| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.45 |
| Score | 0% | 69% |
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 42 | |
| 53 | |
| 46 | |
| 45 |
The equation for this sequence is:
an = an-1 + 3(n - 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 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46
The __________ is the greatest factor that divides two integers.
greatest common multiple |
|
greatest common factor |
|
least common multiple |
|
absolute value |
The greatest common factor (GCF) is the greatest factor that divides two integers.
If all of a roofing company's 12 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 8 complete crews out on jobs?
| 1 | |
| 19 | |
| 12 | |
| 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 12 workers at the company now and that's enough to staff 4 crews so there are \( \frac{12}{4} \) = 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 12 workers so they need to add 24 - 12 = 12 new staff for the busy season.
4! = ?
4 x 3 x 2 x 1 |
|
4 x 3 |
|
5 x 4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
What is \( \frac{49\sqrt{16}}{7\sqrt{4}} \)?
| \(\frac{1}{7}\) \( \sqrt{4} \) | |
| 4 \( \sqrt{7} \) | |
| 7 \( \sqrt{4} \) | |
| 4 \( \sqrt{\frac{1}{7}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{49\sqrt{16}}{7\sqrt{4}} \)
\( \frac{49}{7} \) \( \sqrt{\frac{16}{4}} \)
7 \( \sqrt{4} \)