| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.08 |
| Score | 0% | 62% |
Convert 0.0007589 to scientific notation.
| 7.589 x 104 | |
| 75.89 x 10-5 | |
| 7.589 x 10-5 | |
| 7.589 x 10-4 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.0007589 in scientific notation is 7.589 x 10-4
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 205.8 | |
| 145.5 | |
| 179.6 | |
| 163.8 |
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 9 = \( \frac{5 \times 9}{100} \) = \( \frac{45}{100} \) = 0.45 errors per hour
So, in an average hour, the machine will produce 9 - 0.45 = 8.55 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 8.55 = 179.6 error free parts were produced yesterday.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
PEDMAS |
|
distributive |
|
commutative |
|
associative |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
Solve for \( \frac{2!}{6!} \)
| 4 | |
| \( \frac{1}{4} \) | |
| \( \frac{1}{6} \) | |
| \( \frac{1}{360} \) |
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:
\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)
Damon loaned Latoya $1,400 at an annual interest rate of 8%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,470 | |
| $1,442 | |
| $1,414 | |
| $1,512 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $1,400
i = 0.08 x $1,400
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,400 + $112