| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
Convert y-5 to remove the negative exponent.
| \( \frac{-5}{y} \) | |
| \( \frac{-1}{y^{-5}} \) | |
| \( \frac{-1}{-5y^{5}} \) | |
| \( \frac{1}{y^5} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
Convert 0.0006561 to scientific notation.
| 6.561 x 10-3 | |
| 65.61 x 10-5 | |
| 6.561 x 10-4 | |
| 6.561 x 105 |
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:
0.0006561 in scientific notation is 6.561 x 10-4
What is \( \frac{4}{7} \) ÷ \( \frac{2}{8} \)?
| \(\frac{1}{16}\) | |
| 16 | |
| 2\(\frac{2}{7}\) | |
| \(\frac{1}{3}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{7} \) ÷ \( \frac{2}{8} \) = \( \frac{4}{7} \) x \( \frac{8}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{7} \) x \( \frac{8}{2} \) = \( \frac{4 x 8}{7 x 2} \) = \( \frac{32}{14} \) = 2\(\frac{2}{7}\)
The total water usage for a city is 10,000 gallons each day. Of that total, 17% is for personal use and 34% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 1,700 | |
| 3,400 | |
| 8,400 | |
| 1,600 |
34% of the water consumption is industrial use and 17% is personal use so (34% - 17%) = 17% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{17}{100} \) x 10,000 gallons = 1,700 gallons.
If a mayor is elected with 83% of the votes cast and 69% of a town's 36,000 voters cast a vote, how many votes did the mayor receive?
| 20,617 | |
| 13,662 | |
| 18,133 | |
| 15,401 |
If 69% of the town's 36,000 voters cast ballots the number of votes cast is:
(\( \frac{69}{100} \)) x 36,000 = \( \frac{2,484,000}{100} \) = 24,840
The mayor got 83% of the votes cast which is:
(\( \frac{83}{100} \)) x 24,840 = \( \frac{2,061,720}{100} \) = 20,617 votes.