| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.30 |
| Score | 0% | 66% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 35% larger than the original. By what percentage has the area of the logo increased?
| 17\(\frac{1}{2}\)% | |
| 35% | |
| 20% | |
| 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 35% the radius (and, consequently, the total area) increases by \( \frac{35\text{%}}{2} \) = 17\(\frac{1}{2}\)%
How many hours does it take a car to travel 20 miles at an average speed of 20 miles per hour?
| 1 hour | |
| 3 hours | |
| 8 hours | |
| 4 hours |
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 time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{20mi}{20mph} \)
1 hour
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = 7 or a = -7 |
|
a = 7 |
|
a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
The total water usage for a city is 15,000 gallons each day. Of that total, 23% is for personal use and 37% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 13,000 | |
| 7,000 | |
| 8,800 | |
| 2,100 |
37% of the water consumption is industrial use and 23% is personal use so (37% - 23%) = 14% more water is used for industrial purposes. 15,000 gallons are consumed daily so industry consumes \( \frac{14}{100} \) x 15,000 gallons = 2,100 gallons.
What is \( \frac{4}{7} \) ÷ \( \frac{4}{8} \)?
| 8 | |
| \(\frac{1}{7}\) | |
| \(\frac{3}{35}\) | |
| 1\(\frac{1}{7}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{7} \) ÷ \( \frac{4}{8} \) = \( \frac{4}{7} \) x \( \frac{8}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{7} \) x \( \frac{8}{4} \) = \( \frac{4 x 8}{7 x 4} \) = \( \frac{32}{28} \) = 1\(\frac{1}{7}\)