Ashley has earmarked at most $210,000 for investment in three mutual funds: x dollars in a money market fund, y dollars in an international equity fund, and z dollars in a growth-and-income fund. The money market fund has a rate of return of 4%/year, the international equity fund has a rate of return of 6%/year, and the growth-and-income fund has a rate of return of 15%/year. Ashley has stipulated that no more than 30% of her total portfolio should be in the growth-and-income fund and that no more than 55% of her total portfolio should be in the international equity fund. To maximize the return on her investment P (in dollars), how much should Ashley invest in each type of fund?

A laguerre equation is any differential equation of the form xy"+(1-x)y'+ny=0 where n is an integer. Solve the Laguerre equation with n = 1, that is solve xy"+(x-1)y'+y=0 about the singlular point x=0.

The table below shows the quantity measured for 12 samples (in kg). Create an xbar-chart and an R-chart and plot the values for the 12 samples. Comment on whether or not the process is in control or not. Also create an upper and lower spec limit for the data that results in a Cpk of at least 2.33.

Sample

Day 1
64.43
63.40
65.58
65.03
65.42
68.99
68.63
67.34
67.00
64.07
65.64
63.73
Day 2
65.53
67.43
66.63
64.54
64.76
65.43
65.67
67.27
67.55
63.14
65.69
68.54
Day 3
64.36
65.95
64.07
68.78
65.79
66.60
67.77
66.18
63.07
68.02
63.59
66.37
Day 4
64.75
68.94
66.50
64.33
68.50
66.91
67.52
67.80
66.72
68.79
65.34
68.57
Day 5
66.09
64.38
63.57
68.16
65.64
67.89
67.32
65.88
63.40
63.43
64.09
65.58
Day 6
63.15
64.27
64.22
66.70
68.55
64.78
67.70
63.53
68.52
68.95
64.75
63.56
Day 7
68.24
65.59
64.50
67.50
65.73
66.78
68.16
67.59
65.93
65.99
64.28
66.38
Day 8
66.59
67.14
64.72
65.05
64.35
68.79
66.59
64.50
64.02
66.41
63.15
65.63

What a Workbook!

You will create a math demonstration that teaches how to solve application problems related to systems of equations and factoring polynomials.  

Requirements:

1. Three different application problems involving setting up and solving a system of equations.
   1. Basic
   2. Mixture
   3. Distance, Rate, and Time
2. Three different application problems involving setting up and solving an equation using factoring of polynomials.
   1. Geometric
   2. Pythagorean Theorem
   3. Consecutive Integers
3. One problem per page.
   1. Clear Problem Statement
   2. Step by Step solution to problem
   3. Clear and detailed explanation of how solution was arrived at.
   4. Visual appeal

Determine the general solution of the differential equations. Write out the solution ? explicitly as a function of ?.

(a) 3?^2?^2 ??/?? = 2?−1

(b) 2 ??/?? + 3? = ?^−2? − 5

1. Prove or Disprove: If n is a nonnegative integer, then 5 | (2*4ⁿ + 3*9ⁿ)

Would a logistic regression analysis reveal the keys to improving customer retention?

Examine the enclosed results of logistic regression of Retained on Esent and on Eclickrate, and then discuss the results and make recommendations on how to improve customer retention.

Prove or disprove whether the function f: Z x Z -> Z x Z given by f(x,y) = (2x+y, 3x-6y) is injective, surjective or both.

1. Explain why the graphs of tangent and cotangent have vertical asymptotes

2. Explain why the graphs of cosecant and secant have vertical asymptotes

3. Sketch a graph of y=3sec(2x)y=3sec(2x) by hand, in other words, without a graphing utility. Include 2 periods, and include the asymptotes.

10? + 50? + 20? + 10? = 100

5? + 15? + 75? − 25? = 200

25a − 15? − 5? = 300

10? + 20? − 30? + 100? = 400

how to do flowchart using gauss elimination and lu decomposition method

proof ring of fraction step by step (in general)

Micron Inc. can invest $5,000,000 in a new technology. Micron’s CFO is concerned about uncertainty of the future interest rates. She believes that future interest rates may be either 12% or 7% into foreseeable future. The risk-neutral probability that interest rates will be at 7% is 60%. The one-year risk-free interest rate is 5%; the rate on a risk-free 20-year bond is 10% and the rate on an equivalent 20-year callable bond is 8.5%.
New project will provide Micron an annual cash flows of $570,000 per year for the next 20 years. Should Micron accept this project? Why or why not?

Explain the importance of scientific notation. Why is it necessary even when using calculators or computers? Provide three real-world examples where scientific notation is used, how it is used, and why. Finally, post three facts that include information about extremely large or small numbers that require scientific notation.