| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.97 |
| Score | 0% | 59% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 40% larger than the original. By what percentage has the area of the logo increased?
| 22\(\frac{1}{2}\)% | |
| 20% | |
| 15% | |
| 37\(\frac{1}{2}\)% |
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 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 3 to 2 and the ratio of baseball to basketball cards is 3 to 1, what is the ratio of football to basketball cards?
| 7:1 | |
| 9:2 | |
| 5:1 | |
| 5:6 |
The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.
What is \( \sqrt{\frac{64}{81}} \)?
| 2\(\frac{1}{3}\) | |
| \(\frac{8}{9}\) | |
| \(\frac{3}{8}\) | |
| 1\(\frac{2}{7}\) |
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:
\( \sqrt{\frac{64}{81}} \)
\( \frac{\sqrt{64}}{\sqrt{81}} \)
\( \frac{\sqrt{8^2}}{\sqrt{9^2}} \)
\(\frac{8}{9}\)
Convert z-2 to remove the negative exponent.
| \( \frac{1}{z^2} \) | |
| \( \frac{-1}{-2z} \) | |
| \( \frac{-2}{z} \) | |
| \( \frac{1}{z^{-2}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
|
least common multiple |
|
least common factor |
|
greatest common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.