| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.27 |
| Score | 0% | 65% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 65% larger than the original. By what percentage has the area of the logo increased?
| 22\(\frac{1}{2}\)% | |
| 37\(\frac{1}{2}\)% | |
| 32\(\frac{1}{2}\)% | |
| 20% |
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 65% the radius (and, consequently, the total area) increases by \( \frac{65\text{%}}{2} \) = 32\(\frac{1}{2}\)%
What is (y2)2?
| 80 | |
| y0 | |
| y4 | |
| 2y2 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(y2)2\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for division |
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commutative property for division |
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commutative property for multiplication |
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distributive property for multiplication |
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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
Roger loaned Jennifer $100 at an annual interest rate of 7%. If no payments are made, what is the total amount owed at the end of the first year?
| $107 | |
| $103 | |
| $108 | |
| $102 |
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 $100
i = 0.07 x $100
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $100 + $7A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 50% off." If Roger buys two shirts, each with a regular price of $37, how much money will he save?
| $9.25 | |
| $18.50 | |
| $7.40 | |
| $12.95 |
By buying two shirts, Roger will save $37 x \( \frac{50}{100} \) = \( \frac{$37 x 50}{100} \) = \( \frac{$1850}{100} \) = $18.50 on the second shirt.