| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
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Simplify \( \frac{28}{80} \).
| \( \frac{5}{13} \) | |
| \( \frac{7}{20} \) | |
| \( \frac{5}{8} \) | |
| \( \frac{5}{6} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{80} \) = \( \frac{\frac{28}{4}}{\frac{80}{4}} \) = \( \frac{7}{20} \)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 35% off." If Roger buys two shirts, each with a regular price of $49, how much money will he save?
| $17.15 | |
| $2.45 | |
| $4.90 | |
| $24.50 |
By buying two shirts, Roger will save $49 x \( \frac{35}{100} \) = \( \frac{$49 x 35}{100} \) = \( \frac{$1715}{100} \) = $17.15 on the second shirt.
What is \( \frac{3}{8} \) - \( \frac{6}{10} \)?
| -\(\frac{2}{9}\) | |
| 1 \( \frac{9}{15} \) | |
| 2 \( \frac{6}{40} \) | |
| 1 \( \frac{9}{40} \) |
To subtract 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 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 5}{8 x 5} \) - \( \frac{6 x 4}{10 x 4} \)
\( \frac{15}{40} \) - \( \frac{24}{40} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{15 - 24}{40} \) = \( \frac{-9}{40} \) = -\(\frac{2}{9}\)
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 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?
| 29 | |
| 18 | |
| 14 | |
| 22 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{55}{100} \) = \( \frac{55 x 15}{100} \) = \( \frac{825}{100} \) = 8 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 = \( \frac{8}{\frac{45}{100}} \) = 8 x \( \frac{100}{45} \) = \( \frac{8 x 100}{45} \) = \( \frac{800}{45} \) = 18 shots
to make the same number of shots as the guard and thus score the same number of points.
What is 5b4 x 4b5?
| 9b5 | |
| 20b9 | |
| 9b9 | |
| 20b4 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
5b4 x 4b5
(5 x 4)b(4 + 5)
20b9