| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.35 |
| Score | 0% | 67% |
Solve for \( \frac{2!}{6!} \)
| \( \frac{1}{360} \) | |
| 1680 | |
| 504 | |
| \( \frac{1}{8} \) |
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:
\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)
What is \( \frac{4}{8} \) x \( \frac{2}{5} \)?
| \(\frac{1}{5}\) | |
| \(\frac{3}{10}\) | |
| \(\frac{3}{20}\) | |
| 1 |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{8} \) x \( \frac{2}{5} \) = \( \frac{4 x 2}{8 x 5} \) = \( \frac{8}{40} \) = \(\frac{1}{5}\)
What is the least common multiple of 3 and 11?
| 25 | |
| 33 | |
| 2 | |
| 10 |
The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 have in common.
What is \( \frac{2c^8}{9c^4} \)?
| \(\frac{2}{9}\)c12 | |
| 4\(\frac{1}{2}\)c12 | |
| \(\frac{2}{9}\)c4 | |
| \(\frac{2}{9}\)c2 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{2c^8}{9c^4} \)
\( \frac{2}{9} \) c(8 - 4)
\(\frac{2}{9}\)c4
Convert 8,164,000 to scientific notation.
| 8.164 x 10-6 | |
| 8.164 x 105 | |
| 8.164 x 106 | |
| 8.164 x 107 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
8,164,000 in scientific notation is 8.164 x 106