| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.89 |
| Score | 0% | 58% |
What is 9\( \sqrt{7} \) x 6\( \sqrt{5} \)?
| 54\( \sqrt{35} \) | |
| 54\( \sqrt{5} \) | |
| 15\( \sqrt{35} \) | |
| 15\( \sqrt{5} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
9\( \sqrt{7} \) x 6\( \sqrt{5} \)
(9 x 6)\( \sqrt{7 \times 5} \)
54\( \sqrt{35} \)
The total water usage for a city is 35,000 gallons each day. Of that total, 16% is for personal use and 51% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 16,500 | |
| 3,600 | |
| 1,600 | |
| 12,250 |
51% of the water consumption is industrial use and 16% is personal use so (51% - 16%) = 35% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{35}{100} \) x 35,000 gallons = 12,250 gallons.
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?
| 37\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% | |
| 25% | |
| 15% |
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\(\frac{1}{2}\)%
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
commutative |
|
distributive |
|
PEDMAS |
|
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.
Which of the following is not an integer?
-1 |
|
\({1 \over 2}\) |
|
0 |
|
1 |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.