| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.06 |
| Score | 0% | 61% |
Which of the following is not a prime number?
5 |
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7 |
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2 |
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9 |
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.
If a rectangle is twice as long as it is wide and has a perimeter of 54 meters, what is the area of the rectangle?
| 50 m2 | |
| 162 m2 | |
| 32 m2 | |
| 98 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 54 meters so the equation becomes: 2w + 2h = 54.
Putting these two equations together and solving for width (w):
2w + 2h = 54
w + h = \( \frac{54}{2} \)
w + h = 27
w = 27 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 27 - 2w
3w = 27
w = \( \frac{27}{3} \)
w = 9
Since h = 2w that makes h = (2 x 9) = 18 and the area = h x w = 9 x 18 = 162 m2
Convert a-2 to remove the negative exponent.
| \( \frac{-2}{-a} \) | |
| \( \frac{1}{a^2} \) | |
| \( \frac{-2}{a} \) | |
| \( \frac{2}{a} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
Bob loaned Betty $1,200 at an annual interest rate of 2%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,212 | |
| $1,248 | |
| $1,224 | |
| $1,284 |
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 $1,200
i = 0.02 x $1,200
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,200 + $24\({b + c \over a} = {b \over a} + {c \over a}\) 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 division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).