| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.95 |
| Score | 0% | 59% |
Which of the following statements about exponents is false?
all of these are false |
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b1 = b |
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b1 = 1 |
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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).
What is \( \frac{3}{6} \) - \( \frac{2}{14} \)?
| 2 \( \frac{2}{42} \) | |
| \(\frac{5}{14}\) | |
| \( \frac{2}{42} \) | |
| 2 \( \frac{1}{7} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 7}{6 x 7} \) - \( \frac{2 x 3}{14 x 3} \)
\( \frac{21}{42} \) - \( \frac{6}{42} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{21 - 6}{42} \) = \( \frac{15}{42} \) = \(\frac{5}{14}\)
Which of the following is a mixed number?
\({5 \over 7} \) |
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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.
On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 25 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?
| 28 | |
| 29 | |
| 39 | |
| 23 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{55}{100} \) = \( \frac{55 x 25}{100} \) = \( \frac{1375}{100} \) = 13 shots
The center makes 45% 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 = \( \frac{13}{\frac{45}{100}} \) = 13 x \( \frac{100}{45} \) = \( \frac{13 x 100}{45} \) = \( \frac{1300}{45} \) = 29 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{-6y^5}{2y^3} \)?
| -3y2 | |
| -\(\frac{1}{3}\)y8 | |
| -\(\frac{1}{3}\)y-2 | |
| -\(\frac{1}{3}\)y2 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-6y^5}{2y^3} \)
\( \frac{-6}{2} \) y(5 - 3)
-3y2