| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
How many hours does it take a car to travel 75 miles at an average speed of 25 miles per hour?
| 8 hours | |
| 3 hours | |
| 7 hours | |
| 5 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{75mi}{25mph} \)
3 hours
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 9 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 118.4 | |
| 114.2 | |
| 99.8 | |
| 97.9 |
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 7 = \( \frac{5 \times 7}{100} \) = \( \frac{35}{100} \) = 0.35 errors per hour
So, in an average hour, the machine will produce 7 - 0.35 = 6.65 error free parts.
The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 6.65 = 99.8 error free parts were produced yesterday.
What is \( 9 \)\( \sqrt{32} \) + \( 5 \)\( \sqrt{2} \)
| 45\( \sqrt{32} \) | |
| 14\( \sqrt{2} \) | |
| 41\( \sqrt{2} \) | |
| 45\( \sqrt{16} \) |
To add these radicals together their radicands must be the same:
9\( \sqrt{32} \) + 5\( \sqrt{2} \)
9\( \sqrt{16 \times 2} \) + 5\( \sqrt{2} \)
9\( \sqrt{4^2 \times 2} \) + 5\( \sqrt{2} \)
(9)(4)\( \sqrt{2} \) + 5\( \sqrt{2} \)
36\( \sqrt{2} \) + 5\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
36\( \sqrt{2} \) + 5\( \sqrt{2} \)What is the greatest common factor of 20 and 48?
| 17 | |
| 10 | |
| 3 | |
| 4 |
The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 3 factors [1, 2, 4] making 4 the greatest factor 20 and 48 have in common.
Simplify \( \sqrt{80} \)
| 9\( \sqrt{5} \) | |
| 6\( \sqrt{10} \) | |
| 4\( \sqrt{5} \) | |
| 9\( \sqrt{10} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{80} \)
\( \sqrt{16 \times 5} \)
\( \sqrt{4^2 \times 5} \)
4\( \sqrt{5} \)