| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.87 |
| Score | 0% | 57% |
Which of the following statements about exponents is false?
b1 = b |
|
all of these are false |
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b1 = 1 |
|
b0 = 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).
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 5 to 2 and the ratio of baseball to basketball cards is 5 to 1, what is the ratio of football to basketball cards?
| 9:6 | |
| 25:2 | |
| 5:2 | |
| 1:2 |
The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.
Convert y-3 to remove the negative exponent.
| \( \frac{1}{y^3} \) | |
| \( \frac{-1}{-3y^{3}} \) | |
| \( \frac{-1}{-3y} \) | |
| \( \frac{3}{y} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 65% of his shots. If the guard takes 30 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?
| 37 | |
| 70 | |
| 63 | |
| 42 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{65}{100} \) = \( \frac{65 x 30}{100} \) = \( \frac{1950}{100} \) = 19 shots
The center makes 45% 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 = \( \frac{19}{\frac{45}{100}} \) = 19 x \( \frac{100}{45} \) = \( \frac{19 x 100}{45} \) = \( \frac{1900}{45} \) = 42 shots
to make the same number of shots as the guard and thus score the same number of points.
What is (a2)5?
| 2a5 | |
| a7 | |
| 5a2 | |
| a10 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(a2)5