| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.59 |
| Score | 0% | 52% |
What is \( 7 \)\( \sqrt{32} \) + \( 3 \)\( \sqrt{2} \)
| 10\( \sqrt{2} \) | |
| 10\( \sqrt{32} \) | |
| 10\( \sqrt{16} \) | |
| 31\( \sqrt{2} \) |
To add these radicals together their radicands must be the same:
7\( \sqrt{32} \) + 3\( \sqrt{2} \)
7\( \sqrt{16 \times 2} \) + 3\( \sqrt{2} \)
7\( \sqrt{4^2 \times 2} \) + 3\( \sqrt{2} \)
(7)(4)\( \sqrt{2} \) + 3\( \sqrt{2} \)
28\( \sqrt{2} \) + 3\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
28\( \sqrt{2} \) + 3\( \sqrt{2} \)What is \( \frac{6}{2} \) - \( \frac{3}{4} \)?
| 2\(\frac{1}{4}\) | |
| 2 \( \frac{1}{4} \) | |
| 1 \( \frac{1}{4} \) | |
| 1 \( \frac{5}{10} \) |
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 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 2}{2 x 2} \) - \( \frac{3 x 1}{4 x 1} \)
\( \frac{12}{4} \) - \( \frac{3}{4} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{12 - 3}{4} \) = \( \frac{9}{4} \) = 2\(\frac{1}{4}\)
Which of the following statements about exponents is false?
b1 = b |
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b1 = 1 |
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all of these are false |
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b0 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 70% 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?
| 19 | |
| 21 | |
| 23 | |
| 20 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{70}{100} \) = \( \frac{70 x 15}{100} \) = \( \frac{1050}{100} \) = 10 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 = \( \frac{10}{\frac{50}{100}} \) = 10 x \( \frac{100}{50} \) = \( \frac{10 x 100}{50} \) = \( \frac{1000}{50} \) = 20 shots
to make the same number of shots as the guard and thus score the same number of points.
Which of the following is an improper fraction?
\({2 \over 5} \) |
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\(1 {2 \over 5} \) |
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\({a \over 5} \) |
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\({7 \over 5} \) |
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.