| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.08 |
| Score | 0% | 62% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 75% larger than the original. By what percentage has the area of the logo increased?
| 37\(\frac{1}{2}\)% | |
| 17\(\frac{1}{2}\)% | |
| 15% | |
| 22\(\frac{1}{2}\)% |
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 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%
Find the average of the following numbers: 14, 8, 13, 9.
| 9 | |
| 11 | |
| 16 | |
| 6 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{14 + 8 + 13 + 9}{4} \) = \( \frac{44}{4} \) = 11
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 15% off." If Charlie buys two shirts, each with a regular price of $40, how much money will he save?
| $12.00 | |
| $8.00 | |
| $6.00 | |
| $14.00 |
By buying two shirts, Charlie will save $40 x \( \frac{15}{100} \) = \( \frac{$40 x 15}{100} \) = \( \frac{$600}{100} \) = $6.00 on the second shirt.
What is the least common multiple of 8 and 16?
| 16 | |
| 31 | |
| 83 | |
| 29 |
The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 have in common.
What is \( 6 \)\( \sqrt{28} \) - \( 2 \)\( \sqrt{7} \)
| 12\( \sqrt{4} \) | |
| 4\( \sqrt{196} \) | |
| 10\( \sqrt{7} \) | |
| 4\( \sqrt{45} \) |
To subtract these radicals together their radicands must be the same:
6\( \sqrt{28} \) - 2\( \sqrt{7} \)
6\( \sqrt{4 \times 7} \) - 2\( \sqrt{7} \)
6\( \sqrt{2^2 \times 7} \) - 2\( \sqrt{7} \)
(6)(2)\( \sqrt{7} \) - 2\( \sqrt{7} \)
12\( \sqrt{7} \) - 2\( \sqrt{7} \)
Now that the radicands are identical, you can subtract them:
12\( \sqrt{7} \) - 2\( \sqrt{7} \)