Let g(x)=−6x^6+29x^5+126x^4+135x^3+576x^2+76x−96. Given that -2i
is a root of g(x) and that g(x) has at least...
Let g(x)=−6x^6+29x^5+126x^4+135x^3+576x^2+76x−96. Given that -2i
is a root of g(x) and that g(x) has at least one rational root,
find all the real roots of g(x) in increasing order.
Let X = {1, 2, 3, 4, 5, 6} and let ∼ be given by {(1, 1),(2,
2),(3, 3),(4, 4),(5, 5),(6, 6),(1, 3),(1, 5),(2, 4),(3, 1),(3, 5),
(4, 2),(5, 1),(5, 3)}.
Is ∼ an equivalence relation? If yes, write down X/ ∼ .
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...
Let R(x) = ( 2x^2 − 8x + 6 ) / (x^2 + 6x + 8)
a) Find all x such that R(x) is undefined. Find all x such that
R(x) = 0. Evaluate R(0). Graph R(x) indicating all vertical and
horizontal asymptotes and x and y intercepts.
b) Find the intervals on which ( x^2 + 2x + 12 ) / (x − 2) ≥ 2x
+ 5.
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....
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...
[4 5 5 2 4 4 6 3 3 7 5 3 6 3 4 4 6 5 4 5 3 7 5 5 4 2 6 5 6
6]
This is my dataset
Find mean, median, mode, variance, standard deviation,
coefficient of variation, range, 70th percentile,
3rdquartile of the data and skewness and define what
each of these statistics measure. For example, mean is a measure of
the central tendency, what about the rest?
Use Chebyshev’s rule to find...