| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.00 |
| Score | 0% | 60% |
A machine in a factory has an error rate of 7 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 171 | |
| 88.3 | |
| 172 | |
| 111.6 |
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 6 = \( \frac{7 \times 6}{100} \) = \( \frac{42}{100} \) = 0.42 errors per hour
So, in an average hour, the machine will produce 6 - 0.42 = 5.58 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 5.58 = 111.6 error free parts were produced yesterday.
Which of the following is an improper fraction?
\({7 \over 5} \) |
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\({a \over 5} \) |
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\(1 {2 \over 5} \) |
|
\({2 \over 5} \) |
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.
Solve 4 + (3 + 5) ÷ 4 x 2 - 22
| \(\frac{3}{8}\) | |
| \(\frac{2}{3}\) | |
| 4 | |
| 1\(\frac{3}{5}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
4 + (3 + 5) ÷ 4 x 2 - 22
P: 4 + (8) ÷ 4 x 2 - 22
E: 4 + 8 ÷ 4 x 2 - 4
MD: 4 + \( \frac{8}{4} \) x 2 - 4
MD: 4 + \( \frac{16}{4} \) - 4
AS: \( \frac{16}{4} \) + \( \frac{16}{4} \) - 4
AS: \( \frac{32}{4} \) - 4
AS: \( \frac{32 - 16}{4} \)
\( \frac{16}{4} \)
4
a(b + c) = ab + ac defines which of the following?
distributive property for division |
|
commutative property for multiplication |
|
distributive property for multiplication |
|
commutative property for division |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 5 to 2 and the ratio of baseball to basketball cards is 5 to 1, what is the ratio of football to basketball cards?
| 1:8 | |
| 9:1 | |
| 7:8 | |
| 25:2 |
The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.