| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.15 |
| Score | 0% | 63% |
Which of the following statements about exponents is false?
all of these are false |
|
b1 = b |
|
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).
Which of the following is not an integer?
0 |
|
-1 |
|
1 |
|
\({1 \over 2}\) |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
What is \( \frac{2}{9} \) x \( \frac{1}{8} \)?
| \(\frac{2}{9}\) | |
| \(\frac{1}{6}\) | |
| \(\frac{1}{36}\) | |
| \(\frac{1}{18}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{9} \) x \( \frac{1}{8} \) = \( \frac{2 x 1}{9 x 8} \) = \( \frac{2}{72} \) = \(\frac{1}{36}\)
What is \( \frac{4b^6}{2b^4} \)?
| \(\frac{1}{2}\)b2 | |
| 2b\(\frac{2}{3}\) | |
| \(\frac{1}{2}\)b10 | |
| 2b2 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{4b^6}{2b^4} \)
\( \frac{4}{2} \) b(6 - 4)
2b2
The total water usage for a city is 40,000 gallons each day. Of that total, 25% is for personal use and 38% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 3,100 | |
| 4,250 | |
| 5,200 | |
| 3,000 |
38% of the water consumption is industrial use and 25% is personal use so (38% - 25%) = 13% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{13}{100} \) x 40,000 gallons = 5,200 gallons.