At 9 cents per kilowatt-hour of electric power. Analyze how much money you would save in a year (365 days) if you went from non-energy efficient to energy efficient appliances. Calculate how much per appliance and then a total of your savings. appliance washing machine- usage per day 1 hours, watts used per hour 3000 watts washing machine usage per day 1 hours, watts used per hour 1500 watts Refrigerator usage per 24 hours watts per hour 100 Refrigerator usage per 24 hours watts used per hour 75 Dishwasher usage per day 1 hour watts used per hour 1500 watts Dishwasher usage per day 1 hour watts used per hour 1200 watts

Let S(t) be the price of dollar at time t, i.e. the number of euros per dollar. The behavior of S(t) through time is modeled by ??(?) ?(?) = ??? + ???(?) for a standard Brownian motion and real value µ and σ > 0. Now, let ?(?) = 1 ?(?) be the exchange rate of euro against the dollar. Show that U(t) satisfies the following stochastic differential equation. ??(?) ?(?) = (?2 − ?)?? − ???(?) # please help me with this question in detail, in an organized way . And please do not simply copy other's solution#

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)

cos(θ) − sin(θ) = 1

Your farm encompasses 500 acres, and you are planning to grow soybeans, corn, and wheat in the coming planting season. Fertilizer costs per acre are: $5 for soybeans, $2 for corn, and $1 for wheat. You estimate that each acre of soybeans will require an average of 5 hours of labor per week, while tending to corn and wheat will each require an average of 2 hours per week. Based on past yields and current market prices, you estimate a profit of $10,500 for each acre of soybeans, $7,000 for each acre of corn, and $3,500 for each acre of wheat. You can afford to spend no more than $3,000 on fertilizer, and your farm laborers can supply 3,000 hours per week. How many acres of each crop should you plant to maximize total profits?

In this event, will you be using all the available labor?

Yes No    

Let g(x)=−6x^6+29x^5+126x^4+135x^3+576x^2+76x−96. Given that -2i is a root of g(x) and that g(x) has at least one rational root, find all the real roots of g(x) in increasing order.

3) Now you will plan for your retirement. To do this we need to first determine a couple of values.

a. How much will you invest each year? Even $25 a month is a start ($300 a year), you’ll be surprised at how much it will earn. You can choose a number you think you can afford on your life circumstances or you can dream big. State what you will use for P, r, and n to earn credit. (3 points)

The typical example of a retirement investment is an I.R.A., an Individual Retirement Account, although other options are available. However, for this example, we will assume that you are investing in an I.R.A. (for more information see: http://en.wikipedia.org/wiki/Individual_Retirement_Account ) earning 8% interest compounded annually. (This is a good estimate, basically, hope for 10%, but expect 8%. But again this is just one example; I would see a financial advisor before investing, as there is some risk involved, which explains the higher interest rates.) List your P, r, and n to earn points for this question.

b. Determine the formula for the accumulated amount that you will have saved for retirement as a function of time and be sure to simplify it as much as possible. You need to be able to show me what you used for r, n, and P so that I can calculate your answers. Plug in those values into the formula and simplify the equation. (5 points)

c. Graph this function from t = 0 to t = 50. (6 points) Ways to show graphs: ? Excel ? Hand draw, take a pic with phone and import it into your document as a picture. ? Online graphing calculator program (try googling free graphing calculators or use one listed in the Tech websites from Module 1)

d. When do you want to retire? Use this to determine how many years you will be investing. (65 years old is a good retirement-age estimate). You need to say how old you are (Age 29) if you are retiring when you are 65 or tell me how long until you retire. State what you will use for t. (2 points)

e. Determine how much you will have at retirement using the values you decided upon above. (5 points)

f. How much of that is interest? (4 points)

g. Now let’s say you wait just 5 years before you start saving for retirement, how much will that cost you in interest? How about 10 years? How about just 1 year? (10 points) Now you need to consider if that is enough. If you live to be 90 years old, well above average, then from the time you retire, to the time you are 90, you will have to live on what you have in retirement (not including social security). So if you retired at 65, you will have another 25 years where your retirement funds have to last.

h. Determine how much you will have to live on each year. Note, we are neither taking into account taxes nor inflation (which is about 2% a year). (5 points) Let’s look at this from the other direction then, supposing that you wanted to have $50,000 a year after retirement.

i. How much would you need to have accumulated before retirement? (5 points)

j. How much would you need to start investing each year, beginning right now, to accumulate this amount? A “short-cut” to doing this is to first compute the effective yield at your retirement age, then divide this amount into Part (i). This is the amount you well need to invest each year. (5 points)

k. That was just using $50,000, how much would you want to have each year to live on? Dream big or reasonable depending on your occupation! Now using that value, repeat parts (i) and (j) again. You need to state what you would want to live on and it needs to be something besides $50,000. (10 points)

Your answer to (k) would work, if you withdrew all of your retirement funds at once and divided it up. However, if you left the money in the account and let it draw interest, it is possible that the interest itself would be enough to live on, or at the very least if you had to withdraw some of the principle, the remaining portion would still continue to earn interest. Essentially, what you have found is the upper bound for the amount of money that you will need to invest each year to attain your financial goals.

l. Finish by summarizing what you have learned in the entire project and consider setting a goal towards saving for retirement. (Your answer should be in complete sentences free of grammar, spelling, and punctuation mistakes.) This should be a paragraph not one sentence. (10 points)

Just because two or more values are different does not mean that they are different in a statistically significant manner. Researchers rely on the p values that are generated for each of their statistical tests to determine significance. If the p value is larger than the alpha, then they are not different in a statistically significant manner, and therefore the values are not considered different. In this journal activity, consider these concepts in terms of the differences between null and alternative hypotheses, and discuss this question: What is the difference between failing to reject the null hypothesis and having evidence to support the alternative hypothesis?

Complete the table to determine the balance A for P = $1200 dollars invested at rate r = 6% for t = 10 years and compounded n times per year. (Round your answers to two decimal places.)

Argument A

Since all triangles have three sides, and an isosceles triangle is a triangle, it follows that an isosceles triangle has three sides.

Argument a is:

inductive/deductive;

valid/invalid/strong/weak;

sound/unsound/cogent/uncogent?

Argument B

There is a large crack in Philadelphia's Liberty Bell. From this, we can conclude that there was a defect in the bell's craftsmanship.

Argument B is:

inductive/deductive;

valid/invalid/strong/weak;

sound/unsound/cogent/uncogent?

Argument C

Paleontologists now agree that the Tyrannosaurus Rex was actually a peaceful, plant-eating dinosaur. Therefore, it is probably true that the Tyrannosaurus Rex was not a meat-eater.

Argument C is:

inductive/deductive;

valid/invalid/strong/weak;

sound/unsound/cogent/uncogent?

What does a sampling distribution have to do with a confidence interval?

Maximization applications

A farmer has 100 acres of land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital. The farmer has at most 800 hours of labor and $2400 of capital available. If the profit from an acre of wheat is $80 and from an acre of corn is $100, how many acres of each crop should she plant to maximize her profit?

Consider the following scenario:

A drum used for percussion has sides modeled by a hyperbola. Suppose the total height of the drum is known. The diameter at the top of the drum is 16 inches, and the minimum diameter is 7 inches, occurring at a height of 9 inches. Assume that the center of the hyperbola occurs at the height where the diameter is the least.

Choose your own value for the height of the drum based on the scenario above and address the following:

1. Draw a graph or figure to represent this situation.
2. Describe how the concepts from this module can be applied in this case.
3. Determine the equation of a hyperbola that models the sides of the drum.
4. Provide another example of a scenario that involves the same concept.

DISCUSS UNDERSTANDING HOW TO SOLVE AN EQUATION ALGEBRAICALLY AND GRAPHICALLY.

A farmer raises only sheep and geese. She wants to raise at least 16 animals, including 7 sheep. She spends $34 to raise a sheep and $15 to raise a goose, and she has $1020 availble for this project. Write a system of inequalities that describe all the given conditions. Graph the feasible region.

Compound Interest In Exercises 17 and 18, determine the time necessary for $1000 to double if it is invested at interest rate compounded (a) annually, (b) monthly, (c) daily, and (d) continuously

17. r = 11%

18. r = 10 1/2%