There are 120 ways to choose an unordered group of three people from ten. There are 720 ways to assign three distinct roles from ten people. The difference

AnswerStatistics & Probability

Combinations versus permutations

There are 120 ways to choose an unordered group of three people from ten. There are 720 ways to assign three distinct roles from ten people. The difference

ComparisonStatistics & Probability

Choosing between combinations and permutations

There are 120 ways to choose an unordered group of three people from ten. There are 720 ways to assign three distinct roles from ten people. The difference

GuideStatistics & Probability

Area

Area is the measure of a two-dimensional surface.

DefinitionGeometry

Percentage

A percentage is a ratio expressed as a number of parts per hundred.

DefinitionPercentages

Volume

Volume is the measure of three-dimensional space occupied by a solid or available inside a container.

DefinitionGeometry

Are two 20% discounts equal to 40%?

Two discounts apply to different bases. Start with a price of 100. A 20% discount leaves 80; a second 20% discount removes 16 and leaves 64. The total redu

AnswerPercentages

Successive discounts versus an added discount

Two discounts apply to different bases. Start with a price of 100. A 20% discount leaves 80; a second 20% discount removes 16 and leaves 64. The total redu

ComparisonPercentages

Combining discounts correctly

Two discounts apply to different bases. Start with a price of 100. A 20% discount leaves 80; a second 20% discount removes 16 and leaves 64. The total redu

GuidePercentages

How do you calculate a discount?

Multiply the original price by the discount percentage divided by 100, then subtract that saving from the price.

AnswerPercentages

How do you calculate the area of a circle?

Square the radius and multiply by π: area = πr².

AnswerGeometry

How do you calculate percentage decrease?

Subtract the new value from the original, divide by the original, and multiply by 100.

AnswerPercentages

How do you calculate percentage increase?

Subtract the original value from the new value, divide by the original value, and multiply by 100.

AnswerPercentages

How do you calculate a percentage?

Divide the part by the whole and multiply by 100. For example, 20 out of 80 is 25%.

AnswerPercentages

How do you calculate triangle area?

Multiply the base by its perpendicular height and divide by two.

AnswerGeometry

Understanding Percentage Change

Percentage change compares a difference with its original value. The starting value is the reference point.

GuidePercentages

How Percentages Work

A percentage describes a quantity per hundred. It lets you compare shares even when the underlying totals differ.

GuidePercentages

What is the difference between percent and percentage points?

Percentage points measure the difference between two percentages. Percent change measures that difference relative to the starting percentage.

AnswerPercentages

What was the original price before a 20% increase?

If a price after a 20% increase is 120, the original price was 100: divide 120 by 1.20. Subtracting 20% of 120 produces 96 because it uses the new price as

AnswerPercentages

Percentage increase versus reversing an increase

If a price after a 20% increase is 120, the original price was 100: divide 120 by 1.20. Subtracting 20% of 120 produces 96 because it uses the new price as

ComparisonPercentages

Finding an original value after a percentage change

If a price after a 20% increase is 120, the original price was 100: divide 120 by 1.20. Subtracting 20% of 120 produces 96 because it uses the new price as

GuidePercentages

Volume Formulas and Measurement

Volume measures three-dimensional space. Cubic units express how many unit-sized cubes occupy a solid or container.

GuideGeometry

What is 20% of 80?

20% of 80 is 16. Write 20% as 0.20, then multiply 0.20 by 80.

AnswerPercentages