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### 82 Cards in this Set

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 Steps for finding the equation of a line -find the slope y2-y1/x2-x1 -plug one of the points, and the slope into y=mx+b -solve for b -plug m and b into y=mx+b ***CAN USE LINREG IF IT WORKS parallel lines same slope perpindicular lines opposite reciprocal slope horizontal lines y=# slope=0 vertical lines x=# slope=undefined word problems y= x=everything else set up 2 points-----LINREG equilibrium point set equations equal, solve, plug x into one rate of_____as a function of ____? whatever follows last blank=what will go in the x spot cost c(x)=mx+b negative to profit revenue r(x)=p * x profit p(x)=r(x)-c(x) break-even point -set r(x)=c(x) -solve for x -plug into revenue to find y-coordinate demand line only line with negative slope profit line negative fixed cost ---only one that goes across the x axis find value of k that will give the following no solution? #x-#y=# kx+#y=# #/k=-#/# solve for k setting up word problems? -always read the problem first -look at the last statement, this will tell you what to use for column headings -all the other categories will be row headings -define the variables -set up your equations Gauss-Jordan in the calculator? to find 1s?---(flip over)Rc---->Rc to find zeros?---(change - signs) Rc+Rr---->Rr if there is a letter in the matrix and it asked if its row reduced form? make up a number----CANT BE 0, 1 if there is a bar between the matrix and it asks if its in row reduced form? only put numbers before the line in the matrix solve the following systems of equations? matrix--->rref 1)add the variables to the top of each column 2) write the variables at the lower left corner 3) then examine what you have: ( in this order --contradiction--no solution --doesnt match: infinite solution--letter missing? give it a t --matches: one solution in order to use matrix multiplication the _____ have to match up labels a matrix equation must have an _____ equal sign for the following systems of equations: a) rewrite the system as a matrix equation B)use matrix inverses to solve leontief input-output models production side=top---columns consumption side=side--rows if a matrix asks the dollar amount of goods required to produce a $amount of all goods? just add up the entire row to solve for x [X]=([I]-[A])^-1[D] (prouduction)=output [X]-[D] (consumption)=input Steps for solving linear programming problems 1)for reverse shading, flip over the inequalities 2)cover up x and y 3)draw the line 4)shade 5)label the corners 6)draw the table corner---coordinate---max or min 7) find all intersection points (RREF) 8)evaluate the last column bounded region will have both max and min unbounded region only a minimum n=? i? pv? pmt? fv? p/y=cy= n=number of periods per year*number of years i=interest reate, percentage pv=starting amount/loan pmt=amount of periodic payments fv=ending amount/savings p/y=number of periods per year interest earned (fv)-(pmt)(n) interest paid (pmt)(n)-(pv) simple use simple interest a=p(1+rt) eqn:0=a-p(a+rt) effective use effective rate eff (I, p/y) no key word use the list and the TVM solver continuous a=pe^rt eqn: 0=a-pe^rt equity$ amount you own of the house effective rate when interest rate isn't given use TVM solver to solve for I then eff (I, p/y) effective rate when money is deposited at % compounded continuously e^r-1 set: { } a collection of objects universal set: U the set that contains all possible ovjects element: cool e an object from the set empty set a set that contains no elements. This is a subset of all set venn diagram a graphical representation of sets circles in the venn diagram ircles boxes in venn diagram universal sets subset: sideways U with line under it A is a subset of B, only if each element of A, is also in B ( or in other words, the set A is made from the stuff in set B proper subset: sideways U a is a subset of B a cannot equal b union combine a and b together keyword: OR intersection what A and B have in common keyword:and complement whats not in A keyword: not disjoint two sets that have nothing in common # of subset 2^n # of elements in the set n # of proper subsets 2^n-1 when doing venn diagram always label circles with letters then do chart---dont forget pokemon row rref 3 basic rules for probability 1)the largest value for probability is 1 2)the smallest value for probability is 0 3)the sum of all possible probabilities is 1 p (event)= the number of ways the event can occur/the total number of outcomes probability equation # want/total multiplication primciple general rule:ORDER MATTERS-items must be selected one at a time problem types: -repeats -different categories -anything in a line or row -problems involving numbers or letters equation: _*_*_*_*_*_*_ Combinations general rule: ORDER DOESNT MATTER: these items can be selected as a group problem types: -cards -committess -samples: a sample is a small group selected from a larger group equation: C(n,r)=n!/r!(n-r)! and multiply or add not, at least one subtract overcount divide birthday problems n=# of periods x=# of people none: p(n,x)/n^x @ least 2: 1-p(n,x)/n^x binomial -only 2 outcomes -fixed # of trials -probability of success is constant -independents trials if it meets one of the last 2 you can ignore the other test for independence p(a) * p(b) = p(a upside down U b) tree diagram rules -always start at the beginning -dont skip around -as you travel the branches, multiply -if you start over, add -for conditional probability, always use: p(a/b)=p(a upside down u B)/p(b) stochastic matrix -each number in the matrix is > or equal too 0 -the sum of each column is 1 Markov chain the process in which the probabilities associated with the outcomes at any stage of the experiment depend only on the outcomes of the preceding stage if the number pi works in a situation, it is _____ continuous----cant be finite or infinite if the number pi doesn't work it is ________ not a continuous function finite has a start and stop infinite neverending odds # for: # against probability # for/ total # standard deviation this is used to describe how data is distributed about the mean. The closer to the mean the data is, the smaller the value for standard deviation best way to find the standard deviation is to use the calculator entering data: press stat, hit enter, x---> L1, P(x)---> L2 press stat, ----> to calc, hit enter, 2nd L1, a comma, and 2nd L2 chebychevs inequality 1)draw a number line with the mean at the center, include the 2 endpoints 2) take the endpoint on the right end, plug it into the following equation: right endpoint=mean+k standard deviation 3) solve for k 4)choose your equation by shading: shading in middle: prob=1-1/k^2 shading on outside: prob=1/k^2 bell curves 1) always draw the picture 2)shade the appropriate area 3) use one of the following normalcdf(start, stop, u, o) -1e99, 1e99 or if you choose the x given area option, InvNorm (area to the left, u, o) normal approximation to the binomial distribution 1) find the mean and the standard deviation u=n*p o=square root of (n*p*(1-p)) 2) draw the picture 3)error correction: you want to add or subtract .5 to x 4) use one of the calc commands