| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.28 |
| Score | 0% | 66% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 55% larger than the original. By what percentage has the area of the logo increased?
| 35% | |
| 27\(\frac{1}{2}\)% | |
| 20% | |
| 15% |
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 55% the radius (and, consequently, the total area) increases by \( \frac{55\text{%}}{2} \) = 27\(\frac{1}{2}\)%
Which of the following is a mixed number?
\({5 \over 7} \) |
|
\({a \over 5} \) |
|
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
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.
Simplify \( \frac{40}{52} \).
| \( \frac{10}{13} \) | |
| \( \frac{10}{11} \) | |
| \( \frac{2}{7} \) | |
| \( \frac{7}{18} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{40}{52} \) = \( \frac{\frac{40}{4}}{\frac{52}{4}} \) = \( \frac{10}{13} \)
What is 6\( \sqrt{9} \) x 5\( \sqrt{3} \)?
| 30\( \sqrt{9} \) | |
| 30\( \sqrt{3} \) | |
| 11\( \sqrt{9} \) | |
| 90\( \sqrt{3} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
6\( \sqrt{9} \) x 5\( \sqrt{3} \)
(6 x 5)\( \sqrt{9 \times 3} \)
30\( \sqrt{27} \)
Now we need to simplify the radical:
30\( \sqrt{27} \)
30\( \sqrt{3 \times 9} \)
30\( \sqrt{3 \times 3^2} \)
(30)(3)\( \sqrt{3} \)
90\( \sqrt{3} \)
Roger loaned Frank $1,300 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?
| $91 | |
| $48 | |
| $42 | |
| $63 |
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 $1,300
i = 0.07 x $1,300
i = $91