| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.33 |
| Score | 0% | 67% |
In a class of 33 students, 10 are taking German and 15 are taking Spanish. Of the students studying German or Spanish, 6 are taking both courses. How many students are not enrolled in either course?
| 23 | |
| 14 | |
| 13 | |
| 27 |
The number of students taking German or Spanish is 10 + 15 = 25. Of that group of 25, 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 25 - 6 = 19 who are taking at least one language. 33 - 19 = 14 students who are not taking either language.
What is 5y2 + 2y2?
| 7y4 | |
| 7y2 | |
| 3y-2 | |
| 7y-4 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
5y2 + 2y2
(5 + 2)y2
7y2
A circular logo is enlarged to fit the lid of a jar. The new diameter is 75% larger than the original. By what percentage has the area of the logo increased?
| 37\(\frac{1}{2}\)% | |
| 15% | |
| 35% | |
| 20% |
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 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%
What is the greatest common factor of 68 and 16?
| 16 | |
| 4 | |
| 3 | |
| 12 |
The factors of 68 are [1, 2, 4, 17, 34, 68] and the factors of 16 are [1, 2, 4, 8, 16]. They share 3 factors [1, 2, 4] making 4 the greatest factor 68 and 16 have in common.
What is 3y4 x 5y5?
| 15y20 | |
| 15y5 | |
| 15y9 | |
| 8y20 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
3y4 x 5y5
(3 x 5)y(4 + 5)
15y9