Formula Sheet
MATH 113
Trigonometry
'Ii'igonometric mctions of Important Angles
r ans 811! cm tan
0 0 0 1 0
30 1r/6 1/2 /2 5/3
45 "/4 Ji/2 5/2 1
60 1r/3 7/2 1/2 J5
90 1r/ 2 1 0 undened
I Fundamental Identities
sin20+cos20= 1
1+oot20=csc29
sin(9) = sin9
AP
Statistic
s
Chen Tingjing
[email protected]
Confidence Interval for a
Population Mean
2
Example 9.7 Cosmic Radiation
t Distributions
One-Sample t Confidence Interval
15/9/27
homework
9.34
15/9/27
9.41
AP
Statistic
s
Chen Tingjing
[email protected]
Large-Sample Confidence Interval for a
Population Proportion
Because of sampling variability, rarely is
the point estimate from a sample exactly
equal to the true value of the population
characteris
AP Statis
tics
Chen Tingjing
[email protected]
Large-Sample Confidence Interval for a
Population Proportion
Because of sampling variability, rarely is t
he point estimate from a sample exactly e
qual to the true value of the population cha
ract
Summary for discussion (page 63)
1. From our discussion, we reached a consensus that it would be easy to obtain
a simple random sample of students at our school. From our perspective, the
most challenging work for simple random sample of all students in t
AP Statis
tics
Chen Tingjing
[email protected]
9.1 Point Estimation
A point estimate of a population characte
ristic is a single number that is
based on sample data and represents a pl
ausible value of the characteristic.
How to get a point est
2011 AP STATISTICS FREE-RESPONSE QUESTIONS
Formulas
(I)
Descriptive Statistics
xi
n
x
1
sx
1
n
xi
x yi
xi
y
b1
r
x
xi
1
2
1
x
sx
yi
y
sy
sy
sx
yi
sb
y
b1 x
1
n
n2 1
b1 x
b1
r
2
n2 1 s 2
2
n1 1
b0
b0
x
n1 1 s2
1
sp
y
xi
yi
n
2
xi
x
2
2
-3-
2011 AP STATISTI
In the book How to slowly kill yourself and others in America, the author
Laymon uses the concept of an album to connect all tracks which are his
experiences with different people to show how a black person suffers from the
racism in America. Through the
Math 113 - Calculus II] Practice Exam 1 Spring 2003
Name: SOLUTIONS
1. Match each function to one of the given graphs. and no one of the glwn contour
diagrams. The plots ate given In a semi-we handout.
'14
0:
A!
ulss
v
U
D
"I
N
+
531
2 l
_ '1
"L
+
A
NI?
Math 113 - Calculus 11] Exam 1 Practice Problems Fall 2005
Name: _
1. Match each function to one of the given graphs, and to one of the given contour
diagrams. The plots are given in a separate handout.
Contout
Graph Diagram 2. (3) Consider the function
Questionnaire
1. Have you registered for any AP Exam?
A. Yes (Please continue answering this questionnaire) 42
B. No (This is the end of the questionnaire. Thanks for your participation. ) 8
2. How many AP exams did you register?
A. 1-2 21
B. 3-4 17
C. 5-
Group 5
!
SURVEY OVERVIEW
!
2012530513 2012530122
2012530412
2013530424
Our group choose The Survey and Analysis on the AP Exams Registration of
Shenzhen Middle School IC Freshmen as our topic. We analyze and research the
senior one students attitudes, u
Chapter 16
1. Section 1
a. understand the definition of a vector field.
b. Associate functions with their vector field (this is a bit hard to study
for, just trust yourself)
c. Give examples of velocity field, force field, maybe another
d. A conservative
CH 14 PARTIAL DERIVATIVES
Section 7 Maximum and Minimum Values
Summary
In this section the old is new again where we find the maxima and minima values using
derivatives. Sometimes critical points (first deriv =0) are not extrema, so we check for that. Fin
Western Michigan University
ScholarWorks at WMU
Center for the Study of Ethics in Society Papers
Center for the Study of Ethics in Society
9-1993
Why Does Utilitarianism Seem Plausible?
John Dilworth
Western Michigan University
Follow this and additional
Why Not Utilitarianism?
,
A lot of very smart non-philosophers are attracted to some form of
utilitarianism. Some of these people, like Ilya Somin and Mike Rappaport
are generally sympathetic to the idea of bleeding heart libertarianism, but
think that ut
Department of Economics
Colgate University
Dean Scrimgeour
Fall 2016
ECONOMICS 252: MACROECONOMICS
FINAL PAPER
Your assignment is to write a paper about some theme developed in Mohamed El-Erians
book The Only Game in Town. You may give a more complete exp
Variable
countryname
ppp_xr_2010
milex2010_lcu
milex2010_usd
Description
Country Name
Purchasing Power Parity Exchange Rate, 2010
Military Expenditure, 2010, local currency units
Military Expenditure, 2010
Units
Source
Price in LCU/Price in USD
Local Curr
Macro Update 2
November 2, 2016
Rachel Huang & Eric Hong
The past month has been a good month overall for the overall economic activity shows
improvement, with the stable labor market and slightly growing inflation.
My assessment of overall economic activ
Given the data and news stories released in this past month, has your overall assessment of
overall economic activity improved, deteriorated, or remained the same as compared to the
previous month? In a short paragraph, justify your answer.
Export,
Consum
I picked China simply just because it is where I am from and also, Chinese economy is
distinguished for its so-called socialist market economy which is different from many
western economies that are capitalist.
Chinese starts its rapid economy development
9/17/13
2010.igem.org/Team:USTC/Project/survey
Below are the results of the questionnaire answered by people before the talk.
SURVEY OVERVIEW
ur survey includes two parts, one conducted before our campus talk and the other aﬂer that. 106 students
took
Math 113 - Calcullm II] Final Exam Practice Problems Spring 2003
I. Let
giny. :) = V213 + y? + 49.
(8) Describe the shapes of the level surfaces of 9
(b) In three different graphs. sketch the three tress sections to the level surface
g(r.y.:) ' l for Wlll
Math 3 - Calculus lll Chapter 16 Pracca Problems Fall 2003
1. Suppose the integral of some function I over a region R in the plane is given in polar mor-
dinntm 33 v
.3 .1
l I r2 d0dr.
. u . 0
(:5) Sketch the region of integration R in the my plane.
(b) C
12.5: Lines and Planes in R3
Lecture 4
Marius Ionescu
September 10, 2012
Marius Ionescu ()
12.5: Lines and Planes in R3
September 10, 2012
1 / 13
The vector equation of a line
A line L is determined when we know a point P0 (x0 , y0 , z0 ) on
L and the dir
The Dot Product
Lecture 2
Marius Ionescu
August 31, 2012
Marius Ionescu ()
The Dot Product
August 31, 2012
1/9
The Dot Product
If a = a1 , a2 , a3 and b = b1 , b2 , b3 , then the dot product
of a and b is the number
a b = a1 b1 + a2 b2 + a3 b3 .
Marius Io
The Cross Product
Lecture 3
September 7, 2012
()
The Cross Product
September 7, 2012
1/7
Properties
Given two vectors a and b we want to build a vector a b called
the cross product of a and b with the following properties:
The vector a b is orthogonal to
14.3: Partial Derivatives
Marius Ionescu
October 12, 2012
Marius Ionescu ()
14.3: Partial Derivatives
October 12, 2012
1 / 13
Partial derivative of f
with respect to x
Denition
Marius Ionescu ()
14.3: Partial Derivatives
October 12, 2012
2 / 13
Partial de
14.4: Tangent Planes and Linear Approximations
Marius Ionescu
October 15, 2012
Marius Ionescu ()
14.4: Tangent Planes and Linear Approximations
October 15, 2012
1 / 13
Tangent Planes
Denition
Marius Ionescu ()
14.4: Tangent Planes and Linear Approximation