| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.35 |
| Score | 0% | 67% |
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 8 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 156.8 | |
| 138.2 | |
| 149.9 | |
| 132.3 |
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 9 = \( \frac{4 \times 9}{100} \) = \( \frac{36}{100} \) = 0.36 errors per hour
So, in an average hour, the machine will produce 9 - 0.36 = 8.64 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 8.64 = 138.2 error free parts were produced yesterday.
Which of the following is not an integer?
0 |
|
1 |
|
-1 |
|
\({1 \over 2}\) |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
Which of the following is an improper fraction?
\({a \over 5} \) |
|
\({2 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
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 menswear store is having a sale: "Buy one shirt at full price and get another shirt for 45% off." If Roger buys two shirts, each with a regular price of $19, how much will he pay for both shirts?
| $10.45 | |
| $20.90 | |
| $29.45 | |
| $22.80 |
By buying two shirts, Roger will save $19 x \( \frac{45}{100} \) = \( \frac{$19 x 45}{100} \) = \( \frac{$855}{100} \) = $8.55 on the second shirt.
So, his total cost will be
$19.00 + ($19.00 - $8.55)
$19.00 + $10.45
$29.45
Simplify \( \frac{20}{56} \).
| \( \frac{1}{3} \) | |
| \( \frac{5}{14} \) | |
| \( \frac{5}{12} \) | |
| \( \frac{1}{2} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{20}{56} \) = \( \frac{\frac{20}{4}}{\frac{56}{4}} \) = \( \frac{5}{14} \)