| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 60% larger than the original. By what percentage has the area of the logo increased?
| 32\(\frac{1}{2}\)% | |
| 30% | |
| 15% | |
| 25% |
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 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%
Convert b-5 to remove the negative exponent.
| \( \frac{-5}{b} \) | |
| \( \frac{-5}{-b} \) | |
| \( \frac{1}{b^5} \) | |
| \( \frac{-1}{-5b^{5}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is 6z6 x 7z6?
| 13z12 | |
| 42z12 | |
| 42z36 | |
| 42z0 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
6z6 x 7z6
(6 x 7)z(6 + 6)
42z12
If the ratio of home fans to visiting fans in a crowd is 2:1 and all 46,000 seats in a stadium are filled, how many home fans are in attendance?
| 31,500 | |
| 32,500 | |
| 20,667 | |
| 30,667 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
46,000 fans x \( \frac{2}{3} \) = \( \frac{92000}{3} \) = 30,667 fans.
What is (x3)5?
| x-2 | |
| x2 | |
| x15 | |
| 5x3 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(x3)5