find the minimum and maximum values of z=9x+8y, if possible for the following set of constrains: 4x+3y>=12 x+3y>=6 x>=, y >= please show how to get corners

Let T be a graph. Suppose there is a unique path between every pair of vertices in T. Prove that T is a tree.

Can I do this using the contraposative? Like Let u,v be in T and since I am assuming T to not be a tree this allows cycles to occur thus the paths must not be unique. Am I on the right track?

After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only two women among the last 22 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women. Help her address the charge of gender discrimination by finding the probability of getting two or fewer women when 22 people are hired, assuming that there is no discrimination based on gender. (Report answer accurate to 8 decimal places). P(at most two) = .00021 Incorrect Because this is a serious claim, we will use a stricter cutoff value for unusual events. We will use 0.5% as the cutoff value (1 in 200 chance of happening by chance). With this in mind, does the resulting probability really support such a charge?

To process a workpiece 10 operations are interchangeable in their order. The
economic-technological evaluation of each variant lasts 1h. How long would the overall rating take to find the optimal machine layout?

How many Morse alphabet characters can be formed when a character is out
a) exactly five elements b) should consist of at most five elements?

In the vicinity of a resort 15 hiking trails are to be marked by two colored, parallel lines.
How many colors do you need at least if the same color pairs are allowed and the arrangement of the lines does not matter?

Solve the following system of linear equations:

−p + q + 2r = 8 (1)

p + q + 2r = 0 (2)

2q − 2r = 2 (3).

The sum of the values of p, q and r of the solution is

Create the following 3D plot in boxed format using MAPLE. Include a title and the code for the plot in the same page.

-3 spheres of radius 5 centered at (0,-8,0) , (0,8,0) and (0,0,0)

Create the following 3D plot in boxed format using MAPLE. Include a title and the code for the plot in the same page.

-A pair of concentric cylinders about the z axis, with a height of 7.

In a small job shop department there are four jobs to be assigned to three workers. The table below indicates the weekly costs incurred by assigning each worker to each job. The objective is to find the optimal assignment that will minimize the total cost.

Worker/Job │   I      II     III    IV

A     │ 12      10    11    15

  B     │ 13      16    14    12

  C     │ 11 12    13    10

      Formulate this problem as a linear programming model to find the optimal assignment to minimize the total cost. Please show your definition of decision variables needed clearly for this formulation. Do not ever try to solve this formulation.

1) How many positive integers are greater than 140, less than 30800 and relatively prime to 280.

Consider the vector space P₂ := P₂(F) and its standard basis α = {1,x,x^2}.

1Prove that β = {x−1,x^2 −x,x^2 + x} is also a basis of P₂

2Given the map T : P2 → P2 defined by T(a + bx + cx2) = (a + b + c) + (a + 2b + c)x + (b + c)x²
compute [T]^β_α.

3 Is T invertible? Why

4 Suppose the linear map U : P2 → P2 has the matrix representation

(1 0 0

0 2 0

0 0 4)

Compute [UT]^α_α and complete the following formula
(UT)(a+bx+cx²) =

Suppose V is a finite dimensional inner product space. Prove that every orthogonal operator on V , i.e., <T(u),T(v)> = <u,v>, ∀u,v ∈ V , is an isomorphism.

Suppose we have a mass of 12 pounds on a spring which stretches by 1/2 foot from the weight. If we have a forcing function g(t) = cos(8t), no damping, and y(0) = y ′ (0) = 0, describe the motion of the system. Our mass is 12/32 = 3/8, and k = mg/L = 12/(1/2) = 24. USE DETERMINANT METHOD.

Hi. I want matlab code that implements a mimo system

that uses the mmse and zf methods with Rayleigh fading.

Thank you.

Exercise 3.1.5: Expressing sets in set builder notation. About Express each set using set builder notation. Then if the set is finite, give its cardinality. Otherwise, indicate that the set is infinite. PLEASE show some explanation how you got answer. Thanks!

(a)

{-2, -1, 0, 1, 2}

(b)

{ 3, 6, 9, 12, .... }

(c)

{ -3, -1, 1, 3, 5, 7, 9 }

(d)

{ 0, 10, 20, 30, ...., 1000 }

Exercise 3.2.4: A subset of a power set.

(a)

Let X = {a, b, c, d}. What is { A: A ∈ P(X) and |A| = 2 }?

(b)

Let A = {1, 2, 3}. What is {X ∈ P(A): 2 ∈ X}?

The past few modules introduced various ways to solve a differential equation, separation of variables, integrating factor, and exact equations. As you can see, you need skills from previous coursework, in particular algebraic manipulation and both differentiation and integration, to solve these equations. How do these skills translate to differential equations? In a general sense, explain how algebra, differentiation, and integration skills are necessary to classify and solve first-order ODEs. Include an example in your explanation.