| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.50 |
| Score | 0% | 70% |
A machine in a factory has an error rate of 2 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 141.1 | |
| 102.9 | |
| 160.7 | |
| 115.2 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{2}{100} \) x 5 = \( \frac{2 \times 5}{100} \) = \( \frac{10}{100} \) = 0.1 errors per hour
So, in an average hour, the machine will produce 5 - 0.1 = 4.9 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 4.9 = 102.9 error free parts were produced yesterday.
In a class of 23 students, 11 are taking German and 13 are taking Spanish. Of the students studying German or Spanish, 6 are taking both courses. How many students are not enrolled in either course?
| 21 | |
| 15 | |
| 5 | |
| 19 |
The number of students taking German or Spanish is 11 + 13 = 24. Of that group of 24, 6 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 24 - 6 = 18 who are taking at least one language. 23 - 18 = 5 students who are not taking either language.
Convert z-3 to remove the negative exponent.
| \( \frac{-1}{z^{-3}} \) | |
| \( \frac{-3}{z} \) | |
| \( \frac{-1}{-3z} \) | |
| \( \frac{1}{z^3} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
Which of the following is a mixed number?
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
|
\({a \over 5} \) |
|
\({5 \over 7} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
4! = ?
4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
|
5 x 4 x 3 x 2 x 1 |
|
4 x 3 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.