| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.46 |
| Score | 0% | 69% |
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?
| 32\(\frac{1}{2}\)% | |
| 37\(\frac{1}{2}\)% | |
| 20% | |
| 17\(\frac{1}{2}\)% |
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 65% the radius (and, consequently, the total area) increases by \( \frac{65\text{%}}{2} \) = 32\(\frac{1}{2}\)%
What is \( \frac{3}{3} \) - \( \frac{4}{7} \)?
| \( \frac{7}{21} \) | |
| \( \frac{5}{21} \) | |
| \( \frac{8}{21} \) | |
| \(\frac{3857}{9000}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 7}{3 x 7} \) - \( \frac{4 x 3}{7 x 3} \)
\( \frac{21}{21} \) - \( \frac{12}{21} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{21 - 12}{21} \) = \( \frac{9}{21} \) = \(\frac{3857}{9000}\)
4! = ?
5 x 4 x 3 x 2 x 1 |
|
4 x 3 x 2 x 1 |
|
4 x 3 |
|
3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
Alex loaned Diane $600 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?
| $642 | |
| $648 | |
| $630 | |
| $654 |
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 $600
i = 0.07 x $600
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $600 + $42Simplify \( \frac{20}{68} \).
| \( \frac{1}{2} \) | |
| \( \frac{5}{17} \) | |
| \( \frac{5}{16} \) | |
| \( \frac{7}{16} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{20}{68} \) = \( \frac{\frac{20}{4}}{\frac{68}{4}} \) = \( \frac{5}{17} \)