| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.64 |
| Score | 0% | 53% |
If the ratio of home fans to visiting fans in a crowd is 4:1 and all 40,000 seats in a stadium are filled, how many home fans are in attendance?
| 32,000 | |
| 24,667 | |
| 27,000 | |
| 26,400 |
A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:
40,000 fans x \( \frac{4}{5} \) = \( \frac{160000}{5} \) = 32,000 fans.
What is the distance in miles of a trip that takes 9 hours at an average speed of 25 miles per hour?
| 240 miles | |
| 135 miles | |
| 60 miles | |
| 225 miles |
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 distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 25mph \times 9h \)
225 miles
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 40% of his shots. If the guard takes 20 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?
| 14 | |
| 24 | |
| 18 | |
| 32 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{40}{100} \) = \( \frac{40 x 20}{100} \) = \( \frac{800}{100} \) = 8 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 = \( \frac{8}{\frac{25}{100}} \) = 8 x \( \frac{100}{25} \) = \( \frac{8 x 100}{25} \) = \( \frac{800}{25} \) = 32 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( 8 \)\( \sqrt{8} \) - \( 8 \)\( \sqrt{2} \)
| 64\( \sqrt{16} \) | |
| 64\( \sqrt{2} \) | |
| 0\( \sqrt{4} \) | |
| 8\( \sqrt{2} \) |
To subtract these radicals together their radicands must be the same:
8\( \sqrt{8} \) - 8\( \sqrt{2} \)
8\( \sqrt{4 \times 2} \) - 8\( \sqrt{2} \)
8\( \sqrt{2^2 \times 2} \) - 8\( \sqrt{2} \)
(8)(2)\( \sqrt{2} \) - 8\( \sqrt{2} \)
16\( \sqrt{2} \) - 8\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
16\( \sqrt{2} \) - 8\( \sqrt{2} \)If a rectangle is twice as long as it is wide and has a perimeter of 42 meters, what is the area of the rectangle?
| 18 m2 | |
| 72 m2 | |
| 98 m2 | |
| 128 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 42 meters so the equation becomes: 2w + 2h = 42.
Putting these two equations together and solving for width (w):
2w + 2h = 42
w + h = \( \frac{42}{2} \)
w + h = 21
w = 21 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 21 - 2w
3w = 21
w = \( \frac{21}{3} \)
w = 7
Since h = 2w that makes h = (2 x 7) = 14 and the area = h x w = 7 x 14 = 98 m2