| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.95 |
| Score | 0% | 59% |
Find the average of the following numbers: 13, 5, 13, 5.
| 13 | |
| 6 | |
| 11 | |
| 9 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{13 + 5 + 13 + 5}{4} \) = \( \frac{36}{4} \) = 9
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?
| 50 m2 | |
| 162 m2 | |
| 18 m2 | |
| 98 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
If \(\left|a\right| = 7\), which of the following best describes a?
a = -7 |
|
none of these is correct |
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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).
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 35% of his shots. If the guard takes 25 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?
| 32 | |
| 16 | |
| 20 | |
| 14 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{35}{100} \) = \( \frac{35 x 25}{100} \) = \( \frac{875}{100} \) = 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.
If \( \left|x + 6\right| \) + 1 = -9, which of these is a possible value for x?
| -8 | |
| -11 | |
| -16 | |
| -3 |
First, solve for \( \left|x + 6\right| \):
\( \left|x + 6\right| \) + 1 = -9
\( \left|x + 6\right| \) = -9 - 1
\( \left|x + 6\right| \) = -10
The value inside the absolute value brackets can be either positive or negative so (x + 6) must equal - 10 or --10 for \( \left|x + 6\right| \) to equal -10:
| x + 6 = -10 x = -10 - 6 x = -16 | x + 6 = 10 x = 10 - 6 x = 4 |
So, x = 4 or x = -16.