| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.01 |
| Score | 0% | 60% |
Cooks are needed to prepare for a large party. Each cook can bake either 2 large cakes or 13 small cakes per hour. The kitchen is available for 4 hours and 24 large cakes and 220 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 11 | |
| 10 | |
| 7 | |
| 8 |
If a single cook can bake 2 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 2 x 4 = 8 large cakes during that time. 24 large cakes are needed for the party so \( \frac{24}{8} \) = 3 cooks are needed to bake the required number of large cakes.
If a single cook can bake 13 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 13 x 4 = 52 small cakes during that time. 220 small cakes are needed for the party so \( \frac{220}{52} \) = 4\(\frac{3}{13}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 5 = 8 cooks.
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 60% 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?
| 26 | |
| 27 | |
| 30 | |
| 54 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{60}{100} \) = \( \frac{60 x 25}{100} \) = \( \frac{1500}{100} \) = 15 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 = \( \frac{15}{\frac{50}{100}} \) = 15 x \( \frac{100}{50} \) = \( \frac{15 x 100}{50} \) = \( \frac{1500}{50} \) = 30 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \sqrt{\frac{49}{9}} \)?
| 2\(\frac{1}{3}\) | |
| 1 | |
| 1\(\frac{2}{7}\) | |
| 4\(\frac{1}{2}\) |
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:
\( \sqrt{\frac{49}{9}} \)
\( \frac{\sqrt{49}}{\sqrt{9}} \)
\( \frac{\sqrt{7^2}}{\sqrt{3^2}} \)
\( \frac{7}{3} \)
2\(\frac{1}{3}\)
What is the least common multiple of 6 and 12?
| 29 | |
| 34 | |
| 12 | |
| 23 |
The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 have in common.
a(b + c) = ab + ac defines which of the following?
distributive property for division |
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commutative property for multiplication |
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commutative property for division |
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distributive property for multiplication |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.