| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.77 |
| Score | 0% | 55% |
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 7 to 2 and the ratio of baseball to basketball cards is 7 to 1, what is the ratio of football to basketball cards?
| 3:6 | |
| 1:6 | |
| 49:2 | |
| 7:4 |
The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.
a(b + c) = ab + ac defines which of the following?
commutative property for division |
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commutative property for multiplication |
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distributive 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.
What is \( 5 \)\( \sqrt{28} \) + \( 2 \)\( \sqrt{7} \)
| 7\( \sqrt{4} \) | |
| 10\( \sqrt{7} \) | |
| 12\( \sqrt{7} \) | |
| 10\( \sqrt{4} \) |
To add these radicals together their radicands must be the same:
5\( \sqrt{28} \) + 2\( \sqrt{7} \)
5\( \sqrt{4 \times 7} \) + 2\( \sqrt{7} \)
5\( \sqrt{2^2 \times 7} \) + 2\( \sqrt{7} \)
(5)(2)\( \sqrt{7} \) + 2\( \sqrt{7} \)
10\( \sqrt{7} \) + 2\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
10\( \sqrt{7} \) + 2\( \sqrt{7} \)A machine in a factory has an error rate of 7 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 131.6 | |
| 136.7 | |
| 140.8 | |
| 76.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{7}{100} \) x 7 = \( \frac{7 \times 7}{100} \) = \( \frac{49}{100} \) = 0.49 errors per hour
So, in an average hour, the machine will produce 7 - 0.49 = 6.51 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 6.51 = 136.7 error free parts were produced yesterday.
Solve for \( \frac{6!}{5!} \)
| \( \frac{1}{1680} \) | |
| 6 | |
| 4 | |
| 7 |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{6!}{5!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{6}{1} \)
6