Managing Retail Productivity and Profitability

Question: Discuss about the Managing Retail Productivity and Profitability. Answer: Introduction: The company Bellamys Australia, formerly known as the Tasmanian Pure foods had been started up a Tasmanian Family in the year 2004. The company offers a wide variety of the organic food and products for the toddlers, young babies and children. The company provides a wide variety of products ranging from the birth to the childhood of an early age. Bellamy believes the providing of nutrition that is uncomplicated in nature. The company provides the best food that is nutritious and wholesome for the care of the children. It always has the pursuit of providing the purest form of food to nourish the mild and gentle stomachs of the younger generations (Vickerstaff and Johal 2014). The company has a belief in the instilling of the healthy and mindful food choices for the babies in the path of growing healthy and intelligent children and adults in the near future. The company is a certified company by the NASAA, the most leading organic certifier of the nation. The company makes and packs all the products in Australia and maintains the highest requirements of the safety of food wherever in the world. The families at any places in the country have a trust and confidence that the products produced in Australia, will surely have a highest quality of the products (Cotching et al. 2014). The company has ingredients sourced out with a commitment of utilizing the most fresh, higher quality and certified ingredients being organic in nature. The company also focuses on the maintenance of the most economical, social and ecological sustainability in the mind that extends the preparation and packaging of the organic foods. The company is listed on the Australian Stock Exchange and the company takes control of the Corporate Governance structure. The following are maintained by the company: The crucial link between the corporate culture and governance is maintained by the company. The diversity in the composition of the Board is presented by the company and the innovation for the competitive environment and technological advancements and the growth of the security of the same (Berry and Gribble 2016). The environmental, governance and social considerations has been reported by the company and the same has been reported and managed under the exposures of risks and responsibilities of social structure. There is a continuous disclosure of the series of the developments and other important information in the company. The oversight of the management and important foundations are presented in the accounts of the company (Bamber and Parry 2014). Analysis of the company Particulars 2014 2015 2016 Net Profit Margin 5.59% 12.62% 5.68% Return on asset ratio 11.75% 18.79% 5.12% Return of ordinary shareholders equity(B/D) 14.92% 24.98% 9.13% Net profit margin ratio: The ratio helps in measuring the total of net profits produced with the amount of sales. The higher the ratio, the better is the position of profitability of the company. The revenue of Bellamy marked a change of a downfall of 7% in approx from the year 2015 to 2016. Even though, the company had been able to increase the ratio from 6% to 12% in 2014 and 2015 respectively, it became unsuccessful in the year 2016 (Holland et al. 2016). Thus, there must be effective control in maintaining the same for the better performance and profitability. Return on assets: The ratio measures the net profits created by the amount of total assets i.e. the average of the opening and closing amount of the total assets. The return on assets ratio considers the effective management of the assets to construct profits throughout a stage. In 2015, the year marked a successful increase in the return that meant a good situation for the financial position of the company. In 2016, there was a major downfall in the ratio i.e. again a major defect in the effectiveness of the procedures of a business (Johal et al. 2014). Return on common stockholders equity ratio: The return of the equity determines the success of the company in earning the incomes for benefitting the ordinary investors of the company. The company has again showed a decline in the ratio i.e. the profitability as it has shown a decline from 25% to 9% in the years 2015 to 2016 respectively (pi?ka 2016). Particulars 2014 2015 2016 Accounts receivable turnover 5.91 2.44 4.70 Inventory Turnover 6.29 18.79 5.12 Accounts receivable turnover: It is the ratio that measures the receivables from the debtors and the time decides the efficiency of the ratio. The more the ratio, the more the efficiency of collecting the receivables and the company is efficient as the ratio is 4.70 i.e. 5 times approx in a year. Inventory turnover: the ratio measures the movement of the inventory and the ratio compares the cost of goods sold or cost of sales with the average inventory of the company. The movement of the inventory is represented by the ratio and the higher the ratio, the more efficient the company. The ratio has decreased from 19 to 5 in the year 2015 and 2016 that must be checked and controlled by the management (Karunaratne et al. 2014). Short-term solvency Ratios Particulars 2014 2015 2016 Current Ratio 4.68 3.62 1.85 Quick Ratio 3.59 2.76 0.73 Current ratio: The current ratio must be 2 in minimum for the best effectiveness; the company is maintaining the liquidity. The company had a ratio of 5 and 4 in approx for the years 2014 and 2015 that has decreased in the year 2016. Hence, the ratio must be maintained. Quick ratio: It is also known as acid test and computes the position of convertibility in meeting the current liabilities and assets, thus making it better for evaluating in comparison to the current ratio. It has a conservative nature in contrast to the current ratio and the same helps towards demarcating and ruling the stock and prepaid expenses leading to a structuring of conversion difficulty to get the cash ready for availability. The better position of a business is the result of a greater quick ratio. The ratio has declined i.e. 0.73 from 2.76 in the years 2015 and 2016 respectively, to a bad position that needs to be checked and controlled (Laffy and Walters 2016). Long-term solvency Ratios Particulars 2014 2015 2016 Debt-to-equity ratio 0.01 0.00 0.17 Debt-to-total assets 0.01 0.00 0.08 Debt to equity ratio: The ratio calculates the total debts by the total equity possessed by the company. The ratio helps in the determination of the solvency of the company in viewing the meeting of the debts or borrowings with the possessed equity of the company. The debt to equity ratio is too low that represents that the debts are too low and easily met by the company which is definitely a sign of a best policy used by the management and the company (Maynard 2013). Debt to total assets: The ratio considers the total debts divided by the total assets i.e. the position of the company in maintaining the debts of the company through the total amount of assets present. The company is maintaining the debts as the ratio is zero in the years and hence the company is being able to manage the debts from the total assets of the organization (Moustafa 2014). Market based Ratios Particulars 2014 2015 2016 Price earnings ratio 1.23 0.31 0.59 Dividend yield 0.00 0.19 1.47 Earning yield 0.82 3.22 1.70 Price/Earnings ratio: The market price and the Earning per share of the company are measured by the division of the price to earnings. The price to earnings ratio specifies the price expected from the earnings of a stock. Higher Price/Earnings ratio more often than not indicates a positive performance and makes the investors invest in stocks. The ratio has increased from 2015 to 2016 and thus, it must control and manage the same (O'Hare 2013). Earnings yield: The yield obtained by the earnings or the total profits of the firm determines the ratio of the earnings yield. The higher the ratio, the better are the earnings and the yields from the above. The yield has decreased but is at a stable level and hence must try to enhance or maintain the same. Dividend yield: The ratio measures the total cash dividends circulated to the ordinary shareholders and that is comparative to the per share market value of the firm. The ratio has increased comparatively and must try to maintain and keep up the position. Conclusions The company is maintaining its efficiency of paying off its debts and also the position of liquidity. Based on the above evaluation, it has been found that Bellamy has been going through tough financial situations. Even though, it is recovering from such conditions in the current year, there are various lacks in the other scenarios discussed above. For providing effective information to the investors, dividend yield ratio and price/earnings ratio have been computed and evaluated critically. After the conduction of such critical evaluation, it is found that Bellamy has not paid any dividend to its investors over the two-year period due to fall in net income. Thus, investing in this organisation might not assure the investors to obtain yearly returns, which would further attribute to their investments. Along with this, the price/earnings ratio obtained suggests that the share price of Bellamy is highly overvalued with unstable rate of return. References Bamber, M. and Parry, S., 2014.Accounting and Finance for Managers: A Decision-making Approach. Kogan Page Publishers. Berry, N.J. and Gribble, K.D., 2016. Health and nutrition content claims on websites advertising infant formula available in Australia: A content analysis.Maternal child nutrition. Cotching, W.E., Oliver, G., Downie, M., Corkrey, R. and Doyle, R.B., 2014. Land use and management influences on surface soil organic carbon in Tasmania. Soil research, 51(8), pp.615-630. Holland, K., Lindop, S. and Zainudin, F., 2016. Tax Avoidance: A Threat to Corporate Legitimacy? An Examination of Companies Financial and CSR Reports. Johal, P., Vickerstaff, B. and McAuliffe, E., 2014.Unlocking Financial Accounting. Routledge. Karunaratne, S.B., Bishop, T.F.A., Odeh, I.O.A., Baldock, J.A. and Marchant, B.P., 2014. Estimating change in soil organic carbon using legacy data as the baseline: issues, approaches and lessons to learn.Soil Research,52(4), pp.349-365. Laffy, D. and Walters, D., 2016.Managing Retail Productivity and Profitability. Springer. Maynard, J., 2013.Financial accounting, reporting, and analysis. Oxford University Press. Moustafa, A.E., 2014. The Debatable Distance between Theory and Practice: An Analysis of Financial Ratios Theory. O'Hare, J., 2013.Analysing Financial Statements for Non-specialists. Routledge. pi?ka, J., 2016. Market Concentration and Profitability of the Grocery Retailers in Central Europe.Central European Business Review,5(3), pp.5-24. Vickerstaff, B. and Johal, P., 2014.Financial Accounting. Routledge.

AA Meeting Report free essay sample

The meeting that I attended was called â€Å"The Way of Life Group†. It took place at Palos Methodist Church, 12101 S Harlem Ave on Monday, January 20, 2014 at 7:00 PM. There were about twenty to thirty people at the meeting. They were all very friendly and welcoming to me as an observer. There were new members and older members and everyone was very open about their situation and dependence on alcohol. Overall, the participants were of all ages, ethnicities, and there was an even amount of men and women. The biggest thing that I noticed about the participants that were at the meeting was that they did not look like my perception of someone who was suffering from alcohol dependence. They were like average people that I would meet during everyday life or someone that I could even see as a friend. It never occurred to me that these individuals would be normal everyday people. I assumed that they would be dysfunctional and unable to participate in the meeting, but many of them looked healthy and were happy to participate and talk at the meeting. Testimonial There was an individual who gave a testimonial. This individuals name was Maurine and her sobriety date was September 28, 2005, at the age of 50. She has completed her recovery, but continues to return to help others with her story and because she believes it helps her to be a stronger person. She grew up on the South side. Her father was also an alcoholic, but he was not an everyday drinker. Maurine stated that she believe that her father being an alcoholic had caused a lot of problems in her later years. She caused a lot of problems for herself that caused her daughter to stop speaking to her for five years. She is a social worker and has been ever since she graduated college. However, her drinking problem had gotten so bad that one day she was in the hospital and had to be visited by a social worker, or as she stated â€Å"a social worker to see the social worker†. This was the turning point when Maurine realized that she was suffering from alcohol dependence. When she got out the hospital, she called the number of A. A. and she went to her first meeting at a church. The only reason that she stayed and went through A. A. was the fact that there was someone who waited for her at the end of the meeting. He invited her to another meeting and stated that he would be there. She did not believe in the A. A. process, but she still went to the meeting and she was surprised at the fact that there was someone willing to support her. She stated that they told her to take her recovery one day at a time, but she was happy if she could just make it fifteen minutes at a time. Maurine said that now she is embarrassed by her past and that it was hard and scary for her to get through the process. Nevertheless, she listened to the people at the meetings and felt that she could connect to the people who would speak at the meetings. She got divorced because of the fact that the person she was with would not stop drinking and she believed that it would be problematic to her recovery. The biggest thing that she believed helped her through her recovery was the fact that people in A. A. would actually did the things that they said they would and that she enjoy the time with the people she meet at A. A. The people she spent time with now did not require the type of excitement that she needed when she was drinking, but at the same time they could have fun together. After her life of alcohol and â€Å"excitement†, she finally was able to trust people and moreover she was able to trust herself. She does not dwell on her problems as much anymore and she believe that she is not the same person that she was before. Maurine believe that the only reason she was so successful was because of the fact that she kept coming to the A. A. meetings. She stated that she will keep coming back as long as she can to help other and because she does not want to become someone who falls back on their dependency of alcohol. Issues Addressed The issues that were addressed during this meeting all revolved around the twelve steps and traditions. The individuals at the meeting worked hard to promote these steps and traditions so that all the newcomers were aware of them and understand them. However, I think that the biggest issues that were addressed at this meeting were encouraging the newcomers that there is something greater than them that will help them with their alcoholism and the fact that the group always be there for those willing to make a change for the better with their dependence on alcohol. I think that both of these issues are extremely important. I believe without a strong spirituality an individual will have a hard time in life and will turn to other outlets like alcohol to find a way to cope. Also I believe that having a support group to help you through your hard times will give an individual a better chance at success and being able to overcome their dependence on whatever drug they may use, like alcohol. Both of these issues seemed like important things and I was glad to see that they were addressed during the A. A. meeting that I attended. Role of a Sponsor The sponsor helps the individual through their journey in A. A. They are supposed to guide them through AA with the twelve steps and help them to become more connected to the program. They help encourage the patient to attend meetings and help them have a positive attitude throughout the process. They should not make the individuals dependent on them. Instead, they should help the individual to understand for themselves how to use the twelve step program to be successful in their journey and then be able to help others do the same. They help to promote a better life for the person they have sponsored so that they will not have any need or desire to drink again. The sponsor should be there to answer question for the individual, but at the same time the sponsor does not have all the answers. The sponsor acts as a friend and a mentor for the newcomer in A. A. (Whelan, 2009). The â€Å"Big Book† In the A. A. meeting, there were a lot of times where the â€Å"Big Book† was brought up by the people attending the meeting. The full name of this book is Alcoholics Anonymous: The Story of How Thousands of Men and Women Have Recovered from Alcoholism. It is currently on its fourth edition and the first edition was written by William Wilson and Bob Smith. This book contains the twelve steps and twelve traditions in the beginning part of the book. It contains stories of men and women who have recovered from alcoholism. This book acts as a guideline for individuals who are in A. A. and helps them to see others who have been successful in overcoming the problem. This is important because it helps the individual suffering with alcohol dependence and let them know they are not alone in this journey and there were many before them who were successful. (Alcoholics Anonymous World Services, Inc. , 2014) 12 Steps and 12 traditions During the A. A. meeting, the twelve steps and twelve traditions were explained. To begin, the twelve steps included: 1. We admitted we were powerless over alcohol – that our lives had become unmanageable. 2. Came to believe that a Power greater than ourselves could restore us to sanity. 3. Made a decision to turn our will and our lives to the care of God as we understood Him. 4. Made a searching and fearless moral inventory of ourselves. 5. Admitted to God, to ourselves, and to another human being the exact nature of our wrongs. Were entirely ready to have God remove all these defects of character. 7. Humbly asked Him to remove our shortcomings. 8. Made a list of all persons we had harmed, and became willing to make amends to them all. 9. Made direct amends to such people wherever possible, except when to do so would injure them or others. 10. Continued to take personal inventory and when we were wrong promptly admitted it. 11. Sought through prayer and meditation to improve our conscious contact with God as we understood Him, praying only for knowledge of His will for us and the power to carry that out. Having has a spiritual awakening as the result of these steps, we tried to carry this message to alcoholics, and to practice these principles in all our affairs. Next the twelve traditions were discussed in the A. A. meeting as well. These twelve traditions included: 1. Our common welfare should come first; personal recovery depends upon A. A. unity. 2. For our group purpose there is but one ultimate authority – a loving God as He may express Himself in our group conscience. Our leaders are but trusted servants; they do not govern. 3. The only requirement for A. A. membership is a desire to stop drinking. 4. Each group should be autonomous except in matters affecting other groups or A. A. as a whole. 5. Each group has but one primary purpose – to carry its message to the alcoholic who still suffers. 6. An A. A. group ought never endorse, finance, or lend the A. A. name to an related facility or outside enterprise, lest problems of money, property, and prestige divert us from our primary purpose. 7. Every A. A. group ought to be fully self-supporting, declining outside contributions. 8. Alcoholics Anonymous should remain forever nonprofessional, but our service centers may employ special workers. 9. A. A. , as such, ought never be organized; but we may create service boards or committees directly responsible to those they serve. 10. Alcoholics Anonymous has no opinion on outside issues; hence the A. A. name ought never be drawn into public controversy. 11. Our public relations policy is based on attraction rather than promotion; we need always maintain personal anonymity at the level of press, radio, and films. 12. Anonymity is the spiritual foundation of all our traditions, ever reminding us to place principles before personalities. Response to Experience I thought this experience was extremely helpful. It taught me not to stereotype individuals. I was surprised by how friendly everyone was to me and how open they were to each other. This experience has taught me never to judge someone before I know their background and to try to be more understanding of others. I felt almost ashamed because I had unknowingly judged these individuals before I even meet them. However, overall I believe that this A. A.  meeting experience was positive and allowed me to see a new world that I might never see elsewhere. The things that I will take into my nursing practice with me from this experience are to be less judgmental and let the patient tell me their story before I decide how I feel about them. I think that this idea can be applied to any patient, not just patients that suffer from alcohol dependence. I believe that the best way for me to be a good and caring nurse is to put this idea into practice right away and to make sure that if I do have judgment towards a patient when I care for them. Other Treatments Some other treatments that are available for individuals who suffer from alcoholism include pharmacological, biological and social therapy. These treatments follow two goals. The first goal is providing a safe way to detox the individual and the second is encouraging the individual to want to recovery from their illness. The treatment usually depends on the patient and what they are going through because not all patient need to deal with withdrawal management. Drugs like Librium, Valium, Serax, Ativan and many other drugs can help the withdrawal symptoms, but overall the health of patient should be reviewed no matter what treatment is given. (Varcarolis Halter, 2009) There are many other types of treatments that are available for patients. Some of these therapies include avoiding individuals and places that cause you to drink, join a group like A. A, look for help from family and friends, look for new hobbies to help or join a church, and exercise can also be helpful to the patient (Edmundson, 2013). These are just some ways to help individuals who are having trouble with alcohol dependence. If the patient is experiencing alcohol withdrawal, they should be treated with some kind of medication. No matter what the treatment is, it should be specific to the patient and their needs. Conclusion Overall, A. A. meetings are an excellent idea because they provide support and leadership to individuals that are in need of help with their dependency issues. The experience was very helpful to me and allowed me to how A. A. members help people with a similar problem to get their life together and get rid of their addiction. I would defiantly recommend A. A. to anyone who is suffering with an alcohol addiction.

Sugar Dbq free essay sample

Just as how sugar and its tropical imports were dependent on each other, the slave and sugar trades were as well. As long as sugar was in demand, so were the slaves. And as long as slaves were used, sugar would keep being produced. The only way sugar was produced was by slavery. Readers realize this statement is true when analyzing document H. The document contains a list of requirements when owning a five acre plantation. When owning a five acre plantation it is a requirement to own at least 300 slaves. Illustrations of African slaves working on sugar production are shown in Document J, which is composed of two illustrations. The first is an 1823 illustration of a plantation, where only African slaves worked. The slaves are planting and working on a field, and most of these slaves were male. The second illustration is of a mass sugar production in a nineteenth century boiling house circa 1820, again all of the slaves are African, and this time most of the slaves were women, but both the first and the second illustrations had overseers watching the slaves. We will write a custom essay sample on Sugar Dbq or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Clearly the most successful and beneficial plantations owned plenty of slaves, because more slaves equal more sugar produced, which in the end means more money. This was shown in document I, the wealthiest plantation owners owned at most 2,183 slaves in the 1830s. Additionally, because the African slaves were used regularly, they were not at as high of a price. The average price for a male West African Slave was sixteen euros in 1768, while the average price for a male British Caribbean slave was 41 euros in that same year. This shows how much African slaves were regularly used, if they weren’t used as often, they would be much higher in price like the Caribbean slaves. Everything has a consequence. The sugar trade’s success did come with a price. Because slaves became a requirement to sugar production, they didn’t have a nice lifestyle like we have today. A simple explanation of this is in document D, even though document D was written anonymously it is most likely that this author was a slave considering the biased tone, however, the document does not lie. If sugar was not consumed it would not be imported – if it were not imported it would not be cultivated, if it was not cultivated there would be an end to the slave trade; so that the consumer of sugar is really the prime mover, the grand cause of all the horrible injustice which attends the capture, of all the shocking cruelty which accompanies the treatment, of the wretched African Slave. † It becomes obvious in t his document that slavery wasn’t a happy life. Another consequence of the slave life is shown in document k. It is to the cheapness of the labour of these poor people that those costly and extensive works, which are necessary in a sugr plantation are derived. † Slaves were not paid for their labor, slaves only had an original price when sold to a master, after that slaves worked without pay. However slaves were not the only ones who lived with consequences. Document E explains the health consequences for consuming sugar. â€Å"Children greatly injure their gums and teeth by eating sugar, and sweet things, whereas (cavity filled) teeth and corroded gums are most evidently owing to improper food for children. Sugar if consumed too much, could affect the health of children and most likely adults as well. All in all, the sugar trade had consequences which included slavery and the health of the general public. In conclusion, The sugar trade was most successful due to the hi gh consumer demand and the slave trade. This is shown by the evidence of sugar’s addictive properties and its easy use as a sweetener with certain goods. However sugar does have its health and slavery issues, not allowing Africans and other slaves to live they life they deserve.

Writing an Outline For Essay in College

Writing an Outline For Essay in CollegeIf you are writing a sample for essay in college, it is important to have a good outline. A sample for essay in college must include some useful ideas. An outline will help the reader be able to follow the written piece in the best way possible.The outline must contain important information such as the topic of the sample, the goals of the reader, the location of the samples, the writing style, and an end of the sample. The writers can include these things in the sample outline for an essay in college because it gives them a chance to see what to include. This outline is also a great way to get their ideas out of their heads and into the paper.First of all, they need to know what the basic idea of the project is. This is important because it can save them time when it comes to writing the outline. It will also allow them to have a good idea of the main ideas in the paper. If they already know the basic idea then they will be able to get a better idea of what they want to write.They should also find out what the goal of the sample is. They should know the main goal that is not just for the sample but also for the grade. This way they will know that they are accomplishing the main goal.Location is important for this kind of outline because they need to know where to start. Having an outline for an essay in college will make it easier for them to write. They will not have to hunt down the main idea on their own.They should also include a writing style. There are different writing styles and they need to know which one they are writing. Having a good writing style will make the sample easier to write because it will look more professional.When they are done with the samples, they should have a good idea of what to write. Having a good idea of what to write is very important. It will also allow them to be more organized.Lastly, they should finish writing each paragraph. This is to make sure that they are finished writing each p aragraph. They should have no gaps between the paragraphs to make sure that they don't forget to put the details in their paragraphs.

The Moral Of Everyman Essays - Everyman, Morality Play, Heaven

The Moral Of Everyman The Moral of Everyman Everyman, an English morality play, is an allegory of death and the fate of the soul. Summoned by Death, Everyman calls on Fellowship, Goods and Strength for help, but they desert him. Only Good Deeds and Knowledge remain faithful and lead him toward salvation. Everyman represents, in a worldly sense; every man. The play unfolds as he wrestles with his own qualities, whether they be good or evil. The way Everyman reacts to these qualities is impressive as they morally obligate him to do good or tempt him to do evil. Everyman can be pulled towards Heaven or Hell and it is not until Death knocks at his door that he begins to follow the path towards Heaven. Every character represents a different characteristic of the main character, Everyman. The characters are symbolic. For example, Beauty, Strength, and Discretion are some different characteristics that were expressed in Everyman. It is true that these characteristics make up a person, but they are not the most important. The most important characteristic in a person is doing good deeds. Knowledge also makes up who a person can be. Everyman had many important characteristics in his life, but, when Everyman went to the afterlife, the only thing that went with him was his knowledge, and good deeds. Death was an important character in Everyman. Death symbolized a messenger of God. He was the figure that went down to earth to retrieve Everyman and take him to the afterlife. Death was a significant part of Everyman because he motivated Everyman to find something to accompany him on his eternal journey to heaven or to hell. All of the characters that Everyman pleads with to be his companion forsake him. Only one character, Good Deeds, holds true to his word to accompany Everyman. When Everyman makes his reckoning to God, his good deeds are the only things that speak for him. In the end, Everyman's soul is saved, but only by the grace of God. For He and He alone decides who is admitted to His Kingdom. The strong influence of the Roman Catholic Church at that time period was evident in the references to Mary and Good Deeds. For they believed that good deeds could get you into heaven. Believing that you could gain entrance into heaven by simply doing good deeds is a foolish belief. For as Christians, we know that Ephesians 2:8 and 9 says, ?For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast.?

Reflections, Translations, and Rotations on SAT Math Coordinate Geometry Guide

Reflections, Translations, and Rotations on SAT Math Coordinate Geometry Guide SAT / ACT Prep Online Guides and Tips If it's always been a dream of yours to shift around graphs and points on the $x$ and $y$ axes (and why not?), then you are in luck! Points, graphs, and shapes can be manipulated in the coordinate plane to your heart's content. Want to scoot that triangle a little to the left? Flip it? Spin it? With reflections, rotations, and translations, a lot is possible. This will be your complete guide to rotations, reflections, and translations of points, shapes, and graphs on the SAT- what these terms mean, the types of questions you'll see on the test, and the tips and formulas you'll need to solve these questions in no time. Before You Continue Reflection, rotation, and translation problems are extremely rare on the SAT. If you're aiming for a perfect score (or nearly) and want to grab every last point you can, then this is the guide for you. But if you still need to brush up on your fundamentals, then your time and energy is better spent studying the more common types of math problems you'll see on the test. Remember, each question is worth the same amount of points, so it is better that you can answer two or three questions on integers, triangles, or slopes than to answer one question on rotations. So if you've got everything else nailed down tight (or you just really, really like coordinate geometry), then lets talk reflections, rotations, and translations! What is a Reflection? Just like how your image is reflected in a mirror, a graph or a flat (planar) object can be reflected in the coordinate plane. It can be reflected across the x-axis, the y-axis, or any other line, invisible or otherwise. This line, about which the object is reflected, is called the "line of symmetry." Most SAT reflection questions will ask you to identify a shape that is symmetrical about a line that you must imagine or draw yourself. These questions should be simple enough so long as you pay attention to the details. For example, The diagram below shows the Greek letter pi. Each side of the figure is reflected identically about a vertical line of symmetry. Of the letters shows bellow, which has both a vertical and a horizontal line of symmetry? A. B. C. D. E. Now, we are being asked for a letter that has BOTH a vertical AND a horizontal line of symmetry (even though the example, pi, only has a vertical line of symmetry). If you are going too quickly through the test, you might be tempted to find the letter with only a vertical line of symmetry like the example picture. Doing this, however, would lead you to select the wrong answer choice. So, now that we know that we must find a letter that is symmetrical both vertically and horizontally, let us examine our options. You can either draw lines of reflection in your mind or on the page, but we will draw it out here. Let us test our options by first giving them a vertical line of symmetry. If they fail the vertical test, then they will automatically be eliminated, with no need to test if they have a horizontal line of symmetry. (Remember, we are looking for a letter that has both.) So let us draw a potential vertical line of symmetry through each of our answer choices, starting with answer choice A. We can see that rho does not have a vertical line of symmetry, as each half is not a perfect reflection of one another. We can eliminate answer choice A. Each half of gamma is also not symmetrical with the other half. We can eliminate answer choice B. Mu is symmetrical about itself vertically and if you were going quickly through the test, you may be tempted to stop here. But we know we must also find a horizontal line of symmetry. Mu does not have a horizontal line of symmetry, so we can now eliminate answer choice C. Eta, as well, has a vertical line of symmetry. Let us see if it also has a horizontal one as well. Success! Eta is symmetrical, whether the line of symmetry is vertical or horizontal. We can stop here, as we have found our correct answer choice. Our final answer is D. Nature showing off its coordinate geometry skills. Clearly. What is a Rotation? Objects in the coordinate plane can also be rotated (turned) clockwise or counterclockwise. Imagine that we can adjust the object with our hands- it will spin, while still lying flat, like a piece of paper on a tabletop. To rotate an object, we must pick a point to act as the center point for our rotation. This center point of our rotation does NOT have to be the center of the shape, however; there must always be a center to our rotation, but we can pick any point to act as this center. Let us look at a visual demonstration of this. First, let's look at a shape that has a center of rotation at the center of the shape itself. Now we can see how the movement of the object changes as the center of rotation shifts. Here, we have a center of rotation as a point on the outline of the shape. But though any point can act as a center of rotation, you will almost always be asked to rotate an object "about the origin." This means that the origin (coordinates $(0,0)$) will act as your center of rotation. The angle about which the object moves is called the angle of rotation. As we rotate an object, the angle of rotation will be: Positive when we move the object counterclockwise Negative when the object is rotating clockwise. A positive angle of rotation. A negative angle of rotation. Through both objects ended up in the same place, one was rotated +180Â ° and the other was rotated -180Â °. If you are asked to rotate an object on the SAT, it will be at an angle of 90 degrees or 180 degrees (or, more rarely, 270 degrees). These are nice numbers that evenly divide the coordinate plane into 4 parts, and each of these degree measures has a standard rule of rotation. Let us look at these rotation rules. Note: if you're a little shaky on the different quadrants of the $xy$-coordinate plane and where $x$ and $y$ are positive and negative, you should take a couple of minutes to read through our article on the four graph quadrants before going to the next section of this guide. Put your cudgels away and we'll prove we're not fakirs. Rotation Rules and Formulas You can determine the new coordinates of your point if you rotate your object by a certain angle about the origin. [Note: these formulas only work when rotating a point or a series of points about the origin- they will not work if rotating the object about any other center of rotation.] Each of the three degree measures- 90, 180, or 270- will shift the coordinates of your original point to a different, calculable, position on the graph. If rotating counterclockwise (a positive angle of rotation), you can use these rules to find your new coordinate points. For example, let us start with a set of coordinates at $(4, 6)$ and rotate the point. Here we have our original coordinates of $(4, 6)$ For 90 degree rotations: $(a, b)$ = $(-b, a)$ If our original coordinates of (4, 6) are rotated 90Â °, the new coordinates will be (-6, 4). For 180 degree rotations: $(a, b)$ = $(-a, -b)$ If our original coordinates of $(4, 6)$ are rotated 180Â °, the new coordinates will be $(-4, -6)$. For 270 degree rotations: $(a, b)$ = $(b, -a)$ If our original coordinates of $(4, 6)$ are rotated 270Â °, the new coordinates will be $(6, -4)$. (And, of course, a 360 degree rotation will bring you right back to the beginning at $(a, b)$ again!) If our original coordinates of $(4, 6)$ are rotated 360Â °, the new coordinates will be the same, $(4, 6)$. â™ ª You spin me right round, baby, right round â™ ª What is a Translation? If we continue to think of the shape as a piece of paper lying flat on a table (on the coordinate plane), a translation is the act of sliding it along the coordinate plane in a particular direction. The shape can be translated up or down (or both!) any amount of distance along the plane. It maintains its shape and bearing, but is simply located elsewhere in the plane. The way to notate that a translation is to occur is by saying: $T_{a,b}(x,y)$ This means that your final coordinates for this point will be: $(x + a, y + b)$ For example, What is the new point for $T_{-3, 4}(2, -6)$? A. $(-5, 10)$B. $(-1, 2)$C. $(1, -2)$D. $(-5, -10)$E. $(-1, -2)$ We know that we must add together our translated points to the corresponding $x$ and $y$ values of our original coordinates. So: $T_{-3, 4}(2, -6)$ $(2 + -3, -6 +4)$ $(-1, -2)$ Our new coordinates for this point are at $(-1, -2)$. You can see why this is true if we look at it on a graph. We are starting at the coordinates $(2, -6)$. Now, we are traveling -3 spaces along the $x$-axis and +4 spaces along the $y$-axis. By tracing this, we can find our new coordinates. Our final answer is E, $(-1, -2)$. Typical Reflection, Rotation, and Translation Problems Again, these types of questions are extremely rare on the SAT, and the odds likely that you will not see any reflection, rotation, or translation problems at all on your test. That said, there are three different types of reflection/rotation/translation problems that will show up, when they appear at all. These questions will be either a reflection, rotation, or translation questions about: #1: Points#2: Shapes in the coordinate plane#3: Function graphs Let's look at all three. Points Points are the simplest objects to be rotated, reflected, or translated, because there is only one component- the single point. Any point on the coordinate plane will have an $x$-coordinate and a $y$-coordinate, but you will still have far fewer moving parts when dealing with a point rotation than with any other kind of rotation, reflection, or translation. Shapes Shapes are slightly more complicated to reflect or rotate than points are for the sheer reason that shapes are made up of several points (and the lines connecting those points). This means that any shape rotation/reflection/translation will require more consideration and care, in order to make sure all your pieces are properly aligned. It is often much easier, when working with modified shapes, to map out the positions of the points alone. Don't worry about the lines- mark the proper position of the new coordinates for the points and the lines will sort themselves out. For instance, let us say that we must rotate a trapezoid +90 degrees. The particular question may ask you to find the slope of one of the new lines of the rotated shape, identify a new coordinate point, or anything else. But first, we must rotate our figure. The easiest way to do this is to simply map the new coordinate points according to our rotating rules. We know that a 90 degree rotation will transform all of our coordinates from $(a, b)$ to $(-b, a)$, so let's find them. Each given coordinate point will transform like so: $(1, 1)$ = $(-1, 1)$ $(3, 4)$ = $(-4, 3)$ $(7, 4)$ = $(-4, 7)$ $(9, 1)$ = $(-1, 9)$ Now we can simply connect the lines and find our new trapezoid, allowing us to answer any question we need to about it. Function Graphs Finally, function graphs can be reflected or translated just like shapes and points, though NOT rotated. (Why can't functions be rotated? If a function were rotated, it would fail the vertical line test and no longer be a function.) A reflected function. A translated function. Functions cannot be rotated! This fails the vertical line test and so is no longer a function. Function Translations We can either translate our function vertically (up and down) or horizontally (left and right), or a combination of the two. The way we do this is by modifying our inputs and outputs (for more on how functions work, including inputs and outputs, check out our guide to SAT functions.) We can translate our function up or down by adding or subtracting from our output. Adding to output translates the graph up. Subtracting from the output moves the graph down. On the other hand: Adding to the input will shift the graph left Subtracting from the input will shift the graph to the right Function Reflections We can also reflect our function about a line of symmetry along the $x$ or $y$-axis. Making the output negative makes the function reflect across the $\bi x$-axis (inverts it about the $x$-axis). Making the input negative makes the function reflect across the $\bi y$-axis. If this is a lot of new information for you, don't stress. These types of questions are, again, so rare that the odds are you won't see them on your test. Only try to memorize these rules if you feel comfortable doing so. Strategies for Reflection and Translation Problems Though no two reflection/translation/rotation problems are exactly alike, there are a few tips and tricks to follow for any kind you may come across. #1: Draw Your Own Graphs Especially when dealing with a problem that requires a reflection or a translation, it is always a good idea to take a moment to sketch out a graph of the object's old and new positions in space. This allows you to work with the problem on the page instead of in your head, which is especially useful if you are asked to find information other than simply identifying a new coordinate point (a feat in and of itself!). For instance, you might be asked to find the slope of a reflected line, or the product of two translated $x$-coordinates, or anything else the SAT might think of. Without making your own drawings and diagrams, it can be easy to become confused, fall for bait answers, and lose precious points. #2: Drill Your Rotation Formulas When working with translations or reflections, it is simple enough to draw your own picture and line up your corresponding points, but when it comes to rotations, it can be much harder to visualize the movement of the point or the object. Even when you've mapped out the original point, rotations are often much trickier than they appear. Unless you have a paper cut-out of your point, shape, or function and want to spend your time spinning your scratch paper around in circles, it's better to simply memorize your rotation rules for 90, 180, and 270 degrees. #3: Double-check, double-check, (triple-check) Rotations, reflections, and translations may seem simple (and, indeed, the underlying principles are not overly complex), but the difficulty in solving these kinds of problems is in just how easy it is to mis-map a coordinate point or two. Nothing is more frustrating than when you know how to solve a problem, but go too quickly or too carelessly and so get the question wrong. So make sure you double-check that you've properly shifted your coordinates before you bubble in that final answer. Test Your Knowledge 1. 2. The graph $y = f(x)$ is shown below. What could be the graph of $y = f(x + 3)$? A. B. C. D. E. Answers: E, A Answer Explanations: 1. If we draw an imaginary vertical line through every letter in the answer options, we can see that all but one are symmetrical about that vertical line. Only the letter E has a different shape to it on each side of the vertical line. Our final answer is E. 2. We know that adding to the input or output will shift our graph and translate it somewhere else. In this case, we are adding to the input, which, you'll recall, translates our graph to the left. We are making no additional changes, so its vertical position will remain unchanged. The only answer choice that shows us a graph that maintains the vertical position and is shifted to the left is answer choice A. Here is the starting position of the function. And here it is shifted to the left in answer choice A. Our final answer is A. Yay! You did it! The Take-Aways Though quite rare to see, the surprise rotation or reflection question can throw a wrench in the works if you are unprepared for it. But nothing the SAT can put on the test is insurmountable (and, indeed, the test is designed to give you opportunities to succeed). Once you've got your understandings down tight and know not only the difference between all your terms, but how to properly take down any kind of coordinate geometry question the SAT can throw at you, you will be well on your way to earning that perfect score. What's Next? You've taken on one of the more obscure SAT math topics, but have you made sure that you have a solid understanding of all the rest of the math topics the SAT will test you on? As always, it is better to get as many points as possible (as accurately as possible), so now might be a good time to catch up on your understanding of circles, triangles, and integers, both basic and advanced. Want to know two of the most invaluable math strategies? Check out our guides on how to use plugging in numbers and plugging in answers to make sense of some of the trickiest SAT problems out there. Looking to get that perfect score? Our team has your back with our guide to getting a perfect 800 on the SAT math, written by a perfect-scorer. Want to learn more about the SAT but tired of reading blog articles? Then you'll love our free, SAT prep livestreams. Designed and led by PrepScholar SAT experts, these live video events are a great resource for students and parents looking to learn more about the SAT and SAT prep. Click on the button below to register for one of our livestreams today!

The British Inventor and Industrial Designer Sir James Dyson

The British Inventor and Industrial Designer Sir James Dyson British industrial designer, Sir James Dyson is best known as the inventor of the Dual Cyclone bagless vacuum cleaner, which works on the principle of cyclonic separation. In laymans terms, James Dyson invented a vacuum cleaner that wouldnt lose suction as it picked up dirt, for which he received a  Ã¢â‚¬â€¹U.S. patent  in 1986 (U.S. Patent 4,593,429). James Dyson is also well known for his manufacturing company Dyson, which he founded after failing to sell his vacuum cleaner invention to the major manufacturers of vacuum cleaners. James Dysons company now outsells most of his competition. James Dysons Early Products The bagless vacuum cleaner was not Dysons first invention. In 1970, while he was still a student at Londons Royal College of Art, James Dyson co-invented the Sea Truck, with sales amounting to 500 million. The Sea Truck was a flat-hulled, high-speed watercraft that could land without a harbor or jetty. Dyson also produced: the Ballbarrow, a modified wheelbarrow with a ball replacing the wheel, the Trolleyball (also with a ball) which was a trolley that launched boats, and the land seafaring capable Wheelboat. Inventing Cyclonic Separation In the late 1970s, James Dyson began inventing cyclonic separation to create a vacuum cleaner that would not lose suction as it cleaned, inspired by his Hoover brand vacuum cleaner that kept clogging and losing suction as it cleaned. Adapting technology from the air filter in his Ballbarrow factorys spray-finishing room, and supported by his wifes art teacher salary, Dyson made 5172 prototypes to perfect his bright pink G-Force cleaner in 1983, that was first sold by catalog in Japan. (see additional images for photo) Say Goodbye to the Bag James Dyson was unable to  sell his new bagless vacuum cleaner design to an outside manufacturer or find a UK distributor as he originally intended, in part because nobody wanted to rock the huge market for replacement cleaner bags. Dyson manufactured and distributed his own product and a brilliant television advertising campaign (Say Goodbye to the Bag) that emphasized the end to replacement bags sold Dyson vacuum cleaners to consumers and sales grew. Patent Infringement However, success often leads to copycats. Other vacuum cleaner manufacturers began to market their own version of a bagless vacuum cleaner. James Dyson had to sue Hoover UK for patent infringement winning $5 million in damages. James Dysons Latest Inventions In 2005, James Dyson adapted the wheel ball technology from his Ballbarrow into a vacuum cleaner and invented the Dyson Ball. In 2006, Dyson launched the Dyson Airblade, a fast hand dryer for public bathrooms. Dysons most recent invention is a fan without external blades, the Air Multiplier. Dyson first introduced Air Multiplier technology in October 2009 offering the first real innovation in fans in more than 125 years. Dyson’s patented technology replaces fast-spinning blades and awkward grilles with loop amplifiers. Personal Life Sir James Dyson was born on May 2, 1947, in Cromer, Norfolk, England. He was one of three children, whose father was Alec Dyson. James Dyson attended Greshams School in Holt, Norfolk, from 1956 to 1965. He attended the Byam Shaw School of Art from 1965 to 1966. He attended the Royal College of Art in London from 1966 to 1970 and studied furniture and interior design. He went on to study engineering. In 1968, Dyson married Deirdre Hindmarsh, an art teacher. The couple has three children: Emily, Jacob, and Sam. In 1997, James Dyson was awarded the Prince Phillip Designers Prize. In 2000, he received the Lord Lloyd of Kilgerran Award. In 2005, he was elected as a Fellow at The Royal Academy of Engineering. He was appointed a Knight Bachelor in the New Years Honours December 2006. In 2002, Dyson set up the James Dyson Foundation to support design and engineering education among young people. Quotes I just want things to work properly.A lot of people give up when the world seems to be against them, but thats the point when you should push a little harder. I use the analogy of running a race. It seems as though you can’t carry on, but if you just get through the pain barrier, youll see the end and be okay. Often, just around the corner is where the solution will happen.