Gravimetric Analysis Definition

Gravimetric analysis is a collection of  quantitative analysis laboratory techniques  based on the measurement of an analytes mass. One example of a  gravimetric analysis technique  can be used to determine the amount of an ion in a solution by dissolving a known amount of a compound containing the ion in a solvent to separate the ion from its compound. The ion is then precipitated or evaporated out of solution and weighed. This form of gravimetric analysis is called precipitation gravimetry. Another form of gravimetric analysis is volatization gravimetry. In this technique, compounds in a mixture are separated by heating them to chemically decompose the specimen. Volatile compounds are vaporized and lost (or collected), leading to a measurable reduction on the mass of the solid or liquid sample. Precipitation Gravimetric Analysis Example In order for gravimetric analysis to be useful, certain conditions must be met: The ion of interest must fully precipitate from solution.The precipitate must be a pure compound.It must be possible to filter the precipitate. Of course, there is error in such an analysis! Perhaps not all of the ion will precipitate. They may be impurities collected during filtration. Some sample may be lost during the filtration process, either because it passes through the filter or else is not recovered from the filtration medium. As an example, silver, lead, or mercury may be used to determine chlorine because these metals for insoluble chloride. Sodium, on the other hand, forms a chloride that dissolves in water rather than precipitates. Steps of Gravimetric Analysis Careful measurements are necessary for this type of analysis. Its important to drive away any water that may be attracted to a compound. Place an unknown in a weigh bottle that has its lid cracked open. Dry the bottle and sample in an oven to remove water. Cool the sample in a desiccator.Indirectly weigh a mass of the unknown in a beaker.Dissolve the unknown to produce a solution.Add a precipitating agent to the solution. You may wish to heat the solution, as this increases the particle size of the precipitate, reducing loss during filtration. Heating the solution is called digestion.Use vacuum filtration to filter the solution.Dry and weigh the collected precipitate.Use stoichiometry based on the balanced chemical equation to find the mass of the ion of interest. Determine the mass percent of the analyte by dividing the mass of analyte by mass of unknown. For example, using silver to find an unknown chloride, a calculation might be: Mass of dry unknown chloride: 0.0984Mass of AgCl precipitate: 0.2290 Since one mole of AgCl contains one mole of Cl- ions: (0.2290 g AgCl)/(143.323 g/mol) 1.598 x 10-3 mol AgCl(1.598 x 10-3)x(35.453 g/mol Cl) 0.0566 g Cl (0.566 g Cl)/(0.0984 g sample) x 100% 57.57% Cl in unknown sample Note lead would have been another option for the analysis. However, if lead had been used, the calculation would have needed to account for the fact one mole of PbCl2 contains two moles of chloride. Also note, error would have been greater using lead because lead is not completely insoluble. A small quantity of chloride would have remained in solution instead of precipitating.

How an Understanding of Human Growth and Development Can...

I. Introduction A. In my essay will explain how an understanding of human growth and development can assist the counsellor in responding to the needs of the client. I have chosen three theories in three different models. My first model is psychodynamic and I will look at Sigmund frauds theory of development. The second model is humanistic and I will be covering Rogers and Maslow. My last model I will cover in this essay is social Erikson’s lifespan development theory. My essay will look at the theories and the application of each theory and I shall explain how an understanding of human growth and development can assist the counsellor in responding to the needs of the client. II.†¦show more content†¦12-18 is the genital stage. Young adults develop interests in the opposite sex, like previously in the phallic stage. the body is changing in terms of the growing of pubic hair growing, periods, in young males semen being produced .because of social restrictions adolescents shift their sexual energies to other forms of interaction such as sport, friendships and career mapping(Gerald Corey). If this stage is not managed with positivity and acceptance then personality disorders can take place. And the last stage is 18-35 the genital continued. The genital sage is the longest stage and continues to 60 +.becoming and being an adult .freedom to do as you please, love who you want, work where you want no parental restriction, a person has now become an adult (Gerald Corey). Responsibilities are taken, intimate relationships are formed and the capacity to want to understand others is formed (Gerald coyer).if the stages were inadequate, not positive then there can be problems, fraud calls these problems fixations. As noted earlier there are 5 stages, oral, anal, phallic, latency and genital. Successful completion of stages determines how the next stage is managed. An example would be a caregiver did not meet the needs of a child in the oral stage, in terms of the giving of food (breastfeeding). The child may later develop trust issues, personality disorders due to the wanting feeling, the pleasure principle of the id has an impact because theShow MoreRelatedRoles and Functions of the Guidance Counsellor1482 Words   |  6 PagesROLES AND FUNCTIONS OF THE GUIDANCE COUNSELLOR Guidance Counsellors are professionals who work in and out of the school system. Outside of the school system these professionals focus and interest is more on counselling and as a result are called counsellors. Guidance Counsellors form a part of the helping profession. 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Only you can call me into aliveness. Each time youre kind, and gentle, and encouraging, each time you try to understand because you really care, my heart begins to grow wings, very small wings, very feeble wings, but wings! Extract from Poem Please Hear What I am not

Analysis or Current Ethical Dilemma in Health Care Free Essays

There are many types of ethical dilemmas that plague the medical field but never is a dilemma more important than when dealing with life and death. In situations such as these, one must follow their own moral compass. When the case involves an entire hospital going against their religious mandates for the life of a woman, the decision becomes that much more difficult. We will write a custom essay sample on Analysis or Current Ethical Dilemma in Health Care or any similar topic only for you Order Now This paper will analyze the situation one Phoenix hospital found themselves in and the repercussions it suffered because of it decision. St. Joseph’s Hospital and Medical Center in Phoenix, Arizona is a hospital internationally recognized for their neurology department. They have treated high profile patients such as Brett Michaels and Muhammad Ali, but neither has gained the hospital quite the publicity as a woman seeking treatment in November 2009. Alongside neurology, St. Joseph’s Hospital also has a noted obstetrics department and this is where the woman was treated. In late November 2009, a terminally ill woman came to the obstetrics unit suffering from pulmonary hypertension. She was 11 weeks pregnant. During the course of diagnosis, it was found that the pregnancy was exacerbating her illness by worsening her hypertension to the point of placing the patient in immediate danger of death. Doctors determined the only course of action to save the woman was to abort her pregnancy. With St. Joseph’s being a Catholic hospital, this decision went against their guidelines. The decision was taken before an ethics committee which decided to proceed with the procedure. The rationale for the committee’s choice was that they were seeking specifically â€Å"to save the woman’s life, not to end the pregnancy. (Clancy, 2010, p. 1) As a result of performing the procedure, the hospital was stripped of its Catholic status. The problem identified in this situation can be posed in one question; does the religious affiliation of a hospital have the right to dictate the care of a patient? Had the ethics committee gone the other way and decided not to abort the pregnancy, this would have prohibited the woman’s right to live. One should take into account that the patient sought treatment at a Catholic hospital and she should have been aware of their belief system. However one doesn’t know if the patient came to this specific hospital because of its Catholic mission or whether she had no choice in the matter. In either case, is it not a hospitals first duty to provide the best care possible for their patients? The best care for this patient was to abort her pregnancy but the guidelines of the hospital would rather have seen the patient die trying to save both. My personal values and ethical position in this case lead me to side with the hospital. I have always been a proponent of the pro-life ideal and this instance is no exception. The principles I advocate for the strongest are respect for the patients autonomy and beneficence. Keeping these principles in mind, the patient made an informed decision about her care and the hospital needed to respect that decision. As far as beneficence, the cost to benefit ratio was analyzed and a conclusion was reached that benefited the patient most. Utilitarianism is a theory I would apply to this case. Doing the greatest good for the greatest amount of people and saving those you can save. Sometimes the end does justify the means. This not to say that religion plays no part in treating patients, but it is my firm belief that if the Catholic guidelines had prohibited the patient to receive the abortion, two lives would have been lost. When making a serious choice in a case like this, it is important to factor in alternate resolutions. The first alternate resolution is the most obvious and would have had the highest priority; transfer the patient to a facility that has no abortion restrictions. This would have been the best case scenario; however the patient was not stable enough to be relocated and may have died in transit. Another alternate decision would have been to attempt to wait out the patient’s condition and treat her medically. Do to patient confidentiality, the specifics of the patient’s condition are not known. Based on the testimony of doctors at St. Joseph’s, the woman was in critical condition and had this approach been followed, the consequences would have been fatal to both mother and child. This information makes medical management the lowest in alternative priority. When faced with difficult ethical dilemmas, it is best to have a plan of action to assist in decision-making. A step by step approach often works best because it allows the decider to breakdown a stressful choice into workable parts. First one must identify the problem and ask the appropriate questions: What? Who? How? The second step is to identify one’s own personal values toward the dilemma. The third, fourth and fifth steps include coming up with reasonable alternative, examining them and then predicting the possible outcomes of those decisions. In the sixth step, one should prioritize the alternative choices to better identify the most acceptable one. The seventh step is where the final decision is made based on all the information gathered and a plan is created. The plan is then implemented in the eighth step. The final ninth step is when one evaluates the end result and determines if the decision made was the right thing. In evaluation of this particular ethical dilemma, the right thing was done. The decision to forsake the values of Catholicism to save the woman’s life was the right thing to do. The hospital agrees and therefore lost its Catholic status because they stated that they would have made the same choice again. (Kurtz, 2010) Dealing with ethics can be a tricky thing to navigate which is why it is paramount to have a good sense of one’s own moral compass. This is not the last dilemma this hospital will face but following solid ethical values and principles, they should feel confident in their ability to provide the best care to the patients they treat. How to cite Analysis or Current Ethical Dilemma in Health Care, Papers

Shapiro Chapter Solutions Essay Example

Shapiro Chapter Solutions Paper Economic profit measures true increments to value, but is hard to assure. Accounting profit is correlated with economic profit, but not perfectly so. Accounting profit can be measured much more easily. B. What is the relationship between accounting rate of return and economic rate of return? Answer: The accounting rate of return is the ratio of after-tax profit to average book investment. Economic rate of return is the ratio of after-tax economic profit to the market value of the investment Economic profit equals cash accruals to the asset combined with changes in its market value. 2. In 1991, ATT laid a transatlantic fiber optic cable costing $400 million that an handle 80,000 calls simultaneously. What is the payback on this investment if ATT uses just half its capacity while netting one cent per minute on calls? Answer: 5210 Million per year assuming the half capacity is for 24 hours a day, 365 days per year. The annual payback is then 53%. 3. The satisfied owner off new $15,000 car can be expected to buy another ten cars from the same company over the next 30 years (an average of one every three years) at an average price of $15,000 (ignore the effects of inflation). We will write a custom essay sample on Shapiro Chapter Solutions specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Shapiro Chapter Solutions specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Shapiro Chapter Solutions specifically for you FOR ONLY $16.38 $13.9/page Hire Writer If the net profit margin on these cars is 20 percent, how much should an auto manufacturer be willing to spend to keep its customers satisfied? Assume a 9 percent discount rate. Answer: At a 20 percent profit margin, the auto company will earn an annuity to about $3,000 every three years for the next 30 years. Discounted at 9 percent, this annuity is worth $9,402, assuming that the tires new car is purchased three years from today. Hence, an investment to keep customers satisfied will have a positive NAP as long as the amount spent is less than $9,402. Thus, a car company should be willing to spend LIP to $9,402 in present value terms to keep its customers satisfied. A trick is available to calculate the present value of this annuity)h Recognize that an annuity received every three years for 30 years and discounted at 9 percent is equivalent to a 10-year annuity discounted at 29. 5029 percent since each cash flow term is discounted at (I . 09)3 = 1295029. 4. Demonstrate that the following project has internal rates of return of O percent, 100 percent, and 200 percent. Year $1,200 12 13 I Cash flow +7,200 1-13,200 Answer: To demonstrate that an AIR calculation is valid, compute the net present value at the AIR. A valid AIR yields O. I Year | -400. 00 -488. 89 | +88. 9 10 Cash Flow 112 1 13 1 14 I I Total 1-1,200 I-I ,200 | -600 1-1,650 +450 5. During 1990, DOD Chemical generated the following returns on investment in its different business units: Business unit 116. 6 16. 7 Return on Investment (h) I Chemicals/Performance Products I I Consumer Specialties Plastics 12. 7 I Hydrocarbons/Energy Other 111. 15. 2 11. 6 I I DOD Chemical overall Given these returns, which of the business units should DOD invest additional capital in? What additional information would you need in order to make that decision? Answer: These figures tell you what DOD earned in 1990. In order to decide on future investments, you need the following information: 1. Whether these returns are representative of those expected to be earned in the future in these different divisions, What matters for investment decommissioning are projected future returns, not past returns. To the extent that these returns vary widely from year to year-?which they do in the chemical business-?historical return data for one year are meaningless. One reason these data may be misleading is that they are based on historical cost figures for investment. You really want to calculate returns on the replacement cost of sets Inflation will cause asset values to be understated, which will lead the return on investment to be overstated. 2. The cost of capital for these divisions. Each division is likely to have its own risk and, hence, its own cost Of capital. A high return could just indicate a high degree of risk and, therefore, a high required return. What matters is the projected return relative to the cost Of capital. A high projected return that is less than the risk-adjusted cost of capital will yield a negative NAP investment. Conversely, a low projected return that exceeds the cost Of capital Will yield a costive NAP investment. 3. The marginal return on investment in each division. Even if the figures for, say, the plastics and chemical/performance products divisions exceed their cost of capital and are representative of those expected to be earned in the future, that does not automatically justify additional investment in those divisions. These figures tell us the average ROI; for investment purposes you need the marginal ROI. That is, what matters tort investment purposes is not the return on past investments but the return on future investments. As we have seen, many companies (e. G. Monsanto, Philip Morris) have divisions that yield high returns on past investments but very low returns on incremental investments. 4, The extent to which these divisions sell to one another, DOD Chemical is a vertically-integrated company. Its hydrocarbons/energy unit sells to its downstream plastics unit, which in turn sells to its consumer specialties unit. Thus, the profitability of these units depends critically on the prices at which these internal transactions take place. Gore example, the hydrocarbons/energy unit may be showing a low ROI simply because it sells petroleum to the plastics unit at 3 below-market price. That is, the hydrocarbons unit may be very profitable but its profits are showing up in the plastics unit in the form of a low price on raw materials. This is a form Of cross-subordination. Disentangling the true profitability of the different units of a vertically-integrated company like DOD turns out to be a very difficult task, but it is a necessary one for capital budgeting purposes. What matters is how profitable investments are from the standpoint of the overall company, not from the standpoint of the units undertaking those investments, 5, The returns associated with specific assets and activities within each vision. What matters from an investment standpoint is not just how well each division can be expected to do in the future but hove well specific projects within each division can be expected to do. For example, certain products within the profitable plastics division may be earning a return while others are only earning a 2% return. Similarly, certain investments may be expected to yield a high return relative to their rockiness, whereas others have little chance of a significant payoff. At the same time, the low-return hydrocarbons/newer division may have some very high-return projects, which are masked by a lot of value- storing activities elsewhere. Without detailed data on the returns associated with each divisions various activities, customers, and products, one cant say where investment dollars would be best spent. CHAPTER 2: PROBLEMS 1. A firm is considering investing in a project with the following cash flows: I cash Flows 1 15 1 16 117 1 18 II I-I sass. O 2,000. 00 | 3,000. 00 4,000. 00 | 3,500. 00 13,000. 00 1 ,oho. O | 1,818. 18 12,479. 4 13,005. 26 12,390. 55 11,862. 76 11,128. 95 1513. 16 1466. 51 1,818. 18 4,297. 52 17,302. 78 9,693. 33 Ill 12,685. 04 | 13,664. 70 2. The pennon Oil Co. Just decide whether it is financially feasible to open an oil well off the coast of China. The drilling and rigging cost for the well is The well is expected to yield 585,000 barrels of oil a year at a net profit to pennon of $5 a barrel for four years. The well will then be effectively depleted but must be capped and secured at a cost of Pennon requires an annual rate of return of 14 percent on its investment projects. Should Pennon open the well? (Assume all Of a years production occurs at the end Of the year. ) Answer: Net annual profit = = $2. MM. IV(Production) $2_MM _ 2. MM _ 2. 9137 = 58. MM. IV(Capping) = SO. MOM _ = 4 _ 0. 5921 = $2. MM. IV(Drilling) 55. MM. NAP = IV(Production) ? IV'(Capping) = 9. MM 2. MM 5. MM $1. MM. The well should be drilled, since the present value of the benefits exceeds the present value of the costs, The term NAP (Net Present Value) refers precisely to the difference in present value between the benefits and the costs of a project, 3. Jack Nicolas, the golfing pro and real estate developer, is thinking Of acquiring an 800-acre property outside Atlanta that he intends to turn into an exclusive community for 600 families, The cost of this property and the necessary improvements is $30 million. After setting aside a mandatory 25 percent of the property as green space, he figures he can sell the remaining lots for an average of $90,000 an acre. By putting in a golf course on the 200 acres of green space, Nicolas believes he can instead sell the lots for an average of $140,000 an acre. The golf course, including clubhouse, has a projected price tag of $6 million. In either event, the project is expected to take eight years to sell out at a rate of 75 lots per year. Jack Nicolas faces a marginal tax rate of 40 percent and can write off his land and development costs by prorating these costs against each lot old. A. If his required return is 14 percent, should Jack Nicolas go ahead with the initial project (i. E a community With no golf course)? Answer: The initial project, a community With no golf course, requires an initial outlay of $MM, and reaps 6. MM per year for 8 years in the absence of taxes and depreciation. The present value of the decision at r 14% and t -40% can be determined from the following formula: b. Should he put in the golf course? Answer: With the golf course, the cost is MM, and pretax revenues are 10. MM per year. The same calculations as above can be made with the new data: NAP = + (1 -? Nicolas should build the golf course (exactly as we exp ected), a b, * An alternate display is illustrative: Tax ( @ 40%) Choosing Only Twit Golf Course I Annual Sales I Ann. Amortization I I Ann. Pretax Profit I I Ann. After Profit 4. 638864 I cost I Present Value 37,574. 798 .NET Present Value 4. The Coin Coalition is trying to get the U. S. Government to replace the dollar bill with a gold-colored dollar coin. One argument is cost savings. A dollar bill costs 2. 6 cents to produce and lasts only about 17 months, A dollar coin, on the other hand, while costing 6 cents to produce, lasts for 30 years. About 1. 8 billion dollar bills must be replaced each year, The start-up costs of switching to a dollar coin are likely to be quite high, however. These costs have not been estimated. A. What are the projected average annual cost savings associated with switching from the dollar bill to a dollar coin? Answer: Since each dollar bill in circulation lasts an average of I . 42 years (17/1 2), and 1. 8 billion are replaced each year, this must mean that there are about 2. 556 billion dollar bills in circulation. The cost of replacing I billion dollar bills each year at a cost per bill of 2. 5 cents is $46. Million. Since the dollar coin lasts 30 years, only about 85. 2 million (2. 556 billion/30) coins must be replaced each year at an annual cost of $5. 1 million. Thus, the annual cost savings comes to approximately $41. 7 million. B. Taking into account only the cost savings estimated in part a, how high can the start-up costs for this replacement project be and still yield a positive NAP for the LIST. Government? Else an 8 percent discount rate. Answer: The present value of the cost savings perpetuity estimated in part a, discounted at 8 percent, is $41 or $521. 25 million. Hence, the start- p costs for replacing the dollar bill with a dollar coin can be as high as $521. 25 million in present value terms and this project will still yield a positive net present value. . Recent Census Bureau data show that the average income to a college- educated person was $34,391 versus ASS,CLC for those without college. At the same time, the annual tuition at public universities was $1,566 versus $7,693 for private colleges. In the following questions, assume there is no difference in income between public and private university graduates. A. Based on thes e figures, what is the payback period for a college education, akin into account the four years of lost earnings while being in college? Do these calculations for both public and private colleges. Answer: Based on the figures presented, the lost income during four years of college is 4 * 524,701 = 598,804 (if they dont go to college they earn Nan-college incomes). The cost of the four years of college at a public (private) university is 56,264 ($30,772). Combining these figures yields a total (undiscovered) cost for a public university of $105,068. For a private college. This cost comes to $129,576. The income advantage to a college education is 59,690 (534,391 . $24,701). From radiation, it takes 105,068/3,690 = 10. 4 years to recover the cost of a public university education. The equivalent figure for a private college is 129,576/9,690 13. 37 years. B. Assuming college graduation at age 22 and retirement at age 65, what is the internal rate of return on a college degree from a public university? A private university? Answer: For a public university, the cash flows are four years of annual net cash outflows equal to $26,267 ($1 ,566 + $24,701) and then 43 years of net cash in flows equal to $9,690 annually, Whether all these cash flows occur at the beginning or end of the year, the AIR equals 7. Percent (the timing of the cash flows doesnt matter because you are just multiplying the NAP-?which must equal zero-?by a constant). Poor a private university, the cash flows are four years of annual net cash outflows equal to $32,394 ($7,693 + $24, 701) and then 43 years of net cash inflows equal to 59,690 annually. The AIR based on these numbers is 6. 32 percent. C. Assuming a 7 percent discount rate, and the same working life as in part b, what is the net present value of a college degree from a public university? A private university? Answer: Assuming all cash flows occur at the end Of the year (here the timing goes matter), the NAP for a public university education is $10,878. For a private college, the WV is . $9,876. 6. The Fun Foods Corporation must decide on what new product lines to introduce next year, After-tax cash flows are listed below along with initial investments. The firms cost of capital is 12 percent and its target accounting rate of return is 20 percent, Assume straight-line depreciation and an asset life of five years. The corporate tax rate is 35 percent. All projects are independent. I Project | $1,250 | 1,200 I Yearly I Investment $3,000 I s,coo 11,200 | 55,000 12,400 $800 17,500 ,000 $1,000 1,250 4,000 14 | 5350 | 600 a. Calculate the accounting rate of return on the project. Which projects are acceptable according to this criterion? (Note: Assume net income is equal to after-tax cash flow less depreciation. ) I Project A Total AT Cash Flow I Total Depreciation I Net Income Avgas Net Income | 5400 shoo 11400 1280 Project B 116750 7500 9250 Project C 18400 14000 | 4400 1880 Cacti Rate of return (Average Net Income Average Book NV) ABA = Total depreciation/2. I 49. % Projects 8 and C are acceptable based on a 20% accounting rate of return. B. Calculate the payback period. All projects with a payback of fewer than four years are acceptable. Which are acceptable according to this criterion? Answer: Assuming depreciation effects are included in the cash flows: Payback A (years) 4. 53, Payback B Payback C 3,42_ Projects B and C are acceptable. Assuming depreciation h as not been included: Payback A (years) = 4. 06, Payback B = 2. 73, Payback C = 3. 06. Projects B and C are c. Calculate the projects Naps. Which are acceptable according to this criterion? Answer: NAP IV(After Tax Cash Flows) -? Initial Investment Assuming depreciation has already been incorporated: NAP A?$742. 2, NIB- 33801. 83, C 51574. 01. Projects B and C are acceptable. If depreciation has not been incorporated, and all writers Gang be used: NAP = IV(After Tax Cash Flows)-? Nit NV IV(Deep Tax Shield) NAP A- $518. 95, NAP B = ASSESS,34, NAP C = $2583. 34, All projects are acceptable. D. Calculate the projects IR, Which are acceptable according to this Answer: AIR is the discount rate that makes NAP = 0. Depreciation included: AURA= 7. 0%, AIR 27. %, Projects B and C are acceptable. (AIR > 12%) Depreciation not included: AURA= 15. 43%, All projects are acceptable. (AIR > 12%) e. Which projects should be chosen? Answer: The firm should follow the guidelines of the NAP rule. 7. Aptest, Inc. , is negotiating with the U. S. Department of Housing and urban Development (HUT) to open a manufacturing plant in South Central L. A. , the scene of much of the rioting in April 1992. The proposed plant will cost $3. 5 million and is projected to generate annual after-tax profits of $550,000 million over its estimated tour-year elite. Depreciation is straight-line over the tour-year period and Aptest;s tax rate is 35 percent, However, given the risks involved, Aptest is looking for a tax-exempt government subsidy. According to Aptest, the subsidy Just be able to achieve any of the following four objectives: (l) Provide a 2-year payback. (2) Provide an accounting rate of return of 35 percent. (3) Raise the plants AIR to 22 percent. (4) Provide an NAP of $1 million when cash flows are discounted at 18 percent. A. Poor each alternative suggested by Aptest, develop a subsidy plan that minimizes the costs to HUT of achieving Pates objective. You can schedule the subsidy payments at any time over the four-year period. Answer. Here are the alternatives With their costs: Payback. The annual cash flow,s are the sum of after-tax profits plus depreciation of $306,250 or $856,250. The sum of the first two years cash flows is $1 , 712,500. To bring the payback to two years will require a subsidy of $1 ; $1 Since the computation of payback is insensitive to when the subsidy is paid, as long as it happens within the two-year period, the present value of its cost can be minimized by providing it at the end of year 2. AIR. The accounting rate of return is 31. 43% In order to bring this up to 35%, it is necessary to bring average annual income up to $612,500 , 750,000), an average annual increase of 62,500. The subsidy will equal $250,000 Since the computation of AIR is insensitive to when the busily is received, its present value can be minimized by providing it at the end of the four years. AIR. With a subsidy of at time O, thereby lowering its net investment to Aptest will get its AIR up to 22%. Any delay will result in a correspondingly higher required subsidy (it will accrue at the rate of 22% annually. Or example, if the subsidy were to be provided at the end Of the first year, it would have to equal $1 ? 1. 22) to get Aptest AIR up to 22%. Hence, HELD Will minimize its costs Of getting Pates AIR up to 22% by providing the subsidy immediately instead of waiting. NAP. The NAP of the project, discounted at 18%, is (1,196,635). Hence, a subsidy equal to $1 , 196,635 that is paid up front will just pr ovide a zero NAP when discounted at 18%. The subsidy will rise at the rate of 18% annually if it is paid in a future year. B. Which of the four subsidy plans would you recommend to HUT if it uses a 15 percent discount rate? Answer. The winning subsidy plan is that associated with the AIR criterion, go paying $250,000 at the end of the tour-year period, the present value of Huts cost when discounted at will be $142,938. 8. The Fast Food chain is trying to introduce its new Hot and Spicy line of ambushers. One plan (S) will include a big media campaign but less in-house production capability. The other plan (L) will concentrate on a more gradual roll- out of the project but will involve more investment in personnel training and so forth.

An Introduction to Brownian Motion

An Introduction to Brownian Motion Brownian motion is the random movement of particles in a fluid due to their collisions with other atoms or molecules. Brownian motion is also known as pedesis, which comes from the Greek word for leaping. Even though a particle may be large compared to the size of atoms and molecules in the surrounding medium, it can be moved by the impact with many tiny, fast-moving masses. Brownian motion may be considered a macroscopic (visible) picture of a particle influenced by many microscopic random effects. Brownian motion takes its name from the Scottish botanist Robert Brown, who observed pollen grains moving randomly in water. He described the motion in 1827 but was unable to explain it. While pedesis takes its name from Brown, he was not the first person to describe it. The Roman poet Lucretius describes the motion of dust particles around the year 60 B.C., which he used as evidence of atoms. The transport phenomenon remained unexplained until 1905 when Albert Einstein published a paper that explained the pollen was being moved by the water molecules in the liquid. As with Lucretius, Einsteins  explanation served as indirect evidence of the existence of atoms and molecules. At the turn of the 20th century, the existence of such tiny units of matter was only a theory. In 1908, Jean Perrin experimentally verified Einsteins hypothesis, which earned Perrin the 1926 Nobel Prize in Physics for his work on the discontinuous structure of matter. The mathematical description of Brownian motion is a relatively simple probability calculation, of importance not just in physics and chemistry, but also to describe other statistical phenomena. The first person to propose a mathematical model for Brownian motion was Thorvald N. Thiele in a paper on the least squares method that was published in 1880. A modern model is the Wiener process, named in honor of Norbert Wiener, who described the function of a continuous-time stochastic process. Brownian motion is considered a Gaussian process and a Markov process with continuous path occurring over continuous time. What Is Brownian Motion? Because the movements of atoms and molecules in a liquid and gas is random, over time, larger particles will disperse evenly throughout the medium. If there are two adjacent regions of matter and region A contains twice as many particles as region B, the probability that a particle will leave region A to enter region B is twice as high as the probability a particle will leave region B to enter A. Diffusion, the movement of particles from a region of higher to lower concentration, can be considered a macroscopic example of Brownian motion. Any factor that affects the movement of particles in a fluid impacts the rate of Brownian motion. For example, increased temperature, increased number of particles, small particle size, and low viscosity increase the rate of motion. Brownian Motion Examples Most examples of Brownian motion are transport processes that are affected by larger currents, yet also exhibit pedesis. Examples include: The motion of pollen grains on still waterMovement of dust motes in a room (although largely affected by air currents)Diffusion of pollutants in the airDiffusion of calcium through bonesMovement of holes of electrical charge in semiconductors Importance of Brownian Motion The initial importance of defining and describing Brownian motion was that it supported the modern atomic theory. Today, the mathematical models that describe Brownian motion are used in math, economics, engineering, physics, biology, chemistry, and a host of other disciplines. Brownian Motion Versus Motility It can be difficult to distinguish between a movement due to Brownian motion and movement due to other effects. In biology, for example, an observer needs to be able to tell whether a specimen is moving because it is motile (capable of movement on its own, perhaps due to cilia or flagella) or because it is subject to Brownian motion. Usually, its possible to differentiate between the processes because Brownian motion appears jerky, random, or like a vibration. True motility appears often as a path, or else the motion is twisting or turning in a specific direction. In microbiology, motility can be confirmed if a sample inoculated in a semisolid medium migrates away from a stab line. Source Jean Baptiste Perrin - Facts. NobelPrize.org, Nobel Media AB 2019, July 6, 2019.

The Complete Guide to AP Human Geography FRQs

The Complete Guide to AP Human Geography FRQs SAT / ACT Prep Online Guides and Tips The free-response section is the hardest part of any AP test. Although AP Human Geography is much more straightforward than some other humanities AP exams, if you don't have your stuff down, the free-response section can still hit you where it hurts. In this article, I'll take you through the structure of the free-response section, some tips for answering AP Human Geography FRQsstrategically, examples of what actual questions look like, and a few places where you can find the best practice materials. AP Human Geography Free-Response Section Format There are three questions on the free-response section, each worth the same percentage of your score.You’ll have an hour and 15 minutes to answer all three questions.Free-response prompts will ask you to: Demonstrate an understanding of geographic models Analyze and evaluate geographic concepts Cite and explain examples of various geographic processes Synthesize different topics covered in the curriculum Most free-response questions have multiple parts, and you can earn anywhere from 6-10 raw points on each of them.It’s usually fairly obvious where the points are earned on these questions, as you’ll see in the examples in the upcoming sections. How to Answer AP Human Geography FRQs Before we get into examples with answer explanations, I’ll give you some essential steps for answering these types of questions.AP Human Geography free-response questions are typically pretty straightforward so you can attack them in a methodical fashion. Here's a sample question from the 2015 exam that I'll use as a reference so you can see how the different steps apply: Step 1: Read the Introductory Statement Before you start in on the first part of the question, make sure you read the short introductory blurb.It sets up the topic you’ll be analyzing and gives you firmer ground to stand on when addressing the rest of the question. In the sample question above, the introductory statement makes it clear that the question will deal with refugees and the political and social origins of mass emigration. Reading all the introductory statements for the three free-response questions in the section before you start answering any of them can help you decide where to begin.If you see a topic that is especially familiar, you might go for that question first because you’ll be able to answer it the fastest. Step 2: Identify the Key Command In each part of the question, underline what it’s asking you to do.Common examples of key commands include â€Å"compare,† â€Å"describe,† â€Å"identify,† and â€Å"explain.†It’s helpful to underline these words to keep yourself on track when responding to the question.This is also useful because it will get you in the habit of paying closer attention to the differences between each of these tasks. For example, a question that asks you to â€Å"identify† something will merit a much more succinct answer than one that asks you to â€Å"describe† it.In part A of the sample question, the key command is "define," meaning you could just give a one sentence answer that clearly outlines what a refugee is. For part B, the key command is "discuss," which denotes a longer answer that elaborates on each reason for refugees leaving their countries of origin. In part C, the key commands are "identify and explain," which would mean a very succinct answer followed by greater detail. The final part of the question asks you to "explain" two economic impacts, which means a couple of sentences of further clarification for each example you give.You’ll save time and earn points if you’re careful to make these distinctions! Step 3: Hit the Points Now it’s time to answer the question.Make an estimate of how many points are possible in this part of the question.For example, if a question tells you to give two examples of how a concept applies to a certain country’s economic landscape, there are likely two points that you can potentially earn for that part of the question.In the sample question, you can see relatively clearly that part A is worth one point, part B is worth three points, part C is worth two points, and part D is worth two points. Part C is the only tricky part - notice that you're only asked for one reason, but you must identify AND explain it. There is typically one point available for completing each key command.After making this determination, write a clear answer that addresses all of the points thoroughly and will make it easy for the grader to find your responses. Step 4: Reread and Double Check When you’ve finished writing your answer, reread the question and your response to make sure you’ve done everything it asked you to do.If you’re satisfied, move onto the next part of the question, and repeat the process of identifying key commands and hitting all the possible points.After you finish the last part, check over all of your answers for that question one last time to ensure that everything is the way you want it to be. Then you can move onto the next free-response question. Review your answers with a second, more critical eye. I think this picture is photoshopped, but I don't know for sure because I don't feel like Googling "can you have two pupil/iris combos within one eyeball?" Just kidding, I did Googleit, and it's probably not a thing, but not even the internet knows for sure.OoOoOoOo. AP Human Geography FRQ Examples In this section, I'll go through the answers to two different free-response questions that were asked on real AP Human Geography tests within the last couple of years. Here's the first question: For this question, a knowledge of the most prevalent geographic models and theories is very important.You need to be able to relate one of these models to the economic development of a specific country.This question requires almost all the skills listed in the first section of this guide. As you may have guessed, there were three points possible for the answer to the first part.Here are some examples of differences between the two models that you could identify and compare: Rostow’s five-stage model says that national economies are developing forward over time (never moving backward) while Wallerstein’s core-periphery model says that countries are static or can move backward in development. Rostow’s model says that international trade may help countries to grow economically while Wallerstein’s model says that international trade strengthens development in core countries and constrains development in peripheral countries. Rostow’s model provides a national-level analysis while Wallerstein’s model provides an international-level analysis. For part B, you need to show that you can apply these models in the context of Mexico and Brazil, countries that are in the midst of fully developing and modernizing their economies.One point would be earned for identifying a stage or part of one of the models, and a second point would be earned for explaining that stage or part.For example, you could talk about Stage 4, or the Drive to Maturity, in Rostow’s model.This stage is exemplified by increased manufacturing specialization and integration into the global economy. For part C, you would have to identify two examples of the core-periphery concept below the national level.One example might be a core city and its peripheral suburbs.Another example might be a core productive area surrounded by a less developed or impoverished periphery. Now, let’s take a look at a second example with an image component: Forpart A, we have to consult the map and determine one characteristic that the shaded countries have in common.Examples of characteristics you could mention include: They’re all developing countries. They’re former colonies. They all use plantation or small-scale agriculture. They’re all equatorial countries. Part A was worth one point.Notice that this only requires a very broad understanding of the nature of these countries or a basic knowledge of climate in different parts of the world. For part B, you could earn two points for identifying each impact of coffee farming.Possibilities include: Economic development:Coffee farming leads to increased employment, growth in GNP, development of infrastructure, improved foreign exchange, increased global trade and better international relations. Environmental impacts:Coffee farming causes harmful effects from agricultural chemicals, water use issues, deforestation, biodiversity loss, and soil erosion. You could also talk about how coffee farming might lead to too much economic dependence on a single commodity and cause the land to be used for commercial agriculture rather than food. Part C was also worth two points, one for identifying a way that increased consumption affects coffee-producing countries and one for explaining the effect in more detail.For example, you might say that increased consumption leads to increased production.This, in turn, means more resources dedicated to coffee production, the adoption of new technologies related to the industry, increased profit, and the introduction of new producers into the coffee industry. Finally, for part D, you have to explain a specifically urban change in the developed world related to coffee production.You might say that more coffee shops will start to spring up in urban areas.That gets you one point.Then, you could earn a second point if you got into a more specific discussion about how the placement of coffee shops is related to geographic theories.You might explain it in the context of consumer proximity, central place theory, and diffusion. How to Practice AP Human Geography FRQs You can find plenty of sample AP Human Geography free-response questions (and their corresponding answer guidelines) online.The College Board site has real test questions that were administered between 2004 and 2015 with sample responses and scoring guidelines.This is the best resource for free response questions because you can be sure that they’re accurate representations of what you’ll see on your exam in terms of content and difficulty level.There’s nothing wrong with using free-response questions crafted by test prep companies for preliminary practice, but you should always incorporate real questions into your studying at frequent intervals. Barron’s has a free practice test that you can take in timed or practice mode depending on how serious you’re feeling.It might be good to make use of the timed mode when you’re close to the real test so you can get an accurate feel for the conditions.It has three free-response questions just like the actual AP test, and you can consult scoring guidelines to check your answers (the multiple-choice portion of the test is scored automatically, but you have to do a little more work for free response).If you’re not averse to spending a bit of money ($25), you might also register with Learnerator to get access to a bunch of additional AP Human Geography practice free-response questions. It's time to fly free! Go, respond. It is your destiny. What's Next? If you want an overview of the whole exam with examples of multiple-choice and free-response questions, take a look at my survey of the AP Human Geography test including study tips and sample questions. Looking for more resources to use in preparing for this test? Check out my ultimate study guide for AP Human Geography! If you want more free response practice, you might consider getting a review book to supplement the online resources listed in this article. Here's a list of the best review books for AP Human Geography.

Use elements of minimum core in applying theories and principles for Essay

Use elements of minimum core in applying theories and principles for planning and enabling inclusive learning and teaching - Essay Example This process can be applied in any of the phases and it should be continuous, meaning that there is no limitation to the number of cycles that can be made in a learning situation. According to this theory, with no limitations, one would simply go on repeating the same mistakes. According to the theory, individuals learn in four ways and they are likely to develop one mode of learning more than others. Thus learning is by concrete experience, by observation and reflection, by experimenting actively, and by active conceptualization. These four processes can be applied by learning facilitators or teachers (Coffield, et al. 2004). This can be applied in literacy and language. For example, in reading one can use readable, accessible texts also teaching learners explicitly how they can develop comprehension skills using activities that are related to their texts. Learners are also encouraged to highlight the main words also ideas in texts, successful questioning, setting the picture, as we ll as stimulating previous reading prior to any reading so as to offer learners’ great chances of decoding the text, will also work. There are other diverse theories and principles that have been developed to aid in understanding planning and enabling inclusive learning and teaching. The minimum core elements can be applied in enabling inductive learning and teaching. One of these elements is the use of reinforcement. It is vital that the teachers integrate positive reinforcement to learning and teaching. Positive reinforcement includes rewards given to students and positive remarks made by the teachers. This can be given to encourage behaviour, achievements and notable improvements (Curzon 2003). This is important in learning as it is important how learners view themselves, their self esteem and being aware of their strengths and weaknesses affects their learning ability. The learners’ degree of motivation as well as engagement in learning and the phase