| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.65 |
| Score | 0% | 53% |
What is \( 8 \)\( \sqrt{63} \) + \( 2 \)\( \sqrt{7} \)
| 10\( \sqrt{63} \) | |
| 26\( \sqrt{7} \) | |
| 16\( \sqrt{7} \) | |
| 10\( \sqrt{441} \) |
To add these radicals together their radicands must be the same:
8\( \sqrt{63} \) + 2\( \sqrt{7} \)
8\( \sqrt{9 \times 7} \) + 2\( \sqrt{7} \)
8\( \sqrt{3^2 \times 7} \) + 2\( \sqrt{7} \)
(8)(3)\( \sqrt{7} \) + 2\( \sqrt{7} \)
24\( \sqrt{7} \) + 2\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
24\( \sqrt{7} \) + 2\( \sqrt{7} \)On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 65% of his shots. If the guard takes 15 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?
| 24 | |
| 16 | |
| 18 | |
| 26 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{65}{100} \) = \( \frac{65 x 15}{100} \) = \( \frac{975}{100} \) = 9 shots
The center makes 50% 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 = \( \frac{9}{\frac{50}{100}} \) = 9 x \( \frac{100}{50} \) = \( \frac{9 x 100}{50} \) = \( \frac{900}{50} \) = 18 shots
to make the same number of shots as the guard and thus score the same number of points.
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?
| 37\(\frac{1}{2}\)% | |
| 25% | |
| 32\(\frac{1}{2}\)% | |
| 20% |
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 the least common multiple of 5 and 7?
| 35 | |
| 14 | |
| 31 | |
| 22 |
The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 have in common.
What is \( \frac{3}{8} \) - \( \frac{9}{16} \)?
| -\(\frac{3}{16}\) | |
| 1 \( \frac{4}{12} \) | |
| \( \frac{9}{15} \) | |
| 1 \( \frac{8}{16} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 2}{8 x 2} \) - \( \frac{9 x 1}{16 x 1} \)
\( \frac{6}{16} \) - \( \frac{9}{16} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{6 - 9}{16} \) = \( \frac{-3}{16} \) = -\(\frac{3}{16}\)