 153.9 | |
| 175.8 | |
| 100.8 | |
| 213.4 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{5}{100} \) x 9 = \( \frac{5 \times 9}{100} \) = \( \frac{45}{100} \) = 0.45 errors per hour
So, in an average hour, the machine will produce 9 - 0.45 = 8.55 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 8.55 = 153.9 error free parts were produced yesterday.
Which of these numbers is a factor of 20?
| 10 | |
| 11 | |
| 20 | |
| 2 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 20 are 1, 2, 4, 5, 10, 20.
What is \( \frac{3}{6} \) x \( \frac{2}{9} \)?
| \(\frac{1}{9}\) | |
| \(\frac{2}{27}\) | |
| \(\frac{2}{21}\) | |
| \(\frac{2}{35}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{6} \) x \( \frac{2}{9} \) = \( \frac{3 x 2}{6 x 9} \) = \( \frac{6}{54} \) = \(\frac{1}{9}\)
Solve for \( \frac{5!}{6!} \)
| \( \frac{1}{336} \) | |
| 4 | |
| \( \frac{1}{210} \) | |
| \( \frac{1}{6} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)
Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 18 small cakes per hour. The kitchen is available for 2 hours and 28 large cakes and 470 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 17 | |
| 14 | |
| 95 | |
| 15 |
If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 28 large cakes are needed for the party so \( \frac{28}{10} \) = 2\(\frac{4}{5}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 18 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 18 x 2 = 36 small cakes during that time. 470 small cakes are needed for the party so \( \frac{470}{36} \) = 13\(\frac{1}{18}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 14 = 17 cooks.