| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.40 |
| Score | 0% | 68% |
Solve for \( \frac{2!}{4!} \)
| \( \frac{1}{7} \) | |
| \( \frac{1}{56} \) | |
| \( \frac{1}{3024} \) | |
| \( \frac{1}{12} \) |
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:
\( \frac{2!}{4!} \)
\( \frac{2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4 \times 3} \)
\( \frac{1}{12} \)
What is the least common multiple of 5 and 9?
| 45 | |
| 2 | |
| 14 | |
| 31 |
The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 have in common.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 40% off." If Charlie buys two shirts, each with a regular price of $25, how much money will he save?
| $2.50 | |
| $1.25 | |
| $10.00 | |
| $11.25 |
By buying two shirts, Charlie will save $25 x \( \frac{40}{100} \) = \( \frac{$25 x 40}{100} \) = \( \frac{$1000}{100} \) = $10.00 on the second shirt.
A bread recipe calls for 2\(\frac{1}{4}\) cups of flour. If you only have \(\frac{3}{4}\) cup, how much more flour is needed?
| 2 cups | |
| 1\(\frac{1}{2}\) cups | |
| \(\frac{3}{4}\) cups | |
| 1\(\frac{7}{8}\) cups |
The amount of flour you need is (2\(\frac{1}{4}\) - \(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{18}{8} \) - \( \frac{6}{8} \)) cups
\( \frac{12}{8} \) cups
1\(\frac{1}{2}\) cups
A triathlon course includes a 400m swim, a 30.5km bike ride, and a 5.9km run. What is the total length of the race course?
| 36.8km | |
| 28.1km | |
| 50.9km | |
| 40.5km |
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 + 30.5km + 5.9km
total distance = 36.8km