| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 72.8 | |
| 125.1 | |
| 116.4 | |
| 134.4 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{4}{100} \) x 7 = \( \frac{4 \times 7}{100} \) = \( \frac{28}{100} \) = 0.28 errors per hour
So, in an average hour, the machine will produce 7 - 0.28 = 6.72 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 6.72 = 134.4 error free parts were produced yesterday.
If \(\left|a\right| = 7\), which of the following best describes a?
a = -7 |
|
none of these is correct |
|
a = 7 |
|
a = 7 or a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
What is \( \frac{45\sqrt{49}}{9\sqrt{7}} \)?
| 5 \( \sqrt{7} \) | |
| \(\frac{1}{5}\) \( \sqrt{7} \) | |
| 7 \( \sqrt{\frac{1}{5}} \) | |
| 7 \( \sqrt{5} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{45\sqrt{49}}{9\sqrt{7}} \)
\( \frac{45}{9} \) \( \sqrt{\frac{49}{7}} \)
5 \( \sqrt{7} \)
The total water usage for a city is 45,000 gallons each day. Of that total, 12% is for personal use and 32% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 4,650 | |
| 9,000 | |
| 4,900 | |
| 12,400 |
32% of the water consumption is industrial use and 12% is personal use so (32% - 12%) = 20% more water is used for industrial purposes. 45,000 gallons are consumed daily so industry consumes \( \frac{20}{100} \) x 45,000 gallons = 9,000 gallons.
Which of the following is an improper fraction?
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({2 \over 5} \) |
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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.