| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.47 |
| Score | 0% | 69% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 45% larger than the original. By what percentage has the area of the logo increased?
| 15% | |
| 22\(\frac{1}{2}\)% | |
| 17\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% |
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 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%
What is the distance in miles of a trip that takes 4 hours at an average speed of 15 miles per hour?
| 45 miles | |
| 60 miles | |
| 90 miles | |
| 125 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 15mph \times 4h \)
60 miles
What is the least common multiple of 2 and 4?
| 6 | |
| 5 | |
| 3 | |
| 4 |
The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 have in common.
What is 2x4 - 6x4?
| 4x4 | |
| 8x8 | |
| -4x4 | |
| 8x4 |
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:
2x4 - 6x4
(2 - 6)x4
-4x4
Solve for \( \frac{5!}{2!} \)
| \( \frac{1}{336} \) | |
| \( \frac{1}{60480} \) | |
| 60 | |
| 210 |
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:
\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60