THE IMPACT OF TRADE ON LABOUR Essay Example | Topics and Well Written Essays - 2250 words

THE IMPACT OF TRADE ON LABOUR - Essay Example Then it has collected some data of international trade volume and unemployment rate of a developing and a developed nation to find out whether any strong relationship does exist between the two variables. On the basis of its research, the study has come to the conclusion that trade does not significantly affect labor market in real world. Introduction: According to the Economic theory, we know that there are gains from trade. But these gains are reflected as net gains. Despite there been a secular increase in both exports and imports and has been regarded as a percentage of Gross National Product which is considered to be beneficial for the economy and also though the increased exports have generated additional employment opportunities, but still these changes have been accompanied by reduced employment opportunities and adjustment burdens for workers in import-competing industries. The workers had to adapt themselves to the new working environment of changing demand conditions in th e import competing industries which involve extended periods of job research, restraining and relocation which demands to be a bit costly venture. As per the analysis, women and the minorities, the less educated and the lower paid groups, as compared to men, had to take more burdens on themselves and they were not in a position to afford the cost even. Since the last two decades, quite a number of developing countries have undergone liberalization of their trade regimes. The proponents of such liberalization have argued that one of the chief beneficiaries of greater openness to trade is the workers in these countries. Basically, trade liberalization with abundant supply of labor has encouraged producers to reallocate output towards labor intensive goods. Hence the resulting increase in the demand for labor, given the labor market conditions, has translated into some condition of an increase in employment and wages. The logic behind this argument has been totally justified and compel ling and has been supported by the proponents of early liberalization as the Newly Industrialized Economies of East Asia like Hong Kong, Korea, Singapore and Taiwan. According to Robbins in the year 1996, and Wood in 1997, recent episodes of trade liberalization have appeared not to have been associated with large improvements in prospects for the typical worker. The apparent divergence between the expectations of liberalization advocates and the recent evidence has been explained by various factors. For example, the liberalization in trade has lead to an inflow of new technologies from abroad. But in this case, the growing evidence suggests that the new technologies are increasingly skill biased and therefore according to the recent episodes of trade liberalization that may lead to an increased demand for workers but that will comprised of less number of workers who are highly skilled, as per Wood in 1997. ( Wood, 1997) On the other way, the available evidence may be incomplete in some important ways. As for example, it has been highly observed that the short run effects of liberalization are likely to be adverse for aggregate labor, even among the proponents of trade liberalization. It takes a lot of time for resources to get reallocated in new firms and industries and it is also possible that the available time series is not enough to capture the effects of trade fully. In a similar way, the number of countries that have been taken into observation may not be the most appropriate ones.

Modern Irony Essay Example for Free

Modern Irony Essay Since the beginning of time, man has attempted to unravel the seemingly infinite mysteries of life. The English playwright Tom Stoppard has written plays that address the existence of fate (or a predestined outcome for every human being) and controlling ones own destiny. His plays also deal with the many other uncertainties that arise during a normal persons life; such as sex, how we know things, etc. (Tom Stoppard) Stoppards utilization of satire and drawn parallels mirror the image of lifes faults and intricacies. His plays serve to show people the humor and irony that life presents. During the time that Stoppard wrote his first play, Rosencrantz and Guildenstein, society was experiencing a social upheaval. The late sixties was a time of experimentation and existentialism. People were asking questions about their very existence in a way never before seen. In this climate, Stoppard saw the opportunity to begin writing plays that dealt with the issues of the time (Overview of Tom Stoppard). He took a whimsical spin though, on the method in which he delivered it. He embarked on the continuing journey of a great literary tradition, but diverged from its path by ridiculing it. His desire to write plays was not a spontaneous venture; during this era, many people wanted to express their thoughts and feelings, and plays were a common medium. Stoppard observed this and pondered if success and knowledge could be his as well. The general question being asked around this time was Why are we here? Man has always sought an answer to this question, but now more than ever was it expressed in literature and plays. Stoppards craft shows a propensity for humor, which offers a more light-hearted viewpoint of this previously serious and mundane subject. Stoppard asks the question of not only Why are we here? but also How are we here? as well. He explores the intricacies of life in an attempt to derive a meaning. His comical touch alleviates the heavy association of philosophy though. Whether or not his question is answered is secondary to the method in which we view it. In Stoppards eyes, it is more important to live rather than to comprehend why we live. This approach brought fanfare to Stoppard, as society saw his style as fresh; and a tangible device to which they could relate. Literary history has had a heavy impact on Stoppards method and conceptual presentation. He admits to being swooned by such masterpieces as Waiting for Godot by Samuel Beckett, and The Love Song of J. Alfred Prufock by T. S. Elliot. The ideas that he extracted from these artists and their works helped him divulge his own style to which he could further literature. A parallel may be drawn between Waiting for Godot and Stoppards Rosencrantz and Guildenstein are Dead. Both works feature two men, and their journey in existentialism. Becketts version has them waiting for a surreal character (Godot) that, in the end, never appears. The characters are portrayed as confused, and the play takes on an air of severe depression. The play is very much an appeal to the audience, as they too are overcome by this depression. The characters slowly fade away, emotionless and unexcitable. Stoppards version though has his characters embark on a journey; a fruitless journey, but a goal to meet none the less. Beckett disarms his audience, while Stoppard embraces them into his play; making the audience feel at home and comfortable. Stoppard diffuses the rather heavy atmosphere belied by Beckett with satire and a whimsical wit. For example, In Rosencrantz and Guildenstein are Dead, Stoppard portrays the idea of death as a game. He does this in an attempt to show the audience that it is not to be feared. He achieves this by his satirical depiction of the internal play within Hamlet by Shakespeare. The characters in the play perish, and then the actual characters die in the exact same manner. The audience can identify with death, as all humans are concerned with their own demise. They take away though, a much less serious approach in viewing it. The other author, Elliot, often depicted his characters as stumbling and indecisive. One of his most famous works, The Love Song of J. Alfred Prufrock, deals with a man who is enamored with the variables and uncertainties of approaching a woman that he admires. In the poem, Prufrock realizes that only he cares about his decision, and whether he chooses to pursue her or not, will not matter. He sees himself as part of his own world; in which he is the sole occupant. He, sadly, is only coherent enough in his world though to realize how much he is potentially missing by not being completely immersed in it. He cannot solve this problem though, and continues wandering and pondering till the end of time. Stoppard took away from Elliot a similar stance to character development. He portrays his characters as aware, but not completely in tune with their surroundings. The effect is one of dismay, but comical as well. Stoppards portrayal is more humorous in nature, displaying them as bungling and unresponsive. This is exemplified in his play, Rosencrantz and Guildenstein are Dead. His characters attempt to divulge the plan and their purpose as designated by the King (Claudius), but are unable to fully grasp its meaning. These literary greats do not contribute the fabulous humor that Stoppard has developed though. His humorous elements can best be equated to his passion for the Theatre of the Absurd. This type of theater came into popularity during the 1950s and 1960s; and was applied to plays that portrayed the human situation without purpose and with absurd plot elements. This form was a reemergence of an attempt towards awareness of mans purpose in life; the sense of wonder that man has always had concerning how things work and why. In some respect, it was anti-theater, as it went against the basic premise of regular theater. It was illogical and usually had very little or no plot (Culik). Stoppards fascination with this art form had a profound impact on his own personal style. Sigmund Freud, a proponent of the Absurd, said, In trying to burst the bounds of logic and language, the absurd theater is trying to shatter the enclosing walls of the human condition itself. (Culik) This confirms the spatial concepts that the theater was attempting to portray, and Stoppards comedic element is based upon this illogical and removed nature. The play Rosencrantz and Guildenstein are Dead is a satirical look upon the much more staunch play Hamlet. It delves into the lives of two supporting characters named Rosencrantz and Guildenstein. The characters unimportance is exemplified in the play by their lack of understanding and baffling thought patterns. This play shows Stoppards portrayal of artificiality of theater. The performance is not about the actual play, but the context of the play; the idea of attending the performance. The characters appeal directly to the audience, instead of becoming immersed in its story and plot. The effect is comical, as the play begins with them merely spinning coins and making bizarre implications towards the audience. Rosencrantz has spun the coin and received heads nearly 85 times. His humorous portrayal of the law of averages is his justification for his luck. This is the plays first look into why things happen. The characters are unable to come to a proper conclusion though; and the path that Rosencrantz begins upon (the law of averages) cannot be farther removed from the truth. The play continues with these hilarious situations, finally having the pair receive their mission from Claudius the King. The pair ponders why they have received the mission, and why they must complete it. Stoppard constantly asserts that a play is being read. ; instead of allowing the reader to delve into a story. He makes the reader think of Hamlet, and its tragic implications; and applies a humorous tone to it. In the end of the play, Rosencrantz and Guildenstein are supposedly murdered (the English king is instructed to execute them, but their actual deaths are not witnessed), but instead of a grand exit, they merely fade away. Stoppard shows through this that the characters had served only a menial and insignificant purpose. The reader is unable to sympathize with the characters demise, as the play is portrayed with a comical tone. This disservice to death with satire is both eye widening and thought provoking. A person is assaulted with the moral implications of death, instead of offering a deaf sympathy to the characters grief. Stoppards ability to allow the playgoers to analyze what they feel is his greatest achievement in the work; not the story itself. Stoppards play Arcadia is another intelligent play that provokes the reader to appraise mans life long debacles. In the play, the characters attempt to grasp the mysteries of sex, and a path towards knowledge that leads to an understanding of the future. The latter is portrayed as an equation developed by Thomasina, in an attempt to control her own destiny. Her professor, Septimus, also contributes to the equation by way of a lesson to his student, Thomasina. He explains to her that the loss of knowledge isnt the end of the world; as it is rediscovered eventually in the future. This subject is an explanation of humanitys technological progression and our knowledge. The play attempts to allow the reader to grasp the many unknown or misunderstood concepts in life. Mysteries such as sex can only be acquired through practice and progression of time. Stoppard appeals to the general public that things cannot be instantly understood; they must be studied and experimented with to fully grasp the full meaning. These mysteries will eventually be solved, but it shall take time and patience; nothing is instantaneous in life. Stoppards inclusion of Thomasinas equation is both humorous and practical in its implication. Thomasinas goal was to create an equation that could more or less tell the future. It is humorous to surmise that a simple equation can predict the future with numbers. The limitless variables and uncertainties in life will forever impede such an advancement. Stoppard attempts to explain that life itself is intangible; it can neither be predicted nor reduced to a simple equation. Stoppards plays contain many useful outlooks on how a person should view their life on earth. People are always concerned with the future and their own death (and when it will occur). Stoppard believes that man shouldnt view life with such a critical eye; and instead should accept certain facts to be true. Man is powerless concerning the ability to control life. There are many uncertainties in life that are both humorous and infinitely escapable to the human mind. His plays show inept characters driven into the ground by their consumption of the study of life. Stoppard suggests through his characters comical adventures that life is for living, and the consequence of a life spent longing and pondering equates to a life disenfranchised of pulp and meaning. The meaning which man longs for cannot be quantified; it must be experienced to break the surface of significance. Works Cited Stoppard, Tom. Arcadia. Stoppard, Tom. Rosencrantz and Guildenstern Are Dead. Tom Stoppard. DISCovering Biography. Online Edition. Gale, 2003. Student Resource Center. Thomson Gale. 17 January 2005Â  http://galenet.galegroup.com/servlet/SRC

The Necessity of Marrying Well in Jane Austens Sense and Sensibility E

In Jane Austen’s Sense and Sensibility, the necessity of marrying well is one of the central themes. In Austen’s era a woman’s survival depended on her potential to acquire an affluent partner. This meant a choice of marrying for love and quite possibly starve, or marry a securing wealthy person, there was a risk of marrying someone who you might despise. Passage One, portrays the relationship between Marianne and Willoughby. Marianne was blinded by her love, ‘He was exactly formed to engage Marianne’s heart.’ Marianne is someone who can show no concern for wealth if she believes she has found true love. Willoughby was estimated to be ‘Faultless as in Marianne’ Willoughby was all that Marianne fancied, her affection for him was beyond everything else. This is rather ironic for Willoughby the man she loves holds a wholly contradicting viewpoint on the matter. Willoughby is willing to sacrifice even the greatest of loves if it cannot secure status and wealth. Passage one also indicates the necessity of marrying well. Mrs. Dashwood illustrates a shallow reaction to the situation ...

Symbol and Symbolism of Water in Toni Morrisons Beloved Essay

The Powerful Symbol of Water in Beloved Water. It expresses its’ power in the form of hurricanes and flash floods. It displays its gentleness, washing dirt off a child's scabbed knee. Water has been used to quench the thirst of many longing throats; and it has been the cause of death to those who unfavorably crossed its path. It possesses the power of total destruction, yet it holds the bases of all life. Generally, water has symbolized cleanliness and renewal. In the Bible, water was used in Baptism, cleansing the soul of original sin and offering a new life in the light of God. Water in itself is a natural purifier, washing the dirt from our bodies. Water is a symbol of transition-from dirty to clean. In Beloved, Morrison uses water to introduce a transition between stages in a character's life. Water separates one stage of a character's life from another. Paul D.'s escape from Alfred, Georgia was directly helped and represented by the rain that had fallen in the past weeks. Paul D. was sent to Alfred, George because he tried to kill Brandywine, his master after the schoolteacher. In Alfred, he worked on a chain gang with forty-five other captured slaves. They worked all day long with "the best hand-forged chain in Georgia" threading them together. They slept in a cell dug out of the earth. A man's breaking point was challenged everyday. It was hell for Paul D. Then it rained. Water gave Paul D. his freedom. The rain raised the water level in the in-ground cell so they could dive, "down through the mud under the bars, blind groping," in search of the other side (p. 110). One by one each of the forty-s... ...d that Beloved was Sethe's child. Sethe broke water to represent Beloved's second birth. Sethe was now whole again. She had found the child that she had lost. The water symbolized the beginning of her life with Beloved. Sethe could now begin sharing her life with Beloved again. She could Ice-skate, take walks, or just begin to love her child again. Beloved describes the struggle and challenge of former slaves trying to deal with an unforgettable past. Their brave journey carries them through tragic times full of torment and torture, and joyful times full of love and tenderness. Beloved teaches the lesson of never giving up. Water denotes a change for the better--from dirty to clean--where a person rebounds from life's tragedies. It symbolizes hope and reassurance that life will improve.

Outlining an Informative Speech: Anabolic Steroids

| Outlining an Informative SpeechAnabolic Steroids in Sports| | | OUTLINE OF SPEECH ATTENTION-GETTING OPENER An athlete is a person who is trained or skilled in exercises, sports, or games requiring physical strength, agility, or stamina. Athletes train and practice year-round to prepare for the competition and challenges. Most high school, college, amateur and professional athletes participate in sports for the opportunity to pit their abilities against those of their peers, and to experience the satisfaction that comes from playing to their potential. Others do so to satisfy a desire for recognition and fame.Unfortunately all this creates some athletes who are determined to win at any cost. Have you heard or know of anyone who has used anabolic steroids? PREVIEW Today I will give you some interesting facts about the use of anabolic steroids in sports. I Description and definition II Reasons for using III Famous Athletes IV Effects V Solutions BODY TRANSITION: To better understand m y report, first we should know what anabolic steroids are. I Description and definition A. A group of usually synthetic hormones that are derivatives of testosterone, are used medically especially to promote tissue growth B.Are sometimes abused by athletes to increase the size and strength of their muscles and improve endurance C. Non-medical use of anabolic steroids is illegal and banned by most major sports organizations D. In January 2005, the Anabolic Steroid Control Act was amended with the Controlled Substance Act that added anabolic steroids to the list of controlled substances and makes possession of the substances a federal crime TRANSITION: You may be asking by now, what are the reasons that make athletes use these drugs? II Reasons for using A. To gain advantage B. Lack of self esteem C.Peer, competitive, fan and media pressure TRANSITION: Now, I will mention some famous athletes that used, during their careers and competitions, anabolic steroids. I’m sure you know most of them. III Famous Athletes who used anabolic steroids A. Heidi Krieger B. Ben Johnson C. Mark McGwire D. Florence Griffith Joyner E. Brian Bosworth F. Arnold Schwarzenegger G. John Kordic H. Danny Harris I. Lyle Alzado TRANSITION: Ok, I will now proceed to mention some of the harmful effects that this drug has on the athletes that use and abuse them. IV Effects A. Damage to the kidneys and liver B.Alteration of the balance of the natural hormones C. Some male users form breasts D. Serious acne problems E. When used by teens it can cause stunted growth F. Genital changes, water retention, yellow eyes, coronary artery disease, high blood pressure, and changes in cholesterol levels G. Ligament injuries and sterility H. Women run the risk of male pattern baldness I. Coma and death J. HIV transmission K. Withdrawal symptoms L. Depression TRANSITION: After mentioning the harmful effects, I will explain some solutions that should be taken to reduce the use of this dangerous drug by all athletes.V Solutions A. Legal 1. Restrictive laws 2. Penalties B. Education: Change of athlete’s attitude 3. Thorough knowledge of the sport's physical demands and requirements 4. Maintenance of a healthy lifestyle 5. Appreciation of the satisfaction that comes from participation TRANSITION: After my presentation, you should now understand why some athletes use anabolic steroids and the effects this drug has on them. SUMMARY Now, you understand the most important facts of anabolic steroids in sports. I Description and definition II Reasons for using III Famous Athletes IV EffectsV Solutions Concluding Remarks In conclusion, any athlete of any age should be educated in light of the hazard and negative effects that the anabolic steroids has on a body. Some athletes persist in taking them, believing that these substances provide a competitive advantage. But beyond the issues of popularity or legality is the fact that anabolic steroids can cause serious physical and psycholo gical side effects. ACTUAL SPEECH INTRODUCTION I. An athlete is a person who is trained or skilled in exercises, sports, or games requiring physical strength, agility, or stamina.Athletes train and practice year-round to prepare for the competition and challenges. Most high school, college, amateur and professional athletes participate in sports for the opportunity to pit their abilities against those of their peers, and to experience the satisfaction that comes from playing to their potential. Others do so to satisfy a desire for recognition and fame. Unfortunately all this creates some athletes who are determined to win at any cost. Have you heard or know of anyone who has used anabolic steroids? II. Today I will give you some interesting facts about the use of anabolic steroids in sports.A. Description and definition B. Reasons for using C. Famous Athletes D. Effects E. Solutions TRANSITION: To better understand my report, first we should know what anabolic steroids are. BODY Ana bolic steroids are â€Å"any of a group of usually synthetic hormones that are derivatives of testosterone, are used medically especially to promote tissue growth, and are sometimes abused by athletes to increase the size and strength of their muscles and improve endurance†. Non-medical use of anabolic steroids is illegal and banned by most major sports organizations.In January 2005, the Anabolic Steroid Control Act was amended with the Controlled Substance Act that added anabolic steroids and prohormones (a precursor to a hormone) to the list of controlled substances and makes possession of the substances a federal crime. TRANSITION: You may be asking by now, what are the reasons that make athletes use these drugs? TRANSITION: Now, I will mention some famous athletes that used, during their careers and competitions, anabolic steroids. I’m sure you know most of them. Over the years many professional athletes have been focus of the media, after being caught using anabol ic steroids.To name only a few, here are some examples. Heidi Krieger proved herself one of the world's top athletes in the 1980s, winning medal after medal in the shot put for East Germany. Heidi Krieger, the 1986 European women's shot-put champion, became Andreas Krieger after a sex-change operation in 1997. He said he had been fed so many steroids by his coaches without his knowledge that physical and emotional problems began. We remember when Ben Johnson was stripped of his gold medal in the 1988 Seoul Olympics. Many athletes that were seen as heroes had their problems with anabolic use.Good examples of athletes that were made to look like heroes were Mark McGwire and Florence Griffith Joyner. Flo Jo was suspected of drug abuse when she won her gold medals in the Olympics. She was tested ten years after the Olympics and came up negative, but most steroids are out of a person's system within weeks. She was idolized by millions, so no other discussions came up on the topic of her drug use until her death. She was said to have died in a fit of epileptic seizures. Later investigations showed she died of cardiac problems, a health problem that can be brought on by steroid use.According to CBS News, other examples of professional athletes that used steroids were Brian Bosworth, Arnold Schwarzenegger, and John Kordic. American Danny Harris ranked number one in the hurdles in 1991, failed a drug test, and was suspended for four years. The best known case of steroid use was Lyle Alzado. Lyle, the former defensive end, had an inoperable brain tumor that left his once-massive body ravaged. He blames years of heavy use of steroids and human growth hormones. Alzado took steroids almost daily for nearly 20 years. This prolonged use killed him.TRANSITION: Ok, I will now proceed to mention some of the harmful effects that this drug has on the athletes that use and abuse them. The negative effects of this drug are many. Some of the negative effects of the drugs are damage to the kidneys and liver. A person can also alter the balance of the natural hormones. This can cause detrimental affects to the body. The effects of your natural hormones being out of balance can last several years after being off the drugs. Some male users form breasts due to the use of steroids. Because of the increase in testosterone, steroids can cause serious acne problems.When used by teens it can cause stunted growth. Other side effects include genital changes, water retention, yellow eyes, coronary artery disease, ligament injuries, high blood pressure, and changes in cholesterol levels, sterility and liver disease. The list goes on and on. Women that use steroids run the risk of male pattern baldness. Some effects of steroids are even worse. Some people fall into comas after injecting the drugs, some may even die from the injections. Sometimes, athletes who use anabolic steroids may share the needles, syringes or other equipment they use to inject these drugs.By sharing ne edles, syringes or other equipment, a person becomes a high risk for HIV transmission. HIV is the virus that causes AIDS. Athletes who use steroids can also experience withdrawal symptoms when they quit. The symptoms include mood swings, depression, fatigue and irritability, loss of appetite, insomnia, and aggression. Depression can even lead to suicide attempts, if untreated. TRANSITION: After mentioning the harmful effects, I will explain some solutions that should be taken to reduce the use of this dangerous drug by all athletes.The attitude of winning at any cost embraced by some athletes must be redirected and replaced by personal dedication to the sport; a thorough knowledge of the sport's physical demands and requirements; maintenance of a healthy lifestyle; and, an appreciation of the satisfaction that comes from participation. Our athletes should be educated since their early age about the effects and consequences of using anabolic steroids. There should be also restrictive laws and penalties for the athletes that are caught using this drug, no matter their fame or money.TRANSITION: After my presentation, you should now understand why some athletes use anabolic steroids and the effects this drug has on them. CONLUSION I. Now, you understand the most important facts of anabolic steroids in sports. a. Description and definition b. Reasons for using c. Famous Athletes d. Effects e. Solutions II. In conclusion, any athlete of any age should be educated in light of the hazard and negative effects that the anabolic steroids has on a body. Some athletes persist in taking them, believing that these substances provide a competitive advantage.But beyond the issues of popularity or legality is the fact that anabolic steroids can cause serious physical and psychological side effects. VISUAL AIDS 1. List of ideas a. Power point presentation of pictures of anabolic steroids, famous athletes that have used the drug, and their pictures before and after using them. b. Short captions or tapes of the athletes during their performances. 2. Power point, because the captions or tapes can be inserted in the presentation. 3. The visual aid could be used as guide in each of the transitions.

Algebraic Operations on ACT Math Strategies and Formulas

Algebraic Operations on ACT Math Strategies and Formulas SAT / ACT Prep Online Guides and Tips Variables, exponents, and more variables, whoo! ACT operations questions will involve all of these (and so much more!). So if you ever wondered what to do with or how to solve some of those extra long and clunky algebra problems (â€Å"What is the equivalent to ${2/3}a^2b - (18b - 6c) +$ †¦Ã¢â‚¬  you get the picture), then this is the guide for you. This will be your complete guide to ACT operations questions- what they’ll look like on the test, how to perform operations with multiple variables and exponents, and what kinds of methods and strategies you’ll need to get them done as fast and as accurately as possible. You'll see these types of questions at least three times on any given ACT, so let's take a look. What Are Operations? There are four basic mathematical operations- adding, subtracting, multiplying, and dividing. The end goal for any particular algebra problem may be different, depending on the question, but the operations and the methods to solve them will be the same. For example, when solving a single variable equation or a system of equations, your ultimate objective is to solve for a missing variable. However, when solving an ACT operations problem, you must use your knowledge of mathematical operations to identify an equivalent expression (NOT solve for a missing variable). This means that the answer to these types of problems will always include a variable or multiple variables, since we are not actually finding the value of the variable. Let’s look at two examples, side-by-side. This is a single variable equation. Your objective is to find $x$. If $(9x-9)=-$, then $x=$? A. $-{92/9}$B. $-{20/9}$C. $-{/9}$D. $-{2/9}$E. $70/9$ This is an ACT operations problem. You must find an equivalent expression after performing a mathematical operation on a polynomial. The product $(2x^4y)(3x^5y^8)$ is equivalent to: F. $5x^9y^9$G. $6x^9y^8$H. $6x^9y^9$J. $5x^{20}y^8$K. $6x^{20}y^8$ (We will go through exactly how to solve this problem shortly) Let's break down each component of an operations problem, step-by-step. (Also, bonus French braid lesson!) Operation Question How-To's Let us look at how to identify operations questions when you see them and how to solve for your answer. How to Identify an Operations Problem As we said before, the end goal of an operations problem is not to solve for a missing variable. Because of this, you can identify an operations problem by looking at your answer choices. If the question involves variables (instead of integers) in the given equation and in the answer choices, then it is likely you are dealing with an operations problem. This means that if the problem asks you to identify an â€Å"equivalent† expression or the â€Å"simplified form† of an expression, then it is highly likely that you are dealing with an operations problem. How to Solve an Operations Problem In order to solve these types of questions, you have two options: you can either solve your problems by using algebra, or by using the strategy of plugging in numbers. Let’s begin by looking at how algebraic operations work. First, you must understand how to add, multiply, subtract, and divide terms with variables and exponents. (Before we go through how to do this, be sure to brush up on your understanding of exponents and integers.) So let us look at the rules of how to manipulate terms with variables and exponents. Addition and Subtraction When adding or subtracting terms with variables (and/or exponents), you can only add or subtract terms that have the exact same variable. This rule includes variables with exponents- only terms with variables raised to the same power may be added together (or subtracted). For example, $x$ and $x^2$ CANNOT be combined into one term (i.e. $2x^2$ or $x^3$). It can only be written as $x + x^2$. To add terms with variables and/or exponents, simply add the numbers before the variable (the coefficients) just as you would add any numbers without variables, and keep the variables intact. (Note: if there is no coefficient in front of the variable, it is worth 1. $x$ is the same thing as $1x$.) Again, if one term has an additional variable or is raised to a different power, the two terms cannot be added together. Yes: $x + 4x = 5x$ $10xy - 2xy = 8xy$ No: $6x + 5y$ $xy - 2x - y$ $x + x^2 + x^3$ These expressions all have terms with different variables (or variables to different powers) and so CANNOT be combined into one term. How they are written above is as simplified as they can ever get. Multiplication and Division When multiplying terms with variables, you may multiply any variable term with another. The variables do not have to match in order for you to multiply the terms- the variables instead are combined, or taken to an additional exponent if the variables are the same, after multiplying. (For more on multiplying numbers with exponents, check out the section on exponents in our guide to advanced integers) $x * y = xy$ $ab * c = abc$ $z * z = z^2$ The variables in front of the terms (the coefficients) are also multiplied with one another as usual. This new coefficient will then be attached to the combined variables. $2x * 3y = 6xy$ $3ab * c = 3abc$ Just as when we multiplying variable terms, we must take each component separately when we divide them. This means that the coefficients will be reduced/divided with regard to one another (just as with regular division), as will the variables. (Note: again, if your variables involve exponents, now might be a good time to brush up on your rules of dividing with exponents.) $${8xy}/{2x} = 4y$$ $${5a^2b^3}/{15a^2b^2} = b/3$$ $${30y + 45}/5 = 6y + 9$$ When working on operations problems, first take each component separately, before you put them together. Typical Operation Questions Though there are several ways an operations question may be presented to you on the ACT, the principles behind each problem are essentially the same- you must manipulate terms with variables by performing one (or more) of the four mathematical operations on them. Most of the operations problems you’ll see on the ACT will ask you to perform a mathematical operation (subtraction, addition, multiplication, or division) on a term or expression with variables and then ask you to identify the â€Å"equivalent† expression in the answer choices. More rarely, the question may ask you to manipulate an expression in order to present your equation â€Å"in terms of† another variable (e.g. â€Å"which of the following expressions shows the equation in terms of $x$?†). Now let’s look at the different kinds of operations problems in action. The product $(2x^4y)(3x^5y^8)$ is equivalent to: F. $5x^9y^9$G. $6x^9y^8$H. $6x^9y^9$J. $5x^{20}y^8$K. $6x^{20}y^8$ Here, we have our problem from earlier, but now we know how to go about solving it using algebra. We also have a second method for solving the question (for those of you are uninterested in or unwilling to use algebra), and that is to use the strategy of plugging in numbers. We’ll look at each method in turn. Solving Method 1: Algebra operations Knowing what we know about algebraic operations, we can multiply our terms. First, we must multiply our coefficients: $2 * 3 = 6$ This will be the coefficient in front of our new term, so we can eliminate answer choices F and J. Next, let us multiply our individual variables. $x^4 * x^5$ $x^[4 + 5]$ $x^9$ And, finally, our last variable. $y * y^8$ $y^[1 + 8]$ $y^9$ Now, combine each piece of our term to find our final answer: $6{x^9}y^9$ Our final answer is H, $6{x^9}y^9$ Solving Method 2: Plugging in our own numbers Alternatively, we can find our answer by plugging in our own numbers (remember- any time the question uses variables, we can plug in our own numbers). Let us say that $x = 2$ and $y = 3$ (Why those numbers? Why not! Any numbers will do- except for 1 or 0, which is explained in our PIN guide- but since we are working with exponents, smaller numbers will give us more manageable results.) So let us look at our first term and convert it into an integer using the numbers we selected to replace our variables. $2{x^4}y$ $2(2^4)(3)$ $2(16)(3)$ $96$ Now, let us do the same to our second term. $3{x^5}{y^8}$ $3(2^5)(3^8)$ $3(32)(6,561)$ $629,856$ And finally, we must multiply our terms together. $(2{x^4}y)(3{x^5}{y^8})$ $(96)(629,856)$ $60,466,176$ Now, we need to find the answer in our answer choices that matches our result. We must plug in our same values for $x$ and $y$ as we did here and then see which answer choice gives us the same result. If you are familiar with the process of using PIN, you know that our best option is usually to start with the middle answer choice. So let us test answer choice H to start. $6{x^9}y^9$ $6(2^9)(3^9)$ $6(512)(19,683)$ $60,466,176$ Success! We have found our correct answer on the first try! (Note: if our first option had not worked, we would have seen whether it was too low or too high and then picked our next answer choice to try, accordingly.) Our final answer is again H, $6{x^9}y^9$ Now let us look at our second type of problem. For all real numbers $b$ and $c$ such that the product of $c$ and 3 is $b$, which of the following expressions represents the sum of $c$ and 3 in terms of $b$? A. $b+3$B. $3b+3$C. $3(b+3)$D. ${b+3}/3$E. $b/3+3$ This question requires us to translate the problem first into an equation. Then, we must manipulate that equation until we have isolated a different variable than the original. Again, we have two methods with which to solve this question: algebra or PIN. Let us look at both. Solving Method 1: Algebra First, let us begin by translating our equation into an algebraic one. We are told that the product of $c$ and 3 is equal to $b$. A â€Å"product† means we must multiply $c$ and 3 and so our equation looks like this: $3c = b$ Now we are asked to find the sum of $c$ and 3. This means we must isolate $c$ so that we can add them together. So let us first isolate $c$ by using our knowledge of algebraic operations. $3c = b$ $c = b/3$ Now, we can sum $c$ and 3 by replacing our $c$ with $b/3$. $c + 3$ ${b/3} + 3$ Our answer matches answer choice E. Our final answer is E. Solving Method 2: Plugging in numbers Alternatively, we can use our technique of plugging in numbers. Because our question deals with variables, we can choose our own numbers (so long as they follow the rules of our given information.) We are told that the product of $c$ and 3 is equal to $b$. So let us assign a value to $c$ and use this information to find the value of $b$. So let us say that $c = 4$. (Why 4? Why not!) If $c = 4$, then the product of $c$ and 3 is: $3c = b$ $3(4) = b$ $b = 12$ So, when $c$ equals 4, $b$ equals 12. Now we must find the sum of $c$ and 3. $3 + c$ $3 + (4)$ $7$ Now that we have found our sum, we must identify the answer choice that gives us this sum. All of our answer choices are presented to us in terms of $b$, so we will use our found value of 12 to replace $b$ for each. As with all PIN questions, let us start with the middle answer option. Answer choice C gives us: $3(b + 3)$ We can tell just by looking at it that this will be far larger than 7, but we can always test this out. $3(12 + 3)$ $3(15)$ $45$ We can eliminate answer choice C. Just by glancing, we can see that answer choices A and B will also be larger than 12, which means we can eliminate them as well. Let us try answer choice D. ${b + 3}/3$ ${12 + 3}/3$ $15/3$ $5$ Answer choice D did not match our sum, which means we can eliminate it as well. By process of elimination, we are left with answer choice E, but let us test it to be sure. ${b/3} + 3$ ${12/3} + 3$ $4 + 3$ $7$ Success! We have found the answer choice that matches the sum we found. Our final answer is, once again, E, ${b/3} + 3$. As you can see, the answer to your operations questions will always be in variables and the problem will always require you to interpret and manipulate expressions with variables, but there are always multiple options for how to solve these types of problems. You've got the power to decide how you would like to solve and manipulate your operations problems. Magic! Strategies for Solving Operations Questions Now that we’ve seen the types of operations questions you’ll see on the ACT, let’s review our solving strategies. #1: Use PIN when needed (or to double-check your answer) If you ever feel concerned that you may be going down the wrong path while manipulating your operations problems, or if you simply want to double-check your answer, it's never a bad idea to use the strategy of plugging in numbers. Although it can take a little longer plug in your own numbers for your variables, you'll never have to fear misremembering how to manipulate your exponents, your variables, or your equations as a whole. Once you're able to use real numbers for your variables, the math will be a piece of cake. #2: Focus on one aspect of the term at a time It can become all too easy to lose yourself when working with multiple variables at once, especially when it comes to multiplication and division. The test-makers know this and will provide bait answers for any number of common mistakes. In order to keep all your components organized, focus on just one piece of each expression at a time. First, look at the coefficients, then look at the variables. This will help keep all your moving pieces in order and lessen the odds of mix-ups and mistakes. #3: Eliminate your answer options as you go Operations problems can sometimes mess with your head, not because they are inherently difficult, but because the ACT is a marathon and your brain can get tired and confused (and lazy). This, combined with the fact that all the answer choices generally look quite similar, with only small differences- a minus sign instead of a plus sign, one coefficient difference, etc.- can lead you to select the wrong answer, even when you know what the correct one should be. To avoid this kind of careless error (the worst kind of error!), eliminate your answer choices as you go through your problem. Know that the coefficient for your $y$ value must be 3? Immediately cross out any answer choices that give you anything other than $3y$. It may seem inefficient to solve problems this way, but it will keep your answers much more clear. #4: Keep careful track of your negatives Not only can it be difficult to keep track of multiple variables, but it's even easier to mix-up the proper negative and positive signs. Many students make careless errors with their negative signs and the ACT test-makers are all too aware of this. They will provide all manner of bait answers for anyone who misplaces even a single negative sign, so be very careful. $(a+2b+3c)-(4a+6b-5c)$ is equivalent to: A. $-4a-8b-2c$B. $-4a-4b+8c$C. $-3a+8b-2c$D. $-3a-4b-2c$E. $-3a-4b+8c$ For a problem like this, we are being asked to subtract the entire expression, $4a + 6b - 5c$, from the entire expression, $a + 2b + 3c$. This means that the negative sign will be negating every term in the expression $4a + 6b - 5c$. So we must put a negative sign in front of each term. $4a$ becomes $-4a$ $6b$ becomes $-6b$ $-5c$ becomes $- -5c$ or $+5c$. Now let us put these pieces together with the first expression. $a - 4a = -3a$ $2b - 6b = -4b$ $3c + 5c = 8c$ Our final expression will be: $-3a - 4b + 8c$ Our final answer is E, $-3a - 4b + 8c$. [Note: many (many!) students put a negative sign only in front of the first term in the parenthesis, which in this case the $4a$. If you had done this, you would have gotten: $a - 4a = -3a$ $2b + 6b = 8b$ $3c - 5c = -2c$. This would have given you answer choice C, $-3a + 8b - 2c$. Again the test-makers know this is a common error and there will always be a bait answer to tempt anyone who makes this kind of mistake.] Operations in the "real world." Hyuk, yuk, yuk. Test Your Knowledge Now that we’ve gone through the tips and tricks of operations questions, it’s time to put your knowledge to the test with more real ACT math problems. 1. Which of the following is an equivalent simplified expression for $2(4x+7)-3(2x-4)$? F. $x+2$G. $2x + 2$H. $2x+26$J. $3x+10$K. $3x+$ 2.Which of the following expressions is equivalent to ${1/2}y^2(6x+2y+12x-2y)$? A. $9xy^2$B. $18xy$C. $3xy^2 + 12x$D. $9xy^2-2y^3$E. $3xy^2+12x-y^3-2y$ 3.$t^2-59t+54-82t^2+60t$ is equivalent to: F. $-26t^2$G. $-26t^6$H. $-81t^4+t^2+54$J. $-81t^2+t+54$K. $-82t^2+t+54$ 4.The expression $-8x^3(7x^6-3x^5)$ is equivalent to: A. $-56x^9+24x^8$B. $-56x^9-24x^8$C. $-56x^18+24x^15$D. $-56^18-24x^15$E. $-32x^4$ Answers: H, A, J, A Answer Explanations: 1. As always, we can solve this question using algebra or using PIN. Let us look at both ways. Method 1: Algebra First, we must distribute out our terms. Only afterwards will we subtract them. Let us take each half of our expression by itself. $2(4x + 7)$ $8x + 14$ $ -3(2x - 4)$ $-6x + 12$ (Note: keep careful track of your negatives here, especially in the second half of our expression.) Now, we can put the two together. $8x + 14 - 6x + 12$ $2x + 26$ We cannot go any further, as we have combined all our like terms. Our final answer is H, $2x + 26$ Method 2: PIN As an alternative to algebra, we can always use plugging in numbers. So let us assign our own value to $x$, which we will call 3. (Why 3? Why not!) This means that we will replace any $x$ in our given equation with a 3. $2(4x + 7) - 3(2x - 4)$ $2(4(3) + 7) - 3(2(3) - 4)$ $2(12 + 7) - 3(6 - 4)$ $2(19) - 3(2)$ $38 - 6$ $32$ Now, let us find the answer choice that matches with our found answer of 32, once we replace the $x$ with 3. As usual, when using PIN, let us start with the middle answer option. $2x + 26$ $2(3) +26$ $6 + 26$ $32$ Success! We found our answer on the first try. But remember- when using PIN, always check your other answer options to make sure there are not repeat correct answers. We can see straightaway that answer choices F and G will be too small, since answer choice H was a match. So let us try answer choice J. $3x + 10$ $3(3) + 10$ $9 + 10$ $19$ This answer choice is too small and we can see just by looking that answer choice K will be too small as well (since they only differ by 1). This means we are safe with our answer choice H, as no others produced a match. Our final answer is H, $2x + 26$. As we saw from earlier in the guide and from the example problem above, we can always use algebra or PIN for our operations problems. Knowing that, we will only go through one method each for the rest of our answer explanations. 2: For this problem, let us do our solve using algebra (again, we could also use PIN, but for the sake of brevity, we are only choosing one method for each problem). We are given the equation: ${1/2}y^2(6x + 2y + 12x - 2y)$ Now, let us first make life easier by combining the like terms in the parenthesis. $(6x + 2y + 12x - 2y)$ $(6x + 12x + 2y - 2y)$ $(18x)$ The $y$ terms cancel one another out, so we are left with only $18x$ in the parenthesis. Now, we must multiply our $18x$ by ${1/2}y^2$. As always, when multiplying, we must multiply first the coefficients and then combine them with the combined variables. So: ${1/2}y^2 * 18x$ $(1/2) * 18 = 9$ $y^2 * x = y^2x$ Put the two together and we have: $9y^2x$ So our final answer is A, $9xy^2$ 3: Because we used algebra last time, let us try our hand at solving this question using PIN. Because we are using our own numbers, we don’t have to worry about whether or not we are matching up the right terms, or if we are combining them incorrectly; we can bypass all the mess and use numbers instead. We have one variable, $t$, so let us say that $t = 2$. (Why 2? As always, why not!) $t^2 - 59t + 54 - 82t^2 + 60t$ $(2)^2 - 59(2) + 54 - 82(2)^2 + 60(t)$ $4 - 8 + 54 - 328 + 120$ $-268$ Now, we must find the answer choice that matches our found answer of 102, once we replace $t$ with 2. Let us start in the middle, with answer choice H. $-81t^4 + t^2 + 54$ $-81(2)^4 + (2)^2 + 54$ $-81(16) + 4 + 54$ $-1296 + 58$ $-1238$ We can see just by looking that answer choice G will be too small as well ($-26 * 16 = -416$), and answer choice F will be too large (-26 * 4 = -104). So let us try answer choice J. $-81t^2 + t + 54$ $-81(2)^2 + 2 + 54$ $-81(4) + 56$ $-324 + 56$ $-268$ Success! And we can also see that the only difference between answer choices J and K are the coefficient in front of $t^2$ (-81 vs. -82), so we know that answer K would produce an incorrect and smaller number than answer choice J. Our final answer is J, $-81t^2 + t + 54$ 4: Because we used PIN last time, let us use algebra for this problem. Because we do not have like terms in the parenthesis, we must distribute out our expression using multiplication. $-8x^3(7x^6 - 3x^5)$ $-8x^3(7x^6) - -8x^3(3x^5)$ And take each piece separately. $-8x^3(7x^6)$ = $-8 * 7 = -56$ and $x^3 * x^6 = x^[3 + 6] = x^9$ (for more on this, look to the section on exponents in our advanced integers guide). So, combined, we have: $-56x^9$ And the other half of our expression will be the same. $- -8x^3(3x^5)$ $8x^3(3x^5)$ = $8 * 3 = 24$ and $x^3 * x^5 = x^[3 + 5] = x^8$ So, combined, we have: $24x^8$ Now our equation looks like this: $-56x^9 + 24x^8$ Our final answer is A, $-56x^9 + 24x^8$ (Take care! The only difference between answer choice A and B is the negative sign. If you weren’t careful with your double negatives, you may have fallen for this bait answer.) Ten thousand gold stars for solving your operations problems! The Take-Aways Though operations problems are easy to get wrong if you’re going too quickly through the test (or trying to solve them in your head), the basic elements are the same as any problem with variables- combine like terms, keep your work organized, and use PIN if you feel overwhelmed (or simply want to double-check your answer). You have a multitude of options for solving ACT algebra questions, so don’t be afraid to use them. What’s Next? Still in the mood for math? Well we've got you covered! First, take a gander at exactly what's tested on the ACT math section in order to get a feel for your strong and weak points. Next, dive right into our ACT math guides for any topic you feel you haven't quite mastered (or just any topic you want to refresh). From circles to ratios, slopes to polygons, we've got your back. Running out of time on the ACT math section? Check out our guide on how to help maximize your avaialable time in order to get your best score possible. Nervous about test day? Ease your mind by taking a look at what to do the night before and the day of the test. Trying for a perfect score? Look no further than our guide to getting a perfect 36 on the ACT math, written by a perfect-scorer. Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

How to Get Your Commercial Driver’s License in Michigan and Idaho

How to Get Your Commercial Driver’s License in Michigan and Idaho This article applies to anyone who wants to apply for a CDL in Michigan and Idaho. If you want to learn about getting a CDL in other states, TheJobNetwork has put together a very comprehensive CDL guide on every state of the country. MichiganWho needs a CDL?Any Michigan resident who will  operate the following commercial vehicles is required to obtain a CDL:Single vehicles with a GVWR of 26,001+ poundsCombination vehicles towing a trailer or other vehicles with a GVWR of 10,001+ pounds when the GCWR is 26,001+ poundsVehicles designed to transport 16 or more people (including the driver) or carrying hazardous materials in amounts requiring placardingWho does not need a CDL?Active duty military (including National Guard) with military licenses operating military vehiclesPolice officers and firefighters who meet approved training standards and operate authorized emergency vehiclesFarmers operating vehicles within a 150 mile radius of their farm. However, an F-endorsement is needed by farmers operating combination vehicles whose towing vehicle has a GVWR of 26,001+ pounds. Also, farmers who carry hazardous materials in amounts requiring placarding while operating combination vehicles with a  towing vehicle  that has a GVWR of 26,001+ pounds or a single vehicle with a GVWR of 26,001+ poundsneed a CDL with a hazardous materials endorsement.Individuals operating motor homes or other vehicles used exclusively to transport personal possessions or family members, for non-business purposesObtaining a CDLHere are the steps you must take in order to obtain your CDL.1. Visit a Secretary of State branch office. While there, you must provide:Proof of Social Security number (Social Security card, payroll check stub, W-2 Form).Proof of legal presence in the United StatesIf applying for a hazardous materials endorsement, proof of   Federal Security Threat  Assessment and  U.S. Citizenship or Lawful Permanent Resident2. Complete an application. You will have to certify at this time that you meet medical and driver qualifications.  If you have had any change in your physical condition since your last driver license renewal which may affect your ability to drive, you may need a special form before you can apply for your CDL.At this point, you will also have to prove that you meet driver record eligibility requirements as determined by Secretary of State branch office personnel. 3. Pass the Knowledge Test and a vision test. You must pass all required knowledge tests to first obtain a CLP, which lets you practice driving with another  driver who has a CDL for your vehicle  type. You need a CLP to  take the CDL skills tests (see Step 5).   If you do not pass a knowledge test on your first attempt, you must wait one day to retake the test.4. Pay your CDL fees.5. Schedule your  CDL skills test. Note:  You must wait 14 days after receiving your CDL to take the skills test and converting your CLP into a full  CDL.  You must schedule your skills test at least 2 days in advance.Once you have passed your CDL skills tests, return to the Secretary of State branch office to:6. Pay a correction fee to add CDL privileges to your license.7. Receive your CDL.IdahoWho needs a CDL?In Idaho, you must obtain  a CDL to operate any of the following commercial motor vehicles:Single vehicles with a GVWR of 26,001+ poundsCombination vehicles towing a trailer or other vehicles with a GVWR of 10,001+ pounds when the GCWR is 26,001+ poundsVehicles designed to transport 16 or more people (including the driver) or carrying hazardous materials in amounts requiring placardingWho does not need a CDL?Drivers of vehicles used exclusively to transport personal possessions or family members for non-business or recreational purposes.Military vehicle operators who are considered active-duty military personnelDrivers of firefighting or other emergency equipment used in response to emergencies involving the preservation of life or propertyDrivers of farm vehicles, including family members and farmhands.How to Obtain an Idaho CDLTo apply for a CDL, you must:Be at least 18 years oldHave a valid Idaho non-commercial license (Class D) or have passed all tests required to obtain one.Have one year of driving experienceApplication steps:1. Go to your county driver’s license office and supplyYour current driver’s licenseSocial Security cardProof of Idaho residenceMoney to pay your feesIf you are not a  U.S. citizen or a U.S. national, you should provide proof of lawful presence in the United States2. Your driving record will be checked, fees will be collected, and you will take a  vision and knowledge test.3. After passing these tests, you must make an appointment to take the skills test. A list of Examiners is available at the County DMV and online at www.itd.idaho.gov.When you  take your skills test, you will need to provide  proof of identification, proof of insurance, and your receipt showing you have passe d the written tests and paid the skills test receipt fee.4. Take your skills tests:   the vehicle inspection, the basic control skills test, and the road test. The skills test will take two to three hours to complete and must be taken in a vehicle that is representative of the license class you wish to obtain.5. Obtain your CDL from the County DMV.