| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
Solve for \( \frac{2!}{5!} \)
| \( \frac{1}{6} \) | |
| \( \frac{1}{60} \) | |
| \( \frac{1}{42} \) | |
| 336 |
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:
\( \frac{2!}{5!} \)
\( \frac{2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4 \times 3} \)
\( \frac{1}{60} \)
Which of the following is not an integer?
-1 |
|
\({1 \over 2}\) |
|
1 |
|
0 |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
The total water usage for a city is 35,000 gallons each day. Of that total, 29% is for personal use and 59% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 14,499 | |
| 1,800 | |
| 10,500 | |
| 14,850 |
59% of the water consumption is industrial use and 29% is personal use so (59% - 29%) = 30% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{30}{100} \) x 35,000 gallons = 10,500 gallons.
What is \( 7 \)\( \sqrt{112} \) + \( 4 \)\( \sqrt{7} \)
| 28\( \sqrt{16} \) | |
| 32\( \sqrt{7} \) | |
| 11\( \sqrt{784} \) | |
| 28\( \sqrt{112} \) |
To add these radicals together their radicands must be the same:
7\( \sqrt{112} \) + 4\( \sqrt{7} \)
7\( \sqrt{16 \times 7} \) + 4\( \sqrt{7} \)
7\( \sqrt{4^2 \times 7} \) + 4\( \sqrt{7} \)
(7)(4)\( \sqrt{7} \) + 4\( \sqrt{7} \)
28\( \sqrt{7} \) + 4\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
28\( \sqrt{7} \) + 4\( \sqrt{7} \)What is (z2)5?
| z10 | |
| 5z2 | |
| z7 | |
| z3 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(z2)5