| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.80 |
| Score | 0% | 56% |
Which of the following statements about exponents is false?
b1 = 1 |
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b1 = b |
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all of these are false |
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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).
What is \( \frac{24\sqrt{16}}{8\sqrt{8}} \)?
| 2 \( \sqrt{3} \) | |
| 3 \( \sqrt{\frac{1}{2}} \) | |
| 2 \( \sqrt{\frac{1}{3}} \) | |
| 3 \( \sqrt{2} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{24\sqrt{16}}{8\sqrt{8}} \)
\( \frac{24}{8} \) \( \sqrt{\frac{16}{8}} \)
3 \( \sqrt{2} \)
The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
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greatest common factor |
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least common multiple |
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least common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 8 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 94.9 | |
| 157.9 | |
| 138.2 | |
| 159.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 8 = \( \frac{6 \times 8}{100} \) = \( \frac{48}{100} \) = 0.48 errors per hour
So, in an average hour, the machine will produce 8 - 0.48 = 7.52 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 7.52 = 157.9 error free parts were produced yesterday.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
PEDMAS |
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associative |
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distributive |
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commutative |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.