| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.05 |
| Score | 0% | 61% |
Simplify \( \frac{20}{52} \).
| \( \frac{5}{19} \) | |
| \( \frac{7}{20} \) | |
| \( \frac{5}{12} \) | |
| \( \frac{5}{13} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{20}{52} \) = \( \frac{\frac{20}{4}}{\frac{52}{4}} \) = \( \frac{5}{13} \)
How many 1\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 9 gallon tank to fill it exactly halfway?
| 2 | |
| 3 | |
| 3 | |
| 7 |
To fill a 9 gallon tank exactly halfway you'll need 4\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:
cans = \( \frac{4\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 3
Convert 1,723,000 to scientific notation.
| 1.723 x 106 | |
| 1.723 x 10-5 | |
| 1.723 x 107 | |
| 1.723 x 10-6 |
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:
1,723,000 in scientific notation is 1.723 x 106
A machine in a factory has an error rate of 5 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 | |
| 110.4 | |
| 99.8 | |
| 84.6 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{5}{100} \) x 5 = \( \frac{5 \times 5}{100} \) = \( \frac{25}{100} \) = 0.25 errors per hour
So, in an average hour, the machine will produce 5 - 0.25 = 4.75 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 4.75 = 99.8 error free parts were produced yesterday.
In a class of 23 students, 5 are taking German and 13 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 10 | |
| 20 | |
| 22 | |
| 14 |
The number of students taking German or Spanish is 5 + 13 = 18. Of that group of 18, 5 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 18 - 5 = 13 who are taking at least one language. 23 - 13 = 10 students who are not taking either language.