| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.90 |
| Score | 0% | 58% |
What is -7x7 x 4x3?
| -28x7 | |
| -28x10 | |
| -3x21 | |
| -28x3 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-7x7 x 4x3
(-7 x 4)x(7 + 3)
-28x10
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 10% off." If Frank buys two shirts, each with a regular price of $29, how much will he pay for both shirts?
| $55.10 | |
| $2.90 | |
| $36.25 | |
| $26.10 |
By buying two shirts, Frank will save $29 x \( \frac{10}{100} \) = \( \frac{$29 x 10}{100} \) = \( \frac{$290}{100} \) = $2.90 on the second shirt.
So, his total cost will be
$29.00 + ($29.00 - $2.90)
$29.00 + $26.10
$55.10
A circular logo is enlarged to fit the lid of a jar. The new diameter is 75% larger than the original. By what percentage has the area of the logo increased?
| 15% | |
| 37\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% | |
| 25% |
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 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%
A machine in a factory has an error rate of 8 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 161.9 | |
| 128.3 | |
| 147.4 | |
| 202.4 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{8}{100} \) x 10 = \( \frac{8 \times 10}{100} \) = \( \frac{80}{100} \) = 0.8 errors per hour
So, in an average hour, the machine will produce 10 - 0.8 = 9.2 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 9.2 = 202.4 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.
distributive |
|
associative |
|
commutative |
|
PEDMAS |
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.