Math Sections
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| Experimental Probablity | is probablility based on data collected from repeated trials
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| A toy car manufactor inspected 2000 toy cars at random. The manufactor found no defects in 1899 toy cars. What is the probablity that a car selected at random had no defects? Write the probability as a percent. | Experimental Probablitity: 1899/2000= 0.9495= 94.95= 95%
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| Theoretical Probability | P(event= number of favorable outcomes/number of possible outcomes
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| Suppose a bag contains 2 black, 3 blue, 3 green and 2 red marbles. 1-What is the probability of reaching into the bag randomely selecting a red marble? 2-What is the probability of randomly selecting a red or black marble? | Theroretical Probability:
1- 2/10=1/5 (1.0/5=.2= 20%)
2- 4/10=2/5=.4= 40%
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| Geometric Probability | Desired outcome/Total outcome
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| You purchase 1 raffet ticket. 500 are sold. What is the probablitites? | P (Win) = 1/500, P (loss)= 499/500
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| Tickets sold by class: 9th grade 500 blue tickets 10th grade 650 red tickets 11th grade 700 green tickets What is the probability that the winning ticket was sold by an 11th grader? | P= 700/ (500+650+700)= 700/1850
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| Mutually Exclusive Events | can't occur at the same time
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| If A+B are mutually exclusive events then... | P(A or B)=P (A)+P(B)
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| If A+B are not mutually exclusive events then... | P(A or B)= P(A)+P(B)-P(A and B)
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| 24% of the students at the local high school are seniors, 16% are juniors, 34% are sophomores and 26% are freshmen. If a student is chosen at random from school, what is the probability the student is a senior or a junior? | Mutually Exclusive
P(senior or junior)= P(senior) + P (Junior)
= .24 + .16
= .40
= 40%
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| There are 5 types of fish in the tank at the pet store. 10% of the fish are tiger-striped, 20% are angelfish, 15% are catfish, 30% are tetras, & 25% are zebra fish. What is the probability that Joe gets a zebra fish or a tiger-striped fish? | Mutually Exclusive
P(zebra or tiger)= P(zebra)+P(tiger)
= .25 + .10
= .35
= 35 %
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| Dependent Events | Affect each other
P(A then B)=P(A) P(B after A)
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| A bag contains 6 red and 4 blue marbles. What is the probability of randomly selecting a red, then a blue marble, without replacing the first? | Dependent Event
P(red)=6/10
=3/5
P(blue after red)=4/9
P(A) x P(B after A)
3/5 x 4/9= 12/45 = 4/15
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| Independent Events | Dont influence each other
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| Suppose the letter tiles shown were despoited in a bag. What is the probability of randomly selecting an I and a U? | Independent Event
P(I)=2/15
P(U)=2/15
P(I+U)= 2/15 x 2/15= 4/225
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| Tree Diagram | Suppose you go to a deli which has 3 types of bread, 3 types of meat for possible sandwich combinations. How many combinations can you make? (Answer 9)
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| Counting Principle | When tree diagram is to big (M x N)
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| At the weeding there are 5 salad choices, followed by 6 choices for the main course. How many ways can you choose a salad folloed by a main course? | Counting Principle (5 x 6=30 choices)
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| Chandy throws an even fancier wedding and serves a 5 course meal. There are 3 choices for each course. How many different meals can be chosen? | 1 2 3 4 5 = courses
3 x 3 x 3 x 3 x 3 = 243 meals
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| Find the number of permutations possible for the letters NESTA. | N E S T A
5 x 4 x 3 x 2 x 1= 120
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| Sam, Janet, and Bob wait in line for a concert. In how many wasy could the 3 of thme line up? | 3 x 2 x 1=6
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| Permutations | nPr= n (n-1)(n-2)...
Order Matters!!!
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| Simplify 8P5 | n=8, r=5
8(8-1)(8-2)(8-3)(8-4)
8 x 7 x 6 x 5 x 4
6720
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| Combinations | Order doesn't matter!!
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| Combinations | nCr= n!
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r!(n-r)!
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| A 3 person committe is to be chosen from a group of 15 students. In how many ways can the students be chosen? | 15C3
Answer... 455
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| nCr | Stand for the number of cominations of n objects chosen r at a time
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| nCr | nPr
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rPr
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| There are 7 pizza toppins, you can choose 3. | n=7
r=3
7C3=7P3=7 x 6 x 5= 210
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3P3 3 x 2 x 1 =6 = 35
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| Mean | add them all up and divide by #
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| Mode | # that accures the most
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| Median | Middle #
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| Additives | How many # were added
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| IQR | Q3(median) - Q1(median)
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| Variance | All the numbers individually subtract the mean, then squared. Total them then divided by the additives
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| Standard Deviance | Variance square root
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| Solving cryptarithm | Guess and check
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| The sum of two consecutive terms in arithmetic sequence 2,7, 12, 17... 499. Find the 2 terms. | n=the first
n+5= second term
n + n + 5= 499
2n + 5 =499
2n = 494
n=247, n+5=252
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| Communtative Property | When tow numbers are added, the sum is the same regardless of the order of the addends. For example 4+2=2+4
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| Associative Property | When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (2+3)+4=2+(3+4)
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| Additive Identity Property | The sum of any number and zero is the original number. For example 5+0=5
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| Distributive Property | The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 x (6+3)=4 x 6 + 4 x 3
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| 0/x=0 | All intergers except 0
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| x-10x=-9x -9x=-9x | All intergers
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| x2=-49 | No solution is possible
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| (-x)3 | Neither
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| Higher the power... | lower in value
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| x+y=y+x | Always true
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| x-y=y-x | Sometimes True
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| x-y=x+y | Sometimes True
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| xy=x+y | Sometimes True
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| xy+x2=x(y+2) | Always True
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| x . x=x2 | Always True
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| x+x=x2 | Sometimes True
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| x+y=x | Sometimes True
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| x+1=x | Never True
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| xy=yx | Always True
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| x . 0=x | Sometimes True
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| -(x-y)=-x-y | Sometimes True
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| x0=0 | Never True
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| x/y=y/x | Sometimes True
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| 1/x=0 | Never True
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| 3x+3=x+1 ---- 3 | Always True
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| The difference between 2 even # is an an even # | Always True
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| The product of any two even #'s is an odd # | Never
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| The difference between any two odd numbers is an odd # | Never
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| The product of any two odd # is a odd # | Always
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| If x is greater than y, then 3x is greater than 3y | Always
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| If x is greater than y, then x is greater than -y | Never
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| Teh square of a number, x, is greater than x | Sometimes
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| If 2x is greater than 2y, then x is less than y | Never
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