| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.23 |
| Score | 0% | 45% |
What is \( 2 \)\( \sqrt{8} \) + \( 6 \)\( \sqrt{2} \)
| 8\( \sqrt{4} \) | |
| 8\( \sqrt{16} \) | |
| 12\( \sqrt{2} \) | |
| 10\( \sqrt{2} \) |
To add these radicals together their radicands must be the same:
2\( \sqrt{8} \) + 6\( \sqrt{2} \)
2\( \sqrt{4 \times 2} \) + 6\( \sqrt{2} \)
2\( \sqrt{2^2 \times 2} \) + 6\( \sqrt{2} \)
(2)(2)\( \sqrt{2} \) + 6\( \sqrt{2} \)
4\( \sqrt{2} \) + 6\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
4\( \sqrt{2} \) + 6\( \sqrt{2} \)If the ratio of home fans to visiting fans in a crowd is 2:1 and all 43,000 seats in a stadium are filled, how many home fans are in attendance?
| 36,000 | |
| 32,000 | |
| 28,667 | |
| 29,167 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
43,000 fans x \( \frac{2}{3} \) = \( \frac{86000}{3} \) = 28,667 fans.
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 | |
| 18 m2 | |
| 8 m2 | |
| 50 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 mayor is elected with 84% of the votes cast and 71% of a town's 9,000 voters cast a vote, how many votes did the mayor receive?
| 5,432 | |
| 5,368 | |
| 4,856 | |
| 3,259 |
If 71% of the town's 9,000 voters cast ballots the number of votes cast is:
(\( \frac{71}{100} \)) x 9,000 = \( \frac{639,000}{100} \) = 6,390
The mayor got 84% of the votes cast which is:
(\( \frac{84}{100} \)) x 6,390 = \( \frac{536,760}{100} \) = 5,368 votes.
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 15 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?
| 21 | |
| 20 | |
| 14 | |
| 15 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{40}{100} \) = \( \frac{40 x 15}{100} \) = \( \frac{600}{100} \) = 6 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 = \( \frac{6}{\frac{30}{100}} \) = 6 x \( \frac{100}{30} \) = \( \frac{6 x 100}{30} \) = \( \frac{600}{30} \) = 20 shots
to make the same number of shots as the guard and thus score the same number of points.