| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.01 |
| Score | 0% | 60% |
If \( \left|z - 8\right| \) + 6 = 8, which of these is a possible value for z?
| -7 | |
| -1 | |
| 6 | |
| -11 |
First, solve for \( \left|z - 8\right| \):
\( \left|z - 8\right| \) + 6 = 8
\( \left|z - 8\right| \) = 8 - 6
\( \left|z - 8\right| \) = 2
The value inside the absolute value brackets can be either positive or negative so (z - 8) must equal + 2 or -2 for \( \left|z - 8\right| \) to equal 2:
| z - 8 = 2 z = 2 + 8 z = 10 | z - 8 = -2 z = -2 + 8 z = 6 |
So, z = 6 or z = 10.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
distributive |
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commutative |
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associative |
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PEDMAS |
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.
Which of the following is a mixed number?
\({a \over 5} \) |
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\(1 {2 \over 5} \) |
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\({7 \over 5} \) |
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\({5 \over 7} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 50% 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?
| 21 | |
| 13 | |
| 25 | |
| 11 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{50}{100} \) = \( \frac{50 x 10}{100} \) = \( \frac{500}{100} \) = 5 shots
The center makes 40% 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 = \( \frac{5}{\frac{40}{100}} \) = 5 x \( \frac{100}{40} \) = \( \frac{5 x 100}{40} \) = \( \frac{500}{40} \) = 13 shots
to make the same number of shots as the guard and thus score the same number of points.
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 31,000 seats in a stadium are filled, how many home fans are in attendance?
| 26,000 | |
| 23,250 | |
| 36,000 | |
| 27,500 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
31,000 fans x \( \frac{3}{4} \) = \( \frac{93000}{4} \) = 23,250 fans.