MAT 117 Problem Set 1                               Name: ___________________________

Directions: Show all work and explain your thinking as you solve these problems or write the explanations. Each problem is worth five points.

1. Below are definitions of different math number concepts. Write the concept that goes with each description. (no explanation needed for this problem only).

2. Explain the difference between the expressions 6x⁰ and (6x)⁰. If there is no difference, explain why.

Grading: 2 points: Worked out Problem Mathematically; 3 points: Explanation

3. For a recent year, the United States consumed about 1.0 x 10⁴ of petroleum per second. (Source: U.S. Energy Information Administration)

How many gallons of petroleum did the United States use that year?

Show work for all intermittent steps and Explain each step used to get your answer.

Grading: 1 point: Correct Answer; 2 points: Work; 2 points: Explanation

4. State whether the following statement is true and explain why or why not: A trinomial is always a higher degree than a monomial. Give an example proving your answer is correct.

Grading: 2 points: Correct Answer; 2 points: Explanation; 1 point: Example

5. Explain why x+ 7 is a polynomial, but x+7 is not a polynomial.

Grading: 5 points: Complete explanation

Given the below relational algebra expressions, use domain and tuple relational calculus to specify them:

a. σ_x=z ( R(a,b,c) )

b. π_x,y ( R(x,y,z) )

c. R(x, y) / S(x)

d. R(a,b,c) ∪  S(a,b,c)

e. R(a,b,c) – S(a,b,c)

f. R(d,e,f) ∩ S(d,e,f)

g. R(x,y,z) × S(f,g,t)

Find all x ∈ Z such that x≡2 mod 221 and x≡5 mod 184.

The reader understands derivatives, and knows the definition of instantaneous velocity and knows how to calculate integrals but is struggling to understand them. Use students’ prior knowledge to provide an explanation that includes the concept and physical meaning of the integral of velocity with respect to time. (Give an example)

Reminder: The user is comfortable with the calculations, but is struggling with the concept. To fully address the prompt, emphasize the written explanation in English over the calculation.

Do not copy paste Please type and attach graph or figures(Draw) for better understanding.

Use the Laplace transform to solve the given initial value problem:

y''+3y'+2y=1 y(0)=0, y'(0)=2

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___.

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

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(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.