| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.30 |
| Score | 0% | 66% |
A machine in a factory has an error rate of 9 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 8 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 153.6 | |
| 109.2 | |
| 101.9 | |
| 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:
\( \frac{9}{100} \) x 7 = \( \frac{9 \times 7}{100} \) = \( \frac{63}{100} \) = 0.63 errors per hour
So, in an average hour, the machine will produce 7 - 0.63 = 6.37 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 6.37 = 101.9 error free parts were produced yesterday.
What is \( \sqrt{\frac{4}{49}} \)?
| 1\(\frac{2}{5}\) | |
| 1\(\frac{1}{6}\) | |
| \(\frac{7}{9}\) | |
| \(\frac{2}{7}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{4}{49}} \)
\( \frac{\sqrt{4}}{\sqrt{49}} \)
\( \frac{\sqrt{2^2}}{\sqrt{7^2}} \)
\(\frac{2}{7}\)
Which of the following is a mixed number?
\(1 {2 \over 5} \) |
|
\({5 \over 7} \) |
|
\({7 \over 5} \) |
|
\({a \over 5} \) |
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.
In a class of 18 students, 8 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 13 | |
| 18 | |
| 14 | |
| 6 |
The number of students taking German or Spanish is 8 + 8 = 16. Of that group of 16, 4 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 16 - 4 = 12 who are taking at least one language. 18 - 12 = 6 students who are not taking either language.
Convert 0.0002604 to scientific notation.
| 2.604 x 105 | |
| 2.604 x 10-3 | |
| 0.26 x 10-3 | |
| 2.604 x 10-4 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.0002604 in scientific notation is 2.604 x 10-4