Section 2.2 Equations of Lines
The slope of a line describes how steep the line is.
Lines with positive slopes rise from left to right. Lines with negative slopes fall from
left to right.
Definition o
Section 6.2
Larger Systems of Linear Equations
Example: Solve the Larger Systems
2x + y z = 2
x + 3y + 2z = 1
x+y+z=2
Once you have solved for one variable, use back
substitution to solve for the othe
6.3 Applications of Systems of Linear Equations
For this section, you will be permitted to set up the equations/matrices. You will be permitted
to use a calculator for your solutions.
You will not be
Section 3.3 Applications of Linear Equations
Business Relationships (from section 1.2)
Revenue = (Price per item) x (Number of items)
Cost = Fixed Costs + Variable Costs
Profit = Revenue Cost
Types of
Section 6.1
Systems of Linea Equations
Two or more linear equations make up a System of Linear Equations.
The solution to a system of linear equations is the ordered pair (or pairs) that solve all
equ
Percent Change
(amountin ) _( amnuntin )
latest period previous period
Per hr]: = X 100
een ange amount irt previous period
Simple Interest Fannula
Interest = principal x rate >< time
t' = pr!
(Impo
Mat106 Name: Adi/Kn DC 2 / :Dgnedcth'
Homework 3 Show all Work
1.) Determine without graphing whether the system of equatio
an innite number of solutions. 1.) \- , I'_f_ - \ f,
u 3y=6x+4 2>-\+\/: / "
Mat106 Homeworkl Name Agirlhn ancdel-H
Show all work.
1.) Evaluate the expression 3x2 + Exy $312 for x = 2, y = 5
3(ZZ)+% (25%; (52-):
g: (42) + 360-10
3.) Stopping Distance: A typical cars stopping
b-LJ (p.33
- Arlvim e 1512:1ch-
Matloa Name.
Homework 2 Show all Work
number. 3(x*l-) : 0 x
3 x - l2. : (am (9 + X [3
ZY*I?_=(V 232:6 . .-
Z X = U * 2 X ' Diet Book. the number 029-?
' C [mes Accordin
Chapter One Notes
Statistical Methods - MATH220
What is statistics?
Statistics is the science of conducting studies to collect, organize,
summarize, analyze, and draw conclusions from data.
Collecting
Chapter 2
Section 2-1, 2-2
Frequency Distribution:
Is the organizing of raw data in table form using classes and frequencies.
3 types of Frequency Distributions:
1. Categorical
2. Ungrouped
3. Grouped
Chapter One Notes
Statistical Methods - MATH220
What is statistics?
Statistics is the science of conducting studies to collect, organize,
summarize, analyze, and draw conclusions from data.
Collecting
Review Test Submission: Quiz Unit 1
Content
Question 1
5 out of 5 points
[x1] variables can assume an infinite number of values between any two specific values.
They are obtained by measuring. They o
Relations
Pamela Leutwyler
definition: Let A and B be sets. A binary relation from A to B is a subset of AxB.
example 1: Suppose A is a set of students cfw_Al, Beth, Carl, Donna, Ed
and B is the set
Pamela Leutwyler
An experiment is a procedure that yields one of a given set of results.
The possible results are called outcomes.
The set of all outcomes is called the sample space.
An event is a sub
Pamela Leutwyle
example 1
An urn contains 10 marbles. 3 are red and 7 are blue.
Draw 3 without replacement.
What is the probability that they are all red ?
example 1
An urn contains 10 marbles. 3 are
Conditional Probability
Pamela Leutwyler
The notation p( B | A ) represents the probability that event B occurs IF event A occurs,
sometimes phrased the probability that event B occurs GIVEN THAT even
Finite Probability
Pamela Leutwyler
definition: If S is a finite nonempty sample space of equally likely outcomes,
and E is an event, that is, a subset of S, then the probability of E is p(E) =
|E|
|S
PRACTICE FINAL EXAM for DISCRETE MATHEMATICS solutions
1. Make a truth table for the statement (p r) (r p)
p
T
T
F
r
T
F
T
(p r) (r p)
T
T
T
F
F
T
2. Which of the following is equivalent to the statem
Complements and Unions of Events
Pamela Leutwyler
Roll a single die. S = cfw_ 1, 2, 3, 4, 5, 6
E = theeventthatthedielandsonanevennumber.E = cfw_2,4,6
E = theeventthatthediedoesNOTlandonanevennumber.
ROLL A PAIR OF DICE
AND ADD THE NUMBERS
There are 6 x 6 = 36 equally likely
Possible Outcomes:
(1,1)
(1,2)
(1,3)
(1,4)
(1,5)
(1,6)
(2,1)
(2,2)
(2,3)
(2,4)
(2,5)
(2,6)
(3,1)
(3,2)
(3,3)
(3,4)
(3,5)
(3,
What is the probability that
AT LEAST
2 of the 4 dice
land on the same number
Roll 4 dice
6
x
6
x
6
x
6
= 1296 possible outcomes
What is the probability that at least two land on the same number?
Some
Independence
Pamela Leutwyler
H
*
C
*
*
*
*
*
*
*
*
*
In this example, the probability that a woman
develops heart disease if she smokes is twice
the probability that she develops heart disease.
It im
Math 250 Exam #2 Key (Spring 2016)
1 Newtons Law of Cooling states that T 0 (t) = k[T (t) M ], where M is the temperature of
the oven. Here we have T (0) = 70, T (0.5) = 120, and T (1) = 160. Now,
Z
Z
Math 250 Exam #1 Key (Spring 2016)
1 The initial-value problem
(9 y 2 )y 0 = x2 ,
y(x0 ) = y0 ,
will have a unique solution if
x2
2x2 y
and
f
(x,
y)
=
y
9 y2
(9 y 2 )2
are continuous on some open rect
Math 250 Exam #4 Key (Spring 2016)
1 The IVT is
y 00 + 10y 0 + 16y = 0, y(0) = 1, y 0 (0) = 12.
The auxiliary equation r2 + 10r + 16 = 0 has roots 8 and 2, and so the general solution to
the ODE is
y(
Math 250 Exam #2 Key (Spring 2015)
1 Newtons Law of Cooling states that T 0 (t) = k[T (t) Ta ]. Here we have Ta = 5, T (1) = 55,
and T (5) = 30. Now, noting that T (t) 5 for all t 0,
Z
Z
1
0
T = k(T 5
Math 250 Exam #1 Key (Spring 2017)
1 We have
y0 = p
xy
, y(x0 ) = y0 ,
64
which is an IVP that will have a unique solution if
xy
f (x, y) = p
y 2 64
y2
and
fy (x, y) =
(2y 2 y 128)x
(y 2 64)3/2
are b
Math 250 Exam #3 Key (Spring 2015)
1a We have y 00 + y 0 + 4y = et + et .
1
15
Auxiliary equation: r + r + 4 = 0; roots:
i.
2
2
Start with equation y 00 + y 0 + 4y = et , with nonhomogeneity f (t) =