| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.48 |
| Score | 0% | 70% |
Simplify \( \sqrt{75} \)
| 6\( \sqrt{3} \) | |
| 2\( \sqrt{6} \) | |
| 5\( \sqrt{3} \) | |
| 2\( \sqrt{3} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{75} \)
\( \sqrt{25 \times 3} \)
\( \sqrt{5^2 \times 3} \)
5\( \sqrt{3} \)
What is the next number in this sequence: 1, 3, 5, 7, 9, __________ ?
| 11 | |
| 4 | |
| 7 | |
| 2 |
The equation for this sequence is:
an = an-1 + 2
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 2
a6 = 9 + 2
a6 = 11
4! = ?
4 x 3 x 2 x 1 |
|
4 x 3 |
|
5 x 4 x 3 x 2 x 1 |
|
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.
How many 1 gallon cans worth of fuel would you need to pour into an empty 8 gallon tank to fill it exactly halfway?
| 7 | |
| 3 | |
| 8 | |
| 4 |
To fill a 8 gallon tank exactly halfway you'll need 4 gallons of fuel. Each fuel can holds 1 gallons so:
cans = \( \frac{4 \text{ gallons}}{1 \text{ gallons}} \) = 4
The total water usage for a city is 30,000 gallons each day. Of that total, 21% is for personal use and 56% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 1,900 | |
| 1,400 | |
| 1,950 | |
| 10,500 |
56% of the water consumption is industrial use and 21% is personal use so (56% - 21%) = 35% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{35}{100} \) x 30,000 gallons = 10,500 gallons.