| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.88 |
| Score | 0% | 58% |
In a class of 29 students, 9 are taking German and 10 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 15 | |
| 14 | |
| 18 | |
| 10 |
The number of students taking German or Spanish is 9 + 10 = 19. Of that group of 19, 5 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 19 - 5 = 14 who are taking at least one language. 29 - 14 = 15 students who are not taking either language.
Solve for \( \frac{2!}{6!} \)
| 7 | |
| \( \frac{1}{360} \) | |
| 8 | |
| \( \frac{1}{7} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)
How many 1\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 9 gallon tank to fill it exactly halfway?
| 3 | |
| 6 | |
| 3 | |
| 8 |
To fill a 9 gallon tank exactly halfway you'll need 4\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:
cans = \( \frac{4\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 3
The total water usage for a city is 20,000 gallons each day. Of that total, 33% is for personal use and 66% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 13,500 | |
| 6,600 | |
| 1,550 | |
| 8,800 |
66% of the water consumption is industrial use and 33% is personal use so (66% - 33%) = 33% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{33}{100} \) x 20,000 gallons = 6,600 gallons.
If a mayor is elected with 51% of the votes cast and 63% of a town's 19,000 voters cast a vote, how many votes did the mayor receive?
| 6,105 | |
| 7,541 | |
| 6,584 | |
| 8,140 |
If 63% of the town's 19,000 voters cast ballots the number of votes cast is:
(\( \frac{63}{100} \)) x 19,000 = \( \frac{1,197,000}{100} \) = 11,970
The mayor got 51% of the votes cast which is:
(\( \frac{51}{100} \)) x 11,970 = \( \frac{610,470}{100} \) = 6,105 votes.