| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.48 |
| Score | 0% | 70% |
What is the least common multiple of 3 and 7?
| 11 | |
| 21 | |
| 18 | |
| 4 |
The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 have in common.
What is the next number in this sequence: 1, 2, 3, 4, 5, __________ ?
| 0 | |
| 9 | |
| 4 | |
| 6 |
The equation for this sequence is:
an = an-1 + 1
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 1
a6 = 5 + 1
a6 = 6
What is -4c4 - c4?
| -3c4 | |
| -3c-8 | |
| -5c4 | |
| -5c-4 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
-4c4 - 1c4
(-4 - 1)c4
-5c4
What is \( \frac{-4c^9}{2c^3} \)?
| -\(\frac{1}{2}\)c12 | |
| -2c3 | |
| -2c-6 | |
| -2c6 |
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:
\( \frac{-4c^9}{2c^3} \)
\( \frac{-4}{2} \) c(9 - 3)
-2c6
If all of a roofing company's 4 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 4 complete crews out on jobs?
| 18 | |
| 8 | |
| 4 | |
| 1 |
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 4 workers at the company now and that's enough to staff 2 crews so there are \( \frac{4}{2} \) = 2 workers on a crew. 4 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 4 x 2 = 8 total workers to staff the crews during the busy season. The company already employs 4 workers so they need to add 8 - 4 = 4 new staff for the busy season.