Division Property of Square Roots

For every number a ≥ 0 eh greater than or equal to 0  and b > 0 , a b = a b . b greater than 0 comma . square root of eh over b end root , equals , fraction square root of eh , over square root of b end fraction , .

Trigonometric Ratios

sine   of   ∠ A = length of leg opposite   ∠ A length of hypotenuse cosine of   ∠ A = length of leg adjacent to   ∠ A length of hypotenuse tangent of   ∠ A = length of leg opposite   ∠ A length of leg adjacent to   ∠ A table with 3 rows and 1 column , row1 column 1 , sine , of angle eh equals . fraction lengthoflegopposite . angle eh , over lengthofhypotenuse end fraction , row2 column 1 , cosineof . angle eh equals . fraction lengthoflegadjacentto . angle eh , over lengthofhypotenuse end fraction , row3 column 1 , tangentof . angle eh equals . fraction lengthoflegopposite . angle eh , over lengthoflegadjacentto . angle eh end fraction , end table

The Distance Formula

The distance d between any two points ( x 1 , y 1 )  and  ( x 2 , y 2 ) open , x sub 1 , comma , y sub 1 , close , and , open , x sub 2 , comma , y sub 2 , close  is d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 . d equals . square root of open . x sub 2 , minus , x sub 1 . close squared . plus . open . y sub 2 , minus , y sub 1 . close squared end root . .

The Midpoint Formula

The midpoint M of a line segment with endpoints A ( x 1 , y 1 ) eh open , x sub 1 , comma , y sub 1 , close  and B ( x 2 , y 2 ) b open , x sub 2 , comma , y sub 2 , close  is ( x 1 + x 2 2 , y 1 + y 2 2 ) . open . fraction x sub 1 , plus , x sub 2 , over 2 end fraction . comma . fraction y sub 1 , plus , y sub 2 , over 2 end fraction . close . .

Chapter 11 Rational Expressions and Functions

Inverse Variation

An inverse variation is a relationship that can be represented by a function of the form y = k x , y equals , k over x , comma  where k ≠ 0 . k not equal to 0 .

Chapter 12 Data Analysis and Probability

Mean

The mean of a set of data values = = sum of the data values total number of data values . data values . equals equals . fraction sumofthedatavalues , over totalnumberofdatavalues end fraction . .

Standard Deviation

Standard deviation is a measure of how the values in a data set vary, or deviate from the mean.

σ = ∑ ( x − x ¯ ) 2 n sigma equals . square root of fraction sum . open . x minus , x bar . close squared , over n end fraction end root

Multiplication Counting Principle

If there are m ways to make a first selection and n ways to make a second selection, there are m · n m middle dot n  ways to make the two selections.

Permutation Notation

The expression   n P r sub n , cap p sub r  represents the number of permutations of n objects arranged r at a time.

  n P r = n ! ( x − r ) ! sub n , p sub r , equals . fraction n factorial , over open , x minus r , close . factorial end fraction

Combination Notation

The expression   n C r sub n , cap c sub r  represents the number of combinations of n objects chosen r at a time.

  n C r = n ! r ! ( n − r ) ! sub n , c sub r , equals . fraction n factorial , over r factorial . open , n minus r , close . factorial end fraction

Theoretical Probability

P ( event ) = number of favorable outcomes number of possible outcomes p . open , event , close . equals . fraction numberoffavorableoutcomes , over numberofpossibleoutcomes end fraction

Probability of an Event and Its Complement

P ( event ) + P ( not  event ) = 1 ,  or  P ( not  event ) = 1 − P ( event ) p open , event , close plus p open not , event , close equals 1 comma , or p open , not , event , close equals 1 minus p open , event , close

Odds

Odds in favor of an event = number of favorable outcomes number of unfavorable outcomes Odds against an event = number of unfavorable outcomes number of favorable outcomes table with 2 rows and 1 column , row1 column 1 , cap oddsinfavorofanevent . equals . fraction numberoffavorableoutcomes , over numberofunfavorableoutcomes end fraction , row2 column 1 , cap oddsagainstanevent . equals . fraction numberofunfavorableoutcomes , over numberoffavorableoutcomes end fraction , end table

Experimental Probability

P ( event ) = number of times the event occurs number of times the experiment is done p . open , event , close . equals . fraction numberoftimestheeventoccurs , over numberoftimestheexperimentisdone end fraction

Probability of Mutually Exclusive Events

If A and B are mutually exclusive events, then P ( A  or  B ) = P ( A ) + P ( B ) . p open eh , or b close equals p open eh close plus p open b close .

Probability of Overlapping Events

If A and B are overlapping events, then P ( A  or  B ) = P ( A ) + P ( B ) − P ( A  and  B ) . p open eh , or b close equals p open eh close plus p open b close minus p open eh , and b close .

Probability of Two Independent Events

If A and B are independent events, then P ( A  and  B ) = P ( A ) · P ( B ) . p open eh , and b close equals p open eh close middle dot p open b close .

Probability of Two Dependent Events

If A and B are independent events, then P ( A  then  B ) = P ( A ) · P ( B  after  A ) . p open eh , then b close equals p open eh close middle dot p open b , after eh close .

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