| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
8 members of a bridal party need transported to a wedding reception but there are only 3 2-passenger taxis available to take them. How many will need to find other transportation?
| 5 | |
| 1 | |
| 2 | |
| 8 |
There are 3 2-passenger taxis available so that's 3 x 2 = 6 total seats. There are 8 people needing transportation leaving 8 - 6 = 2 who will have to find other transportation.
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 9 complete crews out on jobs?
| 3 | |
| 19 | |
| 12 | |
| 7 |
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. 9 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 9 x 3 = 27 total workers to staff the crews during the busy season. The company already employs 15 workers so they need to add 27 - 15 = 12 new staff for the busy season.
What is \( \frac{3a^6}{6a^4} \)?
| \(\frac{1}{2}\)a24 | |
| \(\frac{1}{2}\)a2 | |
| 2a10 | |
| \(\frac{1}{2}\)a\(\frac{2}{3}\) |
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:
\( \frac{3a^6}{6a^4} \)
\( \frac{3}{6} \) a(6 - 4)
\(\frac{1}{2}\)a2
What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?
| 31 | |
| 35 | |
| 38 | |
| 22 |
The equation for this sequence is:
an = an-1 + 2(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 + 2(6 - 1)
a6 = 21 + 2(5)
a6 = 31
Simplify \( \sqrt{32} \)
| 4\( \sqrt{2} \) | |
| 6\( \sqrt{4} \) | |
| 3\( \sqrt{2} \) | |
| 8\( \sqrt{2} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{32} \)
\( \sqrt{16 \times 2} \)
\( \sqrt{4^2 \times 2} \)
4\( \sqrt{2} \)