| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.86 |
| Score | 0% | 57% |
Which of the following statements about exponents is false?
all of these are false |
|
b0 = 1 |
|
b1 = 1 |
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b1 = b |
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).
What is the greatest common factor of 36 and 24?
| 6 | |
| 4 | |
| 20 | |
| 12 |
The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24]. They share 6 factors [1, 2, 3, 4, 6, 12] making 12 the greatest factor 36 and 24 have in common.
Jennifer scored 90% on her final exam. If each question was worth 2 points and there were 60 possible points on the exam, how many questions did Jennifer answer correctly?
| 33 | |
| 27 | |
| 13 | |
| 15 |
Jennifer scored 90% on the test meaning she earned 90% of the possible points on the test. There were 60 possible points on the test so she earned 60 x 0.9 = 54 points. Each question is worth 2 points so she got \( \frac{54}{2} \) = 27 questions right.
Convert 78,000 to scientific notation.
| 7.8 x 103 | |
| 7.8 x 10-4 | |
| 78.0 x 103 | |
| 7.8 x 104 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
78,000 in scientific notation is 7.8 x 104
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 35% of his shots. If the guard takes 20 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?
| 26 | |
| 23 | |
| 15 | |
| 18 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{35}{100} \) = \( \frac{35 x 20}{100} \) = \( \frac{700}{100} \) = 7 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 = \( \frac{7}{\frac{30}{100}} \) = 7 x \( \frac{100}{30} \) = \( \frac{7 x 100}{30} \) = \( \frac{700}{30} \) = 23 shots
to make the same number of shots as the guard and thus score the same number of points.