| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| 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 8 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 156.8 | |
| 83.3 | |
| 165.9 | |
| 82.4 |
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 8 = \( \frac{2 \times 8}{100} \) = \( \frac{16}{100} \) = 0.16 errors per hour
So, in an average hour, the machine will produce 8 - 0.16 = 7.84 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 7.84 = 156.8 error free parts were produced yesterday.
How many 15-passenger vans will it take to drive all 39 members of the football team to an away game?
| 7 vans | |
| 8 vans | |
| 5 vans | |
| 3 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{39}{15} \) = 2\(\frac{3}{5}\)
So, it will take 2 full vans and one partially full van to transport the entire team making a total of 3 vans.
What is -8x3 - 9x3?
| 17x-3 | |
| x6 | |
| 17x3 | |
| -17x3 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
-8x3 - 9x3
(-8 - 9)x3
-17x3
The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
|
least common multiple |
|
greatest common factor |
|
least common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 30% larger than the original. By what percentage has the area of the logo increased?
| 37\(\frac{1}{2}\)% | |
| 22\(\frac{1}{2}\)% | |
| 35% | |
| 15% |
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 30% the radius (and, consequently, the total area) increases by \( \frac{30\text{%}}{2} \) = 15%