In a recent survey of 100 women, the following
information was gathered:
#3: Enter Uses B and C, but not A:
13 11 = 2
59 use shampoo A.
51 use shampoo B.
35 use shampoo C.
24 use shampoos A and B.
19 use shampoos A and C.
13 use shampoos B and C.
11 use a
Essential
Essential Lecture Notes for 11.5 & 11.6
11.5 This Document: Analyzing & Graphing Quadratic
Equations in Vertex Form: f(x) = a(x h)2 + k
11.5.A Analyzing Quadratic Equations in Vertex Form
Quadratic Equations in Vertex Form
11.6.A Graphing Quadra
Section 4.1
41. (p. 190)
A certain school has 40 freshman, 30
sophomores, 15 juniors, and 10 seniors.
a. What is the ratio of sophomores to
freshmen?
b. What is the ratio of seniors to freshmen?
Section 4.2
41. (p. 196)
Solve the proportion.
9=1
y
3
1
2
2
5[3(7 t) 4(8 2t)] 20 = 6[2(6 3t) 4]
Detailed Method
Eliminate the inner most parentheses by using the distributive
property, but first convert minus 4 to plus 4
5[(3)(7 t) + (4)(8 2t)] 20 = 6[(2)(6 3t) 4]
5[(3)7 (3)t + (4)8 (4)2t] 20 = 6[(2)6 (2)3t 4]
Sim
When is a radical in simplified form?
A radical is simplified when:
1. The radicand, i.e., the expression under the radical, is simplified.
2. The index cannot be reduced.
3. Any exponents in the radicand must be less than the index; in
exponents in the r
Example 3 (page 527)
The Eureka Lightbulb Company tested a new line of lightbulbs and found their lifetimes to be normally
distributed with a mean life of 98 ( = 98) and a standard deviation of 13 hours ( = 13).
In class we discussed answering question a.
The final step is to remember how an intersection works
Example 4 (p. 419)
Anything that will be in an intersection of two sets, for
example, A B and B , must be in BOTH sets!
To answer Example 4, you must first understand:
The union of A and B: A B
not
Multiply
Multiply and simply.
+
Step
Step 1: Good housekeeping
+
:
+
+
=
+
Step 3: Fully factor all polynomials
Step
=
+
=
i.e. it is fully factored
+
=
=
i.e. it is fully factored
+
Check
Check
+
+
+
=
let
let ' s say
+
+
Step
Step 5: Simplify
+
when
w
REVIEW FINAL
1. Suppose that lim f ( x) 9 and lim g ( x ) 4 . Find the following limit:
lim 14 g( x)
xc
x c
x c
A)
B)
C)
D)
E)
56
126
14
4
9
2. Use properties of limits and algebraic methods to find the limit, if it exists.
x 2 9 x 20
lim
x 2
x2 4x
3
A)
2
Math 457: Introduction to Mathematical Logic
Homework #1
January 13, 2012
We refer to Chapter 2 of the Mathematical Logic lecture notes.
1. Carefully study Exercise 2.2.14 and verify its solution to your own satisfaction. Then, continue by writing sentenc
The K-th Percentile is that number such that K % of all data values are less and (100 - K)
% are larger than it, or to be more precise, at least K% of the sorted values are less than
or equal to it and at least (100 - K) % of the values are greater than o
10.1 Frequency Distributions & Graphs
MTH-120 Grades
A
IIII IIII
B
IIII IIII I
C
IIII IIII IIII I
D
IIII IIII
F
IIII
10.1 Frequency Distributions & Graphs
MTH-120 Grades
A
IIII IIII
9
B
IIII IIII I
11
C
IIII IIII IIII I
16
D
IIII IIII
10
F
IIII
4
10.1 Fre
What
What is the APR at a car dealership that will sell you a used car for
$8,322 with $322 down and 60 monthly payments of $164.90?
(Round your answer to the nearest tenth.)
=
,
To
To use the APR formula, we need to know N, the number of equal
addpayment
Example:CalculatingMonthlyInterestandNewBalance
foraCreditCardusingtheAverageDailyBalanceMethod
Calculate the monthly interest and the new balance at the end of the month for a credit card with an
APR of 18% that uses the average daily balance method havi
Changing a whole number, e.g., 43, from Base 10 to Base 2
The first step is to find the largest power of 2 that
is less than 43.
Since 8 can go into 11 once or 1 time, we write
down a 1 to the right of our new number
So lets review the powers of 2:
101
20
Divide, if possible.
When dividing a number by a fraction, multiply the number and the reciprocal of the fraction; e.g.
Remember: When dividing two fractions, it is always the fraction on the right that you flip!
When multiply two fractions, multiply nume
To answer the questions, we should first convert
the frequency table into a table of raw data.
Raw Data
N
1
2
3
4
5
6
7
8
9
10
Salary
$25,000
$25,000
$25,000
$25,000
$28,000
$28,000
$28,000
$30,000
$30,000
$45,000
Mean
To find the mean, first add all of t
Formula Sheet
Discount Formulas
D=PM
or Discount = Original Price x Markdown
S=PD
or Sale Price = Original Price Discount
C=1M
or Complement of Markdown = 1 Markdown
S = P (1 M)
or Sale Price = Original Price x (1 Markdown)
S=PC
or Sale Price = Original P
Chapter 11
Graphing linear equations (11.3)
In other words
Drawing straight lines on a graph; i.e.,
on
on the x and y axis
Graphing nonlinear equations (11.5)
In other words
Drawing lines that are not straight on a
graph
y axis
This can be called
The C
MATH 457: Introduction to Mathematical Logic
Homework #2
January 27, 2012
We refer to Chapter 2 of the Mathematical Logic lecture notes.
1. Redo Homework #1.
2. Let C be the sentence in item 3(c) on page 30. I.e., C is the solution of
part 3(c) of Exercis