| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.71 |
| Score | 0% | 54% |
Which of the following statements about exponents is false?
b1 = b |
|
b0 = 1 |
|
b1 = 1 |
|
all of these are false |
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).
What is 7b2 + 3b2?
| -4b2 | |
| -4b-2 | |
| 10b2 | |
| 4b2 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
7b2 + 3b2
(7 + 3)b2
10b2
If all of a roofing company's 15 workers are required to staff 5 roofing crews, how many workers need to be added during the busy season in order to send 8 complete crews out on jobs?
| 1 | |
| 9 | |
| 17 | |
| 16 |
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 15 workers at the company now and that's enough to staff 5 crews so there are \( \frac{15}{5} \) = 3 workers on a crew. 8 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 8 x 3 = 24 total workers to staff the crews during the busy season. The company already employs 15 workers so they need to add 24 - 15 = 9 new staff for the busy season.
If \( \left|x - 5\right| \) + 8 = -8, which of these is a possible value for x?
| -6 | |
| -11 | |
| -5 | |
| 1 |
First, solve for \( \left|x - 5\right| \):
\( \left|x - 5\right| \) + 8 = -8
\( \left|x - 5\right| \) = -8 - 8
\( \left|x - 5\right| \) = -16
The value inside the absolute value brackets can be either positive or negative so (x - 5) must equal - 16 or --16 for \( \left|x - 5\right| \) to equal -16:
| x - 5 = -16 x = -16 + 5 x = -11 | x - 5 = 16 x = 16 + 5 x = 21 |
So, x = 21 or x = -11.
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 18 small cakes per hour. The kitchen is available for 4 hours and 22 large cakes and 330 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 5 | |
| 9 | |
| 12 | |
| 7 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 22 large cakes are needed for the party so \( \frac{22}{12} \) = 1\(\frac{5}{6}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 18 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 18 x 4 = 72 small cakes during that time. 330 small cakes are needed for the party so \( \frac{330}{72} \) = 4\(\frac{7}{12}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 5 = 7 cooks.