By using the definition and discussing what is relevant to the situation, interpret each of the following for both the coffee and tea data. Also, compare each for coffee and tea. Be sure to include the relevant information (state the value of or, in the case of the distribution, include the graphs) with each component.

1. Mean
2. Median
3. Modal Interval
4. Range
5. IQR
6. Standard Deviation
7. Distribution of histogram and box plot
8. Slope of each linear model
9. Y-intercept of Coffee vs. Tea
10. Correlation coefficient for each linear model
11. Relevant interpolations or extrapolations
12. Correlation type (from Activity 5) for coffee and tea

Let f:(a, b) → R be a function and n∈N. Assume that f is n-times differentiable and f^(n)(x) = 0 for all x∈(a,b). Show that f is a polynomial of degree at most n−1.

write a descriptive summary on the book "this is our time:everyday myths in the life of the gospel" by trevin wax

A certain dynamical system is governed by the equation x^'' + (x')² + x = 0. Show that the origin is a center in the phase plane and that open and closed paths are separated by the path

2y² = 1- 2x

Find two linearly independent solutions near the regular singular point x₀= 0

x²y'' + (6x + x²)y' + xy = 0

I have a group order 28 is it possible to have an orbit with 6

maybe use sylos thm.

Question C [SD1: 5 Marks]

            A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X₁), age of the individuals (X₂), and the gender of the individual (X₃; zero representing female and one representing male) was performed on a sample of 10 people, and the following results were obtained.

In parts a and b, A is a matrix representation of a linear transformation in the standard basis. Find a matrix representation of the linear transformation in the new basis. show all steps.

a. A = 2x2 matrix with the first row being 2 and -1, and the second row being 1 and 3; new basis = {<1, 2> , < 1, 1> }

b. A = 3x3 matrix with the first row being 2, 1, -1, the second row being, 0, 1, 3, and the third row being -1, 2, 1. new basis = {< 0, -2, 1 > , <1, 2, 0> , <1, 1, 1,>}.

consider the subspace W=span[(4,-2,1)^T,(2,0,3)^T,(2,-4,-7)^T]

Find

A) basis of W

B) Dimension of W

C) is vector v=[0,-2,-5]^T contained in W? if yes espress as linear combantion

Solve the given system of differential equations by systematic elimination. (D + 1)x + (D − 1)y = 6 ; 7x + (D + 6)y = −1

How to determine all the basic solutions of an optimization problem, and classify them as feasible or infeasible?

As an example,

Maximize z= 2x₁ + 3x₂

Subject to:

x₁ + 3x₂ <= 6

3x₁ + 2x₂ <= 6

x₁ + x₂ >= 0

Some solutions are (2,0), (0,2), (0,0), (6/7, 12/7), but are there more solutions? And how do you tell if they are infeasile/feasible? Would you need to graph it?

Consider the set of vectors {(?,?,?) ∈ ?³???ℎ ?ℎ?? ? − 3? + 5? = 0.} Does this set of vectors form a sub-space of ?³?

Let R be the relation on Q defined by a/b R c/d iff ad=bc. Show that R is an equivalence relation. Describe the elements of the equivalence class of 2/3.

Solve the given initial-value problem. y''' − 2y'' + y' = 2 − 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5 2 , y''(0) = − 5 2