| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.75 |
| Score | 0% | 55% |
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?
| 35% | |
| 17\(\frac{1}{2}\)% | |
| 20% | |
| 32\(\frac{1}{2}\)% |
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\(\frac{1}{2}\)%
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 or a = -7 |
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none of these is correct |
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a = -7 |
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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).
Solve 2 + (4 + 3) ÷ 3 x 3 - 42
| \(\frac{4}{5}\) | |
| -7 | |
| \(\frac{6}{7}\) | |
| 2\(\frac{1}{2}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
2 + (4 + 3) ÷ 3 x 3 - 42
P: 2 + (7) ÷ 3 x 3 - 42
E: 2 + 7 ÷ 3 x 3 - 16
MD: 2 + \( \frac{7}{3} \) x 3 - 16
MD: 2 + \( \frac{21}{3} \) - 16
AS: \( \frac{6}{3} \) + \( \frac{21}{3} \) - 16
AS: \( \frac{27}{3} \) - 16
AS: \( \frac{27 - 48}{3} \)
\( \frac{-21}{3} \)
-7
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?
| 9 | |
| 12 | |
| 13 | |
| 10 |
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.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
associative |
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commutative |
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PEDMAS |
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distributive |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.