| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.99 |
| Score | 0% | 60% |
What is 3\( \sqrt{6} \) x 9\( \sqrt{2} \)?
| 27\( \sqrt{2} \) | |
| 12\( \sqrt{6} \) | |
| 54\( \sqrt{3} \) | |
| 27\( \sqrt{8} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
3\( \sqrt{6} \) x 9\( \sqrt{2} \)
(3 x 9)\( \sqrt{6 \times 2} \)
27\( \sqrt{12} \)
Now we need to simplify the radical:
27\( \sqrt{12} \)
27\( \sqrt{3 \times 4} \)
27\( \sqrt{3 \times 2^2} \)
(27)(2)\( \sqrt{3} \)
54\( \sqrt{3} \)
What is \( \frac{3}{8} \) - \( \frac{7}{10} \)?
| -\(\frac{13}{40}\) | |
| 2 \( \frac{9}{15} \) | |
| 1 \( \frac{3}{40} \) | |
| 2 \( \frac{7}{40} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 5}{8 x 5} \) - \( \frac{7 x 4}{10 x 4} \)
\( \frac{15}{40} \) - \( \frac{28}{40} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{15 - 28}{40} \) = \( \frac{-13}{40} \) = -\(\frac{13}{40}\)
If all of a roofing company's 8 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?
| 17 | |
| 8 | |
| 9 | |
| 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 8 workers at the company now and that's enough to staff 2 crews so there are \( \frac{8}{2} \) = 4 workers on a crew. 4 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 4 x 4 = 16 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 16 - 8 = 8 new staff for the busy season.
Convert 2,095,000 to scientific notation.
| 2.095 x 106 | |
| 20.95 x 105 | |
| 2.095 x 10-5 | |
| 2.095 x 107 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
2,095,000 in scientific notation is 2.095 x 106
Which of the following is not an integer?
1 |
|
\({1 \over 2}\) |
|
0 |
|
-1 |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.