| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.27 |
| Score | 0% | 65% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 30% larger than the original. By what percentage has the area of the logo increased?
| 30% | |
| 32\(\frac{1}{2}\)% | |
| 15% | |
| 22\(\frac{1}{2}\)% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 30% the radius (and, consequently, the total area) increases by \( \frac{30\text{%}}{2} \) = 15%
A machine in a factory has an error rate of 3 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 106.7 | |
| 122.8 | |
| 125.1 | |
| 121 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{3}{100} \) x 5 = \( \frac{3 \times 5}{100} \) = \( \frac{15}{100} \) = 0.15 errors per hour
So, in an average hour, the machine will produce 5 - 0.15 = 4.85 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 4.85 = 106.7 error free parts were produced yesterday.
Which of these numbers is a factor of 16?
| 1 | |
| 20 | |
| 12 | |
| 10 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 16 are 1, 2, 4, 8, 16.
Frank loaned Diane $1,100 at an annual interest rate of 7%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,177 | |
| $1,122 | |
| $1,199 | |
| $1,188 |
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 $1,100
i = 0.07 x $1,100
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,100 + $774! = ?
4 x 3 |
|
4 x 3 x 2 x 1 |
|
5 x 4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.