| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 172.8 | |
| 110.4 | |
| 112.8 | |
| 88.2 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 6 = \( \frac{6 \times 6}{100} \) = \( \frac{36}{100} \) = 0.36 errors per hour
So, in an average hour, the machine will produce 6 - 0.36 = 5.64 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 5.64 = 112.8 error free parts were produced yesterday.
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = 7 or a = -7 |
|
a = -7 |
|
a = 7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
What is the next number in this sequence: 1, 4, 7, 10, 13, __________ ?
| 14 | |
| 23 | |
| 20 | |
| 16 |
The equation for this sequence is:
an = an-1 + 3
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
a6 = 13 + 3
a6 = 16
If a mayor is elected with 70% of the votes cast and 40% of a town's 20,000 voters cast a vote, how many votes did the mayor receive?
| 4,480 | |
| 5,600 | |
| 6,160 | |
| 4,800 |
If 40% of the town's 20,000 voters cast ballots the number of votes cast is:
(\( \frac{40}{100} \)) x 20,000 = \( \frac{800,000}{100} \) = 8,000
The mayor got 70% of the votes cast which is:
(\( \frac{70}{100} \)) x 8,000 = \( \frac{560,000}{100} \) = 5,600 votes.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 60% larger than the original. By what percentage has the area of the logo increased?
| 35% | |
| 17\(\frac{1}{2}\)% | |
| 30% | |
| 32\(\frac{1}{2}\)% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%