The Carlson Department store suffered heavy damage when a hurricane struck on August 31. The store was closed for four months (September through December), and Carlson is now involved in a dispute with its insurance company about the amount of lost sales during the time the store was closed. Two key issues must be resolved (1) The Amount of sales Carlson would have made if the hurricane had not struck and (2) whether Carlson is entitled to any compensation for excess sales due to increased business activity after the storm. More than $8 Billion in federal disaster relief and insurance money came into the country, resulting in increased sales at department stores and numerous other businesses.

Table 6.18 gives Carlson's sales data for the the 48 month preceding the storm. Table 6.19 reports total sales for the 48 months preceding the storms for all department stores in the country , as well as total sales in the country for the four months the Carlson's Department Store was closed.

Table 6.18 Sales for Carlson Department store ($Million)

Table 6.19 Department Store Sales for the County ($Million)

Carlson's Manager asked you to analyze these data and Estimates of the lost sales at the Carlson Department Store for the month of September through December. They also asked you to determine whether a case can be made, Carlson is entitled to compensation for excess sales it would have earned in addition to ordinary sales

Managerial Report
Prepare a report for the managers of the Carlson Department Store that summarizes your findings, forecast and recommendations. Include the following:
1. An estimates of sales for Carlson Department Store had there been no hurricanes
2. An estimates of country wide department stores sales had there been no hurricanes
3. An estimates of lost sales for the Carlson Department Store for September through December.

In addition use the countrywide actual department stores sales for September through December and estimates in part (2) to make a case for or against excess storm-related sales

You opened an account and deposited X Dollars on January 1, 2002 in National City Bank. Any balance in the account will earn 5% per year. You withdrew $500 on January 1, 2006 and $500 on January 1, 2008. You closed out this account on January 1, 2011 and received $700. How much did you initially deposit (X) in National City at the time you opened the account?

Use the Divergence Theorem to evaluate

F · dS,

where

F(x, y, z) = z²xi +

+ cos z

j + (x²z + y²)k

and S is the top half of the sphere

x² + y² + z² = 4.

(Hint: Note that S is not a closed surface. First compute integrals over S₁ and S₂, where S₁ is the disk

x² + y² ≤ 4,

oriented downward, and S₂ = S₁ ∪ S.)

Using only real numbers between 0 and 100, inclusive, show the set of three numbers whose product is 64 and whose sum is minimal is give by {4, 4, 4}.

(a) When is an absolute minimum or maximum guaranteed?

(b) State the steps to find an absolute minimum and maximum.

(c) Is the space closed and bounded? Explain.

(d) Use Lagrange Multipliers to find the minimum and maximum

please label and write neatly.

Suppose that Federal Reserve policy leads to higher interest rates in United States

a. How will this policy affect real GDP in short run if the United States is a closed economy (no exports and imports)?

b. How will this policy affect real GDP in short run if the United States is an open economy?

c. How will your answer to part b change if interest rates also rise in the other countries around the world?

On a particular summer day, the temperature is 30 degrees Celsius and the relative humidity is 80% (which means that the partial pressure of water vapor in the ambient air is 80% of the equilibrium vapor pressure of water). A sample of this air is placed in a 1 Liter flask which is then closed and cooled to 5 degrees Celsius. What is the mass in grams of water that still exists as vapor in the flask? How much liquid water in grams condenses out?

A closed rectangular tank 1.2 m high, 2.4 m long and 1.5 m wide is two-thirds full of gasoline (specic gravity 0.8). Calculate the acceleration which may be imparted to the tank so that the bottom front end of the tank is just exposed. Also calculate the total forces on each end of the tank and show that the dierence between these forces equals the unbalanced force necessary to accelerate the liquid mass in the tank.

1. Find the derivative.  

f(x) = x⁶ · 3^x

^2.  Find the absolute maximum and minimum values on the closed interval [-1,8] for the function below. If a maximum or minimum value does not exist, enter NONE.

f(x) = 1 − x^2/3

^3.  Find the derivative.

f(x) = x⁵ · e^6x

Consider the following.

f(x) = -19ln(84x)

Compute f '(x), then find the exact value of f ' (3).

Five kg of oxygen (O​2​), initially at 430°C, fills a closed, rigid tank. Heat transfer from the oxygen occurs at the rate 425 W for 10 minutes. Assuming the ideal gas model with ​k
​ = 1.350 for the oxygen, determine its final temperature, in °C.

Can't seem to find the right equations to use for this one, so I'm getting pretty stumped. Any help would be greatly appreciated