Let o(G) be pq, p > q are primes, prove

(d) Any two non-abelian groups of order pq are isomorphic.

By using Big-m method Minimize z=4x1+8x2+3X3subject to x1+x2>=2, 2x1+x3>=5 and x1,x2,x3>=0

Let X, Y be two topological spaces. Prove that if both are T1 or T2 then X × Y is the same in the product topology. Prove or find a counterexample for T0.

Considering the set X = {1,2,3,4,5,6,7,8}, calculate a Tx topology on X such that the following two conditions are met:
Tx has exactly 8 different elements, that is, | Tx | = | X | = 8
It is possible to find a subspace S of X with three elements, such that the relative topology Ts in S (with respect to Tx) has exactly 8 different elements, that is, | Ts | = | Tx | = | X | = 8

Given f: X - >> S (function of X over S), compute the smallest topology Tf over X, such that f is in C (X, S) with respect to the topology Ts over S. Is it possible to compare Tf with Tx?
Given g: S> -> X (one-to-one function of S in X), compute the smallest topology Tg over S, such that f is in C (S, X) with respect to the topology Tx over X. Is it possible to compare Tg with Ts?

​Tuff-Rider, Inc., manufactures touring bikes and mountain bikes in a variety of frame​ sizes, colors, and component combinations. Identical bicycles are produced in lots of 110. The projected​ demand, lot​ size, and time standards are shown in the following​ table:

The shop currently works 8 hours a​ day, 5 days a​ week, 50 weeks a year. It operates five​ workstations, each producing one bicycle in the time shown in the table. The shop maintains a 15 percent capacity cushion. How many workstations will be required next year to meet expected demand without using overtime and without decreasing the​ firm's current capacity​ cushion?

The number of workstations required next year is___.

​

Verify by direct substitution that the real functions Ψ = Acos (kx - wt) and Ψ = Asin (kx - wt) are not solutions of the SchroÈdinger equation for a free particle.vVerify by direct substitution that the real functions Ψ = Acos (kx - wt) and Ψ = Asin (kx - wt) are not solutions of the SchroÈdinger equation for a free particle.Verify by direct substitution that the real functions Ψ = Acos (kx - wt) and Ψ = Asin (kx - wt) are not solutions of the SchroÈdinger equation for a free particle.Verify by direct substitution that the real functions Ψ = Acos (kx - wt) and Ψ = Asin (kx - wt) are not solutions of the SchroÈdinger equation for a free particle.

In a team of 50 people, 20 pilots are under 40 years old. 15 pilots are over 40 years old. Five of the non-pilots are under the age of 40, the rest are over the age of 40. Find the probability of being a pilot or over 40 when a random person is selected.

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Equation Editor

(2) How many different product codes do not contain W? 

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Equation Editor

(3) How many different product codes contain exactly one V? 

A. Discuss how a strategic investment proposal should be evaluated from a financial and non-financial perspective? Include in your discussion, a consideration of the advantages and disadvantages of each of the methods that you have selected for the financial evaluation.

B. Discuss the usefulness of the Statement of Financial Position and the Statement of Profit and Loss for the strategic business manager? Explain how you should approach the financial analysis of an organization assuming that you have a full set of financial statements and internet access.

C. Evaluate the usefulness of the equity and debt finance to business and discuss the sources of finance that are available to a business. Explain the concept of the weighted average cost
of capital.

Solve the given initial-value problem.

X' =

X, X(0) =

X(t) =

The departure lounge at an airport has ten seats altogether, five on each side. In how many different ways can 4 doctors and 6 nurses sit if

a) they alternate such that no two doctors sit next to each other? [3]

b) the doctors enter the lounge first and occupy the four corner seats and the nurses then follow them and occupy the remaining seats? (4)

The braking distance for a Krazy-Car traveling at 50 mph is normally distributed with a mean of 50 ft. and a standard deviation of 5 ft. Answer the following without using the z table.

a. What is the random variable in this problem? _______________________________

b. If top 3.5% of the cars are going too fast, what would be the braking distance?

c. Find Q1, the median, Q3 and IQR. ________________________________

How is Rubik's cube related to permutation groups?

Consider the integralHC F·dr where F = yi−xj + z3k where C is the triangle with vertices (0,0,3), (1,1,4), (2,0,0), oriented counterclockwise if viewed from above.

a. [2] Represent the equation of the plane containing the triangle in the form z = ax + by + c and find a, b and c.

b. [2] Compute curl F.

c. [4] Compute the original line integral using Stokes’ theorem.