| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
Which of the following statements about exponents is false?
all of these are false |
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b1 = b |
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b0 = 1 |
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b1 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
The __________ is the greatest factor that divides two integers.
absolute value |
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least common multiple |
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greatest common factor |
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greatest common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.
How many 11-passenger vans will it take to drive all 83 members of the football team to an away game?
| 5 vans | |
| 8 vans | |
| 7 vans | |
| 3 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{83}{11} \) = 7\(\frac{6}{11}\)
So, it will take 7 full vans and one partially full van to transport the entire team making a total of 8 vans.
Solve for \( \frac{3!}{4!} \)
| \( \frac{1}{336} \) | |
| \( \frac{1}{4} \) | |
| 120 | |
| 504 |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{3!}{4!} \)
\( \frac{3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4} \)
\( \frac{1}{4} \)
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 55% 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 | |
| 23 | |
| 37 | |
| 34 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{55}{100} \) = \( \frac{55 x 25}{100} \) = \( \frac{1375}{100} \) = 13 shots
The center makes 35% 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 = \( \frac{13}{\frac{35}{100}} \) = 13 x \( \frac{100}{35} \) = \( \frac{13 x 100}{35} \) = \( \frac{1300}{35} \) = 37 shots
to make the same number of shots as the guard and thus score the same number of points.