Use the method of variation of parameters to find the general solution of the differential equation

y''+6y'+5y = 7e^(2x)

describe group homomorphisms from Q8 into Z8.

1. A 60 kg individual needs to work at a MET level of 8 to reach her target heart rate. If the treadmill speed is set at 3.5 mph, what grade is needed? If she exercises for 20 min. at this intensity, how many kcal will she expend?

5A

Research and share two or more real life applications of radial, rotational, or gradient fields.

5B

Explain the concept of divergence and provide an example showing how to calculate the divergence of the vector field chosen in your example.

1. Write notes on Multicollinearity
2. 1. define what the issue is
   2. explain whether, or under what circumstances, it causes a problem for inference in OLS regression
3. 3. explain how it can be detected (if it can)
   4. state what action, if any, you should take to deal with the issue

1. Write notes on omitted variable bias.  
   
2. 1. define what the issue is
   2. explain whether, or under what circumstances, it causes a problem for inference in OLS regression
3. 3. explain how it can be detected (if it can)   
   4. state what action, if any, you should take to deal with the issue.

PLEASE EXPLAIN WHY YOU CHOOSE EACH ANSWER

1). How many distinct ways can a President, Vice President, Secretary and Treasurer be selected from a group of 10 people if no one can hold more than on position?

A). P(10,4)

B). 10 choose 4

C). 10^4

D). 4^10

E). 13 choose 10

F). None of these

2). How many shortest lattice paths are there from (0,0) to (10,4)

A). P(10,4)

B). 10 choose 4

C). 10^4

D). 4^10

E). 13 choose 10

F). None of these

3). At a movie theater with 4 different movies, how many ways can 10 people select a show? They do not have to all go to the same shoe but several poeple can go to the same show.

A). P(10,4)

B). 10 choose 4

C). 10^4

D). 4^10

E). 13 choose 10

F). None of these

The tarot minor arcana deck has 56 cards in four suits (swords, batons, coins, and cups), each having 10 numbered cards and 4 court cards (king, queen, knight, and page). A “spread” is a draw of 9 cards. What is the probability of getting a spread of all court cards?

Creating a Hypothetical Budget – Portfolio Activity

You are paid $11.75/hr. You work 40 hr/wk. Your deductions are FICA (7.65%), Federal tax withholding (10.75%), and state tax withholding (7.5%)

1. Assuming you budget a month as 4 weeks, how much is your total realized income, fixed expenses, and discretionary expenses.
2. If you are able to work 20 hours of overtime the next month and are paid 1.5 times your regular rate, how does this change your budget for that month?
3. How much can you put towards savings each month if you eliminated your discretionary expenses?

Be sure to include in your response:

• A detailed budget showing income and expenses for the two different months.
• Answers to the original questions.
• An explanation for how you calculated the first 40 hours of income and then the additional 20 hours of overtime.

Month 1

Month 2

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1. The value of a European put option must satisfy the following restriction:

??0 ≥????−???? −??0

where ??₀ is the current put price, ??₀ is the current price of the underlying stock, ?? is the exercise price, ?? > 0 is the annualised continuously compounded risk-free rate, and ?? is the time till expiration. Prove by contradiction that the above arbitrage restriction must hold, i.e. show that if the condition does not hold, there is an arbitrage opportunity

Solve it step by step and please with clear handwritten. Be ready to follow the comment

Integrability Topic

Question1. Let g : [0, 1] —> R be defined by if x=0, g(x)=1; if x=m/n (m and n are positive integer with no common factor), g(x)=1/n; if x doesn't belong to rational number, g(x)=0

Use the sequential criterion for continuity to prove that g is discontinuous at every rational number in[0,1]

Question.2 g is continuous at any irrational point in[0,1]. Explain why g is Riemann integrable on[0,1] based on the following fact that

Suppose h:[a,b]→R is continuous everywhere except at a countable number of points in[a,b]. Then h is Riemann integrable on[a,b]

Question.3

Letf:[0,1]→R be defined by f(x)=0 if x=0; f(x)=1 if 0<x<=1 we know that f is integrable on [0,1] Suppose c is a rational number in [0,1]. Compute(f◦g)(c). Now suppose c is an irrational number in[0,1]. Compute(f◦g)(c). Can you recognize the function f◦g:[0,1]→R?

Use R to solve:

Find the approximate solution x' to :

0.89x1 + 0.53x2 = 0.36

0.47x1 + 0.28x2 = 0.19

Find the error x'-x* between the computed solution and the true solution.

Compare the size of this error with the size of the residual r=b-Ax'

Rudin Ch 4, p. 99 #7. If E ⊂ X and if f is a function defined on X, the restriction of f to E is the function g whose domain of definition is E, such that g(p) = f (p) for p ∈ E. Define f and g on 2 by: f (0, 0) = g(0, 0) = 0, f (x, y) = € xy 2 x 2 + y 4 , g(x, y) = € xy 2 x 2 + y 6 if (x, y) ≠ (0, 0). Prove that f is bounded on 2 , that g is unbounded in every neighborhood of (0, 0) and that f is not continuous at (0, 0); nevertheless, the restrictions of both f and g to every straight line in 2 are continuous! .Explain step by step in detal