You can rewrite the percentages as decimals, and figure this out using multiplication. The expression 40% of 20% of 10 is just 0.4 *0.2 * 10 = .08*10 = 0.8.
Candles are a relaxing addition to an evening, they are also dangerous, though, and should never be left unattended.
Excellent. By changing the first comma into a semicolon, you have corrected what was before a comma splice. When you see two independent clauses separated by only a comma, what you are dealing with is a comma splice that creates a run-on sentence. There are a few ways to fix this; changing the comma to a semicolon is one of those ways. You were also correct to notice that the second and third commas in this sentence, those surrounding “though”, are correctly used. Because “though” functions as a parenthetical aside, it should be surrounded by commas.
A student decides to sell lemonade at her school. She knows she will sell 90 glasses of lemonade each day. Each glass will cost her 30 cents to make. What is the minimum price she should charge per glass if she hopes to make $45 profit each day?
The quickest way to the answer is to see that if she sells 90 glasses and makes $45 she is making 50 cents per glass. Therefore she should charge 30 + 50 = 80 cents.
Alternatively, you could solve the following equation:
45 = 90*(x - .30) = 90x - 90*.3 = 90x - 27
The amount of money she makes ($45) is 90 times the difference between the price of the lemonade and the cost of the lemonade (i.e. 90 times her profit per glass). It follows that 90x = 72 and that x = 0.80.
If the angle x is allowed to vary, what is the maximum distance between points A and D that can be attained?
Lining up AC with CD, we add the length of CD(4) to the length of AC. Since ABC is a 3-4-5 right triangle, the length of AC is 5. The maximum distance possible between A and D is 9.
In the figure above, what is the area of triangle XYZ?
Triangle XYZ is made up of two right triangles. Based on the lengths of the sides we can tell that each triangle is a 45-45-90 triangle (the length of the hypotenuse equals the length of a side times the square root of 2).
We now know that the length of XZ is 2, and can solve for the area of triangle XYZ by:
area = (base)(height) area = (2)() area = 2
If a = 3 and b = 4, what is the value of |a| - |b| + |a - b| ?