| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.78 |
| Score | 0% | 56% |
What is \( 3 \)\( \sqrt{32} \) - \( 9 \)\( \sqrt{2} \)
| 3\( \sqrt{2} \) | |
| 27\( \sqrt{2} \) | |
| -6\( \sqrt{64} \) | |
| 27\( \sqrt{64} \) |
To subtract these radicals together their radicands must be the same:
3\( \sqrt{32} \) - 9\( \sqrt{2} \)
3\( \sqrt{16 \times 2} \) - 9\( \sqrt{2} \)
3\( \sqrt{4^2 \times 2} \) - 9\( \sqrt{2} \)
(3)(4)\( \sqrt{2} \) - 9\( \sqrt{2} \)
12\( \sqrt{2} \) - 9\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
12\( \sqrt{2} \) - 9\( \sqrt{2} \)If all of a roofing company's 20 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?
| 18 | |
| 11 | |
| 12 | |
| 6 |
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 20 workers at the company now and that's enough to staff 5 crews so there are \( \frac{20}{5} \) = 4 workers on a crew. 8 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 8 x 4 = 32 total workers to staff the crews during the busy season. The company already employs 20 workers so they need to add 32 - 20 = 12 new staff for the busy season.
Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 11 small cakes per hour. The kitchen is available for 3 hours and 28 large cakes and 470 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?
| 14 | |
| 12 | |
| 15 | |
| 18 |
If a single cook can bake 4 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 4 x 3 = 12 large cakes during that time. 28 large cakes are needed for the party so \( \frac{28}{12} \) = 2\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 11 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 11 x 3 = 33 small cakes during that time. 470 small cakes are needed for the party so \( \frac{470}{33} \) = 14\(\frac{8}{33}\) 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 3 + 15 = 18 cooks.
Which of the following is an improper fraction?
\({2 \over 5} \) |
|
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
What is -8x4 - 3x4?
| -5x-8 | |
| -11x4 | |
| -11x-4 | |
| -5x8 |
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:
-8x4 - 3x4
(-8 - 3)x4
-11x4