Complex Analysis:

Use Rouche's Theorem and Argument Principle to determine the number of roots of p(z)=z^4-2z^3+13z^2-2z+36 which lie in each quadrant of the plane.

(Hint: Consider |z|=5 and |z|=1)

Chapter 1:

A patient is admitted with aortic valve insufficiency. A murmur is auscultated during the assessment and reported to be a grade of IV/VI. Convert the Roman numbers to describe the murmur to Arabic numbers.  

Chapter 2:

A nurse is recording the fluid intake for a client. The following questions pertain to this situation:

A. The nurse notes that the client has drank half of the water in the water pitcher. The pitcher holds 900 mL of water. How many milliliters would the nurse record?

B.  The nurse notes that ¾ of the intravenous (IV) fluids have infused in the past 12 hours. The IV bag contained 1000 mL of fluid at the beginning of the shift. How many milliliters would the nurse record for the IV intake?

C. A nurse has calculated the volume of two medications to be administered by injection. The first medication has a volume of ½ mL, and the second medication has a volume of ¾ mL. What is the total volume of medication?

Chapter 3:

A nurse is preparing a patient for surgery. A preoperative medication is ordered. The following questions pertain to the situation.

A. A nurse has calculated the volume of two medications to administer by injection. The first medication has a volume of 1/2 mL, and the second medication has a volume of 3/4 mL.

The medications will be combined in one syringe. The syringe is calibrated in 0.1-mL increments, so the total volume must be converted from a fraction into a decimal. What is the total volume of medication?

B.   Adult doses are usually rounded to the nearest tenth. Round 1.25 mL to the nearest tenth.

Chapter 4:

A nurse is caring for a patient with a blood clot in the right arm. The following questions pertain to this situation.

A. The pharmacy delivers a heparin bag with 25,000 units of heparin in 250 mL of 0.9% normal saline (NS). How many units of heparin are in 1 mL of NS?

B.  A patient is to take 60 mEq of potassium chloride in six equal doses. How many mEq of potassium will the nurse administer with each dose?

  Chapter 5:

A. The amp of D₅₀ contains a total of 50 mL. Calculate the number of grams contained in the amp of D_50.

     B. A nurse is writing orders she received from the physician over the telephone. The following questions pertain to this situation: The nurse receives an order for one-half of a milligram for a medication. How should the nurse write one-half?

Axe Ski Shop has five large retail stores across three western states. They operate a central warehouse that receives their clothing, ski equipment, and snowboard equipment from various wholesalers. (The central warehouse also has offices for the Axe system employees.) Each retail location currently sends weekly orders to the central warehouse and the warehouse then sends a truck to each location with their weekly orders. This past season was a disaster. Several of the retail locations regularly ran short on ski and snowboard boots, one of the retail locations had excess clothing inventory all winter long, and customers’ special requests to the warehouse either were ignored or were received late. In some cases the items would show up on the weekly delivery but were wrong sizes. Overall, customer satisfaction dropped and online reviews of their stores has reached an all-time low.

To fix these issues Axe’s central management has decided to install a company-wide communication system for their inventory so all five retail locations and the central warehouse can see inventory levels by SKU at all locations. Orders to the warehouse will be automatically generated based on inventory levels which will alleviate several of the issues described above. This new system will also let the retail locations request items shipped from store to store as needed to meet customers’ special requests.

The communication system will be rolled out incrementally to each location over the spring/summer months (shown in Table 1), starting with the warehouse, so that the system is fully functioning by August. Axe wants to purchase and install the optimum number of servers required to run the system but isn’t sure whether they need to install all servers in March or if they can install the servers incrementally as well. The number of employees at each location dictates when server capacity is needed, shown in Table 2. Ultimately, the system needs to handle all company employees. There is variation in server capacity, shown in table 3 below.

Additional cost and budget information includes a maximum budget of $18,000 total for the months of March and April. A discount during these same months is available on the workstation servers (10%) and the full rack servers (25%). Any servers purchased during May-July will not receive a discount.

1. Set up and solve five different optimization spreadsheet models to determine how many servers to purchase during each month, March-July. Answer the following questions:
   1. How many of each server is purchased and when?
   2. What is the total capacity, in number of employees, of the system?
   3. What is the total cost if this purchase schedule is followed?
2. Set up a sixth optimization spreadsheet model that considers the five months as a whole.
   1. How many of each server is purchased and when?
   2. What is the total capacity, in number of employees, of the system?
   3. What is the total cost if this purchase schedule is followed?
   4. How much savings is realized by solving this for the whole five months instead of month by month?
3. If you could relax one of the constraints, could you save Axe even more? Explain the change you would suggest and the resulting solution.

Table 1

Table 2

Table 3

solve by details
y"+y=-1 ,y(0)=0,y(Pi/2)=0
by properties of green function

Define correlation coefficient. Describe in your own words the difference between correlation coefficient and coefficient of determination.

Four hospitals located in one city are cooperating to establish a centralized blood-bank facility to serve them all. On an xy coordinate grid of the city, the hospitals are found at the following locations: Hospital 1 = (x = 5, y = 10), Hospital 2 = (7, 6), Hospital 3 = (4, 2), and Hospital 4 = (16, 3). The expected number of deliveries per month from the blood bank to each hospital is estimated at 450, 1200, 300, and I500, respectively. The travel distances are computed with the metropolitan (i.e., rectilinear) distance metric.

For the location you have selected, how much is the total monthly distance traveled? You can assume that each grid corresponds to a square where each side is exactly one kilometer.

1. Prove that √ 5 is not a rational number and Is it true that √ n is not a rational number for any positive integer n? Explain and show proof of in the answer and show work please.

in the problem given (3 - x)y" + x²y' + (1 + x)y = 0 , x₀=0. find the recurrence relation and the series solution given y(0) = -6 and y'(0)= 2

The question is correct.

Let X be an n-element set of positive integers each of whose elements is at most (2ⁿ - 2)/n. Use the pigeonhole principle to show that X has 2 distinct nonempty subsets A ≠ B with the property that the sum of the elements in A is equal to the sum of the elements in B.

Suppose that a graph G is such that each vertex of G has degree at least 100. Show that G contains a cycle of length at least 101, i.e., a cycle passing through at least 101 vertices.

Listed below are the transactions that affected the shareholders’ equity of Branch-Rickie Corporation during the period 2018–2020. At December 31, 2017, the corporation’s accounts included:

1. November 1, 2018, the board of directors declared a cash dividend of $.80 per share on its common shares, payable to shareholders of record November 15, to be paid December 1.
2. On March 1, 2019, the board of directors declared a property dividend consisting of corporate bonds of Warner Corporation that Branch-Rickie was holding as an investment. The bonds had a fair value of $1.6 million, but were purchased two years previously for $1.3 million. Because they were intended to be held to maturity, the bonds had not been previously written up. The property dividend was payable to shareholders of record March 13, to be distributed April 5.
3. On July 12, 2019, the corporation declared and distributed a 5% common stock dividend (when the market value of the common stock was $21 per share). Cash was paid in lieu of fractional shares representing 250,000 equivalent whole shares.
4. On November 1, 2019, the board of directors declared a cash dividend of $.80 per share on its common shares, payable to shareholders of record November 15, to be paid December 1.
5. On January 15, 2020, the board of directors declared and distributed a 3-for-2 stock split effected in the form of a 50% stock dividend when the market value of the common stock was $22 per share.
6. On November 1, 2020, the board of directors declared a cash dividend of $.65 per share on its common shares, payable to shareholders of record November 15, to be paid December 1.

Required:
1. Prepare the journal entries that Branch-Rickie recorded during the three-year period for these transactions.
2. Prepare comparative statements of shareholders' equity for Branch-Rickie for the three-year period. Net income was $330 million, $395 million, and $455 million for 2018, 2019, and 2020, respectively.