| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
Frank loaned Damon $200 at an annual interest rate of 7%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $27 | |
| $36 | |
| $40 | |
| $14 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $200
i = 0.07 x $200
i = $14
a(b + c) = ab + ac defines which of the following?
distributive property for multiplication |
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distributive property for division |
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commutative 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.
Which of these numbers is a factor of 56?
| 60 | |
| 14 | |
| 17 | |
| 9 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56.
Which of the following is an improper fraction?
\({2 \over 5} \) |
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\({7 \over 5} \) |
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\({a \over 5} \) |
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\(1 {2 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
What is \( 3 \)\( \sqrt{27} \) + \( 3 \)\( \sqrt{3} \)
| 6\( \sqrt{9} \) | |
| 12\( \sqrt{3} \) | |
| 9\( \sqrt{3} \) | |
| 6\( \sqrt{3} \) |
To add these radicals together their radicands must be the same:
3\( \sqrt{27} \) + 3\( \sqrt{3} \)
3\( \sqrt{9 \times 3} \) + 3\( \sqrt{3} \)
3\( \sqrt{3^2 \times 3} \) + 3\( \sqrt{3} \)
(3)(3)\( \sqrt{3} \) + 3\( \sqrt{3} \)
9\( \sqrt{3} \) + 3\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
9\( \sqrt{3} \) + 3\( \sqrt{3} \)