| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.25 |
| Score | 0% | 65% |
What is (x4)4?
| x8 | |
| x16 | |
| x0 | |
| 4x4 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(x4)418 members of a bridal party need transported to a wedding reception but there are only 4 4-passenger taxis available to take them. How many will need to find other transportation?
| 8 | |
| 2 | |
| 5 | |
| 4 |
There are 4 4-passenger taxis available so that's 4 x 4 = 16 total seats. There are 18 people needing transportation leaving 18 - 16 = 2 who will have to find other transportation.
What is the least common multiple of 8 and 16?
| 37 | |
| 78 | |
| 4 | |
| 16 |
The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 have in common.
If a rectangle is twice as long as it is wide and has a perimeter of 12 meters, what is the area of the rectangle?
| 8 m2 | |
| 50 m2 | |
| 18 m2 | |
| 162 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 12 meters so the equation becomes: 2w + 2h = 12.
Putting these two equations together and solving for width (w):
2w + 2h = 12
w + h = \( \frac{12}{2} \)
w + h = 6
w = 6 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 6 - 2w
3w = 6
w = \( \frac{6}{3} \)
w = 2
Since h = 2w that makes h = (2 x 2) = 4 and the area = h x w = 2 x 4 = 8 m2
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 8 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 179.6 | |
| 144.4 | |
| 132.3 | |
| 153.6 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{5}{100} \) x 8 = \( \frac{5 \times 8}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour
So, in an average hour, the machine will produce 8 - 0.4 = 7.6 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 7.6 = 144.4 error free parts were produced yesterday.