| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
Solve for \( \frac{2!}{6!} \)
| 20 | |
| \( \frac{1}{360} \) | |
| 336 | |
| 504 |
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:
\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)
Simplify \( \frac{28}{64} \).
| \( \frac{8}{17} \) | |
| \( \frac{6}{13} \) | |
| \( \frac{7}{16} \) | |
| \( \frac{4}{19} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{64} \) = \( \frac{\frac{28}{4}}{\frac{64}{4}} \) = \( \frac{7}{16} \)
Which of these numbers is a factor of 24?
| 14 | |
| 11 | |
| 1 | |
| 17 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 10% off." If Ezra buys two shirts, each with a regular price of $50, how much money will he save?
| $7.50 | |
| $10.00 | |
| 75 | |
| $5.00 |
By buying two shirts, Ezra will save $50 x \( \frac{10}{100} \) = \( \frac{$50 x 10}{100} \) = \( \frac{$500}{100} \) = $5.00 on the second shirt.
What is 7\( \sqrt{4} \) x 2\( \sqrt{3} \)?
| 9\( \sqrt{3} \) | |
| 28\( \sqrt{3} \) | |
| 14\( \sqrt{4} \) | |
| 9\( \sqrt{4} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
7\( \sqrt{4} \) x 2\( \sqrt{3} \)
(7 x 2)\( \sqrt{4 \times 3} \)
14\( \sqrt{12} \)
Now we need to simplify the radical:
14\( \sqrt{12} \)
14\( \sqrt{3 \times 4} \)
14\( \sqrt{3 \times 2^2} \)
(14)(2)\( \sqrt{3} \)
28\( \sqrt{3} \)