| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.95 |
| Score | 0% | 59% |
Which of these numbers is a factor of 72?
| 2 | |
| 55 | |
| 12 | |
| 33 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
What is \( 2 \)\( \sqrt{80} \) - \( 2 \)\( \sqrt{5} \)
| 4\( \sqrt{16} \) | |
| 6\( \sqrt{5} \) | |
| 4\( \sqrt{400} \) | |
| 4\( \sqrt{80} \) |
To subtract these radicals together their radicands must be the same:
2\( \sqrt{80} \) - 2\( \sqrt{5} \)
2\( \sqrt{16 \times 5} \) - 2\( \sqrt{5} \)
2\( \sqrt{4^2 \times 5} \) - 2\( \sqrt{5} \)
(2)(4)\( \sqrt{5} \) - 2\( \sqrt{5} \)
8\( \sqrt{5} \) - 2\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
8\( \sqrt{5} \) - 2\( \sqrt{5} \)What is \( \frac{3}{5} \) ÷ \( \frac{2}{6} \)?
| 1\(\frac{4}{5}\) | |
| \(\frac{8}{45}\) | |
| 3\(\frac{3}{5}\) | |
| 9 |
To divide fractions, invert the second fraction and then multiply:
\( \frac{3}{5} \) ÷ \( \frac{2}{6} \) = \( \frac{3}{5} \) x \( \frac{6}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{5} \) x \( \frac{6}{2} \) = \( \frac{3 x 6}{5 x 2} \) = \( \frac{18}{10} \) = 1\(\frac{4}{5}\)
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 8 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 133.9 | |
| 135.4 | |
| 97.6 | |
| 176.4 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 9 = \( \frac{6 \times 9}{100} \) = \( \frac{54}{100} \) = 0.54 errors per hour
So, in an average hour, the machine will produce 9 - 0.54 = 8.46 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 8.46 = 135.4 error free parts were produced yesterday.
A triathlon course includes a 100m swim, a 30.3km bike ride, and a 15.3km run. What is the total length of the race course?
| 47.1km | |
| 57.6km | |
| 45.7km | |
| 49.3km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.1km + 30.3km + 15.3km
total distance = 45.7km