| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
Convert z-5 to remove the negative exponent.
| \( \frac{-1}{-5z} \) | |
| \( \frac{1}{z^{-5}} \) | |
| \( \frac{1}{z^5} \) | |
| \( \frac{-1}{-5z^{5}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
Solve for \( \frac{5!}{3!} \)
| 15120 | |
| 9 | |
| 20 | |
| \( \frac{1}{30} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{5!}{3!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{5 \times 4}{1} \)
\( 5 \times 4 \)
20
Roger loaned Charlie $1,000 at an annual interest rate of 7%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $70 | |
| $39 | |
| $45 | |
| $72 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $1,000
i = 0.07 x $1,000
i = $70
What is \( \frac{4a^7}{3a^4} \)?
| 1\(\frac{1}{3}\)a-3 | |
| 1\(\frac{1}{3}\)a3 | |
| 1\(\frac{1}{3}\)a\(\frac{4}{7}\) | |
| 1\(\frac{1}{3}\)a11 |
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:
\( \frac{4a^7}{3a^4} \)
\( \frac{4}{3} \) a(7 - 4)
1\(\frac{1}{3}\)a3
If a mayor is elected with 59% of the votes cast and 44% of a town's 19,000 voters cast a vote, how many votes did the mayor receive?
| 4,514 | |
| 4,932 | |
| 6,019 | |
| 6,604 |
If 44% of the town's 19,000 voters cast ballots the number of votes cast is:
(\( \frac{44}{100} \)) x 19,000 = \( \frac{836,000}{100} \) = 8,360
The mayor got 59% of the votes cast which is:
(\( \frac{59}{100} \)) x 8,360 = \( \frac{493,240}{100} \) = 4,932 votes.