| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.88 |
| Score | 0% | 58% |
Convert 2,509,000 to scientific notation.
| 25.09 x 105 | |
| 2.509 x 10-6 | |
| 2.509 x 106 | |
| 2.509 x 10-5 |
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:
2,509,000 in scientific notation is 2.509 x 106
Which of the following statements about exponents is false?
b1 = b |
|
b0 = 1 |
|
all of these are false |
|
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 total water usage for a city is 45,000 gallons each day. Of that total, 19% is for personal use and 52% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 8,700 | |
| 14,850 | |
| 1,300 | |
| 7,500 |
52% of the water consumption is industrial use and 19% is personal use so (52% - 19%) = 33% more water is used for industrial purposes. 45,000 gallons are consumed daily so industry consumes \( \frac{33}{100} \) x 45,000 gallons = 14,850 gallons.
What is the greatest common factor of 52 and 40?
| 4 | |
| 24 | |
| 23 | |
| 30 |
The factors of 52 are [1, 2, 4, 13, 26, 52] and the factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40]. They share 3 factors [1, 2, 4] making 4 the greatest factor 52 and 40 have in common.
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 65% 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?
| 64 | |
| 27 | |
| 33 | |
| 32 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{65}{100} \) = \( \frac{65 x 25}{100} \) = \( \frac{1625}{100} \) = 16 shots
The center makes 50% 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 = \( \frac{16}{\frac{50}{100}} \) = 16 x \( \frac{100}{50} \) = \( \frac{16 x 100}{50} \) = \( \frac{1600}{50} \) = 32 shots
to make the same number of shots as the guard and thus score the same number of points.