| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.72 |
| Score | 0% | 54% |
The __________ is the greatest factor that divides two integers.
greatest common multiple |
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greatest common factor |
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absolute value |
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least common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.
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 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?
| 33 | |
| 50 | |
| 20 | |
| 18 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{40}{100} \) = \( \frac{40 x 25}{100} \) = \( \frac{1000}{100} \) = 10 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 = \( \frac{10}{\frac{30}{100}} \) = 10 x \( \frac{100}{30} \) = \( \frac{10 x 100}{30} \) = \( \frac{1000}{30} \) = 33 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?
| 128 m2 | |
| 32 m2 | |
| 72 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 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
| 1.8 | |
| 3.6 | |
| 5.4 | |
| 1 |
1
What is \( \frac{3c^5}{9c^3} \)?
| \(\frac{1}{3}\)c-2 | |
| 3c2 | |
| 3c-2 | |
| \(\frac{1}{3}\)c2 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{3c^5}{9c^3} \)
\( \frac{3}{9} \) c(5 - 3)
\(\frac{1}{3}\)c2