Solving proportions Essay Example for Free

Solving proportions Essay Proportions exist in many real-world applications, and in this problem  estimating the size of the bear population on the Keweenaw Peninsula. By comparing  data from two experiments, conservationists are able to predict patterns of animal  increase or decrease. In this situation, 50 bears were captured and tagged and released to  estimate the size of the bear population. A year later, after capturing a random sample of  100 bears only 2 of the bears captured were tagged bears. These proportions will be used  to determine the bear population on the peninsula. This new bear scenario can be solved  by applying the concept of proportions which allows the assumption of the  ratio of  originally tagged bears to the whole population is equal to the ratio of recaptured tagged  bears to the size of the sample. To determine the estimated solution, the bears will be the  extraneous variables that will be defined for solving the proportions used. The ratio of originally tagged bears to the whole population X_2_The ratio of recaptured tagged bears to the sample size 10050 = _2_ This is the proportion set up and ready to solve. X 100  (50)(100), (X)(2)The next step is to cross multiply.  5000 = 2X Divide both sides by 2 2 2  2500 = XThe bear population on the Keweenaw Peninsula is estimated to be  around 2500. The extreme means for this sample were 50 and 100, X and 2.  For the second problem in this assignment, the equation must be solved for Y.  Continuing the discussion of proportions, a single fraction (ratio) exists on both sides  of the equal sign so basically it is a proportion, which can be solved by  cross  multiplying the extremes and means. Y-1 = 3 Original equation solving for Y  X+3 4  4(Y-1) = -3(X+3) Cross multiply both sides  4Y-4 = -3X-9 Add 4 to both sides  4Y = -3X-5 Divide both sides by 4  Y = -3X-5 Final answer for Y  4 4  This is a linear equation in the form of y = mx + b. After comparing the solution  to the original problem, it is noticed that the slope, -3/4 ,is the same number on the right  side of the equation. This indicates that another method exists for solving the sameequation.  Y-1 = 3 Original equation solving for Y  X+3 4  Y-1 = -3(X+3) Multiply both sides by (X+3)  4  Y-1 = -3X-9 Add 1 to both sides  4 4  Y = -3X-5 Final answer  4 4 After solving both of these problems I found it interesting how 2 totally different  equations could be solved with the same basic functions. I also found that everyday life  can incorporate these math functions to solve or estimate daily life events for a number of  different reasons.. REFERENCES References: Elementary and Intermediate Algebra, 4th Ed., Dugopolski

Copland: 1900 through 1942 and Copland: Since 1943 :: Aaron Copland Book Report

Copland: 1900 through 1942 and Copland: Since 1943   Ã‚  Ã‚  Ã‚  Ã‚   In their books: Copland: 1900 through 1942 and Copland: Since 1943, Aaron Copland and Vivian Perlis give a detailed account of the life of one of America’s most influential composers. The books are arranged similarly to the Shostakovich biography that our class reviewed earlier this semester. That is, through personal accounts by Copland himself along with accounts of Copland’s friends and acquaintances, the authors manage to paint an accurate and interesting picture detailing the life of the great composer. When combined, the two books recount Copland’s entire life, dividing it into two periods for the purpose of easier organization and reading.   Ã‚  Ã‚  Ã‚  Ã‚  Copland was born in New York City in 1900. Copland had a large and loving family in New York. His childhood was comfortable, as his father owned a department store where Copland worked for much of his young life. Copland’s mother is described by the composer as "affectionate and a very nice mother to have" (pp. 18) Copland showed an early interest in music, and by the age of eleven, he had surpassed the knowledge of his older sister in the ways of the piano. As a child, he had taken lessons from his sister, but by eleven, he felt that he needed to consult an outside source in order to learn more.   Ã‚  Ã‚  Ã‚  Ã‚  At the age of eighteen, Copland graduated from high school. He pursued his interest in music and began to search for a teacher who could teach him musical harmony. Copland’s piano teacher suggested that he study under Rubin Goldmark who had a studio in Manhattan. Copland found Goldmark to be a very effective teacher. However, Copland and his piano teacher decided to part ways so that Copland could expand his horizons. Under Goldmark, Copland learned very effective methods of composition, but sometimes felt bogged down. Goldmark did not approve of some of Copland’s interest in the more modern musical works, and Copland found this frustrating. After composing a number of "Sonata-form" musical pieces with Goldmark, Copland decided he needed a change of scenery. In 1921, Copland decided to study in France. Even as Copland left his old teacher, Goldmark stressed his traditional ideals. Before Copland’s departure, Goldmark wrote: "I hope you will ma ke more progress in the Sonata form†¦Even if you should fall into the hands of some radicals."(pp. 35)   Ã‚  Ã‚  Ã‚  Ã‚  In France, Copland found a new teacher in Nadia Boulanger.

An Effective Strategy Negotiation

Crouching behind a tight cordon of panda cars, the weather-beaten SWAT team leader, complete with cap, bulletproof vest and loud-hailer, looks up to the third-floor window, clears his throat, and announces: ‘You might as well give yourself up, Kowalski, we've got the place surrounded. ‘ His craggy face is bathed in the soft amber glow of the street light and a small bead of sweat moves slowly down his temple. Kowalski, a wily old stager with deep pockmarks and a broken nose, is having none of it. After all, he has the (rather attractive blonde) hostage securely tied up and there happens to be a fridge full of beer in the office he's holed up in. So it's a complete stalemate. Kowalski and his nemesis are simply going to have to start negotiating. In this case, negotiation is more likely to be resolved in a bloody shoot-out. In the workplace, of course, negotiations generally don't tend to be conducted under such tense or dangerous circumstances. They do, however, take place on a daily, even hourly, basis. In fact, they have become such a regular and ingrained part of working life that participants can readily enter into them without even realising that's what they're doing. Before we proceed, it is probably worth defining our terms, or at least borrowing a definition from personnel consultant Alan Fowler's book, Negotiating, Persuading and Influencing. Fowler explains that ‘negotiation occurs whenever there is an issue that cannot be resolved by one person acting alone; it occurs when the two (or more) people who have to be involved begin with different views on how to proceed, or have different aims for the outcome. There are two situations in which negotiation does not or cannot occur: when one of the persons immediately agrees to what the Other is asking or suggesting; and when one of the two adamantly refuses to even discuss the matter. ‘ You can see that the term covers a multitude of scenarios, from the widely reported collective pay-bargaining conducted by union officials and management representatives, to the more mundane business of negotiating a lease on a property or a supplier's contract. Negotiation is also a key component in inter-office relationships, in instances where managers have no linear authority over a particular colleague but need to persuade them to perform a specific task. Here, the negotiation is a tacit IOU- you've done me a favour, so I'll return it at a later date when you might need it. ‘Managers are doing it all the time,' confirms Roger Moores, an associate of the Industrial Society, who runs courses in negotiation and associated skills. ‘I usually start my courses by asking how many of the people there are negotiators. Not many hands go up but, by the end of the session, they realise they do it all the time. We use the language of negotiation all the time too. It's a language that even children understand, based on the words â€Å"if† and â€Å"then†. â€Å"If you do this for me, then I'll do that. † In theory, it's all wonderfully simple. ‘ Scores of self-help and how-to books have been written on the subject but the theorists by and large fall into two camps. There are experts, such as authors Fowler and Gavin Kennedy, who look at negotiation as a stage-by-stage process, comprising preparation, discussion, proposal, bargaining and finally closing. And then there's the American model, epitomised by the seminal text, Getting to Yes by William Ury, which is more focused on personal relations within the workplace. As Moores rightly points out, the two approaches are by no means mutually exclusive. Though representative bodies such as the Institute of Personnel and Development and the Industrial Society offer dedicated courses on negotiation skills, the majority of managers in small to medium-sized businesses don't have the time or inclination to attend them. A few common-sense pointers, however, go a long way. The first is to recognise when it is actually appropriate to negotiate. ‘If managers negotiated everything, there wouldn't be time to do anything,' reasons Moores. â€Å"There are occasions when orders and dictatorship are required too. ‘ If a matter or issue is definitely worth negotiating, the next step is toassess its merits and how much time you can afford to devote to it. According to all the various pundits, the key to successful negotiation is all in the preparation. They insist that skills and techniques are generally acquired through practice and experience, and that preparatory work and patience will generally stand you in better stead than the gift of the gab or an aggressive stance. There is no point walking into an important negotiation session hoping to wing it. ‘Some people are naturally better [at negotiating] than others,' says Fowler. ‘It requires a certain amount of quick thinking and ability to respond quickly. You also need the confidence to be able to say â€Å"Look, you've raised something new. Can we adjourn this meeting and continue tomorrow, by which time I'll have been able to gather my thoughts? † It's important to know your own style and be comfortable with it. If you're stepping too far outside of yourself, you can end up seeming artificial. ‘ Yet Chris Grice, an assistant director of ACAS, the conciliation and arbitration service which has dragged countless industrial relations negotiations back from the brink, believes negotiation skills are more about nurture than nature. ‘There's a question as to whether negotiating is an art or a science,' he says. You can be taught good negotiation, so I'd say it's a science†¦ Being taught how to mix colours doesn't make you an artist. You can learn about negotiation strategy, how to read a situation, when the tune is right to confront an issue and when to apply a variety of different processes. Preparation is an often neglected area. If you're negotiating about pay, for example, you should be aware of the going rate, affordability and any other interested parties before you go in. You need to be able to anticipate the other party's moves. ‘ While Grice admits that some of the negotiations he is called in to rbitrate are conducted in what he – with admirable understatement – describes as an ‘adversarial atmosphere' (potentially explosive in other words), he reckons that overall he has witnessed as much civility as hostility. This, he believes, is because most of the participants at this level of negotiation tend to be astute practitioners, who realise that prickliness and emotional involvement will only hamper their efforts. ‘Some of the best negotiators are mild-mannered but persuasive people,' says Grice. ‘They know exactly where they want to be and realise they can get there in a civilised manner. After all, you've got more in your toolbox than a hammer. ‘ One problem often leads to another. A manager may feel it necessary to cut overtime. The employees are unhappy and threaten industrial action but the manager should avoid the immediate reaction to sack the ringleader. By doing so, the manager would have two problems to cope with instead of one. It is important to keep one topic in focus at a time. An ‘easy does it' ethos is especially important in small to medium-sized businesses, which rely on establishing and maintaining an ongoing network of reliable suppliers and subcontractors. If parties leave a negotiation feeling hard done by, the relationship is unlikely to be sustainable for any length of time. ‘The main point is to make the person you're negotiating with think that they have achieved the best deal possible,' says Frank Kings, managing director of Sovereign Contracts, a Midlands-based shop-fitting concern, whose clients include IBM, SmithKline Beecham and Warwick University. ‘I'm always looking for repeat business, so negotiation is as much about building a long-term relationship as striking the best deal at that particular moment. One should always try to take a longer-term view. ‘ Susan Croft, a trainer at the Aziz Corporation, which specialises in spoken-communication skills training for business, shares Kings' views. Negotiations, she maintains, are not necessarily confrontational, just a necessary means of ensuring that two or more parties are satisfied with their lot. ‘In a â€Å"win-lose† situation, you may have won the battle but not the long-term war,' Croft says. ‘You don't want the person you're negotiating with to be checking for their arms and legs on the way out. ‘ A degree of emotional detachment is a must. Losing your cool may mean losing the thread and the advantage. Concentration is also essential. The best negotiators are good listeners and observers too. By keeping your eyes and ears open, you can pick up valuable clues as to where the other side is prepared to compromise or where there are flaws in their argument, which you can exploit later. If you are so utterly determined to put across your own points, you may not hear what the other side is saying. Their position may have changed and your initial standpoint may no longer be relevant or valid. Similarly, the other party should not be given too many hints. It is worth keeping your cards close to your chest in a negotiation. Don't give away more information than you have to. Release nuggets sporadically and tactically when you feel they will make the most impact. Be aware of your body language because you might be revealing more than you think through your movements and mannerisms. If you look hard enough and think laterally, there are usually ways and means of clinching a mutually beneficial deal through negotiation. Phil Jones, managing director of Real Time, the London-based interactive design studio, recalls two recent instances where new clients wanted to launch internet web sites but didn't have the requisite budgets. They were the type of high-profile clients and creatively challenging projects that Real Time was keen to get involved in, however. ‘If it's a job you really want to do, you can always find a way of doing it,' maintains Jones. The first was for the Formula 1 motor-racing team, Williams Motorsport: ‘They made the balance up in contra deals, mainly in tickets to some of the major Formula 1 meetings. ‘ The tickets are like gold dust, of course, and can be used as a pat on the back for staff, or as an opportunity to pamper existing clients or woo new ones. Diesel, the Italian clothing manufacturer, which is quietly stealing a march on its rivals in the UK jeans market, approached Real Time towards the end of the financial year, when its promotional budget was running perilously low. Real Time managed to negotiate further projects the following year for completing the initial job an e-commerce site that allows ordering of clothes over the internet – at a cut-price rate. Every job is like that. You have to be flexible to get the business,' says Jones. Indeed, he is currently negotiating a deal with the Football Association for an e-commerce web site dedicated to the UK bid for the 2006 World Cup. Real Time was responsible for the bid's logo and original web site. ‘The FA have a limited budget to spend across a range of media, so I'm talking to them about perhaps receiving a percentage of what's sold from the new site,' he explains. ‘That's really putting your money where your mouth is. ‘ Negotiation, then, is primarily about effective communication. Communicating what you want and what you have to offer, and then marrying that up with another party's requirements. A bit of imagination, flexibility and a well-considered strategy can go along way to meeting these ends. It is also worth remembering that how you put it is often as important as what you're actually saying. ‘You should always try to express things in ways the other parties find palatable, so that no one loses face,' says Grice of ACAS. ‘Packaging is half the battle. ‘

Social Media Paper - 685 Words

SOCIAL MEDIA CURSE Jerome B Miller HUM/186 December 17, 2013 Dr. Rita Carver SOCIAL MEDIA CURSE The last decade gave birth to a huge phenomenon that dramatically changed local and international social entertainment. This new entertaining phenomenon was social media, which came with its share of advantages and disadvantages. A social website called â€Å"My Space† sparked the social site revolution almost ten years ago, and connected millions of people around the world through the internet. Since My Space other popular social sites like Facebook, Instagram, and Twitter have made an incredible explosion on to the growing social scene. Advantages and Disadvantages of Easily Obtainable Information Sometimes easily obtainable information†¦show more content†¦Furthermore, social media gives people the opportunity to keep up with the latest trends and fashion. Twitter and Instagram are two social sites that allow ordinary people to follow the moves of high profile celebrities such as actors, musicians, and sports figures. There have been times when people have been victimized and attacked because of their comments and posts left on social sites, but this is one of the disadvantages of social media. Photos and remarks posted on social sites can sometimes be accessed by employers, but although those photographs and words maybe harmless ones employer can easily take them out of context and find them offensive. A person has to remember that first impressions can lasting impressions. Knowing The Advantages and Disadvantages Knowing the advantages and disadvantages on the uses of social media may alter the way one uses social media by causing them to use more or less privacy settings when online. One might decide to use social media more responsibly, and filter the content that they post on line. 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