n
1. let G=( V , E ) be the graph whose vertices are all 7 vectors of length n over
Z7
in which two vertices are adjacent iff
U V
they differ in precisely one coordinate. Let
n1
be a set of 7
vertices of G, and let W be the set of all vertices of G whose
Quiz #3
Quadratic, Polynomial and Rational Functions
2
(1) Sketch the graph of the equation f ( x )= x 4
2
x 2 x15
Be sure to include dotted lines for any asymptotes (vertical, horizontal and slant) and
label any x- and y-intercepts along with any holes i
Week3 response back
This is from the teacher
5/7/20158:53:17AM
InstructorGrych
Thefollowingquestionisanopportunityforanystudenttodemonstrateadvanced
knowledgeofthisweekstopics.Pleasenotethatifaclassmatehasalreadyposteda
response,youmustchooseanotherquesti
m = [1.6; 1.5];
S = [1.2 .4; .4 1.8];
mvnrnd(m,S,100)
[x]= [0; 1];
FUNCTION [x,y]=generate_gauss_classes(m,S,P,N);
[c]=size(m);
X=[];
y=[];
for j=1:c
t=mvnrnd(m(:,j),S(:,:,j),fix(P(j);
x=[X t];
y=[Y ones(1,fix(P(j)*N)*j];
end
FUNCTION plot_data(X,y,m)
[N]
10. Prove that there is an absolute constant c >0
with the following property. Let
A
n by n matrix with pairwise distinct entries. Then there is a permutation of the rows of
be an
A
so that no column in the permuted matrix contains an increasing subsequen
Quiz #3
Quadratic, Polynomial and Rational Functions
2
(1) Sketch the graph of the equation f ( x )= x 4
2
x 2 x15
Be sure to include dotted lines for any asymptotes (vertical, horizontal and slant) and
label any x- and y-intercepts along with any holes i
Solutions for QUIZ 4
1.
( f h ) (3 )
for f ( 2 x +5 )h ( x )=3|2 x +1|
( f h ) ( x ) =f (3|2 x +1|)=2 (3|2 x+1|) +5
6+2|2 x +1|+5
( f h ) (3 )=11+2|2 (3 ) +1|
11+2|7|
11+14
25
2.
( f g )( x )
for f ( x )=2 x +5g ( x )=x 22 x+ 1
( f g )( x )=f ( x 22 x
10. Prove that there is an absolute constant c >0
with the following property. Let
A
be an n by n matrix with pairwise distinct entries. Then there is a permutation of the
rows of
A
so that no column in the permuted matrix contains an increasing subsequen
10. Prove that there is an absolute constant c >0
with the following property. Let
A
n by n matrix with pairwise distinct entries. Then there is a permutation of the rows of
be an
A
so that no column in the permuted matrix contains an increasing subsequen
Question 2
Table for Constants in Control charts
a) Process standard deviation
( x )=
R
d2
thetable for cons tant for control charts above we can find the value for d 2
for n=5, d 2=2.326 R=12.60
sustitute this valuethe formula , x =
x =
R
d2
12.60
=5.4