# Finite Math Examples

, ,

Find the mean of the binomial distribution using the formula.

The population proportion is the number of true results divided by the total samples .

Fill in the known values.

Simplify the expression.

Fill in the known values to find .

Simplify the denominator.

Rewrite as .

Multiply by .

Simplify.

Combine.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Combine using the product rule for radicals.

Multiply by .

Simplify the numerator.

Multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Rewrite in a factored form.

Factor out of .

Reorder the expression.

Reorder and .

Move .

Reorder and .

Factor out of .

Factor out of .

Factor out of .

Apply the distributive property.

Simplify .

Write as a fraction with denominator .

Multiply and .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine the numerators over the common denominator.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Remove unnecessary parentheses.

Multiply the numerator by the reciprocal of the denominator.

Simplify .

Write as a fraction with denominator .

Multiply and .

Move the negative in front of the fraction.

Cancel the common factor of .

Rewrite.

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Reduce the expression by cancelling the common factors.

Rewrite as .

Multiply by .

Multiply by .

Remove parentheses around .

Cancel the common factor.

Rewrite the expression.

Simplify.

Multiply by .

Multiply and .

Multiply by .

Simplify.

Combine.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Multiply by .

Simplify each term.

Rewrite as .

Remove parentheses around .

Rewrite as .

Remove parentheses around .

Apply the distributive property.

Simplify .

Combine using the product rule for radicals.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Simplify each term.

Remove parentheses around .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Remove parentheses around .

Remove parentheses around .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Rewrite the expression.

Divide by .

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Simplify.

Combine.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Multiply by .

Multiply by .

Factor out of .

Separate fractions.

Evaluate the root.

Divide by .

Divide by .

Multiply by .

Simplify .

Write as a fraction with denominator .

Multiply and .

Simplify the expression.

Move to the left of the expression .

Multiply by .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Simplify the expression.

Rewrite as .

Move the negative in front of the fraction.