| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.67 |
| Score | 0% | 73% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 50% larger than the original. By what percentage has the area of the logo increased?
| 22\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% | |
| 32\(\frac{1}{2}\)% | |
| 25% |
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 50% the radius (and, consequently, the total area) increases by \( \frac{50\text{%}}{2} \) = 25%
If a car travels 100 miles in 4 hours, what is the average speed?
| 15 mph | |
| 45 mph | |
| 70 mph | |
| 25 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Simplify \( \frac{24}{76} \).
| \( \frac{6}{19} \) | |
| \( \frac{1}{2} \) | |
| \( \frac{5}{17} \) | |
| \( \frac{7}{15} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{24}{76} \) = \( \frac{\frac{24}{4}}{\frac{76}{4}} \) = \( \frac{6}{19} \)
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
commutative |
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PEDMAS |
|
associative |
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distributive |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
What is the next number in this sequence: 1, 7, 13, 19, 25, __________ ?
| 35 | |
| 40 | |
| 31 | |
| 22 |
The equation for this sequence is:
an = an-1 + 6
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 6
a6 = 25 + 6
a6 = 31