| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.58 |
| Score | 0% | 72% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 55% larger than the original. By what percentage has the area of the logo increased?
| 20% | |
| 37\(\frac{1}{2}\)% | |
| 35% | |
| 27\(\frac{1}{2}\)% |
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 55% the radius (and, consequently, the total area) increases by \( \frac{55\text{%}}{2} \) = 27\(\frac{1}{2}\)%
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = -7 |
|
a = 7 or a = -7 |
|
a = 7 |
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).
4! = ?
4 x 3 |
|
5 x 4 x 3 x 2 x 1 |
|
4 x 3 x 2 x 1 |
|
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.
What is the next number in this sequence: 1, 6, 11, 16, 21, __________ ?
| 28 | |
| 22 | |
| 30 | |
| 26 |
The equation for this sequence is:
an = an-1 + 5
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 + 5
a6 = 21 + 5
a6 = 26
In a class of 26 students, 13 are taking German and 10 are taking Spanish. Of the students studying German or Spanish, 6 are taking both courses. How many students are not enrolled in either course?
| 9 | |
| 11 | |
| 22 | |
| 16 |
The number of students taking German or Spanish is 13 + 10 = 23. Of that group of 23, 6 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 23 - 6 = 17 who are taking at least one language. 26 - 17 = 9 students who are not taking either language.