| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.70 |
| Score | 0% | 54% |
Which of the following statements about exponents is false?
b1 = 1 |
|
b0 = 1 |
|
b1 = b |
|
all of these are false |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
If all of a roofing company's 16 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 8 | |
| 14 | |
| 10 | |
| 4 |
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 16 workers at the company now and that's enough to staff 4 crews so there are \( \frac{16}{4} \) = 4 workers on a crew. 6 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 6 x 4 = 24 total workers to staff the crews during the busy season. The company already employs 16 workers so they need to add 24 - 16 = 8 new staff for the busy season.
A bread recipe calls for 2\(\frac{7}{8}\) cups of flour. If you only have \(\frac{1}{4}\) cup, how much more flour is needed?
| 2\(\frac{3}{4}\) cups | |
| 2\(\frac{5}{8}\) cups | |
| 1\(\frac{1}{2}\) cups | |
| 1 cups |
The amount of flour you need is (2\(\frac{7}{8}\) - \(\frac{1}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{23}{8} \) - \( \frac{2}{8} \)) cups
\( \frac{21}{8} \) cups
2\(\frac{5}{8}\) cups
If a rectangle is twice as long as it is wide and has a perimeter of 36 meters, what is the area of the rectangle?
| 162 m2 | |
| 128 m2 | |
| 72 m2 | |
| 2 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 36 meters so the equation becomes: 2w + 2h = 36.
Putting these two equations together and solving for width (w):
2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6
Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m2
What is \( \frac{7}{2} \) + \( \frac{8}{8} \)?
| 1 \( \frac{7}{10} \) | |
| 1 \( \frac{9}{16} \) | |
| \( \frac{1}{7} \) | |
| 4\(\frac{1}{2}\) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 4}{2 x 4} \) + \( \frac{8 x 1}{8 x 1} \)
\( \frac{28}{8} \) + \( \frac{8}{8} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{28 + 8}{8} \) = \( \frac{36}{8} \) = 4\(\frac{1}{2}\)