| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.88 |
| Score | 0% | 58% |
Which of the following statements about exponents is false?
all of these are false |
|
b1 = b |
|
b1 = 1 |
|
b0 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 17 small cakes per hour. The kitchen is available for 4 hours and 26 large cakes and 300 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 9 | |
| 13 | |
| 10 | |
| 7 |
If a single cook can bake 5 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 5 x 4 = 20 large cakes during that time. 26 large cakes are needed for the party so \( \frac{26}{20} \) = 1\(\frac{3}{10}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 17 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 17 x 4 = 68 small cakes during that time. 300 small cakes are needed for the party so \( \frac{300}{68} \) = 4\(\frac{7}{17}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 5 = 7 cooks.
What is \( \frac{1}{5} \) x \( \frac{2}{6} \)?
| \(\frac{1}{15}\) | |
| \(\frac{1}{12}\) | |
| \(\frac{3}{49}\) | |
| \(\frac{1}{3}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{5} \) x \( \frac{2}{6} \) = \( \frac{1 x 2}{5 x 6} \) = \( \frac{2}{30} \) = \(\frac{1}{15}\)
Solve for \( \frac{2!}{6!} \)
| 8 | |
| 9 | |
| 504 | |
| \( \frac{1}{360} \) |
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 \( \frac{8}{2} \) - \( \frac{7}{8} \)?
| 2 \( \frac{2}{8} \) | |
| 3\(\frac{1}{8}\) | |
| 2 \( \frac{5}{8} \) | |
| \( \frac{4}{10} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 4}{2 x 4} \) - \( \frac{7 x 1}{8 x 1} \)
\( \frac{32}{8} \) - \( \frac{7}{8} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{32 - 7}{8} \) = \( \frac{25}{8} \) = 3\(\frac{1}{8}\)