| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.30 |
| Score | 0% | 66% |
Which of the following statements about exponents is false?
b0 = 1 |
|
all of these are false |
|
b1 = 1 |
|
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).
4! = ?
5 x 4 x 3 x 2 x 1 |
|
4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
|
4 x 3 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
Convert z-2 to remove the negative exponent.
| \( \frac{1}{z^{-2}} \) | |
| \( \frac{-1}{-2z} \) | |
| \( \frac{-1}{z^{-2}} \) | |
| \( \frac{1}{z^2} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is 9b3 x 5b6?
| 45b9 | |
| 14b6 | |
| 14b18 | |
| 45b6 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
9b3 x 5b6
(9 x 5)b(3 + 6)
45b9
The total water usage for a city is 35,000 gallons each day. Of that total, 10% is for personal use and 41% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 15,500 | |
| 10,850 | |
| 7,350 | |
| 7,000 |
41% of the water consumption is industrial use and 10% is personal use so (41% - 10%) = 31% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{31}{100} \) x 35,000 gallons = 10,850 gallons.