| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.46 |
| Score | 0% | 69% |
4! = ?
4 x 3 |
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3 x 2 x 1 |
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5 x 4 x 3 x 2 x 1 |
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4 x 3 x 2 x 1 |
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.
The __________ is the greatest factor that divides two integers.
least common multiple |
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greatest common multiple |
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greatest common factor |
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absolute value |
The greatest common factor (GCF) is the greatest factor that divides two integers.
If \( \left|x - 1\right| \) - 9 = 9, which of these is a possible value for x?
| -17 | |
| 7 | |
| 16 | |
| 4 |
First, solve for \( \left|x - 1\right| \):
\( \left|x - 1\right| \) - 9 = 9
\( \left|x - 1\right| \) = 9 + 9
\( \left|x - 1\right| \) = 18
The value inside the absolute value brackets can be either positive or negative so (x - 1) must equal + 18 or -18 for \( \left|x - 1\right| \) to equal 18:
| x - 1 = 18 x = 18 + 1 x = 19 | x - 1 = -18 x = -18 + 1 x = -17 |
So, x = -17 or x = 19.
What is the least common multiple of 6 and 14?
| 19 | |
| 84 | |
| 45 | |
| 42 |
The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 have in common.
The total water usage for a city is 30,000 gallons each day. Of that total, 14% is for personal use and 27% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 2,500 | |
| 650 | |
| 3,900 | |
| 7,350 |
27% of the water consumption is industrial use and 14% is personal use so (27% - 14%) = 13% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{13}{100} \) x 30,000 gallons = 3,900 gallons.