| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.29 |
| Score | 0% | 66% |
What is the distance in miles of a trip that takes 9 hours at an average speed of 25 miles per hour?
| 60 miles | |
| 480 miles | |
| 225 miles | |
| 40 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 25mph \times 9h \)
225 miles
Solve for \( \frac{6!}{3!} \)
| 120 | |
| \( \frac{1}{15120} \) | |
| 56 | |
| \( \frac{1}{3024} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{6!}{3!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{6 \times 5 \times 4}{1} \)
\( 6 \times 5 \times 4 \)
120
Which of the following is an improper fraction?
\({7 \over 5} \) |
|
\({a \over 5} \) |
|
\({2 \over 5} \) |
|
\(1 {2 \over 5} \) |
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.
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 9 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 98.3 | |
| 190.1 | |
| 99.8 | |
| 131.9 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{5}{100} \) x 7 = \( \frac{5 \times 7}{100} \) = \( \frac{35}{100} \) = 0.35 errors per hour
So, in an average hour, the machine will produce 7 - 0.35 = 6.65 error free parts.
The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 6.65 = 99.8 error free parts were produced yesterday.
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for division |
|
commutative property for multiplication |
|
commutative property for division |
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distributive property for multiplication |
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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).