6. Let A = {1, 2, 3, 4} and B = {5, 6, 7}. Let f = {(1, 5),(2,
5),(3, 6),(x, y)} where x ∈ A and y ∈ B are to be determined by
you. (a) In how many ways can you pick x ∈ A and y ∈ B such that f
is not a function? (b) In how many ways can you pick x ∈ A and y ∈
B such that f : A → B...
ID
X
Y
1
2
3
2
3
6
3
4
6
4
5
7
5
8
7
6
5
7
7
6
7
8
8
8
9
7
8
10
12
11
Test the significance of the correlation coefficient.
Then use math test scores (X) to predict physics test scores
(Y). Do the following:
Create a scatterplot of X and Y.
Write the regression equation and interpret the regression
coefficients (i.e., intercept and slope).
Predict the physics score for each....
1. Let R be the relation on A = {1, 2, 3, 4, 5} given by R =
{(1, 1),(1, 3),(2, 2),(2, 4),(2, 5),(3, 1),(3, 3),(4, 2),(4, 4),(4,
5),(5, 2),(5, 4),(5, 5)}.
(a) Draw the digraph which represents R.
(b) Give the 0 -1 matrix of R with respect to the natural
ordering.
(c) Which of the five properties (reflexive, irreflexive,
symmetric, antisymmetric, transitive) does R have? Give a brief
reason why or why not each property holds.
2. Let...
5.
(a) Let σ = (1 2 3 4 5 6) in S6. Show that G = {ε, σ, σ^2, σ^3,
σ^4, σ^5} is a group using the operation of S6. Is G abelian? How
many elements τ of G satisfy τ^2 = ε? τ^3 = ε? ε is the identity
permutation.
(b) Show that (1 2) is not a product of 3-cycles. Must be
written as a proof!
(c) If a^4 = 1 and ab = b(a^2) in a...
Given the following dataset x 1
1 2 3 4 5
y 0 2 4
5 5 3
We want to test the claim that there is a correlation between
xand y. The level of cretaine phosphokinase (CPK) in blood samples
measures the amount of muscle damage for athletes. At Jock State
University, the level of CPK was determined for each of 25 football
players and 15 soccer players before and after practice. The two
groups of athletes are trained...
Given the following dataset
x
1
1
2
3
4
5
y
0
2
4
5
5
3
We want to test the claim that there is a correlation between
xand y.
(a) What is the null hypothesis Ho and the alternative
hypothesis H1?
(b) Using α= 0.05, will you reject Ho? Justify your answer by
using a p-value.
(c) Base on your answer in part (b), is there evidence to
support the claim?
(d) Find r, the linear correlation...
2. Consider the following data:
x= 1, 2, 3, 4, 5
y =3, 2, 4, 6, 5
By hand, not using Matlab, and showing your work:
(a) Compute the correlation coefficient.
(b) Find the least-squares line.
(c) Find the standard deviation around the least-squares
line.
Let S = {1, 2, 3, 4, 5, 6, 7} be a sample of an experiment and
let X = {1, 4, 7}, Y = {2, 3, 5}, and Z = {1, 3, 5} be events.
Which of the following statements is correct?
a) X and S are mutually exclusive events.
b) X and Y are mutually exclusive events.
c) X, Y, and Z are mutually exclusive events.
d) Z and Y are mutually exclusive events.
e) X and Z...
Maria says that 4 2/3 x 7 1/5 = 4 x 7 + 2/3 x 1/5. Explain why
Maria has made a good attempt, but her answer is not correct.
Explain how to work with what Maria has already written and modify
it to get the correct answer. In other words, don’t just start from
scratch and show Maria how to do the problem, but rather take what
she has already written, use it, and make it mathematically
correct. Which...