Wednesday, November 27, 2019

A Comprehensive Cheat Sheet for Fractions

A Comprehensive Cheat Sheet for Fractions Fractions Cheat Sheet This cheat sheet provides a basic outline of what you need to know about fractions when you are required to perform computations that involve fractions. Computations refer to addition, subtraction, multiplication and division. You should have an understanding of simplifying fractions and calculating common denominators prior to adding, subtracting, multiplying and dividing fractions. Multiplying Fractions Once you remember that the numerator refers to the top number and the denominator refers to the bottom number of a fraction, you are on your way to being able to multiply fractions. You will multiply the numerators, then multiply the denominators and will be left with an answer that may require one additional step: simplifying. Lets try one: 1/2 x 3/41 x 3 32 x 4 8Therefore the answer is 3/8 Dividing Fractions Again, you need to know that the numerator refers to the top number and the denominator refers to the bottom number. In the case of division of fractions, you will invert the divisor and then multiply. Put simply, turn the second fraction upside down (this is called the reciprocal) and then multiply. Lets try one: 1/2 x 1/31/2 x 3/1 (we just flipped 1/3 to 3/1)3/3 which we can simplify to 1 Notice that I began with Multiplication and Division? If you remember the above, you wont have much difficulty with those two operations as they dont involve calculating the like denominators. However, when subtracting and adding fractions, were are often required to calculate the like or common denominators. Adding Fractions When  adding fractions with the same denominator, you leave the denominator as it is and add the numerators. Lets try one:3/4 9/413/4 Of course, now the numerator is larger than the denominator so you would simplify and have a mixed number:3 1/4 However, when adding fractions with unlike denominators, a common denominator needs to be found prior to adding the fraction. Lets try one:2/3 1/4 (the lowest common denominator is 12)8/12 3/12 11/12 Subtracting Fractions When subtracting fractions with the same denominator, leave the denominator as it is and subtract the numerators. Lets try one:9/4 - 8/4 1/4However, when subtracting fractions without the same denominator, a common denominator needs to be found prior to subtracting the fraction. Lets try one:1/2 - 1/6 (the lowest common denominator is 6) 3/6 - 1/6 2/6 which can be reduced to 1/3 There are times when youll simplify the fractions when it makes sense.

Sunday, November 24, 2019

The magic and illusion Essays

The magic and illusion Essays The magic and illusion Essay The magic and illusion Essay Essay Topic: Invisible Monsters Prospero has a servant in the form of the spirit Ariel. Ariel has lots of special powers himself. He can be invisible and cause lots of apparitions to take place. Sometimes, Ariel is visible to everyone on the stage. Obviously, the audience can see him whenever he appears on stage, but during certain times in the play, he is invisible to different people. To show this in the 17th century would have been very hard. Clues have to be taken from the script which suggests when Ariel was invisible to certain people. Another way of learning when he is visible to different people is to study the way in which he speaks. If he speaks to someone directly, he will normally be visible to them. If he speaks to the audience rather than to the person, he is invisible. A 17th century audience would have to bear this in mind when watching the play. Being very superstitious, they would understand, however, that spirits only appear to certain people at certain times, so it would not be too hard for them to take this on board. An example of Ariel being invisible to only a section of the actors on the stage is in Act 1 Scene 2, when Ariel sings an enchanting song to Ferdinand, luring him to meet Miranda. Neither Miranda nor Ferdinand can see the spirit, but Prospero can, and he talks to Ariel, promising to set him free. In Act 3 Scene 3, Prospero conjures up a banquet for Alonso and the rest of the royal party. Just as the members of the party prepare to eat, the banquet disappears. This would have been very difficult to show in the 17th century. I cannot think of any way 17th century actors would have been able to show this, apart from standing the banquet table on a trap door and then releasing the trap door. This is not a perfect way of showing the table disappear, but it is the only way I can think of showing it in 17th century theatre. Towards the end of the play, a lot is said about Gods of the Ancient Romans, particularly Juno, Ceres and Iris. In most Jacobean masques, there was a lot of emphasis on classical mythology. Prosperos masque is no different. Audiences in 17th century England would have a basic knowledge of Ancient Roman and Greek gods. They would know the names of the gods and what they stood for. Before the masque, Ariel appeared as a harpy to Alonso and his friends. A harpy was part of ancient mythology. A 17th century audience would take the events in The Tempest as gospel. They believed in witchcraft and spirits. The Tempest was all about these things, so the people just took it as a play which included, and may have been based on, real incidents. The inclusion of Caliban within the play gives an insight into 17th century travel. America was a relatively new country as far as Europe was concerned. Europeans considered themselves civilised. When they encountered a new race of people, they were considered uncivilised and savage. This is emphasised in Caliban, who is shown as a monster. He is ridiculed by Prospero an educated and civilised Duke, and when Trinculo discovers him, he considers taking him back to Italy as a sort of freak-show. Were I in England and had but this fish painted, not a holiday fool there but would give a piece of silver: there would this monster make a man; any strange beast there makes a man: when they will not give a doit to relieve a lame beggar, they will lay out ten to see a dead Indian. Europeans did not understand the new race of people that they had found, and because they were different, they were considered dangerous. In the play it is said that Calibans mother was a witch. This adds to the bad attitude of the Europeans to the Native Americans. The Tempest is based around Italy, but Shakespeare still refers to the Englishs attitude towards foreigners, by making Trinculo talk about what it would be like if he were in England. He does not just mention any country in Europe he mentions England. Maybe this is because Shakespeare did not have any knowledge of other European countries attitudes, or perhaps he just thought England was the worst in this way. Things are very different in the 21st century. We no longer believe in superstitions such as witches and evil spirits. There is always the odd person who holds onto old beliefs, but generally, we are rid of those superstitions. Science and mathematics can explain most things that happen. For a world that no longer believes in witches and monsters, we still have a lot to do with these things. We read horror books about beings coming back from the dead; we still celebrate Halloween; we watch films of vampires and witches. In the 17th century, these things would have been taken very seriously. Nowadays, however, it is only for fun that we do these things. Shakespeares plays are still watched the world over, the same plays that were watched when he first wrote them. They have not been changed and so still contain wizards, witches, monsters and spirits within them. However, modern-day directors have to find a way of presenting these magical creatures to a modern-day audience without them appearing comical. As part of the play, the characters must be taken reasonably seriously so that the story can be appreciated. 21st century audiences expect more from a play than they would have done 300 years ago, even if the play were written that long ago. Although modern directors have a somewhat harder task than their 17th century counterparts, they have technology on their side. Technology has increased magnificently since The Tempest was first performed, and this enables directors to create more spectacular special effects. Electricity plays a massive part in these effects. With the use of electricity, different lighting can easily be used for different scenes, to create different atmospheres. The first major part of the play takes place on the ship during the storm. More elegant scenery can be used to create the impression that the actors are indeed on a ship. Special lighting used alongside sound effects, can be used to give the impression of sailing on the sea. Thunder and lighting can be heard in the distance with the aid of a sound recorder. Prospero has a lot of powers. As well as controlling the elements, he has power over human beings. After telling Miranda the story of how they arrived to be on the island, Prospero wishes to talk to Ariel. Miranda does not know of the existence of Ariel, so before he talks to his servant, Prospero sends her to sleep. He does this by making her sit on his magic cloak, and then by a sort of hypnosis, she falls asleep. This act of magic does not require any special effects. All it needs is good acting by the actors playing Miranda and Ferdinand for the audience to believe that it is happening. A lot of the magic events that take place in the Tempest are similar to the one above. Many do not need special effects, and just rely on the talents of the actors. When Prospero freezes Ferdinand, all the actor playing Ferdinand has to do is simply stand still. After the storm, the next magic event that would require some thought would be when Ariel sings a song to Ferdinand about his father. Ariel at this time is invisible to Ferdinand. To make this clear to the audience, Ariel could be suspended by some wires above Ferdinand, so he cannot see the spirit. Alternatively, only Ariels voice could be heard, so it is clear that the spirit cannot be seen. This trick could be used when Ariel overhears Sebastian and Antonio plotting to kill Alonso. He could hover above the traitors in the same way that he did when luring Ferdinand to Miranda. When he sends the group to sleep, he could sprinkle some glitter or some kind of dust over them. That way, it is visible to the audience that something is going on. The main acts of magic are the banquet, the masque and Ariel appearing as a harpy. The banquet and the harpy incident could be shown by the same method. Both are illusions that disappear after being seen by Alonsos group. Both these incidents could be shown by holograms, which could be projected from the back of the theatre onto the stage. Advanced computer imaging could make it seem as if the harpy was talking, then the hologram could simply disappear, making it seem as if the objects were actually on the stage and have vanished. Despite what the audience believes outside a theatre, once inside, they are usually willing to believe anything as long as it makes good theatre. Most people will let go of their normal beliefs if it means that they will enjoy the show more. Directors have to keep this in mind. Maybe the audience will not believe in spirits and witches in everyday life, but if a play they are watching contains these things, they will accept them, as long as they are made reasonably believeable. For a play to be successful, a director has to make sure that the illusions and magic are portrayed as realistically as possible and the audience can believe for a while that these things are real.

Thursday, November 21, 2019

MArketing Essay Example | Topics and Well Written Essays - 2250 words

MArketing - Essay Example However, it has been recommended to focus on the development of broader range of healthy and organic products due to the shift of the consumers’ preferences towards healthier eating habits is a great niche for the company. Starbucks might broaden its existing range of food items by offering innovative and tasty but healthy food items. Also, Starbucks could strengthen significantly its market position by selecting a good â€Å"victim† for M&A. In case of successful acquisition, Starbucks could develop and launch relevant campaign devoted to its healthy product line. Also, as the company is operating through franchising system in the UK’s market it might be helpful to promote its franchising opportunities through launching a broad marketing campaign and participation in various franchising events and exhibitions. By developing its network through franchising, Starbucks will be able to capture a larger market share within a short period of time and thus will be more competitive on the market. Starbucks Corporation is the US-based premier roaster, marketer and retailer of specialty coffee, operating globally (MarketLine Advantage 2014). The company began its story in 1971 in Seattle (Starbucks.com, 2014). Nowadays, its presence is covered by the 19, 767 retail stores operating in 62 countries all over the world (MarketLine Advantage 2014). In addition to purchasing, roasting and selling whole bean coffees, handcrafted coffee, tea and other variety of beverages, the company offers different fresh food items in its stores (MarketLine Advantage 2014). Starbucks also sells its products and licenses trademarks through grocery and national foodservice accounts and licensed stores (MarketLine Advantage 2014). The Food and Beverage sector in the UK’s economy has a broad definition as it is comprised of different sub-sectors (Thornton 2010). The major sub-sectors include: dairy products, soft beverages, frozen and chilled foods,