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82 Cards in this Set
- Front
- Back
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Steps for finding the equation of a line
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-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 |
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parallel lines
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same slope
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perpindicular lines
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opposite reciprocal slope
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horizontal lines
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y=#
slope=0 |
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vertical lines
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x=#
slope=undefined |
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word problems
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y=$$$$
x=everything else set up 2 points-----LINREG |
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equilibrium point
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set equations equal, solve, plug x into one
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rate of_____as a function of ____?
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whatever follows last blank=what will go in the x spot
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cost
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c(x)=mx+b
negative to profit |
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revenue
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r(x)=p * x
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profit
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p(x)=r(x)-c(x)
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break-even point
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-set r(x)=c(x)
-solve for x -plug into revenue to find y-coordinate |
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demand line
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only line with negative slope
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profit line
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negative fixed cost
---only one that goes across the x axis |
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find value of k that will give the following no solution?
#x-#y=# kx+#y=# |
#/k=-#/#
solve for k |
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setting up word problems?
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-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 |
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Gauss-Jordan in the calculator?
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to find 1s?---(flip over)Rc---->Rc
to find zeros?---(change - signs) Rc+Rr---->Rr |
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if there is a letter in the matrix and it asked if its row reduced form?
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make up a number----CANT BE 0, 1
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if there is a bar between the matrix and it asks if its in row reduced form?
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only put numbers before the line in the matrix
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solve the following systems of equations?
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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 |
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in order to use matrix multiplication the _____ have to match up
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labels
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a matrix equation must have an _____
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equal sign
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for the following systems of equations:
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a) rewrite the system as a matrix equation
B)use matrix inverses to solve |
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leontief input-output models
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production side=top---columns
consumption side=side--rows |
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if a matrix asks the dollar amount of goods required to produce a $ amount of all goods?
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just add up the entire row
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to solve for x
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[X]=([I]-[A])^-1[D] (prouduction)=output
[X]-[D] (consumption)=input |
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Steps for solving linear programming problems
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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 |
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bounded region
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will have both max and min
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unbounded region
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only a minimum
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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 |
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interest earned
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(fv)-(pmt)(n)
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interest paid
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(pmt)(n)-(pv)
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simple
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use simple interest
a=p(1+rt) eqn:0=a-p(a+rt) |
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effective
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use effective rate
eff (I, p/y) |
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no key word
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use the list and the TVM solver
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continuous
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a=pe^rt
eqn: 0=a-pe^rt |
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equity
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$ amount you own of the house
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effective rate when interest rate isn't given
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use TVM solver to solve for I then eff (I, p/y)
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effective rate when money is deposited at % compounded continuously
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e^r-1
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set: { }
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a collection of objects
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universal set: U
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the set that contains all possible ovjects
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element: cool e
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an object from the set
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empty set
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a set that contains no elements. This is a subset of all set
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venn diagram
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a graphical representation of sets
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circles in the venn diagram
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ircles
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boxes in venn diagram
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universal sets
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subset: sideways U with line under it
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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
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proper subset: sideways U
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a is a subset of B
a cannot equal b |
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union
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combine a and b together
keyword: OR |
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intersection
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what A and B have in common
keyword:and |
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complement
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whats not in A
keyword: not |
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disjoint
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two sets that have nothing in common
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# of subset
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2^n
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# of elements in the set
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n
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# of proper subsets
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2^n-1
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when doing venn diagram
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always label circles with letters
then do chart---dont forget pokemon row rref |
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3 basic rules for probability
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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 |
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p (event)=
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the number of ways the event can occur/the total number of outcomes
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probability equation
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# want/total
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multiplication primciple
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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: _*_*_*_*_*_*_ |
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Combinations
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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)! |
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and
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multiply
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or
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add
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not, at least one
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subtract
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overcount
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divide
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birthday problems
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n=# of periods
x=# of people none: p(n,x)/n^x @ least 2: 1-p(n,x)/n^x |
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binomial
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-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 |
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test for independence
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p(a) * p(b) = p(a upside down U b)
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tree diagram rules
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-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) |
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stochastic matrix
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-each number in the matrix is > or equal too 0
-the sum of each column is 1 |
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Markov chain
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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
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if the number pi works in a situation, it is _____
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continuous----cant be finite or infinite
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if the number pi doesn't work it is ________
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not a continuous function
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finite
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has a start and stop
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infinite
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neverending
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odds
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# for: # against
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probability
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# for/ total #
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standard deviation
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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
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best way to find the standard deviation is to use the calculator
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entering data: press stat, hit enter, x---> L1, P(x)---> L2
press stat, ----> to calc, hit enter, 2nd L1, a comma, and 2nd L2 |
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chebychevs inequality
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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 |
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bell curves
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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) |
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normal approximation to the binomial distribution
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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 |
