| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.80 |
| Score | 0% | 56% |
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?
| 15% | |
| 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 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%
What is \( 2 \)\( \sqrt{63} \) - \( 2 \)\( \sqrt{7} \)
| 4\( \sqrt{7} \) | |
| 4\( \sqrt{441} \) | |
| 4\( \sqrt{9} \) | |
| 0\( \sqrt{441} \) |
To subtract these radicals together their radicands must be the same:
2\( \sqrt{63} \) - 2\( \sqrt{7} \)
2\( \sqrt{9 \times 7} \) - 2\( \sqrt{7} \)
2\( \sqrt{3^2 \times 7} \) - 2\( \sqrt{7} \)
(2)(3)\( \sqrt{7} \) - 2\( \sqrt{7} \)
6\( \sqrt{7} \) - 2\( \sqrt{7} \)
Now that the radicands are identical, you can subtract them:
6\( \sqrt{7} \) - 2\( \sqrt{7} \)If a car travels 175 miles in 5 hours, what is the average speed?
| 30 mph | |
| 40 mph | |
| 45 mph | |
| 35 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 \( \frac{3}{2} \) - \( \frac{4}{6} \)?
| 2 \( \frac{1}{6} \) | |
| \( \frac{5}{6} \) | |
| \(\frac{5}{6}\) | |
| 2 \( \frac{7}{6} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 3}{2 x 3} \) - \( \frac{4 x 1}{6 x 1} \)
\( \frac{9}{6} \) - \( \frac{4}{6} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{9 - 4}{6} \) = \( \frac{5}{6} \) = \(\frac{5}{6}\)
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 40% of his shots. If the guard takes 10 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 13 | |
| 10 | |
| 7 | |
| 8 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{40}{100} \) = \( \frac{40 x 10}{100} \) = \( \frac{400}{100} \) = 4 shots
The center makes 30% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{4}{\frac{30}{100}} \) = 4 x \( \frac{100}{30} \) = \( \frac{4 x 100}{30} \) = \( \frac{400}{30} \) = 13 shots
to make the same number of shots as the guard and thus score the same number of points.