| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.06 |
| Score | 0% | 61% |
Simplify \( \frac{28}{72} \).
| \( \frac{2}{5} \) | |
| \( \frac{3}{8} \) | |
| \( \frac{7}{11} \) | |
| \( \frac{7}{18} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{72} \) = \( \frac{\frac{28}{4}}{\frac{72}{4}} \) = \( \frac{7}{18} \)
If \( \left|c - 4\right| \) - 9 = -5, which of these is a possible value for c?
| 8 | |
| 3 | |
| -6 | |
| 6 |
First, solve for \( \left|c - 4\right| \):
\( \left|c - 4\right| \) - 9 = -5
\( \left|c - 4\right| \) = -5 + 9
\( \left|c - 4\right| \) = 4
The value inside the absolute value brackets can be either positive or negative so (c - 4) must equal + 4 or -4 for \( \left|c - 4\right| \) to equal 4:
| c - 4 = 4 c = 4 + 4 c = 8 | c - 4 = -4 c = -4 + 4 c = 0 |
So, c = 0 or c = 8.
Find the average of the following numbers: 17, 9, 17, 9.
| 11 | |
| 14 | |
| 13 | |
| 8 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{17 + 9 + 17 + 9}{4} \) = \( \frac{52}{4} \) = 13
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 45% 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?
| 24 | |
| 38 | |
| 28 | |
| 22 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{45}{100} \) = \( \frac{45 x 25}{100} \) = \( \frac{1125}{100} \) = 11 shots
The center makes 40% 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 = \( \frac{11}{\frac{40}{100}} \) = 11 x \( \frac{100}{40} \) = \( \frac{11 x 100}{40} \) = \( \frac{1100}{40} \) = 28 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 36 meters, what is the area of the rectangle?
| 50 m2 | |
| 72 m2 | |
| 8 m2 | |
| 162 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