| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.36 |
| Score | 0% | 67% |
Simplify \( \frac{28}{80} \).
| \( \frac{7}{13} \) | |
| \( \frac{9}{11} \) | |
| \( \frac{7}{20} \) | |
| \( \frac{4}{11} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{80} \) = \( \frac{\frac{28}{4}}{\frac{80}{4}} \) = \( \frac{7}{20} \)
Solve for \( \frac{5!}{3!} \)
| \( \frac{1}{336} \) | |
| \( \frac{1}{56} \) | |
| 336 | |
| 20 |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{5!}{3!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{5 \times 4}{1} \)
\( 5 \times 4 \)
20
A circular logo is enlarged to fit the lid of a jar. The new diameter is 70% larger than the original. By what percentage has the area of the logo increased?
| 20% | |
| 35% | |
| 37\(\frac{1}{2}\)% | |
| 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 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%
| 4.8 | |
| 2.4 | |
| 1.0 | |
| 1 |
1
If a car travels 30 miles in 1 hour, what is the average speed?
| 45 mph | |
| 15 mph | |
| 30 mph | |
| 20 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)