10. The Westchester County Superintendent of Education is responsible for assigning students to the three magnet high schools in her county. She recognizes the need to bus a certain number of students, for several sectors of the county are beyond walking distance to a magnet school. The superintendent partitions the county into five geographic sectors as she attempts to establish a plan that will minimize the total number of student miles traveled by bus. She also recognizes that if a student happens to live in a certain sector and is assigned to the magnet high school in that sector, there is no need to bus him/her since he/she can walk to school. The three magnet schools are located in sectors B, C, and E. The accompanying table reflects the number of magnet high-school-age students living in each sector and the distance in miles from each sector to each school. Each Magnet High School has a capacity of 900 students. Set up the objective function and constraints of this problem, and solve using MS Excel. this question was answered need solver help

Let A = {1, 2, 3}. For each of the following relations state (no proofs required) whether it is (i) both a function and an equivalence relation (ii) a function but not an equivalence relation (iii) an equivalence relation but not a function (iv) neither a function nor an equivalence relation (a) {(1, 1),(2, 2),(3, 3)} ⊆ A × A (b) {(1, 1),(2, 2)} ⊆ A × A (c) {(1, 1),(2, 2),(3, 2)} ⊆ A × A (d) {(1, 1),(2, 2),(2, 3)} ⊆ A × A (e) {(1, 1),(2, 2),(3, 3),(1, 3),(3, 1)} ⊆ A × A

Shown below are rental and leasing revenue figures for office machinery and equipment in the United States over a 7-year period according to the U.S. Census Bureau. Use this data and the regression tool in the data analysis tool pack to run a linear regression. Based on the formula you get from the regression output, answer the following questions: a) What is the forecast for the rental and leasing revenue for the year 2011? b) How confident are you in this forecast? Explain your answer by citing the relevant metrics. Year Rental and Leasing ($ millions) 2004 5,860 2005 6,632 2006 6,543 2007 5,952 2008 5,732 2009 5,423 2010 4,589

can the answer be typed out please?

Consider the transformation W=(1+i)z+3-4i. Consider the rectangle ABCD with vertices: A:(1+i); B:(-1+i) ; C:(-1-i), D:(1-i). Do the following

a. Find the image A'B'C'D' of this rectangle under this transformation

b. Plot both rectangles on graph

c. How do the areas of the two rectangles compare?

d. Describe the transformation geometrically?

e. What are the fixed points of the transformation?

Use pigeonhole principle to prove the following (need to identify pigeons/objects and pigeonholes/boxes):

a. How many cards must be drawn from a standard 52-card deck to guarantee 2 cards of the same suit? (Note that there are 4 suits.)

b. Prove that if four numbers are chosen from the set {1, 2, 3, 4, 5, 6}, at least one pair must add up to 7.

Which of the following statements are true? Check all that apply.

In a total conflict game, there can be more than one saddle point.

"Equating the expected values" method can be applied for any 2x2 total conflict game.

When the maximin and minimax values in a total conflict game are same, there is no pure strategy.

"Method of Oddments" can be used for 2x2 total conflict game only if there is no saddle point in pure strategies.

If there are two saddle points in a total conflict game, the two have the same value.

Prove the theorem in the lecture:Euclidean Domains and UFD's

Let F be a field, and let p(x) in F[x]. Prove that (p(x)) is a maximal ideal in F[x] if and only if p(x) is irreducible over F.

Consider the force, but undamped system described by the initial value problem u'' + u = 3 cos(ωt), u(0) = 0, u'(0) = 0 (a) Find the solution u(t) for ω != 1. (b) Find the solution u(t) for ω = 1 (Resonance)

During a voyage of the old Bass Strait ferry, The Abel Tasman, the Rip at the entrance to Port Phillip Bay caused the navigator some concern. He needed to sail due north, but the current was flowing northwest at 10 km/h. In still water, the Abel Tasman has a maximum speed of 25 km/h. Find the following:

(a) the actual direction of travel if he had simply pointed the boat towards North.

(b) the course necessary to travel in the required direction.

(c) the ship’s velocity relative to Point Lonsdale (a fixed point on land).

The quadratic equation, 2x^2 - 7x - 4 = 0  can be solved by:

• Graphing with or without technology.
• Factoring
• Using the quadratic formula.

Solve the quadratic equation using all three techniques. Rank the techniques in the order in which you would use them to solve this problem. Explain why you chose that particular ranking and summarize the benefits of each method. Explanations, diagrams, examples, formulas and mathematical terminology should all be included in your solution. Be thorough!

Let G be a bipartite graph and r ∈ Z>0. Prove that if G is r-regular, then G has a perfect matching.

HINT:  Use the Marriage Theorem and the Pigeonhole Principle. Recall that G is r-regular means every vertex of G has degree

Please do both problems. They are short.

I will rate for sure. Thanks!

Question# 1

Let p(x) = x^3 + 3x + 1 = (x + 3)^2 (x + 4) in Z5[x].

(a) Perform the following computations in Z5[x]/(p(x)). Give your answers in the form [r(x)] where r(x) has degree as small as possible.

i. [4x] + [3x^2 + x + 2]

ii. [x^2 ][2x^2 + 1]

(b) Show that Z5[x]/(p(x)) has zero divisors

Question #2

Let p(x) = x^3 + x + 1 in Z2[x], and let R = Z2[x]/(p(x)).

(a) Explain briefly how you know that R has 8 elements.

(b) Is R is a field?

(c) Write out the multiplication table for R. (Don’t write out the addition table.) I suggest that you omit the brackets.

Let G be a simple graph. Prove that the connection relation in G is an equivalence relation on V (G)

Plug this into LINGO and provide the objective function value below.

Min 130x1 + 125x2

st

60x1 + 10x2 > = 50

50x1 + 35x2 > = 85

x1, x2 >= 0, both integers