How Airline Companies can be corporate social responsible and be profitable

Question Help Essays

Question Help Essays Question Help Essay Question Help Essay 1)The Seattle Corporation has been presented with an investment opportunity that will yield cash flows of $30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year 10. This investment will cost the firm $150,000 today, and the firm’s cost of capital is 10 percent. What is the payback period for this investment? Payback period Using the even cash flow distribution assumption, the project will completely recover the initial investment after $30/$35 = 0. 86 of Year 5: Payback = 4 + = 4. 86 years. )As the director of capital budgeting for Denver Corporation, you are evaluating two mutually exclusive projects with the following net cash flows: Project X Project Z Year Cash Flow Cash Flow 0 -$100,000 -$100,000 1 50,000 10,000 2 40,000 30,000 3 30,000 40,000 4 10,000 60,000 If Denver’s cost of capital is 15 percent, which project would you choose? NPV Numerical solution: Financial calculator solution (in thousands ): Project X: Inputs: CF0 = -100; CF1 = 50; CF2 = 40; CF3 = 30; CF4 = 10; I = 15. Output: NPVX = -0. 833 = -$833. Project Z: Inputs: CF0 = -100; CF1 = 10; CF2 = 30; CF3 = 40; CF4 = 60; I = 15. Output: NPVZ = -8. 014 = -$8,014. At a cost of capital of 15%, both projects have negative NPVs and, thus, both would be rejected. 3)The capital budgeting director of Sparrow Corporation is evaluating a project that costs $200,000, is expected to last for 10 years and produce after-tax cash flows, including depreciation, of $44,503 per year. If the firm’s cost of capital is 14 percent and its tax rate is 40 percent, what is the project’s IRR? IRR Financial calculator solution: Inputs: CF0 = -200000; CF1 = 44503; Nj = 10. Output: IRR = 18%. 4)St. John’s Paper is considering purchasing equipment today that has a depreciable cost of $1 million. The equipment will be depreciated on a MACRS 5-year basis, which implies the following depreciation schedule: MACRS Depreciation Year Rates 1 0. 20 2 0. 32 3 0. 19 4 0. 12 5 0. 11 6 0. 06 Assume that the company sells the equipment after three years for $400,000 and the company’s tax rate is 40 percent. What would be the tax consequences resulting from the sale of the equipment? Taxes on gain on sale When the machine is sold the total accumulated depreciation on it is: (0. 20 + 0. 32 + 0. 19) ? $1,000,000 = $710,000. The book value of the equipment is: $1,000,000 $710,000 = $290,000. The machine is sold for $400,000, so the gain is $400,000 $290,000 = $110,000. Taxes are calculated as $110,000 ? 0. 4 = $44,000. 5)Ellison Products is considering a new project that develops a new laundry detergent, WOW. The company has estimated that the project’s NPV is $3 million, but this does not consider that the new laundry detergent will reduce the revenues received on its existing laundry detergent products. Specifically, the company estimates that if it develops WOW the company will lose $500,000 in after-tax cash flows during each of the next 10 years because of the cannibalization of its existing products. Ellison’s WACC is 10 percent. What is the net present value (NPV) of undertaking WOW after considering externalities? NPV with externalities Step 1:Calculate the NPV of the negative externalities due to the cannibalization of existing projects: Enter the following input data in the calculator: CF0 = 0; CF1-10 = -500000; I = 10; and then solve for NPV = $3,072,283. 5. Step 2:Recalculate the new project’s NPV after considering externalities: +$3,000,000 $3,072,283. 55 = -$72,283. 55. 6)If one Swiss franc can purchase $0. 71 U. S. dollar, how many Swiss francs can one U. S. dollar buy? Exchange rates Dollars should sell for 1/0. 71, or 1. 41 Swiss francs per dollar. 7)Currently, in the spot market $1 = 106. 45 Japanese yen, 1 Japanese yen = 0. 00966 euro, and 1 euro = 9. 0606 Mexican pesos. What is the exchange rate between the U. S. dollar and the Mexican peso? Exchange rates Find the $ to peso rate: 106. 45 ? 0. 00966 ? 9. 0606 = 9. 3171. $1. 00 = 9. 3171 pesos. 8)A telephone costs $50 in the United States. Today, in the currency markets you observe the following exchange rates: 1 U. S. dollar = 1. 0279 euros 1 euro = 8. 1794 Norwegian krones Assume that the currency markets are efficient and that purchasing power parity holds worldwide. What should be the price of the same telephone in Norway? Purchasing power parity The cost of the telephone in Norway is 50 ? 1. 0279 ? 8. 1794 = 420. 3803 Norwegian krones.

Neoliberal Transition in Latin America Essay Example | Topics and Well Written Essays - 3000 words

Neoliberal Transition in Latin America - Essay Example Economic integration between countries will be examined to see if any neo-liberalism is taking place within the regions of Latin American countries. Discussion includes analysis of manufacturing products and those based on renewable resources mainly in relation to regional development in Chile and the growth of non-traditional exports and labor markets. The paper first examines the origins and thought processes of neo-liberalism. Neo-liberalism maintains people act according to self-interest and that markets yield the most efficient outcome by free trade balances within liberalized capital markets with minimal government intervention in the economy. Karl Marx developed the theory that under capitalism, technical and distributional changes tend to follow specific patterns of evolution. This course of changes coalesces the expansion of output, capital, and employment. (Other mitigating factors include the rise of labor productivity, the real wage, and the capital-to-labor ratio.) Further in the evolution lies difficulty to sustain the progress of labor productivity without resorting to increased amounts of capital investment. The decline of the profit rate creates the conditions for large crises resulting in recessions and unemployment. (These movements and tendencies occur at declining rates of variation (Dumenil & Levy, 2004). Marxist economics is deeply rooted in many Latin countries  and enjoy a strong historical foundation; however, â€Å"with the rise of the Cold War and the increasing United States’ hostility toward  anything remotely progressive, the left in Latin America was first, mildly, and then severely repressed. The list of casualties includes The Arbenz regime in Guatemala; Goulart in Brazil; Allende in Chile and democracy in Uruguay and Argentina† (Noble & Weinstein, 2005).   

What causes inflation Essay Example | Topics and Well Written Essays - 1500 words

What causes inflation - Essay Example It will also look at some of the ways that an individual is able to calculate the inflation rate in an economy. However, the paper will not only focus on the negative side of matters and in conclusion it will also determine what solutions have been brought about on how the economy can avoid such a situation. Introduction Inflation can be described as the increase in the price level of various services and goods within an economy that takes place over a period of time. It should be noted that this increase happens in all sectors of the market meaning that almost goods and services suffer as a result and those in the economy end with a rising expenditure for the same things that they used to buy before (Taylor 89). It may not be very noticeable at first as it is a gradual process and prices do not sky rocket on the first day meaning that many individuals are usually caught off their guard by the situation leading to a financial panic as they realize just what exactly is going on. As a result of inflation, money also loses a fair amount of purchasing power meaning that an individual is able to buy less with a certain amount that before was adequate for his expenditure needs (Svensson 148). Loss of purchasing power of a currency is not good for the economy as this serves to lower the value of a currency as a whole in the end. It is due to this fact that individuals and institutions struggle against any signs of inflation in a bid to avoid from taking place and stopping it in its tracks as early as possible, the sooner the better (Taylor 101). Though inflation is viewed mostly as a negative impact on the economy, it should be noted that there are both positive and negative effects that are associated with this occurrence. Measures of Inflation One is able to identify the onset of inflation in an economy by measuring the inflation rate of that economy. Though there are a number of other ways in which measuring can be done, this is the main method that is used by econ omists on a global scale. Measuring the inflation rate is done by taking note of the yearly change in percentage terms of a price index over a period of time (Abel & Bernanke 93). The price index that is mostly used for these purposes is the consumer index though other can be used as well. The consumer price index is determined by measuring the prices of a selection of various goods and services that are usually bought by the average consumer and include items that may be needed on a daily basis such as foodstuffs and other supplies (Baumol & Blinder 25). High end items are not included in this collection of goods and services as they are first o f all not bought by the typical consumer and second of all not purchased on a regular basis thus they would reflect dishonestly on the final figure that is obtained in the end. Apart from the consumer price index, other indices that are also used to obtain the level of inflation in an economy also include the producer price index. This inde x concentrates on the producers rather than the consumers and determines the amount of money that domestic producers receive for their products over time determining the changes calculated in percentage in the process (Abel & Bernanke 98). The difference between this and the Consumer Price Index is mainly due to issues such as taxes and the intention of profit that will make the

Skills and Experiences Acquired In the Past 12 Months Lab Report

Skills and Experiences Acquired In the Past 12 Months - Lab Report Example Likewise, in the mastering my new language skills, I listened to the podcast as it enabled me to develop a positive feeling for the language in question while also allowing me to learn more and more words. The use of such devices like the podcast enabled me to understand how different sentences are put together hence enabled me to learn my new language skills just like a baby learns to talk a mother’s language (Dyer, Gregersen & Christensen, 2011). Through my inquiry for innovation networks, I found it important since it is like to develop skills for discipline because fostering innovation skills in any area is greatly dependent on the disciplines taught. This will include having the grasp of technical skills, skills in thinking and creativity, behavioral and socials skills. Likewise, through the inquiry, I would like to develop skills in pedagogies which will constitute problem-based learning at the site, cooperative learning, and meta-cognitive learning. This will be tremendously essential to me because it will enable me to focus on different aspects of innovation like design thinking amongst others. In addition, throughout the inquiry, I would like to attain the skills of assessment in order for me to develop and assess various creativity aspects and other habits of the mind related to innovation. Lastly, I would like to develop the skills for international mobility through the inquiry because it will be crucial in enabling me foster skills I have acquired from different sources to match those of the globalized economy (Kuhlthau, Caspari, & Maniotes, 2007). My contribution in the learning process towards innovation networks would be placing myself at the center of what happens in all situations. This will enable me to achieve both cognition and growth as I will be self-regulated hence able to control my mind and emotions to  set various realistic goals and monitor my progress throughout the process.  

Analysis Of Three Theories Soft Hard And Indeterminism Philosophy Essay

Analysis Of Three Theories Soft Hard And Indeterminism Philosophy Essay I am going to compare and analyze the three theories; Soft, hard and indeterminism. I will demonstrate what consequences they have on freewill as well if the universe entire history is predetermined. Strong determinism is the theory that states that every single thing that happens in the universe is determined and governed by the natural law. For example, how earth moves, what movie you chose to see in the cinema. A strong determinist strictly believes that nothing could influence this behavior, in other words our choice or free will does not exist, not even luck. This theory is the strongest theory that supports determinism; this affects freewill very badly, since hard determinism does not believe in free will. This is problematic since how can we have free will if everything is determined and if it is true, would it not create ethical consequences if we have no free will? One might argue that if determinism was true then how can we blame a person who robs a bank? If the universe de termines that he is bound to do that, then he does not have any free will which means we cannot really blame him? There is no right or wrong, nor good or evil if everything is predetermined, this shows the flaws of determinism as a consequence. If determinism may be real, then we are no freer than robots, and since there is no evil or good there is no reason to reward or punish someone. Since this theory rejects ethics, morals and completely disagrees with free will a new concept was created, which is called Soft Determinism. This theory states that determinism is correct; however it tries to make determinism and moral and ethics (and free will) compatible. Since soft determinism believes that everything is determined, it does not believe that our actions are acted freely. Soft determinism in contrast to Hard determinism believes that an action can be voluntary, in other words for something to occur it does not necessarily mean that it cannot have any freedom of choice. One argument may say if I was about to give money to a poor person out of good will and freedom (choice) and then he turned on me with a gun, then it would not mean it would be freedom or soft determinism since I will be forced to do it. An argument would be if a robber were to rob a bank, the soft determinist does not think that his action was caused because he was not free, he did it voluntarily. This theory states that free will is voluntary actions. A hard determinist would argue that this act cannot be free, it must occur. But then again why would the robber rob a bank without any reason? Indeterminism is the theory that states that most events and decisions are occurred by pure chance. In other words, they just happen and have nothing to do with having a determined behavior. They believe that every event is not predictable and this opens a way for us to influence the future and by this we can act freely and have morally responsibilities. The flaw in indeterminism is that if everything happens by chance then free will is unpredictable and happens randomly which cannot hold the person responsible for his choices since he cannot predict when or what will occur. If determinism was true, then it would have several of consequences for free will. Since if we have a determined cause for every action we imply, then our behavior is much like a robot. Since robots do not have any free will and if determinism was true then we people would not either have free will. So by removing all the responsibilities a person have since he cannot control what he is doing, would mean that if someone committed a crime they cannot be blamed since they did not have any freewill. An incompatibilist would argue that if determinism was true then there is no chance of having a free will. Another argument is that soft determinism states that freewill is voluntarily actions, but then again it cannot be free will if our causes are based upon voluntary actions since you are not the first causer. In order to have free will we need to be the first person that causes the choice he makes, so in other words if determinism was true, then we do not cause our choices but that every thing that happens are caused by events and the natural law which he cannot control. Therefore he cannot have freewill since he is not the primary cause of the choices he makes. Finally we come to the question, can we escape the conclusion that the entire history of the universe follows a predetermined path? Well I believe that we cannot escape the conclusion, since I think that the universe cannot come from nothing, and the path its heading is predetermined. I see that everything consisted in the universe is similar to a giant puzzle; if a puzzle bit would act randomly then the puzzle would break. For example, if the atoms in space would act randomly then the end product would not be produced, so every atom needs to have a determined action in order to create things. Just like we have cells in our bodies the immune system is an example, which is consisted of millions of other cells that interacts in a determined way in order to create end products such as; more white cells. That is how I see the universe that our solar system is one cell that exists in trillions of other universes that make up a small piece of the giant puzzle. For example, if my parents ne ver met I would not have existed, so for something to exist there must have been something determine its path. Their genes, education, social life and every factor that have enabled them to meet each other is a direct result of how they met, meaning that the end product is that his was meant to happen. But then, if the future is predetermined then why am I not acting randomly such as deleting everything Ive written so far, draw a huge smile face and send it to MR Hemingway? Well if I was to change the future of my philosophical grade, it would be a direct result of how I am as a person in other words it was meant to happen anyway. The best way for me to think is comparing the universe is with a song, if I pause the song just in the middle I have just heard the past but I know that there is a future that is already determined in that song but it is still unknown, but I can clearly hear that the future is based on the past and this is why I believe that the university is predetermined , and I also believe that in the future we will be able to time travel, just because of this. In conclusion hard determinism denies freedom and believes that everything is determined compared to soft determinism where it still believe that everything is determined however even though our actions are voluntarily. Indeterminism believes that things could happen randomly. All these theories give a consequence to free will, since if determinism was true we would be robots that have no free will at all, we would be people with choices that we cannot decide freely. http://en.wikipedia.org/wiki/Free_will http://plato.stanford.edu/entries/incompatibilism-arguments/#ChoConArg http://www.enotes.com/topic/Indeterminism http://www.lancs.ac.uk/users/philosophy/courses/100/100kant.htm http://www.ucl.ac.uk/~uctytho/dfwVariousKant.htm http://philosophy.tamu.edu/~sdaniel/Notes/freedom1.htm http://www.degree-essays.com/coursework/philosophy-essays/compare-and-contrast-soft-and-hard-determinism-in-respect-to-competing-notion-of-negative-and-positive-freedom/ http://www.blackwellreference.com/public/tocnode?id=g9781405106795_chunk_g97814051067955_ss1-85 http://www.scandalon.co.uk/philosophy/soft.htm http://instruct.westvalley.edu/lafave/FREE.HTM

Ovids Devaluation of Sympathy in Metamorphoses Essay -- Ovid Metamorp

Ovid's Devaluation of Sympathy in Metamorphoses  Ã‚        Ã‚  Ã‚   Ovid reveals two similar tales of incest in the Metamorphoses. First, he describes the non-sisterly love Byblis acquires for her twin brother Caunus. Later, he revisits the incestuous love theme with the story of Myrrha who develops a non-filial love for her father, Cinyras. The two accounts hold many similarities and elicit varying reactions. Ovid constantly tugs at our emotions and draws forth alternating feelings of pity and disgust for the matters at hand. "Repetition with a difference" in these two narratives shows how fickle we can be in allotting and denying sympathy, making it seem less valuable. Both tales begin drawing forth a sense of disgust for the situation in general yet arousing pity for each girl's predicament. Ovid clearly labels the love Byblis and Myrrha pursue illegitimate when he summarizes the moral of Byblis' tale stating, "when girls love they should love lawfully" (Mandelbaum 307) and reveals that "to hate a father is / a crime, but love like [Myrrha's] is worse than hate" (338) before describing Myrrha's tale. By presenting the girls as criminals, Ovid leads us to despise them. He then proceeds to draw out sympathy for Byblis and Myrrha as he describes their unsuccessful attempts to overcome these desires. Byblis dreams intimately about Caunus, but "when she's awake, she does not dare / to let her obscene hopes invade her soul" (308). "[Myrrha] strives; she tries; she would subdue / her obscene love," but she cannot (339). Right away, Ovid makes us question if these situations deserve our sympathy. Byblis and Myrrha compel readers to sympathize with their plight as they orally confess their incestuous passions. They use selective lang... ...d leaves us feeling sorry for Myrrha. Ovid tells this tale of forbidden sin twice to show how inconsistent we are in allotting pity. He begins both tales drawing forth our contempt for the matters at hand, then ends both tales with images that arouse our pity. Throughout each story, our emotions sway between pity and disgust. Even though incest disgusts us, we sympathize with Byblis and Myrrha as they seek incestuous loves. Byblis' broken heart arouses our sympathy, yet Myrrha's "fulfilled heart" disgusts us. Ovid devalues our sympathy by showing how unstable we are with our emotions. Works Cited Mandelbaum, Allen, trans. The Metamorphoses of Ovid. By Ovid. San Diego: Harcourt Brace & company, 1993. Crane, Gregory, ed. Perseus Project. 1995. Tufts University. 6 Oct. 1999 <http://www.perseus.tufts.edu/cgi-bin/text?lookup=ov.+met.+init>      

Learning from the Past

Learning about the past Learning about the past has no value for those of us living in the present. Do you agree or disagree? Use specific reasons and examples to support your answer. There are several views from the people, whether important or not for us keep memorizing the thing that had happened in the past and then try to put on ours life now. For this topic, I would like to discuss about the positive and negative impacts that we can get from that. First of all, there are some proverbs said, the bad experiences are the best teacher that can bring us to live more better in the present or future. For instance, when the first time we learned how to drive a car, probably we might have gotten accident because of lack experiences, but by the time we had already used to it, we will able to drive with easily and pretty sure we know how to handle the car even though the road is treacherous. In addition, learning about the past can make us more efficient either in time or money. Moreover, we can give a good impacts to other people too. In general, the child will always follow in his/her parents behavior during the process of maturity. However, there are also some adverse results that we can get if we still stick with something in the past. People who had ever committed with drugs, they should try to forget it. Otherwise, they will never move on. In my opinion, I agree that learning about something in the past can bring us some value, success will not come without failure, especially old history, that can make our next generation become appreciate about their ancestors and interest to know the history of the world.

Argumentative Essay Sample on Euthanasia

Argumentative Essay Sample on Euthanasia â€Å"If we are to have free will, that free will should include not only how we live our lives, but how long we live them† (Taylor 2003, 30). Euthanasia, the specific term for assisted suicide, has been a century old controversy (Clarfield 2003, 38). Its leader in the controversy is Dr. Jack Kevorkian, who has assisted in over 30 deaths since 1990. Dr. Kevorkian claims that the medical, religious, journalistic and legal communities won’t stop him. Psychologist Joseph Richman says that, â€Å"All suicides, including the â€Å"rational,† can be an avoidance of or substitute for dealing with basic life-and-death issues.† So which is right, helping dying people to achieve their last wish, or waiting for God to do his part while the ill sit there and die slowly and painfully? Euthanasia should be legalized in the United States. Hearing the negatives about euthanasia, the U.S. citizens need to also hear the good points of the topic. The question of who has the right to give or take life has played an important part in the history of technology, with designer babies and altering DNA. But it also contributes to the challenging question of who should be able to take another’s life as in physician’s aide, or euthanasia (Clarfield 2003, 38). In 1972, the Dutch Council of Health did their own study and decided that euthanasia should be legal. They stated that doctors needed to follow rules and regulations to assist with death (Clarfield 2003, 38). Rob Jonquiere states that, â€Å"These reactions are often very hypocritical. Doctors all over the world perform euthanasia, but they don’t report it.† (Kolfschooten 2003, 1352) So even if euthanasia is not legalized, doctors may continue to perform the procedure. So why not legalize euthanasia anyway! â€Å"If your life is yours, then it is no one else’s business if you choose to discontinue having experiences† (Flynn 2003, 25). Then the moral issue comes in. Do individuals lives belong to God? Religious leaders will argue that God had control over everyone’s life until death, and physicians shouldn’t take that into their own hands. Although the conflict of euthanasia seems new, the actual procedure has been around since World War I (Clarfield 2003, 38). It became a strong issue in the 1920’s and 30’s, growing again in the 60’s and 70’s (Clarfield 2003, 38). New laws are still occurring, the last one updated by Dutch euthanasia describes new regulations on April first 2002 (Kolfschooten 2003, 1352). Many supporters of euthanasia also advocated sterilization laws (Payne 2003, 57). But are the supporters agreeing with euthanasia because of their feelings towards the ill? Seventy to eighty percent of people polled that they felt sympathetic towards the terminally ill (Payne 2003, 57). Even if this happens to be true, euthanasia still was morally acceptable in their view s. Just like divorce, marrying outside of a persons’ racial class, and issues dealing with social classes, euthanasia shall overcome obstacles of moral, ethical, and political views with time. People just need to realize that keeping someone alive against their will, happens to be more morally wrong than giving them what they want and rightfully deserve. Although euthanasia is illegal in the United States and its considered a taboo by most; some examples are shown in the following lines that would like to see physician-aided death prevail (Flynn 2003, 24). Freddie, who after being diagnosed with cancer refused chemotherapy as a treatment for the illness. He went in for surgery and had his bladder removed. A few days later the doctors told him that the surgery was unsuccessful, and the cancer had spread to other organs. Freddie’s first week in the hospital was unbearable, waking up to day after day of pain because of laws against assisted suicide. His had spent the last three weeks in the hospital, the last one of which he spent unconscious, hooked up to machines. With a needle in each arm: one to keep him alive, and the other to keep him asleep safe from the pain (Taylor 2003, 29-30). Sidney Cohen was diagnosed with cancer in November and was told that he would die within three months. By January 1st, Sidney was in pain, and bed-bounded praying for euthanasia. He was allowed only to drink water for six weeks, and became desperate, isolated, and frightened (Arthur 2002, 1). Sidney had no reason to live his life, because in his position his life couldn’t be acceptable. People should be able to decide if their life amounts to a â€Å"life not worthy to be lived,† as Dr. Leo Alexander said that the euthanasia debate started with this question. Alexander said that there would be a rising time of death with dignity movement, or assisted suicide, which Oregon has now legalized (Washington 2002, 1). The law legalizing euthanasia became a landmark law for the Oregon people when they received adequate pain relief (Washington 1991, 1). If the option of euthanasia is not available to some, the ill may take their own life as Carol Ezzell did. She did not qualify for physician aide in Holland. So she took her own life in a needlessly vile way, and her loved ones had no chance to say their last goodbyes. Because of Carol’s many years of anguished sickness and the doctors only promising worse to come, she did not see any other solution to her problem (Flynn 2003, 25). That brings us back to the controversy of should euthanasia be legalized? Yeah, there happen to be ways to live longer for those that are not quite on their deathbed, but it is the patient’s decision if they don’t want to live longer. Is it not? Having so many ways to misuse euthanasia, the United States has not passed a bill to legalize. Most doctors today in the United States that have patients in a comatose state do what their family feels happens to be right or with his or her own discretion. And if that is keeping them asleep until their last minutes of life, most doctors consider what they call terminal sedation, legal in the United States (Kolfschooten 2003, 1352). Physicians the world over administer pain-killing drugs to terminally ill patients that have the effect of killing them. The difference is that we do it openly, says Henk Leenen, lawyer of the medical ethics department (Wright 2003, 1061). Doctors can sneak around the euthanasia debate this way. They call it the administration of a sedative medication to ease pain and agony. Doctors in the Netherlands use terminal sedation to get around having to get a second opinion. Although this technique will help the patient out tremendously it is proved that the sleep inducing drugs ends lives early (Kolfschooten 2003, 1352). Using euthanasia properly in the United States, there needs to be a system of rule that is followed religiously. The Netherlands adopted the first laws that allowed euthanasia to be legal. The Dutch euthanasia regulations were set into law on April first of 2002 and Henk Leenen says that all it needs to do to stay legal is follow the guidelines that the Dutch Medical Society introduced, while Europe allows the issue (Wright 2003, 1061). The rules and regulations have to be followed in order to qualify for the procedure in the Netherlands; the rules include these four regulations: (1) that the patient would have to be 21 years of age or older (2) to be of sound mind (3) to be suffering from severe physical pain (4) and to have an incurable ailment (Clarfield 2003, 38). Although the ESA (Euthanasia Society of America) proposed a bill in the United States that would make the patient have to petition the courts and other doctors would have to examine the patient for the treatment before euthanasia to be performed, however the bill did not pass (Clarfield 2003, 38). The United States should come up with rules like the Netherlands did, or just use regulations that they came up with. US doctors or doctors in general are not hanging over the bedside of these ill people trying to save money for the hospital or for the persons’ family (Payne 2003, 57). I think that Wesley Smith stated it best when he said, â€Å"We all age. We fall ill. We grow weak. We become disabled. A day comes when our need to receive from our fellows adds to far more than our ability to give in return. When we reach that stage of life†¦will we still be deemed persons entitled to equal protection under the law?† I certainly hope so. When I get old I want to have the right to choose to end my life. I want my rights that were guaranteed to me in the United States Constitution about my personal freedom. I would like to be able to do what I please without the government running my life. I thought that happens to be what a capitalism government is all about. Being to do what you want, when you want to, without some official questioning your sanity. You can order a custom essay, term paper, research paper, thesis or dissertation on Euthanasia topics at our professional custom essay writing service which provides students with custom papers written by highly qualified academic writers. High quality and no plagiarism guarantee! Get professional essay writing help at an affordable cost.

Complete Guide to Integers on ACT Math (Advanced)

Complete Guide to Integers on ACT Math (Advanced) SAT / ACT Prep Online Guides and Tips Integers, integers, integers (oh, my)! You've already read up on your basic ACT integers and now you're hankering to tackle the heavy hitters of the integer world. Want to know how to (quickly) find a list of prime numbers? Want to know how to manipulate and solve exponent problems? Root problems? Well look no further! This will be your complete guide to advanced ACT integers, including prime numbers, exponents, absolute values, consecutive numbers, and roots- what they mean, as well as how to solve the more difficult integer questions that may show up on the ACT. Typical Integer Questions on the ACT First thing's first- there is, unfortunately, no â€Å"typical† integer question on the ACT. Integers cover such a wide variety of topics that the questions will be numerous and varied. And as such, there can be no clear template for a standard integer question. However, this guide will walk you through several real ACT math examples on each integer topic in order to show you some of the many different kinds of integer questions the ACT may throw at you. As a rule of thumb, you can tell when an ACT question requires you to use your integer techniques and skills when: #1: The question specifically mentions integers (or consecutive integers) It could be a word problem or even a geometry problem, but you will know that your answer must be in whole numbers (integers) when the question asks for one or more integers. (We will go through the process of solving this question later in the guide) #2: The question involves prime numbers A prime number is a specific kind of integer, which we will discuss later in the guide. For now, know that any mention of prime numbers means it is an integer question. A prime number a is squared and then added to a different prime number, b. Which of the following could be the final result? An even number An odd number A positive number I only II only III only I and III only I, II, and III (We'll go through the process of solving this question later in the guide) #3: The question involves multiplying or dividing bases and exponents Exponents will always be a number that is positioned higher than the main (base) number: $4^3$, $(y^5)^2$ You may be asked to find the values of exponents or find the new expression once you have multiplied or divided terms with exponents. (We will go through the process of solving this question later in the guide) #4: The question uses perfect squares or asks you to reduce a root value A root question will always involve the root sign: √ $√36$, $^3√8$ The ACT may ask you to reduce a root, or to find the square root of a perfect square (a number that is equal to an integer squared). You may also need to multiply two or more roots together. We will go through these definitions as well as how all of these processes are done in the section on roots. (We will go through the process of solving this question later in the guide) (Note: A root question with perfect squares may involve fractions. For more information on this concept, look to our guide on fractions and ratios.) #5: The question involves an absolute value equation (with integers) Anything that is an absolute value will be bracketed with absolute value signs which look like this: | | For example: $|-43|$ or $|z + 4|$ (We will go through how to solve this problem later in the guide) Note: there are generally two different kinds of absolute value problems on the ACT- equations and inequalities. About a quarter of the absolute value questions you come across will involve the use of inequalities (represented by or ). If you are unfamiliar with inequalities, check out our guide to ACT inequalities (coming soon!). The majority of absolute value questions on the ACT will involve a written equation, either using integers or variables. These should be fairly straightforward to solve once you learn the ins and outs of absolute values (and keep track of your negative signs!), all of which we will cover below. We will, however, only be covering written absolute value equations in this guide. Absolute value questions with inequalities are covered in our guide to ACT inequalities. We will go through all of these questions and topics throughout this guide in the order of greatest prevalence on the ACT. We promise that your path to advanced integers will not take you a decade or more to get through (looking at you, Odysseus). Exponents Exponent questions will appear on every single ACT, and you'll likely see an exponent question at least twice per test. Whether you're being asked to multiply exponents, divide them, or take one exponent to another, you'll need to know your exponent rules and definitions. An exponent indicates how many times a number (called a â€Å"base†) must be multiplied by itself. So $3^2$ is the same thing as saying 3*3. And $3^4$ is the same thing as saying 3*3*3*3. Here, 3 is the base and 2 and 4 are the exponents. You may also have a base to a negative exponent. This is the same thing as saying: 1 divided by the base to the positive exponent. For example, 4-3 becomes $1/{4^3}$ = $1/64$ But how do you multiply or divide bases and exponents? Never fear! Below are the main exponent rules that will be helpful for you to know for the ACT. Exponent Formulas: Multiplying Numbers with Exponents: $x^a * x^b = x^[a + b]$ (Note: the bases must be the same for this rule to apply) Why is this true? Think about it using real numbers. If you have $3^2 * 3^4$, you have: (3*3)*(3*3*3*3) If you count them, this give you 3 multiplied by itself 6 times, or $3^6$. So $3^2 * 3^4$ = $3^[2 + 4]$ = $3^6$. $x^a*y^a=(xy)^a$ (Note: the exponents must be the same for this rule to apply) Why is this true? Think about it using real numbers. If you have $3^5*2^5$, you have: (3*3*3*3*3)*(2*2*2*2*2) = (3*2)*(3*2)*(3*2)*(3*2)*(3*2) So you have $(3*2)^5$, or $6^5$ If $3^x*4^y=12^x$, what is y in terms of x? ${1/2}x$ x 2x x+2 4x We can see here that the base of the final answer is 12 and $3 *4= 12$. We can also see that the final result, $12^x$, is taken to one of the original exponent values in the equation (x). This means that the exponents must be equal, as only then can you multiply the bases and keep the exponent intact. So our final answer is B, $y = x$ If you were uncertain about your answer, then plug in your own numbers for the variables. Let's say that $x = 2$ $32 * 4y = 122$ $9 * 4y = 144$ $4y = 16$ $y = 2$ Since we said that $x = 2$ and we discovered that $y = 2$, then $x = y$. So again, our answer is B, y = x Dividing Exponents: ${x^a}/{x^b} = x^[a - b]$ (Note: the bases must be the same for this rule to apply) Why is this true? Think about it using real numbers. ${3^6}/{3^4}$ can also be written as: ${(3 * 3 * 3 * 3 * 3 * 3)}/{(3 * 3 * 3 * 3)}$ If you cancel out your bottom 3s, you’re left with (3 * 3), or $3^2$ So ${3^6}/{3^4}$ = $3^[6 - 4]$ = $3^2$ The above $(x * 10^y)$ is called "scientific notation" and is a method of writing either very large numbers or very small ones. You don't need to understand how it works in order to solve this problem, however. Just think of these as any other bases with exponents. We have a certain number of hydrogen molecules and the dimensions of a box. We are looking for the number of molecules per one cubic centimeter, which means we must divide our hydrogen molecules by our volume. So: $${8*10^12}/{4*10^4}$$ Take each component separately. $8/4=2$, so we know our answer is either G or H. Now to complete it, we would say: $10^12/10^4=10^[12−4]=10^8$ Now put the pieces together: $2x10^8$ So our full and final answer is H, there are $2x10^8$ hydrogen molecules per cubic centimeter in the box. Taking Exponents to Exponents: $(x^a)^b=x^[a*b]$ Why is this true? Think about it using real numbers. $(3^2)^4$ can also be written as: (3*3)*(3*3)*(3*3)*(3*3) If you count them, 3 is being multiplied by itself 8 times. So $(3^2)^4$=$3^[2*4]$=$3^8$ $(x^y)3=x^9$, what is the value of y? 2 3 6 10 12 Because exponents taken to exponents are multiplied together, our problem would look like: $y*3=9$ $y=3$ So our final answer is B, 3. Distributing Exponents: $(x/y)^a = x^a/y^a$ Why is this true? Think about it using real numbers. $(3/4)^3$ can be written as $(3/4)(3/4)(3/4)=9/64$ You could also say $3^3/4^3= 9/64$ $(xy)^z=x^z*y^z$ If you are taking a modified base to the power of an exponent, you must distribute that exponent across both the modifier and the base. $(2x)^3$=$2^3*x^3$ In this case, we are distributing our outer exponent across both pieces of the inner term. So: $3^3=27$ And we can see that this is an exponent taken to an exponent problem, so we must multiply our exponents together. $x^[3*3]=x^9$ This means our final answer is E, $27x^9$ And if you're uncertain whether you have found the right answer, you can always test it out using real numbers. Instead of using a variable, x, let us replace it with 2. $(3x^3)^3$ $(3*2^3)^3$ $(3*8)^3$ $24^3$ 13,824 Now test which answer matches 13,824. We'll save ourselves some time by testing E first. $27x^9$ $27*2^9$ $27*512$ 13,824 We have found the same answer, so we know for certain that E must be correct. (Note: when distributing exponents, you may do so with multiplication or division- exponents do not distribute over addition or subtraction. $(x+y)^a$ is not $x^a+y^a$, for example) Special Exponents: It is common for the ACT to ask you what happens when you have an exponent of 0: $x^0=1$ where x is any number except 0 (Why any number but 0? Well 0 to any power other than 0 equals 0, because $0^x=0$. And any other number to the power of 0 = 1. This makes $0^0$ undefined, as it could be both 0 and 1 according to these guidelines.) Solving an Exponent Question: Always remember that you can test out exponent rules with real numbers in the same way that we did in our examples above. If you are presented with $(x^3)^2$ and don’t know whether you are supposed to add or multiply your exponents, replace your x with a real number! $(2^3)^2=(8)^2=64$ Now check if you are supposed to add or multiply your exponents. $2^[2+3]=2^5=32$ $2^[3*2]=2^6=64$ So you know you’re supposed to multiply when exponents are taken to another exponent. This also works if you are given something enormous, like $(x^19)^3$. You don’t have to test it out with $2^19$! Just use smaller numbers like we did above to figure out the rules of exponents. Then, apply your newfound knowledge to the larger problem. And exponents are down for the count. Instant KO! Roots Root questions are fairly common on the ACT, and they go hand-in-hand with exponents. Why are roots related to exponents? Well, technically, roots are fractional exponents. You are likely most familiar with square roots, however, so you may have never heard a root expressed in terms of exponents before. A square root asks the question: "What number needs to be multiplied by itself one time in order to equal the number under the root sign?" So $√81=9$ because 9 must be multiplied by itself one time to equal 81. In other words, $9^2=81$ Another way to write $√{81}$ is to say $^2√{81}$. The 2 at the top of the root sign indicates how many numbers (two numbers, both the same) are being multiplied together to become 81. (Special note: you do not need the 2 on the root sign to indicate that the root is a square root. But you DO need the indicator for anything that is NOT a square root, like cube roots, etc.) This means that $^3√27=3$ because three numbers, all of which are the same (3*3*3), are multiplied together to equal 27. Or $3^3=27$. Fractional Exponents If you have a number to a fractional exponent, it is just another way of asking you for a root. So $4^{1/2}= √4$ To turn a fractional exponent into a root, the denominator becomes the value to which you take the root. But what if you have a number other than 1 in the numerator? $4^{2/3}$=$^3√{4^2}$ The denominator becomes the value to which you take the root, and the numerator becomes the exponent to which you take the number under the root sign. Distributing Roots $√xy=√x*√y$ Just like with exponents, roots can be separated out. So $√30$ = $√2*√15$, $√3*√10$, or $√5*√6$ $√x*2√13=2√39$. What is the value of x? 1 3 9 13 26 We know that we must multiply the numbers under the root signs when root expressions are multiplied together. So: $x*13=39$ $x=3$ This means that our final answer is B, $x=3$ to get our final expression $2√39$ $√x*√y=√xy$ Because they can be separated, roots can also come together. So $√5*√6$ = $√30$ Reducing Roots It is common to encounter a problem with a mixed root, where you have an integer multiplied by a root (for example, $4√3$). Here, $4√3$ is reduced to its simplest form because the number under the root sign, 3, is prime (and therefore has no perfect squares). But let's say you had something like $3√18$ instead. Now, $3√18$ is NOT as reduced as it can be. In order to reduce it, we must find out if there are any perfect squares that factor into 18. If there are, then we can take them out from under the root sign. (Note: if there is more than one perfect square that can factor into your number under the root sign, use the largest one.) 18 has several factor pairs. These are: $1*18$ $2*9$ $3*6$ Well, 9 is a perfect square because $3*3=9$. That means that $√9=3$. This means that we can take 9 out from under the root sign. Why? Because we know that $√{xy}=√x*√y$. So $√{18}=√2*√9$. And $√9=3$. So 9 can come out from under the root sign and be replaced by 3 instead. $√2$ is as reduced as we can make it, since it is a prime number. We are left with $3√2$ as the most reduced form of $√18$ (Note: you can test to see if this is true on most calculators. $√18=4.2426$ and $3*√2=3*1.4142=4.2426$. The two expressions are identical.) We are still not done, however. We wanted to originally change $3√18$ to its most reduced form. So far we have found the most reduced expression of $√18$, so now we must multiply them together. $3√18=3*3√2$ $9√2$ So our final answer is $9√2$, this is the most reduced form of $3√{18}$. You've rooted out your answers, you've gotten to the root of the problem, you've touched up those roots.... Absolute Values Absolute values are quite common on the ACT. You should expect to see at least one question on absolute values per test. An absolute value is a representation of distance along a number line, forward or backwards. This means that an absolute value equation will always have two solutions. It also means that whatever is in the absolute value sign will be positive, as it represents distance along a number line and there is no such thing as a negative distance. An equation $|x+4|=12$, has two solutions: $x=8$ $x=−16$ Why -16? Well $−16+4=−12$ and, because it is an absolute value (and therefore a distance), the final answer becomes positive. So $|−12|=12$ When you are presented with an absolute value, instead of doing the math in your head to find the negative and positive solution, you can instead rewrite the equation into two different equations. When presented with the above equation $|x+4|=12$, take away the absolute value sign and transform it into two equations- one with a positive solution and one with a negative solution. So $|x+4|=12$ becomes: $x+4=12$ AND $x+4=−12$ Solve for x $x=8$ and $x=−16$ Now let's look at our absolute value problem from earlier: As you can see, this absolute value problem is fairly straightforward. Its only potential pitfalls are its parentheses and negatives, so we need to be sure to be careful with them. Solve the problem inside the absolute value sign first and then use the absolute value signs to make our final answer positive. (By process of elimination, we can already get rid of answer choices A and B, as we know that an absolute value cannot be negative.) $|7(−3)+2(4)|$ $|−21+8|$ $|−13|$ We have solved our problem. But we know that −13 is inside an absolute value sign, which means it must be positive. So our final answer is C, 13. Absolutely fabulous absolute values are absolutely solvable. I promise this absolutely. Consecutive Numbers Questions about consecutive numbers may or may not show up on your ACT. If they appear, it will be for a maximum of one question. Regardless, they are still an important concept for you to understand. Consecutive numbers are numbers that go continuously along the number line with a set distance between each number. So an example of positive, consecutive numbers would be: 5, 6, 7, 8, 9 An example of negative, consecutive numbers would be: -9, -8, -7, -6, -5 (Notice how the negative integers go from greatest to least- if you remember the basic guide to ACT integers, this is because of how they lie on the number line in relation to 0) You can write unknown consecutive numbers out algebraically by assigning the first in the series a variable, x, and then continuing the sequence of adding 1 to each additional number. The sum of five positive, consecutive integers is 5. What is the first of these integers? 21 22 23 24 25 If x is our first, unknown, integer in the sequence, so you can write all four numbers as: $x+(x+1)+(x+2)+(x+3)+(x+4)=5$ $5x+10=5$ $5x=105$ $x=21$ So x is our first number in the sequence and $x=21$: This means our final answer is A, the first number in our sequence is 21. (Note: always pay attention to what number they want you to find! If they had asked for the median number in the sequence, you would have had to continue the problem with $x=21$, $x+2=$median, $23=$median.) You may also be asked to find consecutive even or consecutive odd integers. This is the same as consecutive integers, only they are going up every other number instead of every number. This means there is a difference of two units between each number in the sequence instead of 1. An example of positive, consecutive even integers: 10, 12, 14, 16, 18 An example of positive, consecutive odd integers: 17, 19, 21, 23, 25 Both consecutive even or consecutive odd integers can be written out in sequence as: $x,x+2,x+4,x+6$, etc. No matter if the beginning number is even or odd, the numbers in the sequence will always be two units apart. What is the largest number in the sequence of four positive, consecutive odd integers whose sum is 160? 37 39 41 43 45 $x+(x+2)+(x+4)+(x+6)=160$ $4x+12=160$ $4x=148$ $x=37$ So the first number in the sequence is 37. This means the full sequence is: 37, 39, 41, 43 Our final answer is D, the largest number in the sequence is 43 (x+6). When consecutive numbers make all the difference. Remainders Questions involving remainders are rare on the ACT, but they still show up often enough that you should be aware of them. A remainder is the amount left over when two numbers do not divide evenly. If you divide 18 by 6, you will not have any remainder (your remainder will be zero). But if you divide 19 by 6, you will have a remainder of 1, because there is 1 left over. You can think of the division as $19/6 = 3{1/6}$. That extra 1 is left over. Most of you probably haven’t worked with integer remainders since elementary school, as most higher level math classes and questions use decimals to express the remaining amount after a division (for the above example, $19/6 = 3$ remainder 1 or 3.167). But you may still come across the occasional remainder question on the ACT. How many integers between 10 and 40, inclusive, can be divided by 3 with a remainder of zero? 9 10 12 15 18 Now, we know that when a division problem results in a remainder of zero, that means the numbers divide evenly. $9/3 =3$ remainder 0, for example. So we are looking for all the numbers between 10 and 40 that are evenly divisible by 3. There are two ways we can do this- by listing the numbers out by hand or by taking the difference of 40 and 10 and dividing that difference by 3. That quotient (answer to a division problem) rounded to the nearest integer will be the number of integers divisible by 3. Let's try the first technique first and list out all the numbers divisible by 3 between 10 and 40, inclusive. The first integer after 10 to be evenly divisible by 3 is 12. After that, we can just add 3 to every number until we either hit 40 or go beyond 40. 12, 15, 18, 21, 24, 27, 30, 33, 36, 39 If we count all the numbers more than 10 and less than 40 in our list, we wind up with 10 integers that can be divided by 3 with a remainder of zero. This means our final answer is B, 10. Alternatively, we could use our second technique. $40−10=30$ $30/3$ $=10$ Again, our answer is B, 10. (Note: if the difference of the two numbers had NOT be divisible by 3, we would have taken the nearest rounded integer. For example, if we had been asked to find all the numbers between 10 and 50 that were evenly divisible by 3, we would have said: $50−10=40$ $40/3$ =13.333 $13.333$, rounded = 13 So our final answer would have been 13. And you can always test this by hand if you do not feel confident with your answer.) Prime Numbers Prime numbers are relatively rare on the ACT, but that is not to say that they never show up at all. So be sure to understand what they are and how to find them. A prime number is a number that is only divisible by two numbers- itself and 1. For example, 13 is a prime number because $1*13$ is its only factor. (13 is not evenly divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, , or 12). 12 is NOT a prime number, because its factors are 1, 2, 3, 4, 6, and 12. It has more factors than just itself and 1. 1 is NOT a prime number, because its only factor is 1. The only even prime number is 2. Standardized tests love to include the fact that 2 is a prime number as a way to subtly trick students who go too quickly through the test. If you assume that all prime numbers must be odd, then you may get a question on primes wrong. A prime number x is squared and then added to a different prime number, y. Which of the following could be the final result? An even number An odd number A positive number I only II only III only I and III only I, II, and III Now, this question relies on your knowledge of both number relationships and primes. You know that any number squared (the number times itself) will be an even number if the original number was even, and an odd number if the original number was odd. Why? Because an even * an even = an even, and an odd * an odd = an odd ($2*2=4$ $3*3=9$). Next, we are adding that square to another prime number. You’ll also remember that an even number + an odd number is odd, an odd number + an odd number is even, and an even number + an even number is even. Knowing that 2 is a prime number, let’s replace x with 2. $2^2=4$. Now if y is a different prime number (as stipulated in the question), it must be odd, because the only even prime number is 2. So let’s say $y=5$. $4+5=$. So the end result is odd. This means II is correct. But what if both x and y were odd prime numbers? So let’s say that $x=3$ and $y=5$. So $3^2=9$ and 9+5=14$. So the end result is even. This means I is correct. Now, for option number III, our results show that it is possible to get a positive number result, since both our results were positive. This means the final answer is E, I, II, and III If you forgot that 2 was a prime number, you would have picked D, I and III only, because there would have been no possible way to get an odd number. Remembering that 2 is a prime number is the key to solving this question. Another prime number question you may see on the ACT will ask you to identify how many prime numbers fall in a certain range of numbers. How many prime numbers are between 20 and 40, inclusive? Three Four Five Six Seven This might seem intimidating or time-consuming, but I promise you do NOT need to memorize a list of prime numbers. First, eliminate all even numbers from the list, as you know the only even prime number is 2. Next, eliminate all numbers that end in 5. Any number that ends is 5 or 0 is divisible by 5. Now your list looks like this: 21, 23, 27, 29, 31, 33, 37, 39 This is much easier to work with, but we need to narrow it down further. (You could start using your calculator here, or you can do this by hand.) A way to see if a number is divisible by 3 is to add the digits together. If that number is 3 or divisible by 3, then the final result is divisible by 3. For example, the number 23 is NOT divisible by 3 because $2+3=5$, which is not divisible by 3. However 21 is divisible by 3 because $2+1=3$, which is divisible by 3. So we can now eliminate 21 $(2+1=3)$, 27 $(2+7=9)$, 33 $(3+3=6)$, and 39 $(3+9=12)$ from the list. We are left with 23, 29, 31, 37. Now, to make sure you try every necessary potential factor, take the square root of the number you are trying to determine is prime. Any integer equal to or less than a number's square root could be a potential factor, but you do not have to try any numbers higher. Why? Well let’s take 36 as an example. Its factors are: 1, 2, 3, 4, 6, 9, 12, 18, and 36. But now look at the factor pairings. 1 36 2 18 3 12 4 9 6 6 (9 4) (12 3) (18 2) (36 1) After you get past 6, the numbers repeat. If you test out 4, you will know that 9 goes evenly into your larger number- no need to actually test 9 just to get 4 again! So all numbers less than or equal to a potential prime’s square root are the only potential factors you need to test. And, since we are dealing with potential primes, we only need to test odd integers equal to or less than the square root. Why? Because all multiples of even numbers will be even, and 2 is the only even prime number. Going back to our list, we have 23, 29, 31, 37. Well the closest square root to 23 and 29 is 5. We already know that neither 2 nor 3 nor 5 factor evenly into 23 or 29. You’re done. Both 23 and 29 must be prime. (Why didn't we test 4? Because all multiples of 4 are even, as an even * an even = an even.) As for 31 and 37, the closest square root of these is 6. But because 6 is even, we don't need to test it. So we need only to test odd numbers less than six. And we already know that neither 2 nor 3 nor 5 factor evenly into 31 or 37. So we are done. We have found all of our prime numbers. So your final answer is B, there are four prime numbers (23, 29, 31, 37) between 20 and 40. A different kind of Prime. Steps to Solving an ACT Integer Question Because ACT integer questions are so numerous and varied, there is no set way to approach them that is entirely separate from approaching other kinds of ACT math questions. But there are a few techniques that will help you approach your ACT integer questions (and by extension, most questions on ACT math). #1. Make sure the question requires an integer. If the question does NOT specify that you are looking for an integer, then any number- including decimals and fractions- are fair game. Always read the question carefully to make sure you are on the right track. #2. Use real numbers if you forget your integer rules. Forget whether positive, even consecutive integers should be written as x+(x+1) or x+(x+2)? Test it out with real numbers! 6, 8, 10 are consecutive even integers. If x=6, 8=x+2, and 10=x+4. This works for most all of your integer rules. Forget your exponent rules? Plug in real numbers! Forget whether an even * an even makes an even or an odd? Plug in real numbers! #3. Keep your work organized. Like with most ACT math questions, integer questions can seem more complex than they are, or will be presented to you in strange ways. Keep your work well organized and keep track of your values to make sure your answer is exactly what the question is asking for. Got your list in order? Than let's get cracking! Test Your Knowledge 1. 2. 3. 4. 5. Answers: C, D, B, F, H Answer Explanations: 1. We are tasked here with finding the smallest integer greater than $√58$. There are two ways to approach this- using a calculator or using our knowledge of perfect squares. Each will take about the same amount of time, so it's a matter of preference (and calculator ability). If you plug $√58$ into your calculator, you'll wind up with 7.615. This means that 8 is the smallest integer greater than this (because 7.616 is not an integer). Thus your final answer is C, 8. Alternatively, you could use your knowledge of perfect squares. $7^2=49$ and $8^2=64$ $√58$ is between these and larger than $√49$, so your closest integer larger than $√58$ would be 8. Again, our answer is C, 8. 2. Here, we must find possible values for a and b such that $|a+b|=|a−b|$. It'll be fastest for us to look to the answers in order to test which ones are true. (For more information on how to plug in answers, check out our article on plugging in answers) Answer choice A says this equation is "always" true, but we can see this is incorrect by plugging in some values for a and b. If $a=2$ and $b=4$, then $|a+b|=6$ and $|a−b|=|−2|=2$ 6≠ 2, so answer choice A is wrong. We can also see that answer choice B is wrong. Why? Because when a and b are equal, $|a−b|$ will equal 0, but $|a+b|$ will not. If $a=2$ and $b=2$ then $|a+b|=4$ and $|a−b|=0$ $4≠ 0$ Now let's look at answer choice C. It's true that when $a=0$ and $b=0$ that $|a+b|=|a−b|$ because $0=0$. But is this the only time that the equation works? We're not sure yet, so let's not eliminate this answer for now. So now let's try D. If $a=0$, but b=any other integer, does the equation work? Let's say that $b=2$, so $|a+b|=|0+2|=2$ and $|a−b|=|0−2|=|−2|=2$ $2=2$ We can also see that the same would work when $b=0$ $a=2$ and $b=0$, so $|a+b|=|2+0|=2$ and $|a−b|=|2−0|=2$ $2=2$ So our final answer is D, the equation is true when either $a=0$, $b=0$, or both a and b equal 0. 3. We are told that we have two, unknown, consecutive integers. And the smaller integer plus triple the larger integer equals 79. So let's find our two integers by writing the proper equation. If we call our smaller integer x, then our larger integer will be $x+1$. So: $x+3(x+1)=79$ $x+3x+3=79$ $4x=76$ $x=19$ Because we isolated the x, and the x stood in place of our smaller integer, this means our smaller integer is 19. Our larger integer must therefore be 20. (We can even test this by plugging these answers back into the original problem: $19+3(20)=19+60=79$) This means our final answer is B, 19 and 20. 4. We are being asked to find the smallest value of a number from several options. All of these options rely on our knowledge of roots, so let's examine them. Option F is $√x$. This will be the square root of x (in other words, a number*itself=x.) Option G says $√2x$. Well this will always be more than $√x$. Why? Because, the greater the number under the root sign, the greater the square root. Think of it in terms of real numbers. $√9=3$ and $√16=4$. The larger the number under the root sign, the larger the square root. This means that G will be larger than F, so we can cross G off the list. Similarly, we can cross off H. Why? Because $√x*x$ will be even bigger than $2x$ and will thus have a larger number under the root sign and a larger square root than $√x$. Option J will also be larger than option F because $√x$ will always be less than $√x$*another number larger than 1 (and the question specifically said that x1.) Remember it using real numbers. $√16$ (answer=4) will be less than $16√16$ (answer=64). And finally, K will be more than $√x$ as well. Why? Because K is the square of x (in other words, $x*x=x^2$) and the square of a number will always be larger than that number's square root. This means that our final answer is F, $√x$ is the least of all these terms. 5. Here, we are multiplying bases and exponents. We have ($2x^4y$) and we want to multiply it by ($3x^5y^8$). So let's multiply them piece by piece. First, multiply your integers. $2*3=6$ Next, multiply your x bases and their exponents. We know that we must add the exponents when multiplying two of the same base together. $x^4*x^5=x^[4+5]=x^9$ Next, multiply your y bases and their exponents. $y*y^8=y^[1+8]=y^9$ (Why is this $y^9$? Because y without an exponent is the same thing as saying $y^1$, so we needed to add that single exponent to the 8 from $y^8$.) Put the pieces together and you have: $6x^9y^9$ So our final answer is H, 6x9y9 Now celebrate because you rocked those integers! The Take-Aways Integers and integer questions can be tricky for some students, as they often involve concepts not tested in high school level math classes (have you had reason to use remainders much outside of elementary school?). But most integer questions are much simpler than they appear. If you know your way around exponents and you remember your definitions- integers, consecutive integers, absolute values, etc.- you’ll be able to solve most any ACT integer question that comes your way. What’s Next? You've taken on integers, both basic and advanced, and emerged victorious. Now that you’ve mastered these foundational topics of the ACT math, make sure you’ve got a solid grasp of all the math topics covered by the ACT math section, so that you can take on the ACT with confidence. Find yourself running out of time on ACT math? Check out our article on how to keep from running out of time on the ACT math section before it's pencil's down. Feeling overwhelmed? Start by figuring out your ideal score and work to improve little by little from there. Already have pretty good scores and looking to get a perfect 36? Check out our article on how to get a perfect ACT math score written by a 36 ACT-scorer. Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

PDA SIM Essay Example | Topics and Well Written Essays - 750 words

PDA SIM - Essay Example Determining a product’s lifecycle can enable a manager to make decisions of whether to invest more in a project or discontinue an operation. The three products HandHeld Corporation offers are X5, X6, and X7 devices. I noticed that the X7 product had weak sales. As a new CEO working for this business I seek out the advice of my top executives. Teamwork and cooperation are variables that improve the corporate culture and help firms achieve synergy. Synergy is achieved when the whole becomes more important than the sum of its parts (Schermerhorn & Osborn, Hunt, 2003, p.173). My top advisor indicated that the X7 product was in its growth stage. At that point I decided that discontinuing the product was not the right move because investing more in R&D could help increase the demand for the product. I noticed that the market saturation of the product in the first year was only 3%. The X7 product line had negative profitability. The company lost nearly $8.5 million on the X7 this year. The costs were higher than the revenues. I wanted to increase the price by 25% to offset the -17% profitability deficiency, but since the customer care about price I decided to go another direction. The problem with the product was the existence of a high fixed cost of $35 million. If I was able to sell more units then I would have more total profits to offset fixed cost. I lowered the price of the product by 10%. I allocated 50% of the R&D budget to the X7 because it had the lowest market saturation out of the three products. The X5 which was the most saturated product received 20% of the R&D budget and the X6 received the remaining 30%. I increased the price of the X6 hand device by $25 because the customer’s are not worried about price. I decreased the price of the X5 by $25 in order to increase its demand. My score after round 1 was completed was a score of 558,204,736. The 2006 profits were $347,929,621. I was able to turn the X7 into a profitable

Analyzing Psychological Disorders Essay Example | Topics and Well Written Essays - 1750 words

Analyzing Psychological Disorders - Essay Example They assert that all disorders stems primarily form learning or conditioning. The major debate that comes out of these two schools is called the ‘Nature v/s Nurture’ issue. In this work, however, I am going to take the stand of biopsychological perspective which attributes biological, psychological and social causes all to be responsible for disorders. In Part A, Schizophrenia will be analyzed in biopsychological perspective. The symptoms, causal factors and drug therapies for the disorder will also be discussed. In Part B, two other disorders, Anorexia and Anxiety will be analyzed again with the aid of biopsychological perspective and other discussions regarding their relevance to the nature-nurture issue and their treatments. While studying the symptoms of Schizophrenia, various researches have found significant difference in the structure of the brain affected by the disorder. Foremost, problems have been found in structural connectivity in the effected brains. The fluid-filled sacs that surround the brain called lateral ventricles were seen enlarged in brains with Schizophrenia. The volume of the brain is reduced and the cerebral cortex is smaller often times (Cazaban, 2003). The blood flow in frontal regions is lower and the temporal lobe is smaller. The hippocampus, amygdala and limbic system are also found to be smaller by certain researches (Cazaban, 2003). The major part of the brain affected by this disorder is the prefrontal cortex which is associated with memory that results in the disordered though. A major causal factor of Schizophrenia is described to be genetic. A number of recent studies have confirmed that this disorder can be genetically transferred. There is a strong association between the closeness of the blood relationship (i.e. level of gene sharing or consanguinity) and the risk for the disorder (Carson, Butcher, Mineka, & Hooley, 2007 p.501). Several other twin-studies conducted also confirm that people are genetically