Let n be a positive integer. Let S(n) = n sigma j=1 ((1/3j − 2) − (1/3j + 1)). a) Compute the value of S(1), S(2), S(3), and S(4). b) Make a conjecture that gives a closed form (i.e., not a summation) formula for the value of S(n). c) Use induction to prove your conjecture is correct.
In: Advanced Math
3. Write a Matlab script that describes the dynamics of Pressure and Flow in the systemic arteries and Left Ventricle. Assume that :
1) Pressure in the Left atrium (PLA) and in the Systemic Veins (Psv) remain constant.
2) A time dependent LV compliance
3) Opening/Closing of the heart valves instantaneously with the direction of flow (i.e. valves are at an open or closed states. Use parameter values from the handout.
In: Statistics and Probability
A 105‑turn circular coil of radius 2.41 cm and negligible resistance is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is connected to a 14.7 Ω resistor to create a closed circuit. During a time interval of 0.167 s, the magnetic field strength decreases uniformly from 0.481 T to zero. Find the energy, in millijoules, that is dissipated in the resistor during this time interval.
In: Physics
Consider the following family of sets: For any n∈N, we define Q_n={ q \in Q | q= \frac{m} {n^k} for some k, m \in Z}
(That is, Q_n is the set of rational numbers expressed with the denominator that is a power of n.)
a) Is this set closed under addition, subtraction, multiplication, and division?
b) Decide the truth value of the following statement: Q 12 ⊆ Q 18 . Justify.
In: Advanced Math
Cheryl Wilson, president of Rivers Company, considers $48,000 to be a minimum cash balance for operating purposes. As can be seen from the following statements, only $43,000 in cash was available at the end of 2011. Because the company reported a large net income for the year, and also issued bonds and sold some long-term investments, the sharp decline in cash is puzzling to Ms. Feldman.
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Rivers Company Comparative Balance Sheet December 31, 2011, and 2010 |
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| 2011 | 2010 | |||
| Assets | ||||
| Current assets: | ||||
| Cash | $ | 43,000 | $ | 66,600 |
| Accounts Receivable | 233,600 | 246,400 | ||
| Inventory | 275,200 | 212,800 | ||
| Prepaid expenses | 26,600 | 48,600 | ||
| Total current assets | 578,400 | 574,400 | ||
| Long-term investments | 174,000 | 260,000 | ||
| Plant and equipment | 916,000 | 778,000 | ||
| Less accumulated depreciation | 224,000 | 198,400 | ||
| Net plant and equipment | 692,000 | 579,600 | ||
| Total
assets |
$ | 1,444,400 | $ | 1,414,000 |
| Liabilities and Stockholders' equity | ||||
| Current liabilities: | ||||
| Accounts payable | $ | 200,200 | $ | 260,800 |
| Accrued liabilities | 10,800 | 20,600 | ||
| Income taxes payable | 64,400 | 53,000 | ||
| Total current liabilities | 275,400 | 334,400 | ||
| Bonds Payable | 284,000 | 156,000 | ||
| Total liabilities | 559,400 | 490,400 | ||
| Stockholders’ equity: | ||||
| Common stock | 665,000 | 740,000 | ||
| Retained earnings | 220,000 | 183,600 | ||
| Total stockholders' equity | 885,000 | 923,600 | ||
| Total liabilities and stockholders' equity | $ | 1,444,400 | $ | 1,414,000 |
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Rivers Company Income Statement For the Year Ended December 31, 2011 |
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| Sales | $ | 1,360,000 | |
| Cost of goods sold | 850,000 | ||
| Gross margin | 510,000 | ||
| Selling and administrative expenses | 363,800 | ||
| Net operating income | 146,200 | ||
| Non operating items: | |||
| Gain on sale of investments | $34,000 | ||
| Loss on sale of equipment | (11,600) | 22,400 | |
| Income before taxes | 168,600 | ||
| Income taxes | 50,440 | ||
| Net income | $ | 118,160 | |
The following additional information is available for the year 2011:
a. The company sold long-term investments with an original cost of $86,000 for $120,000 during the year.
b. Equipment that had cost $146,000 and on which there was $68,000 in accumulated depreciation was sold during the year for $66,400.
c. The company declared and paid a cash dividend during the year.
d. The stock of a dissident stockholder was repurchased for cash and retired during the year. No issues of stock were made.
e. The company did not retire any bonds during the year.
Required: 1. Using the indirect method, determine the net cash provided by (used in) operating activities for 2011. (Negative amount should be indicated by a minus sign.)
2. Prepare a statement of cash flows for 2011. (Amounts to be deducted and negative amounts should be indicated with a minus sign.)
3. Compute free cash flow for 2011. (Negative amount should be indicated by a minus sign.)
In: Accounting
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Cheryl Wilson, president of Rivers Company, considers $48,000 to be a minimum cash balance for operating purposes. As can be seen from the following statements, only $43,000 in cash was available at the end of 2011. Because the company reported a large net income for the year, and also issued bonds and sold some long-term investments, the sharp decline in cash is puzzling to Ms. Feldman.
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In: Accounting
Assume the that over the past couple of years your investment into a stock that pays no dividends was as follows:
| Year | Starting price | Shares bought/sold |
|---|---|---|
| 2010 | 49.8 | 50 bought |
| 2011 | 55.7 | 100 bought |
| 2012 | 50.7 | 150 sold |
What is your dollar-weighted annual return for over this period for this investment?
Enter answer in percents, to two decimal places.
Bonus exploratory question: how does this compare to the average annual return, or the geometric average annual return?
In: Finance
Suppose you are given the following end of year stock price data for Random Inc. stock. Assume the returns are normally distributed, calculate the probability that an investor will lose more than -3% in a year, Prob(Ret<-3%). (Enter percentages as decimals and round to 4 decimals). Year Price 2005 43.65 2006 44.01 2007 45.77 2008 53.04 2009 45.67 2010 59.05 2011 46.88 2012 49.24 2013 43.99 2014 42.67 2015 48.14
In: Statistics and Probability
Suppose you are given the following end of year stock price data for Random Inc. stock. Assume the returns are normally distributed, calculate the probability that an investor will lose more than -3% in a year, Prob(Ret<-3%). (Enter percentages as decimals and round to 4 decimals). Year Price 2005 43.65 2006 44.01 2007 45.77 2008 53.04 2009 45.67 2010 59.05 2011 46.88 2012 49.24 2013 43.99 2014 42.67 2015 48.14
In: Statistics and Probability
Danny Ferry Co. sells $250,000 of 10% bonds on March 1, 2007. The bonds pay interest on September 1 and March 1. The due date of the bond is September 1, 2010. The bond yield is 12%. Give entries through December 31, 2008.
Round to the nearest dollar.
Instructions:
Prepare all of the relevant journal entries from the time of sale until the date indicated. Use the effective interest method for discount amortization. (Assume the no reversing entries are made.)
In: Accounting