Finite Math Examples

Use the Table to Find the z-Score
, ,
Find the mean of the binomial distribution using the formula.
Find the population proportion.
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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 expression.
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Simplify the denominator.
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Rewrite as .
Multiply by .
Simplify.
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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.
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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 .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Rewrite in a factored form.
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Factor out of .
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Reorder the expression.
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Reorder and .
Move .
Reorder and .
Factor out of .
Factor out of .
Factor out of .
Apply the distributive property.
Simplify .
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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 .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Remove unnecessary parentheses.
Multiply the numerator by the reciprocal of the denominator.
Simplify .
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Write as a fraction with denominator .
Multiply and .
Move the negative in front of the fraction.
Cancel the common factor of .
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Rewrite.
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Reduce the expression by cancelling the common factors.
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Rewrite as .
Multiply by .
Multiply by .
Remove parentheses around .
Cancel the common factor.
Rewrite the expression.
Simplify.
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Multiply by .
Multiply and .
Multiply by .
Simplify.
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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.
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Multiply by .
Multiply by .
Multiply by .
Simplify each term.
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Rewrite as .
Remove parentheses around .
Rewrite as .
Remove parentheses around .
Apply the distributive property.
Simplify .
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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.
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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 .
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Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Simplify.
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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 .
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Write as a fraction with denominator .
Multiply and .
Simplify the expression.
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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.
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Rewrite as .
Move the negative in front of the fraction.
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