| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.65 |
| Score | 0% | 73% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 45% larger than the original. By what percentage has the area of the logo increased?
| 25% | |
| 20% | |
| 30% | |
| 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 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%
What is the next number in this sequence: 1, 8, 15, 22, 29, __________ ?
| 36 | |
| 32 | |
| 45 | |
| 40 |
The equation for this sequence is:
an = an-1 + 7
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 + 7
a6 = 29 + 7
a6 = 36
If all of a roofing company's 9 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 8 complete crews out on jobs?
| 15 | |
| 14 | |
| 9 | |
| 1 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 9 workers at the company now and that's enough to staff 3 crews so there are \( \frac{9}{3} \) = 3 workers on a crew. 8 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 8 x 3 = 24 total workers to staff the crews during the busy season. The company already employs 9 workers so they need to add 24 - 9 = 15 new staff for the busy season.
4! = ?
4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
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5 x 4 x 3 x 2 x 1 |
|
4 x 3 |
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.
Which of the following is a mixed number?
\({a \over 5} \) |
|
\({5 \over 7} \) |
|
\(1 {2 \over 5} \) |
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\({7 \over 5} \) |
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.