Emily Dickinson
I Heard a Fly Buzz when I died (727)
1.
What are the dying person and those around her expecting to find in the room? What appears
instead and why is this ironic?
The dying person and the people around her were anticipating the appearance

CT7 P C 13
Combined Materials Pack
ActEd Study Materials: 2013 Examinations
Subject CT7
Contents
Study Guide for the 2013 exams
Course Notes
Question and Answer Bank
Series X Assignments*
*Note: The Series X Assignment Solutions should also be supplied
wi

2.
The three mean differences that are evaluated by each of the three hypothesis tests that make up a
two factor ANOVA, mean difference of factors the first and the second factors, and the mean
difference of the interactions of the two factors.
The hypoth

a. Overall mean and SD for males and females from all three experiment groups (simple, GNG,
and Choice).
Simple data
Simple
0.7624
38
0.0754
66
0.3735
0.301
0.9545
81
Mean
Standard Error
Median
Mode
Standard Deviation
Mean = 0.7624, SD = 0.9546
GNG data
G

The first plot r = 0.82, the second on the right of it r = 0.00(horizontal line)
The third one (right below the first) r = - 0.92. The fourth one, on its right, r = - 0.76. The last one, r
= 0.66
Based on scatter plot you would expect the correlation to b

MTHM024/MTH714U
Group Theory
Revision Notes
Autumn 2010
Group theory is a central part of modern mathematics. Its origins lie in geometry
(where groups describe in a very detailed way the symmetries of geometric objects)
and in the theory of polynomial eq

26
Tensors
It may seem obvious that the quantitative description of physical processes cannot
depend on the coordinate system in which they are represented. However, we may
turn this argument around: since physical results must indeed be independent of
th

GROUP ACTIONS
KEITH CONRAD
1. Introduction
The symmetric groups Sn , alternating groups An , and (for n 3) dihedral groups Dn
behave, by their very definition, as permutations on certain sets. The groups Sn and An
both permute the set cfw_1, 2, . . . , n

DIHEDRAL GROUPS II
KEITH CONRAD
We will characterize dihedral groups in terms of generators and relations, and describe
the subgroups of Dn .
1. Abstract characterization of Dn
The group Dn has two generators r and s with orders n and 2 such that srs1 = r

HOMOMORPHISMS
KEITH CONRAD
1. Introduction
In group theory, the most important functions between two groups are those that preserve the
group operations, and they are called homomorphisms. A function f : G H between two groups
is a homomorphism when
f (xy

Group Actions
Patrick J. Morandi
There are a number of results of group theory presented in Herstein [1] (the counting
principles in Sections 2.5 and 2.11, Cayleys theorem in Section 2.9 and the Sylow theorems
of Section 2.12, among others) whose proofs f

Vectors & Matrices : suffix notation
A common early vectors question is prove that a (b c) = (a c)b (a b)c, and a typical
first attempt will go something like:
Since x y = (x2 y3 x3 y2 , x3 y1 x1 y3 , x1 y2 x2 y1 ), the first components of each side are
L

Some stuff about integrals and differentials
Line Integrals
Suppose that we have a small bead on a wire. If a constant force pushes the bead along the wire,
then the work done by the force is given by the formula force distance. If the force varies
as the

Arc-length, curvature, torsion, etc.
Suppose that I go for a drive around town, trying to decide which is the scariest corner. If my speed
isnt constant then I might find it hard to tell. For example, if I compare a shallow bend driven at
60mph to a sharp

Jacobians
Suppose we wish to integrate
Z
cos(x2 + y 2 ) dA, where A is the region between two quarter-circles:
A
y
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
A
1
2
x
We decide to change to polar coordinates, by setting x = r cos , y = r s

Hyperbolic functions
CRTM, 2008
Several paths may be followed that each culminate in the appearance of hyperbolic functions. I am
going to define the functions first.
cosh x =
sech x =
ex + ex
;
2
1
;
cosh x
sinh x =
cosech x =
ex ex
;
2
1
;
sinh x
tanh x

1.
a) Probability distribution of X.
X
P(x)
0
114/1676
= 0.0680
1
186/1676
= 0.1110
2
336/1676
= 0.2005
3
251/1676
= 0.1498
4
316/1676
= 0.1885
5
231/1676
= 0.1378
6
149/1676
= 0.0889
7
33/1676
= 0.0197
8
60/1676
= 0.0358
b) Probability that a person rela

1
MAT 150 SLP 5 Assignment and Template
I affirm that this assignment contains all original work. I am familiar with Trident Universitys
Academic Integrity policy located in the Trident Policy Handbook. I affirm that I have not engaged
in direct duplicati

1.
a) True. The probability of an event taking place and the probability of that event not taking
place is impossible.
b) False. If a variance of a data set is zero it implies that all the observations in the data are
identical and not necessarily zero.
c

ABCD UNIVERSITY
SCHOOL OF BUSINESS
ATTACHMENT REPORT
-A Field Attachment Report Done Between May-August 2015 at the WXY INSTITUTE
COURSE: BACHELOR OF SCIENCE IN ECONOMICS AND MATHEMATICS
PRESENTED TO;
DR._ _ _ _ _
1
31st AUG. 2016
DECLARATION
I declare th

By laws
ARTICLE
Name
ARTICLE 2
Objectives
ARTICLE 3
Members
Section 1 . members . Members of the youth group shall be people of aged 18 and above
Section 2. sponser
The youth group sponser should be somebody who is willing to support
the youths in enhanci

1
The air we breathe in contains potentially harmful particles and gases such as dust and
soot, mold, bacteria, viruses and fungi deposit on airway and alveolar surfaces.
Respiratory system has tiny, muscular, hair-like projections (cilia) on the cells th

MATH 1050
HOMEWORK
SET #21, Sections6.1 6.3
1. Factor completely by using the Greatest Common Factor or by grouping :
a)
a 3 a 5 a8
3
2
5
= a (1 + a + a )
= a
b)
3
2
(1 + a
3
)
6 x 3 y 9 x 2 y 2 12 x 2 y
=3 x
c)
(1+ a
2
y(2x +3y + 4)
18 x 12
= 6(3x-2)

Since we wish to know if there is a relationship between frequency of church attendance and the
level of understanding of the basic Christian doctrines (two variables) the appropriate test would
be the Chi-square test of association. This test is used to

1. The order of an ODE is the highest derivative that occurs and the degree of an ODE is the
highest power of the highest derivative that occurs.
ODE
d2 y
dy
x
y 0
2
dx
dx
d4 y
x y ' 3y 4 (y ')3
dx
(y)3 ln x y = 0
Second order
Fourth order
Second ord

Since we wish to know if there is a relationship between frequency of church attendance and the
level of understanding of the basic Christian doctrines (two variables) the appropriate test would
be the Chi-square test association. This test is used to tes

1. Chi-square test of goodness of fit No preference.
The observed frequencies are:
Actual baby
Unrelated baby #1
Unrelated baby #2
The total frequency
36
18
22
is 36+18+22 = 76
The Actual frequencies are calculated as follows:
From the null hypothesis H0,

MATH 1050
HOMEWORK
SET #21, Sections6.1 6.3
1. Factor completely by using the Greatest Common Factor or by grouping :
a) a 3 a 5 a 8
b) 6 x 3 y 9 x 2 y 2 12 x 2 y
c) 18 x 12
d) 9 x 3 x 2 6 x 3
e) 6( x 3) 5a( x 3) =
f)
x( y 2) ( y 2)
g) ab 3a 2b 6
h)

HOMEWORK #2: DATA CONVERSION
1) Convert the following unsigned binary numbers to decimal. (4-points)
a. 1010 11012
=(1x27)+(0x26)+(1x25)+(0x24)+(1x23)+(1x22)+(0x21)+(1x20)
=128+0+32+0+8+4+0+1
=17210
b. 1110 01002
=(1x27)+(1x26)+(1x25)+(0x24)+(0x23)+(1x22)