| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
A machine in a factory has an error rate of 2 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 7 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 87.3 | |
| 144.8 | |
| 149.9 | |
| 172 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{2}{100} \) x 9 = \( \frac{2 \times 9}{100} \) = \( \frac{18}{100} \) = 0.18 errors per hour
So, in an average hour, the machine will produce 9 - 0.18 = 8.82 error free parts.
The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 8.82 = 149.9 error free parts were produced yesterday.
If a rectangle is twice as long as it is wide and has a perimeter of 6 meters, what is the area of the rectangle?
| 128 m2 | |
| 98 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 6 meters so the equation becomes: 2w + 2h = 6.
Putting these two equations together and solving for width (w):
2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1
Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m2
What is \( \frac{5}{3} \) + \( \frac{2}{7} \)?
| 1 \( \frac{5}{21} \) | |
| 2 \( \frac{7}{11} \) | |
| \( \frac{7}{21} \) | |
| 1\(\frac{20}{21}\) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 7}{3 x 7} \) + \( \frac{2 x 3}{7 x 3} \)
\( \frac{35}{21} \) + \( \frac{6}{21} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{35 + 6}{21} \) = \( \frac{41}{21} \) = 1\(\frac{20}{21}\)
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.
Solve for \( \frac{5!}{6!} \)
| \( \frac{1}{6} \) | |
| \( \frac{1}{8} \) | |
| \( \frac{1}{9} \) | |
| \( \frac{1}{120} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)