| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.55 |
| Score | 0% | 71% |
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?
| 15% | |
| 20% | |
| 25% | |
| 30% |
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%
What is (c2)3?
| c | |
| c6 | |
| 2c3 | |
| c-1 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(c2)3Simplify \( \sqrt{75} \)
| 4\( \sqrt{3} \) | |
| 3\( \sqrt{6} \) | |
| 6\( \sqrt{6} \) | |
| 5\( \sqrt{3} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{75} \)
\( \sqrt{25 \times 3} \)
\( \sqrt{5^2 \times 3} \)
5\( \sqrt{3} \)
What is 3y5 x 8y6?
| 24y30 | |
| 24y-1 | |
| 24y11 | |
| 11y30 |
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:
3y5 x 8y6
(3 x 8)y(5 + 6)
24y11
What is the distance in miles of a trip that takes 7 hours at an average speed of 35 miles per hour?
| 385 miles | |
| 225 miles | |
| 245 miles | |
| 210 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 = \( 35mph \times 7h \)
245 miles