| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.45 |
| Score | 0% | 69% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 35% larger than the original. By what percentage has the area of the logo increased?
| 37\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% | |
| 17\(\frac{1}{2}\)% | |
| 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 35% the radius (and, consequently, the total area) increases by \( \frac{35\text{%}}{2} \) = 17\(\frac{1}{2}\)%
What is the least common multiple of 3 and 11?
| 19 | |
| 22 | |
| 33 | |
| 4 |
The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 have in common.
Simplify \( \frac{40}{52} \).
| \( \frac{4}{13} \) | |
| \( \frac{9}{14} \) | |
| \( \frac{10}{13} \) | |
| \( \frac{7}{18} \) |
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:
\( \frac{40}{52} \) = \( \frac{\frac{40}{4}}{\frac{52}{4}} \) = \( \frac{10}{13} \)
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 |
|
a = -7 |
|
a = 7 or a = -7 |
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none of these is correct |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
What is the greatest common factor of 76 and 76?
| 13 | |
| 67 | |
| 76 | |
| 31 |
The factors of 76 are [1, 2, 4, 19, 38, 76] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 6 factors [1, 2, 4, 19, 38, 76] making 76 the greatest factor 76 and 76 have in common.