| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.93 |
| Score | 0% | 59% |
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 43,000 seats in a stadium are filled, how many home fans are in attendance?
| 23,250 | |
| 26,250 | |
| 25,833 | |
| 32,250 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
43,000 fans x \( \frac{3}{4} \) = \( \frac{129000}{4} \) = 32,250 fans.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 65% larger than the original. By what percentage has the area of the logo increased?
| 32\(\frac{1}{2}\)% | |
| 17\(\frac{1}{2}\)% | |
| 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 65% the radius (and, consequently, the total area) increases by \( \frac{65\text{%}}{2} \) = 32\(\frac{1}{2}\)%
In a class of 24 students, 13 are taking German and 5 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 13 | |
| 16 | |
| 11 | |
| 9 |
The number of students taking German or Spanish is 13 + 5 = 18. Of that group of 18, 3 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 - 3 = 15 who are taking at least one language. 24 - 15 = 9 students who are not taking either language.
If \( \left|x - 2\right| \) + 3 = 6, which of these is a possible value for x?
| 12 | |
| 5 | |
| 7 | |
| 1 |
First, solve for \( \left|x - 2\right| \):
\( \left|x - 2\right| \) + 3 = 6
\( \left|x - 2\right| \) = 6 - 3
\( \left|x - 2\right| \) = 3
The value inside the absolute value brackets can be either positive or negative so (x - 2) must equal + 3 or -3 for \( \left|x - 2\right| \) to equal 3:
| x - 2 = 3 x = 3 + 2 x = 5 | x - 2 = -3 x = -3 + 2 x = -1 |
So, x = -1 or x = 5.
Convert y-3 to remove the negative exponent.
| \( \frac{1}{y^{-3}} \) | |
| \( \frac{3}{y} \) | |
| \( \frac{1}{y^3} \) | |
| \( \frac{-1}{-3y^{3}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.