| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.81 |
| Score | 0% | 56% |
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 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 135.8 | |
| 109.4 | |
| 101.9 | |
| 184.1 |
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 - 2 = 22 hours yesterday so you would expect that 22 x 8.37 = 184.1 error free parts were produced yesterday.
Which of the following statements about exponents is false?
b1 = 1 |
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b0 = 1 |
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b1 = b |
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all of these are false |
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).
How many 2 gallon cans worth of fuel would you need to pour into an empty 20 gallon tank to fill it exactly halfway?
| 5 | |
| 10 | |
| 4 | |
| 5 |
To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2 gallons so:
cans = \( \frac{10 \text{ gallons}}{2 \text{ gallons}} \) = 5
If \( \left|x - 7\right| \) + 3 = 3, which of these is a possible value for x?
| 8 | |
| -5 | |
| 9 | |
| 7 |
First, solve for \( \left|x - 7\right| \):
\( \left|x - 7\right| \) + 3 = 3
\( \left|x - 7\right| \) = 3 - 3
\( \left|x - 7\right| \) = 0
The value inside the absolute value brackets can be either positive or negative so (x - 7) must equal + 0 or -0 for \( \left|x - 7\right| \) to equal 0:
| x - 7 = 0 x = 0 + 7 x = 7 | x - 7 = 0 x = 0 + 7 x = 7 |
So, x = 7 or x = 7.
Which of the following is an improper fraction?
\({7 \over 5} \) |
|
\({a \over 5} \) |
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\({2 \over 5} \) |
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\(1 {2 \over 5} \) |
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.