| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
In a class of 22 students, 12 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 6 | |
| 12 | |
| 21 | |
| 22 |
The number of students taking German or Spanish is 12 + 8 = 20. Of that group of 20, 4 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 20 - 4 = 16 who are taking at least one language. 22 - 16 = 6 students who are not taking either language.
The total water usage for a city is 35,000 gallons each day. Of that total, 15% is for personal use and 36% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 950 | |
| 3,250 | |
| 7,350 | |
| 5,950 |
36% of the water consumption is industrial use and 15% is personal use so (36% - 15%) = 21% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{21}{100} \) x 35,000 gallons = 7,350 gallons.
Which of the following is an improper fraction?
\({2 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
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\({a \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
commutative |
|
distributive |
|
PEDMAS |
|
associative |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
What is \( \frac{12\sqrt{9}}{6\sqrt{3}} \)?
| \(\frac{1}{2}\) \( \sqrt{3} \) | |
| 2 \( \sqrt{\frac{1}{3}} \) | |
| 3 \( \sqrt{\frac{1}{2}} \) | |
| 2 \( \sqrt{3} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{12\sqrt{9}}{6\sqrt{3}} \)
\( \frac{12}{6} \) \( \sqrt{\frac{9}{3}} \)
2 \( \sqrt{3} \)