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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