| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
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 30 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 | |
| 48 | |
| 40 | |
| 39 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{40}{100} \) = \( \frac{40 x 30}{100} \) = \( \frac{1200}{100} \) = 12 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 = \( \frac{12}{\frac{25}{100}} \) = 12 x \( \frac{100}{25} \) = \( \frac{12 x 100}{25} \) = \( \frac{1200}{25} \) = 48 shots
to make the same number of shots as the guard and thus score the same number of points.
If a rectangle is twice as long as it is wide and has a perimeter of 12 meters, what is the area of the rectangle?
| 72 m2 | |
| 18 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 12 meters so the equation becomes: 2w + 2h = 12.
Putting these two equations together and solving for width (w):
2w + 2h = 12
w + h = \( \frac{12}{2} \)
w + h = 6
w = 6 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 6 - 2w
3w = 6
w = \( \frac{6}{3} \)
w = 2
Since h = 2w that makes h = (2 x 2) = 4 and the area = h x w = 2 x 4 = 8 m2
4! = ?
4 x 3 |
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4 x 3 x 2 x 1 |
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5 x 4 x 3 x 2 x 1 |
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3 x 2 x 1 |
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.
What is the least common multiple of 6 and 10?
| 30 | |
| 35 | |
| 39 | |
| 45 |
The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 have in common.
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
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a = 7 |
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a = -7 |
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a = 7 or a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).