| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
4! = ?
3 x 2 x 1 |
|
4 x 3 x 2 x 1 |
|
5 x 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.
If a rectangle is twice as long as it is wide and has a perimeter of 18 meters, what is the area of the rectangle?
| 98 m2 | |
| 18 m2 | |
| 2 m2 | |
| 72 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 18 meters so the equation becomes: 2w + 2h = 18.
Putting these two equations together and solving for width (w):
2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3
Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m2
A triathlon course includes a 400m swim, a 30.7km bike ride, and a 9.9km run. What is the total length of the race course?
| 50.2km | |
| 43.5km | |
| 43.6km | |
| 41km |
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 + 30.7km + 9.9km
total distance = 41km
The total water usage for a city is 30,000 gallons each day. Of that total, 19% is for personal use and 49% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 1,700 | |
| 9,000 | |
| 7,700 | |
| 3,900 |
49% of the water consumption is industrial use and 19% is personal use so (49% - 19%) = 30% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{30}{100} \) x 30,000 gallons = 9,000 gallons.
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 40% of his shots. If the guard takes 10 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?
| 15 | |
| 13 | |
| 17 | |
| 8 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{40}{100} \) = \( \frac{40 x 10}{100} \) = \( \frac{400}{100} \) = 4 shots
The center makes 30% 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 = \( \frac{4}{\frac{30}{100}} \) = 4 x \( \frac{100}{30} \) = \( \frac{4 x 100}{30} \) = \( \frac{400}{30} \) = 13 shots
to make the same number of shots as the guard and thus score the same number of points.