| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.89 |
| Score | 0% | 58% |
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 40% 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?
| 10 | |
| 11 | |
| 17 | |
| 12 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{40}{100} \) = \( \frac{40 x 15}{100} \) = \( \frac{600}{100} \) = 6 shots
The center makes 35% 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 = \( \frac{6}{\frac{35}{100}} \) = 6 x \( \frac{100}{35} \) = \( \frac{6 x 100}{35} \) = \( \frac{600}{35} \) = 17 shots
to make the same number of shots as the guard and thus score the same number of points.
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for multiplication |
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commutative property for multiplication |
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distributive property for division |
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commutative property for division |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
The total water usage for a city is 35,000 gallons each day. Of that total, 31% is for personal use and 45% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 2,400 | |
| 3,100 | |
| 4,900 | |
| 14,400 |
45% of the water consumption is industrial use and 31% is personal use so (45% - 31%) = 14% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{14}{100} \) x 35,000 gallons = 4,900 gallons.
What is \( \frac{30\sqrt{36}}{6\sqrt{9}} \)?
| 4 \( \sqrt{5} \) | |
| 5 \( \sqrt{\frac{1}{4}} \) | |
| 4 \( \sqrt{\frac{1}{5}} \) | |
| 5 \( \sqrt{4} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{30\sqrt{36}}{6\sqrt{9}} \)
\( \frac{30}{6} \) \( \sqrt{\frac{36}{9}} \)
5 \( \sqrt{4} \)
What is \( \frac{4}{8} \) - \( \frac{3}{16} \)?
| 2 \( \frac{1}{16} \) | |
| 1 \( \frac{9}{16} \) | |
| \(\frac{5}{16}\) | |
| 2 \( \frac{3}{16} \) |
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 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 2}{8 x 2} \) - \( \frac{3 x 1}{16 x 1} \)
\( \frac{8}{16} \) - \( \frac{3}{16} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{8 - 3}{16} \) = \( \frac{5}{16} \) = \(\frac{5}{16}\)