| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.66 |
| Score | 0% | 53% |
Solve for \( \frac{2!}{3!} \)
| \( \frac{1}{8} \) | |
| 4 | |
| \( \frac{1}{3} \) | |
| 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:
\( \frac{2!}{3!} \)
\( \frac{2 \times 1}{3 \times 2 \times 1} \)
\( \frac{1}{3} \)
\( \frac{1}{3} \)
A triathlon course includes a 400m swim, a 20.3km bike ride, and a 9.4km run. What is the total length of the race course?
| 30.1km | |
| 60km | |
| 37km | |
| 63.2km |
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 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.4km + 20.3km + 9.4km
total distance = 30.1km
What is \( 9 \)\( \sqrt{75} \) - \( 4 \)\( \sqrt{3} \)
| 5\( \sqrt{-16} \) | |
| 41\( \sqrt{3} \) | |
| 36\( \sqrt{225} \) | |
| 36\( \sqrt{75} \) |
To subtract these radicals together their radicands must be the same:
9\( \sqrt{75} \) - 4\( \sqrt{3} \)
9\( \sqrt{25 \times 3} \) - 4\( \sqrt{3} \)
9\( \sqrt{5^2 \times 3} \) - 4\( \sqrt{3} \)
(9)(5)\( \sqrt{3} \) - 4\( \sqrt{3} \)
45\( \sqrt{3} \) - 4\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
45\( \sqrt{3} \) - 4\( \sqrt{3} \)A machine in a factory has an error rate of 8 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 133.3 | |
| 128.8 | |
| 108.3 | |
| 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:
\( \frac{8}{100} \) x 7 = \( \frac{8 \times 7}{100} \) = \( \frac{56}{100} \) = 0.56 errors per hour
So, in an average hour, the machine will produce 7 - 0.56 = 6.4399999999999995 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 6.4399999999999995 = 128.8 error free parts were produced yesterday.
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 30% of his shots. If the guard takes 30 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 39 | |
| 15 | |
| 36 | |
| 23 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{30}{100} \) = \( \frac{30 x 30}{100} \) = \( \frac{900}{100} \) = 9 shots
The center makes 25% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{9}{\frac{25}{100}} \) = 9 x \( \frac{100}{25} \) = \( \frac{9 x 100}{25} \) = \( \frac{900}{25} \) = 36 shots
to make the same number of shots as the guard and thus score the same number of points.