| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 5 to 2 and the ratio of baseball to basketball cards is 5 to 1, what is the ratio of football to basketball cards?
| 5:1 | |
| 7:1 | |
| 1:8 | |
| 25:2 |
The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 40% of his shots. If the guard takes 30 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?
| 48 | |
| 60 | |
| 55 | |
| 46 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{40}{100} \) = \( \frac{40 x 30}{100} \) = \( \frac{1200}{100} \) = 12 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 = \( \frac{12}{\frac{25}{100}} \) = 12 x \( \frac{100}{25} \) = \( \frac{12 x 100}{25} \) = \( \frac{1200}{25} \) = 48 shots
to make the same number of shots as the guard and thus score the same number of points.
a(b + c) = ab + ac defines which of the following?
distributive property for multiplication |
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commutative property for division |
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commutative property for multiplication |
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distributive 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.
Convert 0.0004106 to scientific notation.
| 41.06 x 10-5 | |
| 4.106 x 10-4 | |
| 0.411 x 10-3 | |
| 4.106 x 105 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.0004106 in scientific notation is 4.106 x 10-4
Find the average of the following numbers: 16, 8, 14, 10.
| 12 | |
| 11 | |
| 16 | |
| 15 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{16 + 8 + 14 + 10}{4} \) = \( \frac{48}{4} \) = 12