| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.80 |
| Score | 0% | 76% |
4! = ?
5 x 4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
|
4 x 3 x 2 x 1 |
|
4 x 3 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
Simplify \( \frac{20}{56} \).
| \( \frac{5}{14} \) | |
| \( \frac{4}{11} \) | |
| \( \frac{2}{7} \) | |
| \( \frac{5}{6} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{20}{56} \) = \( \frac{\frac{20}{4}}{\frac{56}{4}} \) = \( \frac{5}{14} \)
How many hours does it take a car to travel 50 miles at an average speed of 50 miles per hour?
| 1 hour | |
| 9 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 = \( \frac{50mi}{50mph} \)
1 hour
If a rectangle is twice as long as it is wide and has a perimeter of 36 meters, what is the area of the rectangle?
| 72 m2 | |
| 2 m2 | |
| 32 m2 | |
| 8 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 36 meters so the equation becomes: 2w + 2h = 36.
Putting these two equations together and solving for width (w):
2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6
Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m2
If a car travels 240 miles in 6 hours, what is the average speed?
| 40 mph | |
| 45 mph | |
| 55 mph | |
| 30 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)