| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.11 |
| Score | 0% | 62% |
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?
| 22\(\frac{1}{2}\)% | |
| 15% | |
| 27\(\frac{1}{2}\)% | |
| 32\(\frac{1}{2}\)% |
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 an improper fraction?
\({2 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({7 \over 5} \) |
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.
If a rectangle is twice as long as it is wide and has a perimeter of 36 meters, what is the area of the rectangle?
| 2 m2 | |
| 98 m2 | |
| 128 m2 | |
| 72 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 36 meters so the equation becomes: 2w + 2h = 36.
Putting these two equations together and solving for width (w):
2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6
Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m2
Monty loaned Frank $100 at an annual interest rate of 6%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $10 | |
| $7 | |
| $24 | |
| $6 |
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 = 0.06 x $100
i = $6
What is \( \frac{4}{5} \) ÷ \( \frac{4}{9} \)?
| 9 | |
| \(\frac{1}{21}\) | |
| 1\(\frac{4}{5}\) | |
| \(\frac{1}{9}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{5} \) ÷ \( \frac{4}{9} \) = \( \frac{4}{5} \) x \( \frac{9}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{5} \) x \( \frac{9}{4} \) = \( \frac{4 x 9}{5 x 4} \) = \( \frac{36}{20} \) = 1\(\frac{4}{5}\)