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| Questions | 5 | 5 |
| Correct | 0 | 2.62 |
| Score | 0% | 52% |
What is (a4)2?
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To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(a4)2On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 10 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?
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guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{55}{100} \) = \( \frac{55 x 10}{100} \) = \( \frac{550}{100} \) = 5 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 = \( \frac{5}{\frac{40}{100}} \) = 5 x \( \frac{100}{40} \) = \( \frac{5 x 100}{40} \) = \( \frac{500}{40} \) = 13 shots
to make the same number of shots as the guard and thus score the same number of points.
Which of the following statements about exponents is false?
b0 = 1 |
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b1 = 1 |
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b1 = b |
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all of these are false |
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).
Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 15 small cakes per hour. The kitchen is available for 3 hours and 38 large cakes and 470 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
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If a single cook can bake 4 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 4 x 3 = 12 large cakes during that time. 38 large cakes are needed for the party so \( \frac{38}{12} \) = 3\(\frac{1}{6}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 15 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 15 x 3 = 45 small cakes during that time. 470 small cakes are needed for the party so \( \frac{470}{45} \) = 10\(\frac{4}{9}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 4 + 11 = 15 cooks.
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