| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
4! = ?
4 x 3 x 2 x 1 |
|
5 x 4 x 3 x 2 x 1 |
|
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.
In a class of 20 students, 6 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 6 are taking both courses. How many students are not enrolled in either course?
| 8 | |
| 12 | |
| 18 | |
| 17 |
The number of students taking German or Spanish is 6 + 12 = 18. Of that group of 18, 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 18 - 6 = 12 who are taking at least one language. 20 - 12 = 8 students who are not taking either language.
A tiger in a zoo has consumed 80 pounds of food in 10 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 120 pounds?
| 5 | |
| 12 | |
| 11 | |
| 9 |
If the tiger has consumed 80 pounds of food in 10 days that's \( \frac{80}{10} \) = 8 pounds of food per day. The tiger needs to consume 120 - 80 = 40 more pounds of food to reach 120 pounds total. At 8 pounds of food per day that's \( \frac{40}{8} \) = 5 more days.
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?
| 27\(\frac{1}{2}\)% | |
| 17\(\frac{1}{2}\)% | |
| 22\(\frac{1}{2}\)% | |
| 30% |
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\(\frac{1}{2}\)%
What is \( \frac{-6c^6}{1c^2} \)?
| -6c4 | |
| -6c\(\frac{1}{3}\) | |
| -\(\frac{1}{6}\)c4 | |
| -6c3 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-6c^6}{c^2} \)
\( \frac{-6}{1} \) c(6 - 2)
-6c4