| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
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a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
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distributive property for division |
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distributive property for multiplication |
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commutative property for division |
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.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 60% larger than the original. By what percentage has the area of the logo increased?
| 17\(\frac{1}{2}\)% | |
| 30% | |
| 32\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 45% 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?
| 23 | |
| 15 | |
| 24 | |
| 25 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{45}{100} \) = \( \frac{45 x 15}{100} \) = \( \frac{675}{100} \) = 6 shots
The center makes 25% 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 = \( \frac{6}{\frac{25}{100}} \) = 6 x \( \frac{100}{25} \) = \( \frac{6 x 100}{25} \) = \( \frac{600}{25} \) = 24 shots
to make the same number of shots as the guard and thus score the same number of points.
Which of the following is not a prime number?
5 |
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2 |
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9 |
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7 |
A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.
What is \( \frac{6}{4} \) + \( \frac{6}{12} \)?
| 2 | |
| \( \frac{3}{12} \) | |
| \( \frac{1}{12} \) | |
| 2 \( \frac{8}{12} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] 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 4 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 3}{4 x 3} \) + \( \frac{6 x 1}{12 x 1} \)
\( \frac{18}{12} \) + \( \frac{6}{12} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{18 + 6}{12} \) = \( \frac{24}{12} \) = 2