| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.85 |
| Score | 0% | 57% |
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 46 | |
| 45 | |
| 53 | |
| 44 |
The equation for this sequence is:
an = an-1 + 3(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46
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 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 122.8 | |
| 114.7 | |
| 194 | |
| 159.8 |
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 - 2 = 22 hours yesterday so you would expect that 22 x 8.82 = 194 error free parts were produced yesterday.
What is \( \frac{2}{3} \) + \( \frac{5}{11} \)?
| \( \frac{7}{12} \) | |
| \( \frac{8}{16} \) | |
| 1\(\frac{4}{33}\) | |
| \( \frac{7}{15} \) |
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 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 11}{3 x 11} \) + \( \frac{5 x 3}{11 x 3} \)
\( \frac{22}{33} \) + \( \frac{15}{33} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{22 + 15}{33} \) = \( \frac{37}{33} \) = 1\(\frac{4}{33}\)
If there were a total of 450 raffle tickets sold and you bought 22 tickets, what's the probability that you'll win the raffle?
| 13% | |
| 3% | |
| 5% | |
| 1% |
You have 22 out of the total of 450 raffle tickets sold so you have a (\( \frac{22}{450} \)) x 100 = \( \frac{22 \times 100}{450} \) = \( \frac{2200}{450} \) = 5% chance to win the raffle.
If a rectangle is twice as long as it is wide and has a perimeter of 54 meters, what is the area of the rectangle?
| 162 m2 | |
| 128 m2 | |
| 72 m2 | |
| 18 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 54 meters so the equation becomes: 2w + 2h = 54.
Putting these two equations together and solving for width (w):
2w + 2h = 54
w + h = \( \frac{54}{2} \)
w + h = 27
w = 27 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 27 - 2w
3w = 27
w = \( \frac{27}{3} \)
w = 9
Since h = 2w that makes h = (2 x 9) = 18 and the area = h x w = 9 x 18 = 162 m2