| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.42 |
| Score | 0% | 68% |
Find the average of the following numbers: 16, 14, 19, 11.
| 14 | |
| 12 | |
| 15 | |
| 18 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{16 + 14 + 19 + 11}{4} \) = \( \frac{60}{4} \) = 15
The total water usage for a city is 40,000 gallons each day. Of that total, 18% is for personal use and 43% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 1,300 | |
| 10,000 | |
| 6,750 | |
| 8,700 |
43% of the water consumption is industrial use and 18% is personal use so (43% - 18%) = 25% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{25}{100} \) x 40,000 gallons = 10,000 gallons.
What is \( \frac{9}{4} \) - \( \frac{4}{12} \)?
| 1\(\frac{11}{12}\) | |
| \( \frac{3}{12} \) | |
| \( \frac{7}{12} \) | |
| \( \frac{2}{12} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 3}{4 x 3} \) - \( \frac{4 x 1}{12 x 1} \)
\( \frac{27}{12} \) - \( \frac{4}{12} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{27 - 4}{12} \) = \( \frac{23}{12} \) = 1\(\frac{11}{12}\)
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 34 students, 11 are taking German and 10 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 14 | |
| 15 | |
| 10 | |
| 26 |
The number of students taking German or Spanish is 11 + 10 = 21. Of that group of 21, 2 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 21 - 2 = 19 who are taking at least one language. 34 - 19 = 15 students who are not taking either language.