Facts About the Number e 2.7182818284590452...

If you asked someone to name his or her favorite mathematical constant, you would probably get some quizzical looks. After a while someone may volunteer that the best constant is pi.  But this is not the only important mathematical constant. A close second, if not contender for the crown of most ubiquitous constant is e. This number shows up in calculus, number theory, probability and statistics.  We will examine some of the features of this remarkable number, and see what connections it has with statistics and probability. Value of e Like pi, e is an irrational real number. This means that it cannot be written as a fraction, and that its decimal expansion goes on forever with no repeating block of numbers that continually repeats. The number e is also transcendental, which means that it is not the root of a nonzero polynomial with rational coefficients. The first fifty decimal places of are given by e 2.71828182845904523536028747135266249775724709369995. Definition of e The number e was discovered by people who were curious about compound interest. In this form of interest, the principal earns interest and then the interest generated earns interest on itself. It was observed that the greater the frequency of compounding periods per year, the higher the amount of interest generated. For instance, we could look at interest being compounded: Annually, or once a yearSemiannually, or twice a yearMonthly, or 12 times a yearDaily, or 365 times a year The total amount of interest increases for each of these cases. A question arose as to how much money could possibly be earned in interest. To attempt to make even more money we could, in theory, increase the number of compounding periods to as high a number as we wanted. The end result of this increase is that we would consider the interest being compounded continuously. While the interest generated increases, it does so very slowly. The total amount of money in the account actually stabilizes, and the value that this stabilizes to is e. To express this using a mathematical formula we say that the limit as n increases of (11/n)n e. Uses of e The number e shows up throughout mathematics. Here are a few of the places where it makes an appearance: It is the base of the natural logarithm. Since Napier invented logarithms, e is sometimes referred to as Napiers constant.In calculus, the exponential function ex has the unique property of being its own derivative.Expressions involving ex and e-x combine to form the hyperbolic sine and hyperbolic cosine functions.Thanks to the work of Euler, we know that the fundamental constants of mathematics are interrelated by the formula eiÃŽ   10, where i is the imaginary number which is the square root of negative one.The number e shows up in various formulas throughout mathematics, especially the area of number theory. The Value e in Statistics The importance of the number e is not limited to just a few areas of mathematics. There are also several uses of the number e in statistics and probability.  A few of these are as follows: The number e makes an appearance in the formula for the gamma function.The formulas for the standard normal distribution involves e to a negative power. This formula also includes pi.Many other distributions involve the use of the number e. For example, the formulas for the t-distribution, gamma distribution, and chi-square distribution all contain the number e.

The Symbolic Language of Dreams - 841 Words

I found the reading The Symbolic Language of Dreams, written by Stephens King, a very interesting story to write about. King stated a quote in his introduction saying that dreams are a useful way that help people find the nature of their problems; or, find answers to their problems in a symbolic way. The purpose of this essay is to show that dreams and imaginations were two main factors in King s successful life. Hence, dreams and imaginations are critical factors when writing; they sure can resolve many issues and expand our thoughts in order to write better and longer books. Without passion writing good books is impossible. King claims that his book Salem s Lot was the perfect example of using a dream in his writings. Dreams are†¦show more content†¦But in the middle, the world is gone and I m able to see better (22). From this we can conclude that King is very passionate about dreaming and writing. King showed us his passion by using beautiful metaphors where he compares dreams to the fish that live in the ocean. He said that deep fish are to surface fish, what deep dreams are to surface thoughts -- meaning that, when we try to get the deep fish to the water surface, theyShow MoreRelatedCarl Jung Symbol1160 Words   |  5 PagesCritical Analysis of Carl Jung’s â€Å"The Importance of Dreams† Jung, one of the most important and most complex psychological theorist of all time, holds the belief that dreams are symbols of human unconsciousness. He finds the very intimate relationship between symbol, unconsciousness and dreams. In his essay â€Å" The Importance of Dreams†, Jung describes that man produces symbols unconsciously and spontaneously, in the forms of dreams. He says that dreams are outlet of unconsciousness. 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Community Health Department Investigation Free Essays

The Health Department received a letter notifying them of a possible health problem in regards to students at Truman and Jackson Middle Schools. It is my duties as a member of the investigative team to find out if there was an increase of absences and for what classes. In looking at the charts it would appear that the absences occurred for the band classes at Truman and Jackson Middle Schools on May 20th. We will write a custom essay sample on Community Health Department Investigation or any similar topic only for you Order Now The chart shows an absent rate of 33% for Truman and 25% for Jackson (â€Å"Independent School District 12 Intranet†). According to the letter from the principal at Truman Middle School she is concerned that a flu outbreak could be the cause of the student’s absences but there is also information from the Health Department inspections that shows restaurants with violations such as: sanitation, food storage, and food preparation. My first hypothesis would be that the students from Truman and Jackson were absent from school on the 20th because they ate at one of the restaurants and caught food poisoning. Several of the students had similar symptoms such as: diarrhea, fever, and vomiting which kept them from attending school. My second hypothesis would be that the students from the two schools came in contact with another which could have lead them to transmitting the flu to one another. This would be supported by the fact that on the calendar of events the students attended the Battle of the Bands on May 19th, which was a day before the absences started taking place. There are six testable questions that could help with the investigation: how close are Truman and Jackson schools, did other band students from Kennedy and Roosevelt report the same symptoms, was there direct contact between the students at Truman and Jackson, were the band students from Kennedy and Roosevelt in contact with the students from Truman and Jackson, was the reported illnesses from students who played the same instrument, and how close are Kennedy and Roosevelt to Truman and Jackson. The following statement: â€Å"The Brentwood Indians basketball team lost the state championship because there is bad stuff in the stars happening with Mars in Aquarius†, is not a suitable hypothesis. In order for â€Å"bad stuff† to be tested we would need to know what exactly it is that they are referring to as â€Å"bad stuff†. How to cite Community Health Department Investigation, Essay examples

International Financial Reporting Standards †Free Samples to Students

Question: Discuss about the International Financial Reporting Standards. Answer: Introduction: A direct quotation in the outside trade markets indicates the estimation of the American dollar is expressed as a for each unit measure of a remote cash. This sort of citation indicates the amount U.S. cash it takes to buy one unit of outside money (Allen, Hemming Potter 2013). This part empowers you to oversee trade rates for every money match utilizing immediate or circuitous citation. The kind of citation utilized is reliant on available standard. You can characterize the kind of citation per customer and money combines (business exchange). Indirect quotation has not been required as of not long ago, on the grounds that immediate citation was normally utilized for trade rates (Avdjiev, McCauley Shin 2016). With the beginning of the double cash period of the European Monetary Union (EMU), backhanded citation is presently utilized inside Europe for trade rates with the euro. Backhanded citation is additionally winding up more generally acknowledged globally. Up to this point, there were numerous restrictions associated with handling aberrant trade rates. Indirect quotation is the place the cost of one unit of outside cash is given in units of nearby money, while roundabout citation is the place the cost of one unit of neighbourhood money is given in units of remote cash (Brigham Ehrhardt 2013). The conversion scale of an outside money is communicated as proportionate to a specific number of units of the household cash. This is typically communicated as the measure of remote cash expected to trade for 1 unit or 100 units of residential money. The more significant the residential cash, the more prominent the measure of remote money it can trade for and the lower the conversion scale. At the point when the local money turns out to be less significant, it can trade for a littler measure of outside cash and the conversion scale drops (Brooke 2016). Under indirect quotation, the ascent and fall of trade rates are straightforwardly identified with the adjustments in estimation of the household money. At the point when the estimation of the household cash rises, the trade rates additionally rise; and when the estimation of the residential money falls, the trade rates fall too. A indirect quotation in the outside trade showcases that communicates the measure of remote cash required to purchase or offer one unit of the residential cash (Cangiano, Curristine Lazare, 2013). An indirect quotation is otherwise called an "amount citation," since it communicates the amount of outside cash required to purchase units of the household money. As such, the local money is the base cash in a backhanded quote, while the remote cash is the counter cash. A indirect quotation is the inverse or complementary of an immediate quote, otherwise called a "value citation," since it communicates the cost of one unit of an outside cash as far as the local money. According to the given problem, the quote in Australia is $0.801, which denotes that 1 AUD is equal to $0.801. Hence, the cost of AUD 250,000 in terms of USD could be computed with the help of the unitary method as follows: AUD 1 = $0.801 AUD 250,000 = $(0.801 x 250,000) = $200,250 Therefore, it could be inferred that the cost of AUD 250,000 would be $200,250. According to the provided question, the bid rate is provided as $1.2772/GBP and the ask rate is provided as $1.2787/GBP. In this scenario, $20,000 has been converted into GBP and then it has been converted back to USD. 1.2772 USD = 1 GBP 1 USD = (1/1.2772) GBP 20,000 USD = (1/1.2772 x 20,000) GBP = 15,659.25 GBP It is assumed that the ask rate is considered for reverting the amount back to USD. In order to convert the above amount back to USD, the following calculation has been made: 1 GBP = 1.2787 USD 15,659.25 GBP = (1.2772 x 15,659.25) USD = 20,023.48 USD In this case, the aim is to earn $1,750 on a round trip transaction by buying at bid rate and selling at the ask rate. From the above calculation, it has been found that a profit of $23.48 has been earned by conversion of 15,659.25 GBP. 23.48 USD = 15,659.25 GBP 1 USD = (15,659.25/ 23.48) GBP 1,750 USD = (15,659.25/23.48 X 1,750) GBP = 1,167,107.44 GBP In this case, the ask rate is considered to find out the amount of USD needed to generate 1,750 USD. Therefore, the amount of USD to be raised is calculated as follows: 1 GBP = 1.2787 USD 1,167,107.44 GBP = (1.2787 x 1,167,107.44) USD = 1,492,380.55 USD The inference of residential money in remote trade showcase is a critical instrument within national bank's toolbox along with maintaining key thought while setting financial strategy. Through implication, in this way, cash levels impacts several financial factors (Cavusgil et al. 2014). It can be deemed that financing cost paid within home loan, the profits on speculation portfolio along with basic needs cost in your nearby general store along with maitaining employment prospects. Cash variances are results of drifting conversion scale framework, which is standard for real economies. Swapping scale of money is deemed to be affected by various key and specialized variables. As these variables are largely in a condition of unending motion, money esteems change starting with one minute then onto the next. In any case, in spite of the fact that a cash's level is to a great extent expected to be controlled by the hidden economy, the tables are frequently turned, as gigantic developments in a money can manage the economy's fortunes. The outside trade showcase is usually known as FOREX, an overall system, which empowers the trades the world over. The accompanying are the principle elements of outside trade showcase, which are really the result of its working: Exchange Function: The essential and most obvious capability of outside trade indicates is the asset exchanges (remote cash) that initiates from a nation then settlement of instalments (Deresky, 2017). It essentially incorporates transformation of cash, in which an aspect of Starting with for exchanging acquiring power that initiates with a nation and ends with other. For instance, India import merchandise from the USA and instalment in dollars, while transformation of rupee to dollar can be supported by FOREX (Dudin et al. 2015). Credit Function: FOREX offers transient credit to shippers for encouraging smooth merchandise stream and ventures from nation to nation. A shipper might use credit for supporting remote buys. For instance, an Indian organization requires purchasing apparatus from USA, might purchase by issuing a trade bill in remote trade platform, with development of three months. Forex Market Participants Customers and Travellers: Buyers may buy merchandise in a remote nation or through web with charge card. The customers pay remote money might be changed over to their home cash on financial record. Voyagers must visit the bank or money trade agency to change with cash (their "home" money) into another ("goal" cash) at the time of using money to pay products and enterprises within the country. Voyagers must understand rates to guarantee they attain reasonable arrangement (Jindrichovska, 2013). Organizations: Organizations frequently must change over monetary standards when they direct exchange from outskirts the country. Huge companies must alter over tremendous measures of money; a multinational organization. This is for instance; General Electric (GE) for example, changes with several billions of dollars all through the years. Financial specialists and Speculators: Financial specialists and examiners require money trade at whatever point they bargain in any outside venture, be it values, securities, bank stores, or land. Financial specialists and theorists additionally exchange monetary standards trying to profit by developments in the cash trade markets (Jung 2017). An extremely short record of certain vital sorts of exchanges led in the outside trade advertises is given underneath. Spot Market: The term spot trade alludes to the class of remote trade exchange, which requires the quick conveyance, or trade of monetary forms on the spot. Practically speaking the settlement happens inside two days in many markets. The rate of trade successful for the spot exchange is known as the spot rate and the market for such exchanges is known as the spot display (Phan, Mascitelli Barut 2014). The forward exchanges is an assertion between two gatherings, requiring the conveyance at some predefined future date of a predetermined measure of outside cash by one of the gatherings, against instalment in residential money be the other party, at the cost settled upon in the agreement. The rate of trade pertinent to the forward contract is known as the forward swapping scale and the market for forward exchanges is known as the forward market (Knights Tinker 2016). The outside trade controls of different nations for the most part manage the forward trade exchanges with a view to checking hypothesis in the remote trades advertise. For instance, business banks are allowed to offer forward cover just concerning real fare and import exchanges. Forward trade offices, clearly, are of gigantic help to exporters and merchants as they can cover the dangers emerging out of swapping scale changes are going into a suitable forward trade contract. With reference to its association with spot rate, the forward rate might be at standard, markdown or premium. In the event that the forward conversion scale cited is correct proportional to the spot rate at the season of making the agreement the forward swapping scale is said to be at standard (Madura, 2015). The forward rate for a cash, say the dollar, is said to be at premium concerning the spot rate when one dollar purchases more units of another money, say rupee, in the forward than in the spot rate on a for e ach annum premise. The forward rate for a cash, say the dollar, is said to be at markdown as for the spot rate when one dollar purchases less rupees in the forward than in the spot showcase. The markdown is likewise generally communicated as a rate deviation from the spot rate on a for every annum premise (Petty et al. 2015). The forward swapping scale is resolved for the most part be the interest for and supply of forward trade. Normally when the interest for forward trade surpasses its supply, the forward rate will be cited at a premium and then again, when the supply of forward trade surpasses the interest for it, the rate will be cited at markdown (McKinney 2015). At the point when the supply is identical to the interest for forward trade, the forward rate will have a tendency to be at standard. While a concentration contract is like a forward contract, there are a few contrasts between them. While a forward contract is carefully fit for the customer be his universal bank, a future contract has institutionalized elements the agreement size and development dates are institutionalized. Prospects taxicab exchanged just on a sorted out trade and they are exchanged aggressively. Edges are not required in regard of a forward contract but rather edges are expected of all members in the fates showcase an underlying edge must be stored into a security record to build up a prospects position (Brooke 2016). While the forward or prospects contract ensures the buyer of the agreement fro m the unfavorable swapping scale developments, it takes out the likelihood of picking up a benefit from positive conversion scale development. A choice is an agreement or money related instrument that gives holder the privilege, yet not the commitment, to offer or purchase a given amount of a benefit as a predefined cost at a predetermined future date (Brooke 2016). An alternative to purchase the fundamental resource is known as a call choice and a choice to offer the basic resource is known as a put choice. Purchasing or offering the fundamental resource through the alternative is known as practicing the choice. The expressed cost paid (or got) is known as the activity or striking cost. The purchaser of an alternative is known as the long and the merchant of a choice is known as the essayist of the choice, or the short. The cost for the alternative is known as premium (Brooke 2016). Types of options: With reference to their activity qualities, there are two sorts of choices, American and European. A European alternative taxi is practiced just at the development or lapse date of the agreement, while an American choice can be practiced whenever amid the agreement. Internationalization is an extremely vital and key choice that an organization takes in its lifetime. Certain essentials should be met before a firm can consider nationalizing and turning into a MNC. The first is high nation engaging quality. The nation ought to have the capacity to offer something that will guarantee an upper hand for the organization or something that can enable the organization to manage its current upper hand (Avdjiev, McCauley Shin 2016). Another essential is the responsibility for capabilities. The organization ought to have a few skills that will enable it to offset the incognizance of remote markets and natural conditions. Likewise, the organization ought to have some hierarchical abilities that will expand the ROI by utilizing the organization's key qualities seriously. These three requirements are basic for choosing the method of internationalization and the method of nation section that will enable the organization to contend in world business. There are numerous techniques embraced by organizations to internationalize and overcome remote markets. The most punctual strategy utilized by firms in their procedure of getting to be MNEs was fares and imports. This may incorporate both stock fares and imports and administration fares and imports. Administration fares and imports might be tourism and transportation, benefit execution and resource utilize. A few administrations acquire instalment for the organizations for the execution of those administrations (Avdjiev, McCauley Shin 2016). For instance, the organizations may pay expenses for turnkey ventures, which are exchanged, to the proprietor once they are operational. Administration contracts likewise acquire the organizations charges for the execution of general and concentrated administration capacities for another. Resource utilize incorporates Licensing, Franchising, and so forth. Authorizing is the way toward enabling another organization to utilize its elusive resourc es like licenses, trademarks, copyrights, or mastery, under contracts known as permitting understandings for which they win sovereignties. Diversifying is the procedure of business in which an organization allows another organization to utilize the trademark as an advantage of the franchisee's business. The franchisor will help the franchisee by providing crude materials, administration administrations and so forth and furthermore will set down rules and gauges that are to be trailed by the franchisee (Cangiano, Curristine Lazare, 2013). The companies might face hurdles in becoming in being multinationals: One of the best authoritative favourable circumstances is mark acknowledgment, which at worldwide levels of business is much esteemed. The organization can spread risks through multinationals. On the off chance that the economy is moderate or request is dropping in one nation, odds are it will be flourishing in another One reason might be to rival bigger organizations and perhaps to get economies of scale. The market for some items if winding up increasingly worldwide particularly with the web thus it is another motivation to multinational organization to survive. The measure of the market serves as multinationals there might be 1 million out of 60 million in the UK who need your item, where as there are billions on the planet thus your market size would increment thus would deal. A firm ends up plainly multinational just when nationals of at least two nations successfully claim the head quarter or parent organization. The idea of acquiring power equality (PPP) has two applications: it was initially created as a hypothesis of swapping scale assurance; however, it is presently principally used to look at expectations for everyday comforts crosswise over nations. From the point of view of swapping scale assurance, PPP is helpful as an update that fiscal arrangement has no long-run affect on the genuine trade rate (Cangiano, Curristine Lazare, 2013). In this way, nations with various swelling rates ought to expect their reciprocal conversion standard to alter to counterbalance these differentials over the long haul. The swapping scale, nevertheless, can veer off steadily from its PPP esteem in light of genuine stuns. To look at expectations for everyday comforts crosswise over nations, PPP trade rates are built by looking at the national costs for a huge wicker bin of merchandise and administrations. These rates are utilized to decipher extraordinary monetary forms into typical money to quantify the obtaining energy of per capita salary in various nations. A PPP swapping scale built in this way is not, be that as it may, a precise measure of the balance estimation of the market-decided swapping scale. Absolute obtaining power equality is a type talked about in A Beginner's Guide to Purchasing Power Parity Theory (PPP Theory) (Brigham Ehrhardt 2013). In particular, it infers that "a heap of products should cost the same in Canada and the United States once you consider the swapping scale". Any differences from same (if products is not that expensive in Canada in comparison to United States), at that point it is ought to expect relative costs and the swapping scale between two nations to move in directions at bushel of merchandise have a similar cost in nations. The thought is communicated in properly within Purchasing Power Parity Theory (PPP Theory) (Allen, Hemming Potter 2013). Relative PPP portrays is in comparison with expansion rates in the nations. In particular, assume swelling rate in Canada is higher in comparison to US, causing cost of a wicker container of products in Canada (Brigham Ehrhardt 2013). Acquiring power equality requires the crate be a similar cost in every nation and this infers Canadian is decreased in comparison to U.S. dollar. The rate change is analysis of the cash should then equal to expansion rates among two nations. The Big Mac Index is distributed by The Economist as a casual method for measuring the buying power equality (PPP) between two monetary forms and gives a trial of the degree to which showcase trade rates result in products costing the same in various nations. References: Allen, R., Hemming, R., Potter, B. (Eds.). (2013).The international handbook of public financial management. Springer. Avdjiev, S., McCauley, R. N., Shin, H. S. (2016). Breaking free of the triple coincidence in international finance.Economic Policy,31(87), 409-451. Brigham, E. F., Ehrhardt, M. C. (2013).Financial management: Theory practice. Cengage Learning. Brooke, M. Z. (2016).Handbook of international financial management. Springer. Cangiano, M. M., Curristine, M. T. R., Lazare, M. M. (2013).Public financial management and its emerging architecture. International Monetary Fund. Cavusgil, S. T., Knight, G., Riesenberger, J. R., Rammal, H. G., Rose, E. L. (2014).International business. Pearson Australia. Cremers, M., Ferreira, M. A., Matos, P., Starks, L. (2016). Indexing and active fund management: International evidence.Journal of Financial Economics,120(3), 539-560. Deresky, H. (2017).International management: Managing across borders and cultures. Pearson Education India. Dudin, M. N., Prokofev, M. N., Fedorova, I. J. E., Frygin, A. V., Kucuri, G. N. (2015). International Practice of Generation of the National Budget Income on the Basis of the Generally Accepted Financial Reporting Standards (IFRS). Jindrichovska, I. (2013). Financial management in SMEs.European Research Studies,16(4), 79. Jung, C. (2017). Public 6 finance and financial management.Public Administration and Policy in Korea: Its Evolution and Challenges, 118. Knights, D., Tinker, T. (Eds.). (2016).Financial institutions and social transformations: International studies of a sector. Springer. Madura, J. (2015).International Financial Management, Abridged. Cengage Learning. McKinney, J. B. (2015).Effective financial management in public and nonprofit agencies. ABC-CLIO. Petty, J. W., Titman, S., Keown, A. J., Martin, P., Martin, J. D., Burrow, M. (2015).Financial management: Principles and applications. Pearson Higher Education AU. Phan, D. H. T., Mascitelli, B., Barut, M. (2014). Perceptions towards international financial reporting standards (IFRS): The case of Vietnam.