| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.41 |
| Score | 0% | 68% |
Bob loaned Ezra $400 at an annual interest rate of 1%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $4 | |
| $90 | |
| $99 | |
| $35 |
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 $400
i = 0.01 x $400
i = $4
What is \( \frac{-9b^8}{6b^2} \)?
| -1\(\frac{1}{2}\)b-6 | |
| -1\(\frac{1}{2}\)b6 | |
| -1\(\frac{1}{2}\)b4 | |
| -1\(\frac{1}{2}\)b\(\frac{1}{4}\) |
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:
\( \frac{-9b^8}{6b^2} \)
\( \frac{-9}{6} \) b(8 - 2)
-1\(\frac{1}{2}\)b6
If all of a roofing company's 6 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 17 | |
| 4 | |
| 6 | |
| 9 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 6 workers at the company now and that's enough to staff 3 crews so there are \( \frac{6}{3} \) = 2 workers on a crew. 6 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 6 x 2 = 12 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 12 - 6 = 6 new staff for the busy season.
What is (z3)3?
| z0 | |
| z9 | |
| 3z3 | |
| z6 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(z3)3a(b + c) = ab + ac defines which of the following?
distributive property for multiplication |
|
commutative property for division |
|
commutative property for multiplication |
|
distributive property for division |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.