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82 Cards in this Set
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Steps for finding the equation of a line

find the slope y2y1/x2x1
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 pointsLINREG 

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)


breakeven point

set r(x)=c(x)
solve for x plug into revenue to find ycoordinate 

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 

GaussJordan 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 numberCANT 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 contradictionno solution doesnt match: infinite solutionletter 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 inputoutput models

production side=topcolumns
consumption side=siderows 

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 cornercoordinatemax 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=ap(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=ape^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^r1


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^n1


when doing venn diagram

always label circles with letters
then do chartdont 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 MATTERSitems 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!(nr)! 

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: 1p(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 _____

continuouscant 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=11/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*(1p)) 2) draw the picture 3)error correction: you want to add or subtract .5 to x 4) use one of the calc commands 