| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.68 |
| Score | 0% | 54% |
What is \( \frac{9}{8} \) + \( \frac{9}{12} \)?
| 1 \( \frac{3}{24} \) | |
| 1\(\frac{7}{8}\) | |
| 2 \( \frac{6}{14} \) | |
| 1 \( \frac{6}{24} \) |
To add 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 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 3}{8 x 3} \) + \( \frac{9 x 2}{12 x 2} \)
\( \frac{27}{24} \) + \( \frac{18}{24} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{27 + 18}{24} \) = \( \frac{45}{24} \) = 1\(\frac{7}{8}\)
Which of the following statements about exponents is false?
b1 = 1 |
|
b0 = 1 |
|
all of these are false |
|
b1 = b |
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 \( \sqrt{\frac{81}{4}} \)?
| 1 | |
| 4\(\frac{1}{2}\) | |
| 1\(\frac{1}{3}\) | |
| 1\(\frac{3}{4}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{81}{4}} \)
\( \frac{\sqrt{81}}{\sqrt{4}} \)
\( \frac{\sqrt{9^2}}{\sqrt{2^2}} \)
\( \frac{9}{2} \)
4\(\frac{1}{2}\)
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 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?
| 23 | |
| 30 | |
| 32 | |
| 36 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{50}{100} \) = \( \frac{50 x 25}{100} \) = \( \frac{1250}{100} \) = 12 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 = \( \frac{12}{\frac{40}{100}} \) = 12 x \( \frac{100}{40} \) = \( \frac{12 x 100}{40} \) = \( \frac{1200}{40} \) = 30 shots
to make the same number of shots as the guard and thus score the same number of points.
If a mayor is elected with 73% of the votes cast and 54% of a town's 12,000 voters cast a vote, how many votes did the mayor receive?
| 4,925 | |
| 5,054 | |
| 4,018 | |
| 4,730 |
If 54% of the town's 12,000 voters cast ballots the number of votes cast is:
(\( \frac{54}{100} \)) x 12,000 = \( \frac{648,000}{100} \) = 6,480
The mayor got 73% of the votes cast which is:
(\( \frac{73}{100} \)) x 6,480 = \( \frac{473,040}{100} \) = 4,730 votes.