| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.51 |
| Score | 0% | 70% |
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?
| 35% | |
| 20% | |
| 25% | |
| 22\(\frac{1}{2}\)% |
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 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%
If a car travels 180 miles in 9 hours, what is the average speed?
| 20 mph | |
| 75 mph | |
| 60 mph | |
| 30 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)What is the least common multiple of 2 and 10?
| 16 | |
| 10 | |
| 8 | |
| 9 |
The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 have in common.
What is -4b4 - 6b4?
| -10b4 | |
| 2b-8 | |
| 2b4 | |
| 10b4 |
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:
-4b4 - 6b4
(-4 - 6)b4
-10b4
What is \( \sqrt{\frac{49}{9}} \)?
| 1 | |
| 2\(\frac{1}{3}\) | |
| \(\frac{5}{6}\) | |
| \(\frac{4}{5}\) |
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:
\( \sqrt{\frac{49}{9}} \)
\( \frac{\sqrt{49}}{\sqrt{9}} \)
\( \frac{\sqrt{7^2}}{\sqrt{3^2}} \)
\( \frac{7}{3} \)
2\(\frac{1}{3}\)