| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.43 |
| Score | 0% | 69% |
4! = ?
4 x 3 |
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3 x 2 x 1 |
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4 x 3 x 2 x 1 |
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5 x 4 x 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.
On average, the center for a basketball team hits 30% 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?
| 31 | |
| 42 | |
| 35 | |
| 37 |
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 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 = \( \frac{11}{\frac{30}{100}} \) = 11 x \( \frac{100}{30} \) = \( \frac{11 x 100}{30} \) = \( \frac{1100}{30} \) = 37 shots
to make the same number of shots as the guard and thus score the same number of points.
Simplify \( \frac{28}{48} \).
| \( \frac{5}{14} \) | |
| \( \frac{9}{14} \) | |
| \( \frac{7}{12} \) | |
| \( \frac{8}{15} \) |
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 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{48} \) = \( \frac{\frac{28}{4}}{\frac{48}{4}} \) = \( \frac{7}{12} \)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 15% off." If Charlie buys two shirts, each with a regular price of $31, how much will he pay for both shirts?
| $38.75 | |
| $44.95 | |
| $57.35 | |
| $4.65 |
By buying two shirts, Charlie will save $31 x \( \frac{15}{100} \) = \( \frac{$31 x 15}{100} \) = \( \frac{$465}{100} \) = $4.65 on the second shirt.
So, his total cost will be
$31.00 + ($31.00 - $4.65)
$31.00 + $26.35
$57.35
A factor is a positive __________ that divides evenly into a given number.
integer |
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mixed number |
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fraction |
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improper fraction |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.