Queen Elizabeth Grammar School Essay Example

Queen Elizabeth Grammar School Essay The Towers of Hanoi is an ancient mathematical game. The aim of this coursework is to try to identify patterns and rules associated with the game and explain them in mathematical terms. The definitions and rules are: Rules: * There are only three positions a disc can be placed. Poles A, B or C. * A disc can only go on top of a larger one. (I.e. Disc A can only go on top of Discs B and C, but Disc B cannot go on top of disc A) We will write a custom essay sample on Queen Elizabeth Grammar School specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Queen Elizabeth Grammar School specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Queen Elizabeth Grammar School specifically for you FOR ONLY $16.38 $13.9/page Hire Writer * The object of the game is to get all the discs to move from pole A to pole B of C in the least number of moves. * Only one disc may be moved at a time. Finding Formula A Number Of Discs Least Number Of Moves Previous term (Doubled) 1 1 2 3 2 3 7 6 4 15 14 5 31 30 6 63 62 7 127 126 8 255 254 From looking at the table it is quite clear that there is a pattern linking the number of discs and the least number of moves. It is clear that there is an element of doubling involved, as the least number of moves nearly doubles each time. When I add the extra column see above, it is clear that there is a doubling element involved. When I look again, I can see that the pattern is the previous term doubled plus 1. This can be expressed mathematically as: Un = 2(Un-1) +1 This can be shown in: 1. For 1 disc, it takes 1 move to move disc A from pole 1 to pole 3; 2. For 2 discs, it takes 3 moves: 2(Un-1) +1 = 2(1) + 1 = 3 3. For 3 discs, it takes 7 moves: 2(Un-1) +1= 2(3) + 1 = 7 4. For 4 discs, it takes 15 moves: 2(Un-1) +1= 2(7) + 1 = 15 5. For 5 discs, it takes 31 moves: 2(Un-1) +1= 2(15) + 1 = 31 To understand how this works, coding is needed to see how a disc moves individually. Coding should show me the patterns involved and then I should be able to justify my formula based on this. Coding is on the next page. Coding Number of Discs: 2 3 4 5 Disc Moving: A A A A B B B B A A A A C C C A A A B B B A A A D D A A B B A A C C A A B B A A E A B A C A B A D A B A C A B A From my coding it is now clearer why that formula is that particular formula. It can be seen that there is symmetry involved in each pattern. The symmetry is always about the name of the bottom disc. I.e. with 3 discs the symmetry is about disc C and this is the bottom disc From the coding, I can also see that the pattern of moves for 2 discs is present in the beginning of 3 discs, 4 discs etc. The pattern for 3 discs is also in the pattern for 4 discs and so on. This is can therefore be explained as: In n number of discs where n is greater than 2, the first three moves will always be ABA. This is because the n-1 discs pattern is included in the n pattern. We have (Un-1), because we take into account the previous terms pattern when making the next tower. We have the 2 term because this pattern is repeated twice, firstly to deconstruct the tower and then to rebuild the tower on top of the bottom disc. We have the +1 term because this is where the bottom disc moves from Pole A to Poles B or C. This can be demonstrated when we move three tiles. ABA This is the move pattern for 2 tiles (Un-1). This allows C to be able to move. C This is when the bottom tile moves and we therefore get the +1 from. ABA This is where the doubling element comes in as well as the n-1 discs moves pattern. This is where the tower is rebuilt on top of disc C. So overall, we get the formula: 2(Un-1) +1 There are limitations to this however. Un-1 has to be an integer because we cannot have 3.5 moves. Un-1 has to also be equal to or greater than 0 and has to be an integer because the formula wouldnt work as the result would be negative and we cannot have a negative number of moves. Formula B Finding the formula that shows how many times a certain disc moves From formula A I now have a basis on which to work. Given a certain number of discs I need to be able to say how many times a desired disc moves. Firstly, I need to analyze my results from the coding. Disc: Disc A Disc B Disc C Disc D Disc E Disc F Total Number of times each disc moves: 3 Discs 4 2 1 7 4 Discs 8 4 2 1 15 5 Discs 16 8 4 2 1 31 6 Discs 32 16 8 4 2 1 63 We can also once again see a pattern here. There is a doubling, well halving element involved depending on which way you look at it. The table above shows how many times a certain disc moves. Whenever a new disc is added to the sequence, such as in Disc 4, the number of moves for Disc A doubles. I.e. As you go down the table the number of moves for each disc doubles. When I look at the results, I notice that they are all from the 2n pattern. Therefore I can come up with the relationship for the number of times each disc moving being: Number of times a certain disc moves = 2n-d with d being the disc number. So in Disc A, the number for d would be 1, as this is the first disc. Disc B would be 2 etc. In the series for 6 discs, the terms would be Disc A: 2n-d = 26-1 = 32 Disc B: 2n-d = 26-2 = 16 Disc C: 2n-d = 26-3 = 8 Disc D: 2n-d = 26-4 = 4 Disc E: 2n-d = 26-5 = 2 Disc F: 2n-d = 26-6 = 1 This therefore works. Now I have to prove that this works. We can see that Disc B always moves half as many times as Disc A. If we do 2n we get how many times Disc A Moves always. If we do 2n-2 we get how many times disc B moves always. This is because as we take more away from 2n we get smaller and smaller until it ultimately converges to 0. Taking 1 away from this halves the number of moves; whereas taking 2 away quarters the number of moves. Disc B always moves less times than Disc A because of the recurring pattern. A has to move more times, because it has to keep going on top of the larger tiles as the rules state. A has more options to move than B because it is smaller. There are limitations to this however, because we cannot have d being greater than n because the formula would not work. It wouldnt work because we cannot have half of a move or a quarter of a move. We cannot also have n being less than 1 because of the same principal. The number of moves and the disc number have to also be an integer because we cannot have Disc A moving 3.5 times. The Link The series above is a geometric series. I know this because the difference is different each time. The general way to write a geometric series is: General: a + ar + ar2 + ar3 + arn-1 The terms: a is the starting number in the sequence. I will use a 6 tiled sequence so my starting number from the table will be 32 as this is the number of times disc A moves. Ratio r This is the amount that a is multiplied to get the next term. So 32 is multiplied by 0.5 to get 16. Our sequence is: S= 32 + 16 + 8 4 +2 +1 To get the sum of a geometric sequence, we need to multiply by the common ratio (0.5) S = a + ar + ar2 + ar3 + + arn-1 rS = a + ar + ar2 + ar3 + +arn-1+ arn S-rS = a arn This can be expressed as S(1-r) = a(1-rn) Divide this by 1-r gives: a(1-rn) S= 1-r Before I can use this information however, I need to determine a formula to get a. I can use the formula I discovered above but just modify it slightly. To get a the formula is: 2n-1 as this is the formula for Disc A always. So the formula above instead of being 2n-d could have also been 2n-1 for the same principals. With n being the disc number you are trying to find. Disc 50 would be 249 and disc 3 would always be 22 and so on. Therefore I can now substitute in my values in a pile of 6 discs to get the formula that links formula A and B. To determine the ratio we have to just see how much the sequence is decreasing each time. 32 + 16+ 8 + 4 + 2 + 1 To get the next term suing the general geometric sequence rule, it says that we have to multiply 32 by a constant. a ar. So: a ar is the same as ar divided by a. 16 = 0.5. This is the ratio. 32 Therefore for the sum of my geometric series, the formula should be: a(1-rn) S= 1-r S = 25(1-0.56) 0.5 S= 31.5 = 63 0.5 Therefore the sum of a 6 termed series is 63. This can be proved by getting the formula for the previous term. S = 24(1-0.55) = 31 0.5 According to my earlier formula (Un = 2(Un-1) +1) when I substitute in I should get the answer 63. 2 x 31 + 1 = 63. This works because of the algebra of the general geometric sequences: S = a + ar +ar2 This is the rule for each term in the sequence: arn-1 or 2n-d I then multiplied by the common ratio (r) rS = ar + ar2 + ar3 This is the rule: arn Then I subtracted the sequence multiplied by the common ratio from the first sequence. This gave: S-rS = a arn = a(1-rn) Therefore S=a(1-rn) (1-r)) Limitations are: S has to be greater than 0 and has to be an integer a has to be positive and an integer r has to be an integer and greater than 0 Extension Work: Finding which pole the pile will be built upon. I have noticed from my work that when I had 3 discs on my pile, disc C landed on where I put disc A to start off with which was on Pole C. When I had 4 discs however, I noticed that the pile finished on where I did not place tile A which was Pole B. This can therefore be expressed as: If the number of discs in the pile to start with is even then the bottom disc will land where you place Disc A to start off with. If the number of discs in the pile is odd however, then the bottom disc in the pile will finish up on the pole where you did not place Disk A. Therefore where you put Disc A can be considered crucial to where you want your pile to land Overview: If I have 25 discs in my pile, I can expect there to be: 33554431 moves involved in the series. Disc A will move 16777216 times; whereas disc y will move only once. The Pile will end up on the pole where you place disc A, so if I leave it on pole B to start with, the pile will end up on Pole B. According to the monks in Hanoi, the world will end in over 500 Million Years. The problems with my investigation: I have realized that there are only 26 letters in the alphabet. With my system of labeling, it is impractical for me to label each disc A, B C etc because I will run out of letters. I will either have to name the poles ABC or call each disc past 26, A1 etc.

How to answer Walk me through your resume in a job interview

How to answer Walk me through your resume in a job interview You’re all excited for your interview and then you get the dreaded question. â€Å"Walk me through your resume,† the interviewer says. â€Å"Walk through it yourself!† you think. â€Å"Can’t you read?† We kid- of course, you can only think this. (Please, only think it!) It may seem like a ridiculous question, but think of it instead as an opportunity. You have a captive audience here to really fill in any holes or gaps on your resume and talk your interviewer through the bullet points while fleshing them out with the details they deserve! Take care, however, that you don’t let your own overconfidence trip you up. Be prepared to give a succinct, non-rambling answer. Also be prepared to have a smooth way of glossing over positions you put on for necessary padding in the hopes that the recruiter wouldn’t read those sections too carefully.Here are a few good tips for preparing to answer this common question.1. Be brief and articulate.Conci sion is your friend. Don’t just wing this answer- practice it with all your other interview prep answers. Remember, you’re probably also being evaluated here on your communication skills. Cut out the â€Å"um†s and set your resume in the context/tone you want without droning on too long about yourself. And whatever you do, don’t let yourself get bogged down with irrelevant extra details that have nothing to do with why your past will make you an ideal candidate for the job you want.2. Keep your eye on the prize.Your job in this answer is to put everything in your resume in the context of the job you’re applying for. Stick to the script! When you’re talking about your background, mine it for little gems that will show just how perfect your history makes you for this position. Explain your career so far in such a way that your interviewer will see how it perfect it makes you for the open job.3. Explain yourself.Some questions undoubtedly come up with any resume, no matter how bulletproof. Try to anticipate any questions or concerns your interviewer might have and have answers prepared. Explain your motivations and what went into the various decisions you’ve made along the way. Try to frame every negative or challenge into a positive. Show yourself to be scrappy and problem-solving when you go over any gaps and potential red flags, as well.4. Anticipate what they want to hear.As much as you want to practice a perfect answer, make sure to also think on the fly. Try to suss out what your interviewer is actually after and incorporate that into your answer. Tailor or fix what you’re about to say what you know they’re after.5. Stay classy.Paint yourself as the best person for the job, but don’t just shine yourself in best, brightest light and trash everyone else. Stay honest. Don’t throw anyone under any buses. Take responsibility for yourself and your actions, and don’t exaggerate you r successes while sweeping all weaknesses under the rug (even though you shouldn’t dwell too long on those)- you just won’t seem believable.6. Think big.When in doubt, frame your answer to be about how  this job is the perfect next step on your career path and how everything in the past has led up to this position.  Don’t forget to show the big picture and highlight your passion and enthusiasm for the position, in addition to your expertise.  Back everything you say up with actual bullet points on your resume. Stick to the script, show off without being too braggy, and the job should be yours!

The ultimate guide for matching your shirts and ties.

The ultimate guide for matching your shirts and ties. Thinking about spicing up your wardrobe from drab to fab? Maybe you should try switching up your shirts and ties. Replacing your shirts and ties with some fun colors and patterns might be just what you need to break you out of the boring office outfit. But before you go all pattern crazy here is what you need to know about mixing colors and patterns†¦and even patterns and patterns. With this simple guide, you will never have to second guess your outfit combinations.  Source [BeckettSimonon]

American political parties, relatively weak compared to similar Essay

American political parties, relatively weak compared to similar nations, why and what are consequences - Essay Example mparison to other highly industrialized society because in reality and practice, the American political parties have always had severe internal divisions. In a two-part system, ideal internal ideological unity could be nothing more than political picture. The political parties are plainly too immense and varied to encourage stable internal unity. Yet, integrated party control confers an electoral incentive for party leadership to downplay, or even vigorously steer clear of, those matters on which the party is divided to protect the outward show of cohesion. In the concern of electoral success and a significant party ticket, party member find motivating incentives to downplay intraparty conflict. Alternatively, it is in my own opinion that the capability of a divided government to provoke resentment rest partly in its capability to generate prospect for intraparty conflict to arise. Moreover, in a divided government system, the prevailing congressional party has the power to compel public concern of those matters most perceptive to the president’s party. Through placing conflict-ridden issues on the agenda, the party dominating Congress compels the president’s party to discuss matters its congressional members would vigorously steer clear of. The typical justification for the irresponsible nature of American political parties is that our very Constitution makes our party system what it is. Richard Hofstadter, the historian, put it in a few words: â€Å"We have a Constitution against parties† (Disch 2002: 62). However, it is also possible that federalism contributes to national and state parties that are primarily self-governing but it is also possible that federalism is the cause. The actual problem is in fact the failure of the political parties to attain an appropriate balance of power within the federal system, which demands a higher nationalization of party influence. Furthermore, it is unfortunate that there is no focus of party leadership in the American

Insurance Is Not Always Beneficial to Emplyees Essay

Insurance Is Not Always Beneficial to Emplyees - Essay Example In the United States, for example, many employees get Insurance policy through their employers where the employers help pay the Insurance policy. When the employer insures one, it is usually through a managed care plan that are health insurance plans that provide health care facilities to members at reduced costs by laying down contracts with medical facilities and health care providers. Employer based Insurance is often much cheaper as compared to buying individual Insurance, hence many people rather have their insurance bill cut from their salaries. The United States unlike other industrialized countries has a different case in that it does not have a national Insurance System. It is important to be insured because one cannot always tell when they are going to need the medical attention. There are vast advantages of getting employee-based health insurance. In the essay, I will look at health insurance in group verses individualized context, explore the advantages of employer based health insurance plan and discuss that insurance is not always beneficial. Group verses Individualized Insurance Employment based Insurance is an example of group based Insurance. ... e of group insurance policy is that it is much easier to obtain in that there are little procedures to be followed, which would in turn delay or even terminate the whole application process like inquiring about the health history of individual members. Group insurance policy is definitely the cheapest form of insurance available. However, as compared to group insurance, there are numerous advantages of individualized insurance plans. Firstly, one is able to customize the provisions they may want included or neglected in their package. They may also choose to regulate on the deductible amount of payment that the insurance company does. It also enables individual to choose the doctor that would be conducting their services. Here the price range may be elevated as compared to group insurers, but the services are better. It may also be exceptionally costly particularly when one runs a high risk being ill or has high health risk qualities. Advantages of Employment Based Health Insurance P lans A health plan would gain more if groups of individuals with low health risks were enrolled in it as compared to unhealthy list of individuals. In the United States where the employee health insurance benefit scheme is purely voluntary, there is a great chance that a group of highly unhealthy individuals are registered in the plan. Insurers would often prefer to enroll a group of individual as compared to the specific individual. Employment based insurance groups are one of the individual groups that are always considered to be formed for the sole purpose to offer their employees health insurance. It does not discriminate and whether the individual in the group posses a high health risk than the other, they will automatically qualify for the system. Not only are employers capable of

The Meaning of American Pie Essay Example for Free

The Meaning of American Pie Essay In the autumn of 1971 Don McLeans elegiac American Pie entered the collective consciousness, and over thirty years later remains one of the most discussed, dissected and debated songs that popular music has ever produced. A cultural event at the peak of its popularity in 1972, it reached the top of the Billboard 100 charts in a matter of weeks, selling more than 3 million copies. By identifying this great success it illustrates that it was no ordinary song. With its boldness, originality and it being thematically ambitious created uncertainty. Presenting the idea that we weren’t entirely sure what the song was about, provoking endless debates over its epic cast of characters. But however open to interpretation the lyrics may have been, the songs emotional resonance was unmistakable: McLean was clearly relating a defining moment in the American experience—something had been lost. Opening with the death of singer Buddy Holly and ending near the tragic concert at Altamont Motor Speedway, we are able to frame the span of years the song is covering—1959 to 1970—as the 10 years weve been on our own of the third verse. It is across this decade that the American cultural landscape changed radically, passing from the relative optimism and conformity of the 1950s and early 1960s to the rejection of these values by the various political and social movements of the mid and late 1960s. American Pie appears to chronicle the course of rock n roll, it is not, as is sometimes suggested, a mere catalogue of musical events. In using the cast of rock n roll players from the 1960s and setting them against the backdrop of Buddy Hollys death, they become polarized—metaphors for the clash of values occurring in America at this time: Holly as the symbol of the happier innocence of the fifties, the rest as symbolic of the sixties growing unrest and fragmentation. And as each verse sums up chronological periods in time—the late 1950s, 1963-66, 1966-68, 1969, 1970—another blow against the happier innocence of another era is registered: another day the music dies. Verse 1 of American Pie looks back from the early seventies and introduces the catalyst for the story about to unfold. â€Å"A long long time ago I can still remember how the music used to make me smile†. The narrator here is nostalgic for a simpler and more optimistic kind of music—a music that can make people smile, and that could help them forget their troubles—and a music that very much represents the happier optimism of the 1950s in America. â€Å"But February made me shiver†, he also identifies Buddy Holly by the month in which he dies. Hollys passing had a profound effect on him, which is displayed throughout the song. The day the music died† this reflects and supports the idea that the day the music died becomes the day the innocence and optimism within America died The chorus is the primary key in understanding American Pie as the theme of America’s lost innocence is clearly stated. â€Å"So bye bye Miss American pie† Miss Amer ican Pie* is as American as apple pie, so the saying goes; she could also be a synthesis of this symbol and the beauty queen Miss America. Either way, her name evokes a simpler time in American life when these icons held more meaning. She is the America of a passing era, and he is bidding her farewell. Drove my Chevy to the levee alludes to a drive along a levee mentioned in a series of popular 1950s Chevrolet television commercials sung by Dinah Shore and which serves as a signpost to that era—just as the Chevrolet itself is a familiar icon of 1950s America. Also, given that a drive to a levee carries the suggestion of romance in a car, we can almost see him on a date here. But the date is over, the levee is dry—someone he once loved has betrayed him; something that once gave him sustenance has evaporated. This’ll be the day that I die† is a rewording of the line â€Å"cause that’ll be the day when I die† from the chorus of Holly’s hit that’ll be the day. This signifies McLean’s way of both mourning the death of that music and way of life, and pointing to Holly as his symbol of it. Verse 2 erupts with the idea that the narrator reaches little further back in time to the days of his youth, the late 1950s—a time of sock hops, pickup trucks and pink carnations—as he courts a woman who ultimately spurns him. This is a fickle lady here, and the narrator questions her loyalties. And can you teach me how to dance real slow? † This is a romantic dance. He is courting her. The slow dance itself is yet another reference to the fifties and the kind of dancing that went out of fashion in the following decade; it also alludes to the slower pace of life in America at this time. This verse helps us to further identity Miss American Pie, whose brief introduction in the chorus needed this additional exposition; and which, along with verse 1 and the chorus, also serves to establish the 1950s as the reference point for the res t of the song. In so doing, McLean characterizes the period primarily through its musical symbol (Holly), using him and the music (those rhythm and blues) as a metaphor for the innocence of the times, and a sacred thing. The day the music died now takes on the significance of a lost faith in the values of a passing era and the sorrow the narrator feels at their passing: blow number two. Having personified America as a woman, Bye bye Miss American Pie now more clearly becomes a farewell to the America he once knew.

Pompey :: essays research papers

Pompey the Great Gnaeus Pompeius, better known as Pompey, was born on September 29, 106 BC. He was four years older than Julius Caesar. Pompey’s father was a rich Roman noble, who was elected to the consul in 89 BC. Pompey distinguished himself as a great leader early in his life. In the civil war between Gaius Marius and Lucius Sulla, Pompey sided with Sulla. Sulla, with the help of Pompey, made some vary impressive defeats in Africa and Sicily. In 79 BC Sulla resigned and died the next year. Two of his patrons, who had fought for him, Pompey and Marcus Crassus, moved to leading military positions in the seventies.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Crassus and Pompey fought together in a battle against a Marian rebel, Quintus Sertorius, and a slave rebellion lead by Spartacus in Italy. They returned, having won, in 71 BC. Pompey then spent time campaigning successfully in Rome before he was elected to consul, with Marcus Crassus for the year 70 BC.  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  After Pompey served his time on Consul he was given command over the Mediterranean, where he did what nobody else had successfully done before. He rid it of Pirates. Pompey, then, went to various places, establishing an ally of the King of Armenia, capturing Jerusalem, and making Syria a Roman duty. Pompey was a great general, but not a very good politician.  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  In 59 BC Pompey returned to Rome to find that tensions with himself and Crassus had grown. Both Crassus and Pompey had large armies, but also pieces of the city that were loyal to them. Cicero, the leader of the sena te, allied himself with Pompey through great flattery. Cicero told Pompey that he must be the protector of the republic. Crassus had other plans, and by 57 BC both men were in Italy with their armies. Before war broke out Julius Caesar stepped in.  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Caesar being a neutral negotiator used these well-known talents and convinced Pompey, Crassus, and Cicero to meet. The men worked out an agreement. This settlement had never been made before among the leaders of Rome. Caesar convinced Crassus and Pompey to join their power and influence with his own. Caesar was a successful leader of Gaul at this time. So the three agreed, and formed what is today known as the First Triumvirate. During this time Pompey married, most likely for political reasons, Julia, Caesar's daughter.  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚     Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Two of the three men returned to Rome and forced the Senate to obey them.

Pepsico Swot Analysis Essay

When making any investment decision, it is important for a potential investor to gain insight into the company. An evaluation of the company’s strengths, weaknesses, opportunities, and threats will help the investor determine if the venture is worth going into (Nickels, McHugh & McHugh, 2010). It also provides details about the internal status of the business and the future growth to expect in the future. SWOT Analysis Conducting a SWOT analysis of PepsiCo will help the company determine where change is possible. If the company is at a turning point, an inventory of its strengths and weaknesses can reveal possibilities. The identified strengths can be built on and used to their full potential and makes can be made to reduce the weaknesses. Potential problems that need to be addressed or at least recognized are identified. It will help PepsiCo discover what it does well, could improve, whether they are making the most of the opportunities around them, and whether there are any changes in the market that may require changes in the business (Nickels et al., 2010). Strengths PepsiCo has a diverse product portfolio that includes foods, snacks, and beverages with annual revenue of over $66 billion. The PepsiCo brands such as Pepsi, Gatorade, Tropicana, Mountain Dew, Lay’s, Aquafina, Sierra Mist, Fritos, and Quaker stand for quality and are well recognized household names. These brands generate over $1 billion each in annual global sales revenue which gives PepsiCo an advantage over its competition that have limited product line (â€Å"Brands,† 2012). Lower sales in one product line because of unforeseeable circumstances can be offset with promoting sales from another product line. PepsiCo’s geographical footprint is another strength of the organization. It currently operates in more than 200 countries worldwide which provides PepsiCo with diverse income sources. In 2011, only 50% of the company’s revenue came from the United States but this did not impact PepsiCo’s overall revenue growth because of the company’s increasing revenue from other parts of the world like Asia, Russia, Europe, and Latin America (â€Å"The Power of PepsiCo,† 2012). Weaknesses With the diverse portfolio of PepsiCo, not all products produced by this  company bear it name and its holdings are still seen by the public as separate entities, not as parts of PepsiCo. Its branding is not obvious and not easily recognized and this is hurting the image of the company. One of its most popular brands, Gatorade, recently changed its name to multiple sub-brands such as â€Å"G Prime 01,† and â€Å"G Series Pro 03 Recover† (Edwards, 2011). PepsiCo is gradually losing its credibility because of its lack of stability in management. The company has a high turnover rate and in the last four years, 26 senior marketing managers have resigned and those that are still with PepsiCo have been moved from one brand to another or from one division to another (Edwards, 2012). The revenue of PepsiCo is over dependent on sales to Wal-Mart. In 2011, approximately 18% of PepsiCo’s North American net revenue was from sales to Wal-Mart (including Sam’s Club). As a result PepsiCo is highly influenced with the business strategies of Wal-Mart (â€Å"The Power of PepsiCo,† 2011). Opportunities PepsiCo is investing its resources by expanding its operation in emerging foreign markets like China and Russia and developing continents like Africa. With the company’s recent purchase of Wimm-Bill-Dann, a Russian food and beverage company with huge market shares in dairy and juice products, PepsiCo will expand greatly its presence in Eastern Europe and Central Asia and is expected to increase its annual sales revenue by $5 billion (â€Å"Pepsi Absorbs Wimm,† 2011). PepsiCo recently signed a partnership agreement with Theo Muller, a German dairy company to sell its dairy products in the US starting with yogurt. PepsiCo will also invest in research to create new dairy products for the US market. This is a great opportunity for PepsiCo to increase its future revenue because it is predicted that annual revenue of $9 billion will be generated by 2016 with nearly 100 million American households expected to buy yogurt products (Steinberg, 2012). Threats PepsiCo faces a strong competition from The Coca-Cola Company, its primary competitor in the carbonated beverage category. These two companies have  had a long history of rivalry since the 1800s with Coca-Cola has a leader for most of the period. PepsiCo recently lost its five-year partnership deal with Dunkin’ Brands to Coca-Cola. Coca-Cola products will now be offered in 7,000 Dunkin’ brands outlets instead of PepsiCo products. In January 2012, Dunkin’ Brands announced the plan to double their outlet stores to 14,000 over the next 20 years. This is a huge revenue loss for PepsiCo (Fisher, 2012). Also in 2010, Diet Coke overtook Pepsi to become the second largest soda brand in the Unites States behind Coke, moving Pepsi to third (Theodore, 2012). There has been a steady decline in carbonated drink sales for the past seven years in the US with total sales dropping one percent in 2011. Americans are now turning to healthier food and drinks like bottled waters to avoid the high sugar contents in soda (â€Å"Soda Sales Fall,† 2012). Even with the diverse portfolio of PepsiCo, this decline in sales of carbonated soda drinks will have a negative impact on its total revenue. United States federal, State, and local laws and other regulatory authority in foreign countries could have a negative impact on the sales and profitability of PepsiCo. PepsiCo’s marketing, manufacturing, and distribution of its products can be affected as a result of what the government dictates. Also Governmental agencies that exist where PepsiCo operates can impose new labeling, accounting standards, product requirement, marketing practices, and taxation requirement. In California, PepsiCo is required to post a warning label on any product sold that contains a substance that the state has found to cause cancer or birth defect. If this type of law is enacted in other states or foreign countries, it would affect the sales of PepsiCo products (â€Å"The Power of PepsiCo,† 2011). Investor Analysis As a result of the SWOT analysis, investing in PepsiCo would yield a positive return on investment. The analysis shows a strong company with increase in earnings for the past five years. PepsiCo’s increasing presence in developing countries is most relevant in the decision to invest. With nearly 72% of the world’s processed food consumption in 2050 predicted to be  happening in developing countries because of increase in population, this will give PepsiCo a competitive edge. Internal and External Stakeholders The success or failure of PepsiCo is determined by how the wants and needs of its internal and external stakeholders are met. The internal stakeholders of PepsiCo are associates, shareholders, and board of directors. The external stakeholders of PepsiCo are consumers, local and foreign communities, retail and food service customers, partners, suppliers, and competitors. PepsiCo meets the needs of its associates by providing a supportive and empowering workplace. The company helps its employees to succeed by helping them develop the skills needed to increase the growth of the company (â€Å"Talent Sustainability,† 2012). The need of the shareholders of PepsiCo is met by striving to deliver top of the line financial performance and providing a high return on their investment (â€Å"Performance,† 2012). In 2011, the dividends paid to PepsiCo’s shareholders was six percent higher than 2010 ((â€Å"The Power of PepsiCo,† 2011). PepsiCo provides its consumers with a diverse list of products that delivers affordability and great taste. The company has recently begun offering consumers a wide range of healthy foods and beverages. Current products are constantly been improved and new products created to meet the changing needs of consumers (â€Å"Stakeholders Engagement,† 2012). Local jobs are created in the developing countries that PepsiCo operates in. PepsiCo provides support for education through PepsiCo Foundation grants. The company is working to protect the water resources they have used in India and working with nonprofit organizations to promote sustainable agricultural practices (â€Å"Stakeholders Engagement’† 2012). Products are delivered directly to retail and food service customers such as grocery stores, gas stations, restaurants, and vending machines. PepsiCo  also assist these stakeholders with marketing services that contributes to the customers’ growth and profit (â€Å"Stakeholders Engagement,† 2012). Conclusion A company’s strength, weaknesses, opportunities, and threats must be analyzed to determine the potential of the return on investment. Even with its weaknesses, PepsiCo is a strong company with earnings growth over the past five years, and has enough cash on hand to maintain its operation. With the new initiatives that PepsiCo is working on, such as expanding its market into developing countries and providing healthier options to its consumers, the company will be able to meet the needs of its stakeholders. References Brands. (2012) Retrieved from http://www.pepsico.com/Brands.html Diet Mountain Dew, Brisk and Starbucks Ready-T0-Drink Beverages Grow to the Billion-Dollar Brands for PepsiCo. (2012, January 26) Retrieved from http://seekingalpha.com/news-article/2139612-diet-mountain-dew-brisk-and-starbucks-ready-to-drink-beverages-grow-to-be-billion-dollar-brands-for-pepsico Edwards, J. (2011, June 22). Pepsi Just Can’t Stop Pulling the Tab After Shaking Up Management. Retrieved from http://www.cbsnews.com/8301-505123_162-42749107/pepsi-just-cant-stop-pulling-the-tab-after-shaking-up-management/ Edwards, J. (2012, May 10). How Pepsi Management Shuffles Led To Sales Collapse. Retrieved from http://www.businessinsider.com/how-pepsis-management-shuffles-led-to-sales-collapse-2012-5?op=1 Fisher, B. (2012, June 12). Pepsi loses Dunkin, Eyes Emerging Markets. Retrieved from http://beta.fool.com/bobbyfisher/2012/06/12/pepsi-loses-dunkin-eyes-emerging-markets/5599/?logvisit=y&source=eptcnnlnk0000001 Nickels, W. G., McHugh, J. M., & McHugh, S. M. (2010). Understanding Business (9th ed.). New York, NY: McGraw-Hill/Irwin. Pepsi Absorbs Wimm-Bill-Dann. (2011) Retrieved from http://rt.com/business/news/pepsi-absorbs-wimm-bill-dann-333/ Performance. (2012) Retrieved from http://www.pepsico.com/Purpose/Performance-with-Purpose.html Stakeholder Engagement. (2012) Retrieved from http://www.pepsico.com/Purpose/Overview/Stakeholder-Engagement.html Steinberg, J. (2012, July 11). PepsiCo Expanding Its American Portfolio With Dairy Products. Retrieved from http://seekingalpha.com/article/714491-pepsico-expanding-its-american-portfolio-with-dairy-products Talent Sustainability. (2012) Retrieved from http://www.pepsico.com/Purpose/Talent-Sustainability.html The Power of PepsiCo – 2011 Annual Report. (2011) Retrieved from http://www.pepsico.com/annual11/downloads/pep_ar11_2011_annual_report.pdf Theodore, S. (2012, August 13). Diet Coke Enters A New Decade: The Carbonated Soft Drink Brand Has Come A Long Way. Retrieved from http://www.mintel.com/blog/diet-coke-enters-new-decade-carbonated-soft-drink-brand-has-come-long-way Tomlinson, S. (2012, March 3). Soda Sales Fall Faster As Americans Turn To Healthier Options. Retrieved from http://www.dailymail.co.uk/news/article-2118291/Soda-sales-fall-faster-Americans-turn-healthier-options.html

Misguided Ink

Tattoos today are becoming very popular within the younger generation. Despite this creative trend of self expression, society still places judgment upon inked individuals. What ever happened to, don't Judge a book by its cover? Unfortunately, people fail to the person who really Lies behind the Ink. Having tattoo's can lead to a lot of misjudgment. Especially In the workplace.An employer might misjudge a potential employee with tattoos for a criminal, without a second thought. Even though it may be true that most prisoners have tattoos, it's not right to put everyone with a tattoo in that category. Even a prisoner with a tattoo could be falsely accused. Also, an employer might consider tattoos as a sign of less Intelligence. Since when does art become a sign of a weak mind? Being creative helps open closed minds. What's on a person's skin should not determine there abilities to work.Eventually, with the growing trend of tattoos, employers are going to have to reconsider there tattoo policies. One day this younger generation will be doing the hiring, it will become rare to not have tattoos. Regardless, there Is still a human being behind the Ink. Toffees make a statement groups, religion, and even memories. Tattoos are transforming into an art form rather than a lowly form according to some perspectives. As humans we have the gift of free will, who has the right to tell us what we can and cannot put on our bodies?Whether we use the gift of free will for good or bad we should not be Judged, since we all have a story to tell whether we express it through a tattoo or on a piece of paper. Tattoo's are a creative way of expressing inner feelings to the world, and can help with self esteem issues ND give someone a boost of confidence. To look down upon someone with tattoo's without knowing the full story behind the ink is like throwing away a flower. It takes a brave individual to express themselves to the world with a permanent line of ink.To be careless about what others may think of there bodied art is rather spontaneous. Judging a person with a tattoo is similar to Judging a child for coloring outside the lines. Coloring outside the lines can give someone the sense of freedom and self. What is even more misjudged is the creator behind the ink. Tattoo artist can be misjudged as well. The effort, thought, and talent that goes into the creating process of the tattoo can be challenging and time consuming.The creative process needs necessary machinery, a body with an idea, an experienced hobby rather than a real profession. Some would fail to realize tattoo artist have earned art degrees, while spending years building a portfolio of beautiful masterpieces of Art is everywhere, without it life would be a blank boring canvas. Some people may themselves as a canvas to splash color on. A tattoo is a way of expressing a feeling or image. Everyone has feelings, there is no need to place Judgment on someone who is tot afraid to express there inner bein g.A piece of art is a unique form of identity, we all want to be noticed, and have different ways of showing it. Its not right to Judge another as one is perfect. Color your own walls and leave no room for Judgment. There is more than what meets the eye, not everything that is seen is as bad as it seems. A open mind can set a soul free. It's not good to let the world define an individual based on there appearance. Don't let the world define beauty. True beauty and strength comes from within the soul, and Ink is only skin deep. Tattoos bleed out character.

POLAR vs BROWN BEAR essays

POLAR vs BROWN BEAR essays There are eight different species of bears found throughout the world: the spectacled bear, the Asiatic black bear, the brown bear (including grizzlies), the polar bear, the sun bear, the American black bear, the sloth bear and the giant panda. Even though most people can distinguish a polar bear from a brown bear by the color of the fur, a lot of people fail to identify all the differences among those two species. Both bears can be perceived as large, clumsy and lumbering beasts with heavily built bodies but short legs, necks and tails. Both of them have rounded ears and noticeably small eyes relative to their large body size. While both of the bears belong to same family, they have several profound differences. They live in different geographical areas, differ in amount of the population, size, physical features, some eating habits, and their The polar bear is found in all of the polar regions of the entire northern hemisphere. This includes Russia, Norway, Greenland, The United States and Canada. Their preferred habitat is in the area where the northern seas meet the shoreline. In this area, there is a constant freezing and thawing of the ice. It is estimated that there are currently somewhere between 20,000 and 40,000 polar bears. The polar bear is the largest member of the bear family, weighing in at between 440 and 1760 pounds with overall body length 11.5 feet. It can grow much larger, however. In fact, there is a record of an adult polar bear weighing over 2200 pounds. Polar bears have a distinctive all white fur which is important camouflage when hunting on the ice pack. Their actual color of the skin is black which is thought to be an adaptation for better heat retention. Compared to the other bears, the neck of polar bear is much longer. This makes it easier for the ...

Alternative Meanings for Hand and Names of Its Parts

Alternative Meanings for Hand and Names of Its Parts Alternative Meanings for â€Å"Hand† and Names of Its Parts Alternative Meanings for â€Å"Hand† and Names of Its Parts By Mark Nichol The human hand is such a quintessential element of our anatomy we wouldn’t be human without ours (specifically, without our prehensile thumbs) that we have applied the word to many literal and figurative senses other than the physiological one, as well as a wealth of idiomatic phrases (too many to list here). Here’s a discussion of alternative meanings of hand, as well as those for its parts. Hand can refer to participation or an offer of assistance, or it denotes a round of applause. It applies to a body part or a component of an object resembling a hand, and a symbol resembling a hand with an outstretched index finger is called a hand, or an index. An aspect, direction, or side is called a hand; on the other hand, the word also refers to the concept of control, possession, or supervision. One can give one’s hand as a pledge (usually, in reference to marriage), and one’s signature or handwriting is called one’s hand. The word denotes ability or skill, or interest or participation or a significant role. In card or other games, hand refers to the cards or game pieces held, to a round in a game, or to a player in a game; by figurative extension, it means â€Å"the strength of one’s position.† In the realm of a rougher game, pugilistics (boxing), or in fighting in general, hand identifies a punch. The creator or producer of a work might be acknowledged as a hand; it could also reference someone with knowledge of or skill in a specific topic, or handiwork or workmanship. The word also applies, more mundanely, to an employee or worker, especially a laborer, or a member of a ship’s crew (or the figurative equivalent). In a sense more akin to tactile connotations, hand describes the feel of a material. Finger, too, has other meanings, including something resembling a finger in shape or function, or a measurement equivalent to the general width of a finger. As a verb, it means to identify or to touch, to extend as a finger would be extended, or to play music using one’s fingers. Likewise, thumb applies to something with a thumblike appearance, and, as a verb, it means â€Å"to leaf through a book or to cause wear by doing so,† or â€Å"to hitchhike or to signal for a ride by holding out one’s thumb.† A knuckle, too, is something that looks like a joint in a bodily appendage (or, in the case of a cut of meat, is that anatomical part from livestock), including a weapon worn on the knuckles and more commonly called brass knuckles. Knuckle can also refer to a part of a hinge or to a structural component with the appearance of a knuckle. To knuckle is to press or rub with one’s knuckles. Palm extends to objects that might remind one of that part of the hand; the palm tree derives its name from resemblance of the fan-shaped leaves to a hand. A palm is also the act of palming; to palm is to conceal with one’s hand or to stealthily give or take something, or, by extension, to commit fraud. It also means to touch with one’s palm, as in the basketball violation of resting a ball in one’s hand during dribbling. Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Vocabulary category, check our popular posts, or choose a related post below:70 "Home" Idioms and ExpressionsRules for Capitalization in TitlesFew vs. Several

The Impact of Global Financial Crisis on the UK Consumer Buying Dissertation

The Impact of Global Financial Crisis on the UK Consumer Buying Behaviour - Dissertation Example Analysis 41 4.2.1.Demographic Findings 41 4.2.2.Descriptive Findings 45 4.2.3.Frequencies of Responses 48 4.2.4.Cross Tabulation of Responses with Respondents’ Income 59 4.3.Regression Results 63 4.4.Chapter Summary 66 Chapter 5: Interpretation of Research Results 67 5.1.Introduction 67 5.2.Interpretation of Results 67 5.3.Thematic Analysis of Interview Responses 67 5.4.Chapter Summary 71 Chapter 6: Conclusion and Recommendations 72 6.1.Conclusion 72 6.2.Recommendations 72 List of References 74 List of Figures Figure 1: Theoretical Framework 18 Figure 2: Risk Attitude and Risk Perception 25 Figure 3: Demographic Findings – Age Group 42 Figure 4: Demographic Findings – Gender 43 Figure 5: Demographic Findings – Marital Status 44 Figure 6: Demographic Findings – Occupation 44 Figure 7: Demographic Findings – Income 45 Figure 8: Regression Findings – Consumption Behaviour vs Psychological Factors 64 Figure 9: Regression Findings – Consumption Behaviour vs Situational Factors 65 Figure 10: Regression Findings – Consumption Behaviour vs Marketing Mix Factors 65 List of Tables Table 1: Risk Attitude and Risk Perception 24 Table 2: New Trends in Consumption Behaviour 27 Table 3: Impact of Financial Crisis on Consumption Behaviour 29 Table 4: Survey Questionnaire Statements 37 Table 5: Interview Questions 38 Table 6: Demographic Findings – Age Group 42 Table 7: Demographic Findings – Gender 42 Table 8: Demographic Findings – Marital Status 43 Table 9: Demographic Findings – Occupation 44 Table 10: Demographic Findings – Income 45 Table 11: Descriptive Findings – Psychological Factors 46 Table 12: Descriptive Findings – Situational Factors 47 Table 13: Descriptive Findings – Marketing Mix Factors 47 Table 14: Descriptive Findings – Consumption Behaviour 48 Table 15: Cross Tabulation – Respondents’ Income vs Responses Against Stateme nts 63 Table 16: Regression Findings 64 Table 17: Thematic Analysis 68 Abstract The researcher of this study aims at investigating how the recent financial crisis of 2008 influenced buying behaviour consumers in the United Kingdom. In this regard, the researcher has decided to adopt a mixed approach which covers both qualitative and quantitative aspects of the research. By opting for a mixed approach, the researcher is able to address the limitations associated with each of the two approaches. The research work has concluded that there is a significant impact of various factors, such as psychological factors, personal factors, social factors, situational factors and marketing mix on the development of consumption behaviour. Moreover, the impact of financial crisis has