| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.89 |
| Score | 0% | 58% |
What is b5 + 7b5?
| 8b5 | |
| 6b5 | |
| -6b-5 | |
| 8b25 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
1b5 + 7b5
(1 + 7)b5
8b5
A tiger in a zoo has consumed 132 pounds of food in 11 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 168 pounds?
| 4 | |
| 11 | |
| 10 | |
| 3 |
If the tiger has consumed 132 pounds of food in 11 days that's \( \frac{132}{11} \) = 12 pounds of food per day. The tiger needs to consume 168 - 132 = 36 more pounds of food to reach 168 pounds total. At 12 pounds of food per day that's \( \frac{36}{12} \) = 3 more days.
Which of the following statements about exponents is false?
b1 = b |
|
all of these are false |
|
b0 = 1 |
|
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).
Simplify \( \frac{32}{80} \).
| \( \frac{5}{14} \) | |
| \( \frac{2}{5} \) | |
| \( \frac{4}{15} \) | |
| \( \frac{7}{19} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{32}{80} \) = \( \frac{\frac{32}{16}}{\frac{80}{16}} \) = \( \frac{2}{5} \)
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 60% 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?
| 15 | |
| 10 | |
| 30 | |
| 21 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{60}{100} \) = \( \frac{60 x 10}{100} \) = \( \frac{600}{100} \) = 6 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 = \( \frac{6}{\frac{40}{100}} \) = 6 x \( \frac{100}{40} \) = \( \frac{6 x 100}{40} \) = \( \frac{600}{40} \) = 15 shots
to make the same number of shots as the guard and thus score the same number of points.