| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
| 1.4 | |
| 1 | |
| 4.2 | |
| 1.8 |
1
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.
Solve for \( \frac{4!}{2!} \)
| 12 | |
| 336 | |
| 56 | |
| \( \frac{1}{3024} \) |
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:
\( \frac{4!}{2!} \)
\( \frac{4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{4 \times 3}{1} \)
\( 4 \times 3 \)
12
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 33,000 seats in a stadium are filled, how many home fans are in attendance?
| 27,500 | |
| 40,833 | |
| 25,833 | |
| 22,500 |
A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:
33,000 fans x \( \frac{5}{6} \) = \( \frac{165000}{6} \) = 27,500 fans.
What is \( \frac{18\sqrt{21}}{9\sqrt{3}} \)?
| \(\frac{1}{2}\) \( \sqrt{\frac{1}{7}} \) | |
| 7 \( \sqrt{2} \) | |
| 2 \( \sqrt{7} \) | |
| \(\frac{1}{7}\) \( \sqrt{2} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{18\sqrt{21}}{9\sqrt{3}} \)
\( \frac{18}{9} \) \( \sqrt{\frac{21}{3}} \)
2 \( \sqrt{7} \)