| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
Find the average of the following numbers: 12, 10, 15, 7.
| 13 | |
| 11 | |
| 6 | |
| 12 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{12 + 10 + 15 + 7}{4} \) = \( \frac{44}{4} \) = 11
Convert x-3 to remove the negative exponent.
| \( \frac{1}{x^{-3}} \) | |
| \( \frac{-1}{x^{-3}} \) | |
| \( \frac{-1}{-3x} \) | |
| \( \frac{1}{x^3} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
Which of the following is an improper fraction?
\({2 \over 5} \) |
|
\(1 {2 \over 5} \) |
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\({a \over 5} \) |
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\({7 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
A machine in a factory has an error rate of 7 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 92 | |
| 167.4 | |
| 141.1 | |
| 202.4 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{7}{100} \) x 9 = \( \frac{7 \times 9}{100} \) = \( \frac{63}{100} \) = 0.63 errors per hour
So, in an average hour, the machine will produce 9 - 0.63 = 8.37 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 8.37 = 167.4 error free parts were produced yesterday.
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for multiplication |
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commutative property for multiplication |
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commutative property for division |
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distributive property for division |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).