Pollution by CO2 Essay Example | Topics and Well Written Essays - 1500 words

Pollution by CO2 - Essay Example Therefore, concentration of CO2 in the atmosphere is being monitored closely in order to prevent effects of global warming (Ramseur & Parker2008, p.27). The need to curb the effects of global warming due to increased greenhouse gases has led to the development of novel devices, which can monitor air pollution by CO2. However, it is worth to mention that some of the methods in use for the monitoring of CO2 tend to be highly sophisticated, and can only be used under exceptional circumstances. Today, majority of the devices that are in use for monitoring of atmospheric CO2 are constructed using Non-Dispersive Infrared gas analyzers. However, there are several other techniques, which use chromatographic and spectrum techniques. It is necessary to note that there is an internationally accepted calibration system that helps in giving a global standard for CO2 measurements (Nowakb & King 2002, p.246). Devices for measuring CO2 pollution Fourier Transform Infrared Spectroscopy (FTIR) This is one of the methods widely used for monitoring atmospheric pollution by CO2. This technique has been in use for decades, and its working principle is based on the identification of the absorption spectrum for different gases. Therefore, FTIR operates by monitoring the whole infrared spectrum in order to identify the different absorption spectrums for gases present. Infrared spectrums produce absorption spectrums for samples that have absorption peaks that correspond to frequencies of bond vibrations within an atom. Every material has a unique combination of atoms, hence the uniqueness in the infrared spectrum produced. Therefore, the use of infrared spectroscopy can help in the quantitative analysis of a material (Xinyi 2012, p. 225). The size of peaks produced by infrared spectrums provides a direct measurement for the quantity of substance present within the test sample, which goes to extents of 10% of CO2 concentrations in the sample. The use of software algorithms has made use o f the infrared spectrum a vital tool for quantitative analysis. The use of FTIR has a number of advantages over other techniques that were in use earlier. These advantages include its nondestructive nature; it also gives precise measurements that do not need any external calibration, has a high operating speed and is of a high sensitivity. Other advantages include its high optical throughput, and its mechanical simplicity.With the help of an interferometer, FTIR measures different infrared frequencies simultaneously. Therefore, this technique is reliable for the identification of air pollution by CO2 based on its unique absorption spectrum (Griffith &Stephen 2000, p.218). Advantages FTIR provides the advantage of measuring up to 50 determinants. The other advantagesincludethe reduced number of interferences, lack of frequent calibration, and a typical range of 2.5-25Â µm. Disadvantages The main disadvantage associated with the use of FTIR is its potential to generate a large amount of data from inferograms, which makes data analysis process cumbersome. The other disadvantage relates to difficulties in obtaining a representative background. Gas chromatography This is an analytic technique that is used in the analysis of a number of gaseous substances. Analysis of gases using gas chromatography requires the gaseous compounds under analysis to have thermal stability and sufficiently

Unethical Business Research Conduct Essay Example for Free

Unethical Business Research Conduct Essay Ethics and the behaviors associated with them have the highest significance for different reasons within a business organization. Companies must ensure they follow all levels of ethical behavior when any activity is performed at their premises; especially activities related to business research. Business research is the systematic inquisition that provides information to direct managerial decisions (Cooper Schindler, 2011). Its purpose is to allow companies access to valuable information on company policies, customer service and consumer buying habits. Business owners can use this information to discover which products and services are important to the public, worker morale and behaviors, as well as what they can do to set themselves apart from the competition. However, wrong methods and/or unethical research conduct can obscure results and lead to the damage of a companies’ process, financial statue and image. An example of unethical business research can be found in the 2004 discrimination lawsuit against the restaurant Cracker Barrel. A number of bad research methods contributed to the courts’ order to convict and discipline the retailer for a number of consumer accusations. The leading cause of the court’s decision was the companies’ bad research and investigations into the basic problems and the flawed information that was turned into the Department of Justice following said investigation. Cracker Barrel Restaurant and Old Country Store, a nationwide retail chain, underwent random testing of its facilities and stores to monitor the possibility of racial bias in customer service. This research and observation was not only to screen for the possibility of racism, but to expand culture and diversity training to employees as part of a settlement with the Department of Justice on May 3, 2004. This agreement was made after a number of African Americans (and other minority groups) customers of the establishment came forward with complaints through the National Association for the Advancement of Colored People or NAACP, stating â€Å" they were made to wait longer for tables, were seated away from white patrons, received inferior service and wer e otherwise discriminated against at Cracker Barrel restaurants† (Fears, 2004). As part of a court agreement, Cracker Barrel conducted its own corporate research into the accusations against its company. They concluded that no wrongdoings were committed, asserting that its company has always maintained anti-discrimination policies to all consumer no matter what gender, race and sexuality they are. Upon the reception of Cracker Barrel’s results, the Justice Department decided to hire an independent auditor to check their claims. The Justice Departments investigation included interviews with approximately 150 persons, [of which consisted] mostly [of] former Cracker Barrel employees; and found that 80 percent stated that they experienced or witnessed discriminatory treatment of customers at a Cracker Barrel restaurant,† according to R. Alexander Acosta, Assistant Attorney General for the Department of Justice’s Civil Rights Division. The conclusion suggested that some managers directed, participated in, and/or encouraged stereotyping and discrim inatory behaviors from employee, Acostas added (Schmit Copeland, 2004). Though this suit ended with the court’s judgment for Cracker Barrel to pay fines and damages to a number of customers and their attorneys, the company’s reputation for discrimination is continuously being investigated a number of private and federal groups, including the Department of Justice, NAACP, and the Equal Employment Opportunity Commission or EEOC. The first issue with the company began with management not taking customer complaints seriously, however, the major issue is how the company went about resolving the issue. Had they taken the time to actually brainstorm and come up with a logical way to resolve the issue, the accusations probably wouldn’t have turned into a class-action lawsuit. And when the Department of Justice demanded the company conduct a private, internal investigation, they should have gone about doing it the right way. However the company and managerial lack of interest in proper investigation and research skills lead them to produce questionable results of value to the case. With this, the Department of Justice chose to proceed with its own investigation to prove or disprove the case and integrity of the company. Reference Cooper, D., Schindler, P. (2011). Business research methods (11th ed.). New York, NY: McGraw- Hill/Irwin. Retrieved from the University of Phoenix eBook website: https://ecampus.phoenix.edu/content/eBookLibrary2/content/TOC.aspx?assetid=8e4d9544-fa8b-4402-8f2d- 624db889e46dassetmetaid=179f7507-93d0-431c-826f-d663a33b6057 Fears, D. (2004). Crackle Barrel, Government Settles Discrimination Suit. The Washington Post Company. Retrieved January 21, 2012 from http://www.washingtonpost.com/wpdyn/articles/A639242004 Schmit, J. Copeland, L. (2004). Cracker Barrel customer says bias was flagrant. USA Today. Retrieved January 20, 2012 from http://usatoday30.usatoday.com/money/companies/2004-05-07-cracker- barrel_x.htm

The Braden Scale :: The Braden Scale

The Braden Scale is a clinically valued tool that is used to predict pressure ulcers. The scale is broken down into six sub-scales; these subscales determine the risk factors associated with skin break down. Multiple aspects of a patients condition are examined, (sensory perception, moisture, activity, mobility, nutrition, friction and shear), to limit the patients susceptibility for skin break down. Since pressure ulcers are a financial burden and a cause for patient discomfort and possible infection, predicting and assessing risk has enormous benefit and significance. This study was conducted to determine the validity of the mobility subscale of the Braden scale. The subscale of mobility is defined as the patients ability to change and control body positions. The research was conducted in a veteran hospital, and participants ranged in age from 45-95 years. The tools that were used were the Braden scale and actigraphy which measures movement. It was placed on the patient’s non-dominant ankle in order to observe the larger movements of the patient. The researcher defined each score in relation to movement. They hypothesized that the increase in movement would cause an increase in score of the mobility subscale. As predicted, the mobility subscale scores increased as movement increased. A similar study to predict risk of ulcers in pediatric patients was conducted to test the validity of using the Braden Q scale. A modified version of the Braden Scale, only containing three subscales, was used to utilize a shorter comparable tool. The Braden Q Scale is a revision of the Braden scale that is applicable in pediatrics. The two tools that were used were: the Braden Q Scale and skin assessments. The sample study consisted of 322 patients who were on bed rest for at least 24 hours. The patients were observed three times per week, for two weeks, and then weekly until discharge, which totaled 887 individual assessments. It was determined that both the Braden Q, as well as the modified Braden Scale was adequate tools to measure skin breakdown. Both studies modified the original Braden Scale to test the validity of their modifications. The first study was based solely on the mobility scale of the Braden scale, while the second study used three of the original sub-scales to prove comparable results to the overall scale. Both studies were designed to simplify the Braden scale in order to determine the effectiveness of the subscales alone.

The Gamma Knife Improves Treatment of Brain Disorders Essay -- Explora

The Gamma Knife Improves Treatment of Brain Disorders Advanced treatment for brain tumors and brain disorders, the Gamma Knife is a tool being utilized to treat thousands of functional brain disorders every year without the danger involved in invasive procedures. Not many people can say they were up and about the same day after treatment of a brain tumor. This is now possible with the Gamma Knife, a technology utilizing gamma rays to treat brain disorders successfully and with no incision. These requirements are essential when trying to treat the disorders in a sensitive organ as the brain, where millimeters may mean the difference between life or death or brain damage. Developed in 1968 by Swedish neurosurgeon Lars Leksell, the Gamma Knife was not used until many years later when advanced diagnostic methods were developed. With the advent of technology such as the MRI and CT scan, the Gamma Knife's full capabilities are finally being realized. Conditions often treated with the technology are arteriovenus malformations, acoustic neuromas, meningiomas, pituitary adenomas, and brain metastases. The risk of surgical complications is non-existent since the procedure is performed without an incision. It is also almost painless; patients usually opt for just local anesthesia and a mild sedative. The patient's head does not even need to be shaved for the procedure. During invasive procedures, surgeons are forced to actually penetrate the brain and work with MRI and CAT scan pictures to locate tumors and remove them. This is often an inaccurate procedure that may leave portions of the tumor still in the brain and require another operation. Another downside to invasive procedure is that tumo... ...Knife is also cost-effective. With no need for long hospital stays or rehabilitation, the procedure is obviously highly recommended by medical-insurance providers. The Gamma Knife is revolutionizing the treatment of brain disorders. Before, when a cancer spread to the brain, it was considered a terminal illness. Now, a patient is able to walk in and be treated in just a half hour. There have not even been any reported deaths or complications resulting from the procedure. It is being bought for use in many hospitals around the world and may be, in the not too distant future, as common as any other surgical procedure performed today. Bibliography http://www.chw.edu/mha/Gamma/gamma.html http://www.chw.edu/mha/Gamma/Q&A.html http://gammaknife.org/technical.html "Magnetic Resonance Imaging", Encarta. Microsoft Corporation, 1997.

Domestic and Global Security Threats

Current domestic and global security threats: The impact on The North Atlantic Treaty Organization (NATO) The North Atlantic Treaty Organization (NATO) was formed to cope with the challenges of a bipolar world. However, today’s global environment faces multi-polar challenges from non-state actors such as terrorists. Threats once considered domestic concerns now affect the world, like global warming and the need to rebuild the infrastructure of unstable states such as Afghanistan and Bosnia.The globalization of modern society has meant the globalization of modern technological threats, including cyberterrorism, as well as increased international competition for scarce energy resources. All of these problems affect NATO members but cannot be addressed with a regionally specific focus. To create a more secure world â€Å"NATO will need to start working in partnership with other multilateral organizations, like the UN, if it hopes to find effective permanent solutions to the secu rity challenges facing the world.Although NATOs presence is often a condition of success, it is increasingly insufficient† by itself when dealing with global security (Goldschmidt 2009). Domestic state concerns, such as internal instability and a lack of resources can have global repercussions. Domestic concerns: Domestic peacekeeping in Afghanistan and global warming Because of the terrorist threat posed to NATO nations by terrorist non-state actors harbored in Afghanistan, NATO cannot shirk the critical role it must play in creating a more stable government, despite Afghanistan’s non-European location.In Afghanistan, â€Å"there is a need for a coordinated effort with development and reconstruction agencies. NATO currently must play both a security and nation-building role. It was not designed for the latter, and cannot hope to create the conditions for military withdrawal without a concerted development effort† with other regional and international organizatio ns such as the United Nations (Goldschmidt 2009).Recently, NATO Secretary General Anders Fogh Rasmussen stated that while Afghanistan security and internal integrity is still challenging and â€Å"Afghanistan will likely face security threats for years to come,† NATO alliance forces within the nation have begun â€Å"transferring security responsibilities to the Afghan government† and can begin a slow withdrawal (Fedynsky 2010). Afghanistan security will remain of grave concern for the Alliance, but the approach taken by NATO has been seen as a useful template for its future 21st century fforts. Said Secretary General Rasmussen: â€Å"It will not be a run for the exit†¦What will happen is that we hand over lead responsibility to the Afghans, and our soldiers will then move into a more supportive role. But I foresee that the Afghan security forces will need our supportive assistance for quite some time† (Fedynsky 2010). NATO will increasingly assume the role , suggests Rasmussen, of a peacekeeping force—keeping the domestic peace for Afghanistan in the interests of global peace.Global warming is of grave concern for all of NATO members, given that wars for the earth’s scarce energy resources can become a fertile source of interstate conflict. Nations with historical animosity to NATO members, such as those in the Persian Gulf, often harbor the greatest reserves of the world’s fossil fuels. Climate change can also result in critical reductions in the food supply and politically destabilizing natural disasters. Global warming has even intensified competition for territory: â€Å"Russia, the US, Canada, Norway and Denmark have all been attracted to the energy supply in the Arctic.Relations between these states has intensified after evidence revealed that global warming was melting the polar ice making, access to the energy supplies easier as jurisdiction over the region is still under dispute† (â€Å"Russia,â⠂¬  Press TV, 2009). â€Å"Climate change could confront us with a whole range of unpleasant developments — developments which no single nation state has the power to contain†¦. dwindling water and food supplies, global warming, and mass migration cause international tensions. [Climate change will] sharpen the competition over resources, notably water.It will increase the risks to coastal regions. It will provoke disputes over territory and farming land. It will spur migration and it will make fragile states even more fragile† warned NATO Secretary General Jaap de Hoop Scheffer (Waterfield 2008). Unspoken by Scheffer was the fact that Russia â€Å"aims to be among the world's top five economies in medium term† and has a strong â€Å"reliance on natural energy supplies such as oil and gas† and a strong interest in expanding its reserves (â€Å"Russia,† Press TV, 2009).Global concerns: Russia, missile shields and cyberterrorism Thus domestic co ncerns such as internal instability and even energy scarcity have global repercussions that affect NATO nations. That is why, despite the end of the Cold War, tensions between NATO member and non-member nations remain bubbling so close to the surface. It has not been forgotten by the Russian leadership that NATO was founded to address the security concerns raised by the now-defunct institutions of the Soviet Union and the Warsaw Pact.Fears of ‘Star Wars’ shield defense systems were reignited in March when Secretary General Rasmussen, warning of the â€Å"looming threat of weapons of mass destruction,† made a case for a missile shield system for all NATO alliance states against â€Å"unconventional weapons and the missiles that [they] could carry†¦Should Iran produce intermediate- and intercontinental-range missiles†¦the whole of the European continent, as well as all of Russia would be in range,† he stated (Brunnstrom 2010).Rasmussen’s del iberate mention of Russia as a potential target for rogue states and terrorist organizations did little to allay the Russia’s fears that a NATO missile shield system would pose a threat to its security. In 2009, before the US announced its abandonment of a missile defense system in the Czech Republic, â€Å"a national security document released by Moscow describe[d] the US and NATO as major threats to the security of the world and Russia† (â€Å"Russia,† Press TV, 2009). Along with its disputes with Russia, cyberterrorism and terrorism have been pressing concerns in framing NATO’s global agenda for the future.The most visible aspect of NATO’s anti-terrorist campaign has been in terms of its military capacity through efforts such as Operation Active Endeavour (OAE), â€Å"a maritime surveillance operation led by NATO’s naval forces to undertake anti-terrorist patrol, escort and compliant boarding in the Mediterranean,† as well as NATO policing assistance protecting the public during high-profile events such as the Olympics and other international sporting events (â€Å"Topic: Terrorism,† NATO, 2010).NATO has also made every effort to deploy new technology in its efforts to subvert terrorist threats such as its Defense Against Terrorism Program of Work (DAT POW) which created the precision air-drop technology currently used in Afghanistan. Since 2007 cyber attacks in Estonia swamped government websites shortly after the Estonian government challenged the Russian government regarding the possession of a national monument, NATO’s awareness has been heightened about the security risks posed by cyberterrorism. The protection of NATO's key information systems in general, and cyber defense in particular, are integral parts of the functions of the Alliance† (â€Å"Topic: Terrorism,† NATO, 2010). In addition to specifically-coordinated military efforts, NATO has attempted to promote information sharing between member nations regarding terrorist threats and counter-terrorist efforts.However, the maintenance of hostilities between NATO and Russia continues to be of concern, given Russia’s fears of NATO missile defense systems, Russia’s desire to expand its territorial outreach for energy reserves, and Russia’s lack of willingness to engage in information exchanges with the Alliance. Russia is a critical partner in fighting global warming and terrorism, particularly because of its size, resources, and the fact that many cyber attacks have been traced to Russia.Building stronger relationships with Russia without compromising NATO’s domestic and global agenda will be a critical challenge for the Alliance in the 21st century.Works CitedBrunnstrom, David. â€Å"Missile Defense Needed Against Growing Threat, NATO Chief Says. † Reuters. March 26, 2009. May 14, 2010. http://www. globalsecuritynewswire. org/gsn/nw_20100326_9638. php Fedynsky, Peter. â€Å"NATO to Transfer Security Tasks to Afghan Government. Global Security. April 23, 2010. May 14, 2010. http://www. globalsecurity. org/military/library/news/2010/04/mil-100423-voa01. htm Goldschmidt, Pierre. Garry Hindle, R. Andreas Kraemer, Fabrice Pothier, Jamie Shea, Michael Stopford , Ashley J. Tellis & Brooks Tigner. â€Å"The Next Generation of Security Threats: Reprogramming NATO? † Carnegie Mellon: Europe. February 24, 2009. May 14, 2010. http://carnegieeurope. eu/events/? fa=1255 Russia: US, NATO main threats to global security. † Press TV. May 13, 2009. May 14, 2010. http://www. presstv. ir/detail. aspx? id=94616 §ionid=351020602 â€Å"Topic: Terrorism† NATO. 2001. May 14, 2010. http://www. nato. int/cps/en/natolive/topics_48801. htm Waterfield, Bruno. â€Å"NATO Chief warns of climate change developments. † The Daily Telegraph. 2008. May 14, 2010. http://www. nysun. com/foreign/nato-chief-warns-of-climate-change-developments/79215/

Complete Guide to Fractions and Ratios on SAT Math

Complete Guide to Fractions and Ratios on SAT Math SAT / ACT Prep Online Guides and Tips You likely had your first taste of working with fractions sometime in elementary school, though it's probably been a while since you've had to deal with how they shift, change, and interact with one another. To refresh, fractions and ratios are both used to represent pieces of a whole. Fractions tell you how many pieces you have compared to a potential whole amount (3 red marbles in a bag of 5, for example), while ratios compare pieces to each other (3 red marbles to 2 blue marbles) or, more rarely, pieces to the whole amount (again, 3 red marbles in 5 total). If this sounds complicated to you right now, don’t worry! We will go through all the principles behind fractions and ratios in this guide. If this seems easy to you right now, definitely check out the practice problems at the end of the guide to make sure you have mastered all the different kinds of fraction and ratio problems you’ll see on the test. The SAT likes to present familiar concepts in unfamiliar ways, so don’t let your mastery of fractions lead you to make assumptions about how you’ll see fractions and ratios on the test. No matter how comfortable you are (or are not) with fractions and ratios right now, this guide is for you. Here, we will go through the complete breakdown of fractions and ratios on the SAT- what they mean, how to manipulate them, and how to answer the most difficult fraction and ratio problems on the SAT. This Guide This guide is seperated into two distinct categories- everything you need to know about fractions and everything you need to know about ratios. For each section, we will go through the ins and outs of what fractions and ratios mean as well as how to manipulate and solve the different kinds of fraction and ratio problems you'll see on the SAT. We will also breakdown how you can tell when an SAT problem requires a ratio or a fraction and how to set up your approach these kinds of problems. At the end, you will be able to test your knowledge on real SAT math questions. The more you prep for the SAT, the more your brain can be Swiss-army-knife-ready for any question the test can throw at you. What are Fractions? $${\a \piece}/{\the \whole}$$ Fractions are pieces of a whole. They are expressed as the amount you have (the numerator) over the whole (the denominator). A pizza is divided into 8 pieces. Kyle ate 3 pieces. What fraction of the pizza did he eat? He ate $3/8$ths of the pizza. 3 is the numerator (top number) because he ate that many pieces of the whole, and 8 is the denominator (bottom number) because there are 8 pieces total (the whole). Math is always more fun when it's delicious. Special Fractions A number over itself equals 1 $3/3=1$ $10/10=1$ $(a+b)/(a+b)=1$ A whole number can be expressed as itself over 1 $5=5/1$ $22/1=22$ $(a+b)/1=a+b$ 0 divided by any number is 0 $0/17=0$ $0/(a+b)=0$ There is one exception to this rule: $0/0=\undefined$. The reason for this lies in the next rule. Any number divided by 0 is undefined Zero cannot act as a denominator. For more information on this check out our guide to advanced integers. But for now all that matters is that you know that 0 cannot act as a denominator. Reducing Fractions If both the numerator and the denominator have a common factor (a number they can both be divided by), then the fraction can be reduced. For the purposes of the SAT, you will need to reduce your fractions to get to your final answer. To reduce a fraction, you must divide both the numerator and the denominator by the same amount. This keeps the fraction consistent and maintains the proper relationship between numerator and denominator. If your fraction is $3/12$, then it can be written as $1/4$. Why? Because both 3 and 12 are divisible by 3. $3/3=1$ and $12/3=4$. So your final fraction is $1/4$ Now let's figure out how to perform the four basic math functions on fractions. Adding or Subtracting Fractions You can add or subtract fractions as long as their denominators are the same. To do so, you keep the denominator consistent and simply add the numerators. $4/15+2/15=6/15$ But you CANNOT add or subtract fractions if your denominators are unequal. $4/15+2/5=?$ So what can you do when your denominators are unequal? You must make them equal by finding a common multiple (number they can both multiply evenly into) of their denominators. In the case of $4/15+2/5$, a common multiple of the denominators 15 5 is 15. When you find a common multiple of the denominators, you must multiply both the numerator and the denominator by the amount it took to achieve that number. Again, this keeps the fraction (the relationship between numerator and denominator) consistent. Think of it as the opposite of reducing a fraction. To get to the common denominator of 15, $4/15$ must be multiplied by $1/1$ Why? Because 15*1=15. $(4/15)(1/1)=4/15$. The fraction remains unchanged. To get to the common denominator of 15, $2/5$ must be multiplied by $3/3$. Why? Because 5*3=15. $(2/5)(3/5)=6/15$. Now we can add them, as they have the same denominator. $4/15+6/15=10/15$ We can further reduce $10/15$ into $2/3$ because both 10 and 15 are divisible by 5. So our final answer is $2/3$. Multiplying Fractions Multiplying fractions is a bit simpler than adding or dividing fractions. There is no need to find a common denominator- you can just multiply the fractions straight across. To multiply a fraction, first multiply the numerators. This product becomes your new numerator. Next, multiply your two denominators. This product becomes your new denominator. $1/4*2/3=(1*2)/(4*3)=2/12$ And again, we reduce our fraction. Both the numerator and the denominator are divisible by 2, so our final answer becomes: $1/6$ Special note: you can speed up the multiplication and reduction process by finding a common factor of your cross multiples before you multiply. $1/4*2/3$ = $1/2*1/3$. Why? Because both 4 and 2 are divisible by 2, we were able to reduce the cross multiples before we even began. This saved us time in reducing the final fraction at the end. So now we can simply say: $1/2*1/3=1/6$. No need to further reduce- our answer is complete. Take note that reducing cross multiples can only be done when multiplying fractions, never while adding or subtracting them! It is also a completely optional step, so do not feel obligated to reduce your cross multiples- you can simply reduce your fraction at the end. Dividing Fractions In order to divide fractions, we must first take the reciprocal (the reversal) of one of the fractions. Afterwards, we simply multiply the two fractions together. Why do we do this? Because division is the opposite of multiplication, so we must reverse one of the fractions to turn it back into a multiplication question. ${2/3}à ·{3/4}$ = $2/3*4/3$ (we took the reciprocal of $3/4$, which means we flipped the fraction upside down to become $4/3$) $2/3*4/3=8/9$ But what happens if you need to divide a fraction by a whole number? If a cake is cut into thirds and each third is cut into fourths, how many pieces of cake are there? *** We start out with $1/3$ of a cake and we need to divide each third 4 more times. Because 4 is a whole number, it can be written as $4/1$. This means that its reciprocal is $1/4$. $1/3à ·4$ = $1/3*1/4=1/12$ Our denominator (the whole) is 12. This means there will be 12 pieces total in the cake. Decimal Points Because fractions are pieces of a whole, you can also express fractions as either a decimal point or a percentage. To convert a fraction into a decimal, simply divide the numerator by the denominator. (The / symbol also acts as a division sign.) $4/5$ = 4/5 = 0.8 Sometimes it is easier to convert a fraction to a decimal in order to work through a problem. This can save you time and effort trying to figure out how to divide or multiply fractions. If $j/k=32$ and $k=3/2$, what is the value of $1/2j$ ? *** As you can see, there are two ways to approach this problem- using fractions and using decimals. We’ll look at both ways. If you were to use fractions, you would set up the problem as a fraction division problem. $k=3/2$ So $j/k=j/{3/2}$ $j/{3/2}$ = $j*2/3$ (remember, we take the reciprocal when we divide) So our full problem looks like this: $2/3*j=32$ Now we must divide 32 by $2/3$ in order to bring it over to the other side and isolate j. This means we need to take the reciprocal yet again. So ${32}/{2/3}$ = $32*3/2=96/2=48$ $j=48$ Now, for the final step, we must take $1/2$ of j. (Note: to "take $1/2$" is the same thing as multiplying by $1/2$.) $48*{1/2}=48/2=24$ Our final answer is 24. Alternatively, we could save ourselves the headache of using fractions and reciprocals and simply use decimals instead. We know that $k=3/2$. Instead of keeping the fraction, let us convert it into a decimal. $3à ·2=1.5$ So $k=1.5$ $j/k=32$ $j/1.5=32$ When you multiply both sides by 1.5, you get: $j=(32)(1.5)=48$ $j=48$ And ${1/2}j={1/2}(48)=24$ So again, our final answer is 24. Percentages After you convert your fraction to a decimal, you can also turn it into a percentage (if needed). So 0.8 from can also be written as 80%, because 0.8*100=80. A pie chart is a useful way of showing relative sizes of fractions and percentages. This shows just how large a fraction $7/10$ (or 70%) truly is. Mixed Fractions Sometimes you may be given a mixed fraction on the SAT. A mixed fraction is a combination of a whole number and a fraction. For example, 7$3/4$ is a mixed fraction. We have a whole number, 7, and a fraction, $3/4$. You can turn a mixed fraction into an ordinary fraction by multiplying the whole number by the denominator and then adding that product to the numerator. The final answer will be ${\the \new \numerator}/{\the \original \denominator}$. 7$3/4$ (7)(4)=28 28+3=31 So your final answer = $31/4$ You must convert mixed fractions into fractions in order to multiply, divide, add, or subtract them with other fractions. In this problem, we began with 5 gallons of water and we ended with 2$1/3$. We must figure out how many gallons we used. 5−2 $5-2{1/3}$ First, let’s get our mixed fraction into a regular fraction. 2$1/3$ = ${[(2*3)+1]}/3={7/3}$ $5/1-7/3$ Now, we need to give each fraction the same denominator. We'll do this by converting $5/1$ into a new fraction with a denominator of 3. $5/1*3/3=15/3$ Finally, we can find the difference between the amounts. $15/3-7/3=8/3$ So we have used up $8/3$rds of the water. Now let’s count how many times the pail was emptied to use up that $8/3$rds of the total water. If you count the dots, the pail was emptied 8 times (the first dot does not count as a time it was emptied- that is merely our starting point). Because the same amount of water was removed each time, we must divide our emptied water by 8. ${8/3}à ·{8/1}$ = $8/3*1/8$ We can now either reduce the cross-multiples (because this is a multiplication problem), which would give us: $8/3*1/8$ = $1/3*1/1$ $1/3*1/1=1/3$ Or we can multiply through and then reduce afterwards: $8/3*1/8=8/24$ $8/12=1/3$ Either way, our final answer is $1/3$; each trip removed $1/3$ of a gallon of water from the tank. Now that we've broken down all there is to know about SAT fractions, let's take a look at their close cousin- the ratio. This shape is called the "golden ratio" and has been studied for thousands of years. It has applications in geometry, nature, and architecture. What are Ratios? Ratios are used as a way to compare one thing to another (or multiple things to one another). If Leslie has 5 white socks and 2 red socks, the white socks and the red socks have a ratio of 5 to 2. Expressing Ratios Ratios can be written in three different ways: A â€Å'to â€Å'B A:B $A/B$ No matter which way you write them, these are all ratios comparing A to B. Different Types of Ratios Just as a fraction represents a part of something out of a whole (written as: ${\a \part}/{\the \whole}$), a ratio can be expressed as either: aâ€Å'part:a â€Å'different â€Å'part OR aâ€Å'part:theâ€Å' whole Because ratios compare values, they can either compare individual pieces to one another or an individual piece to the whole. If Leslie has only 5 white socks and 2 red socks in a drawer, the ratio of white socks to all the socks in the drawer is 5 to 7. (Why 7? Because there are 5 white and 2 red socks, so together they make 5+2=7 socks total.) Some of the many uses of ratios in action (in this case, the ratios are- a part: a different part). Reducing Ratios Just as fractions can be reduced, so too can ratios. Kyle has a stamp collection. 45 of them have pictures of daisies and 30 of them have pictures of roses. What is the ratio of daisy stamps to rose stamps in his collection? *** Right now, the ratio is $45:30$. But they have a common denominator of 15, so this ratio can be reduced. $45/15=3$ $30/15=2$ So the stamps have a ratio of $3:2$ Increasing Ratios Because you can reduce ratios, you can also do the opposite and increase them. In order to do so, you must multiply each piece of the ratio by the same amount (just as you had to divide by the same amount on each side to reduce the ratio). So the ratio of 4:3 can also be $4(2):3(2)=8:6$ $4(3):3(3)=12:9$ And so on. Marbles are to be removed from a jar that contains 12 red marbles and 12 black marbles. What is the least number of marbles that could be removed so that the ratio of red marbles to black marbles left in the jar will be 4 to 3? *** Right now, there are an equal amount of marbles, so the ratio is 12:12 (or 1:1) We know that we have an end ratio of 4:3 that we want to achieve and that each side of the ratio has to be multiplied (or divided) by the same amount to keep the ratio consistent. We want to remove as few marbles as possible, so let us imagine that 4:3 is a reduced ratio. That means we need to see how many total marbles the reduced ratio of 4:3 could possibly be. So both 4 and 3 have to be multiplied by the same amount to maintain their ratio and yet achieve a higher number of total marbles than just their 7 (4+3=7). We can see that 12 is divisible by 4, so the red marbles could conceivably remain unchanged in order to get a new ratio of 4:3. $12/4=3$ Because 4 can go evenly into 12, this will give us the fewest amount of marbles taken away. Because the 4 is multiplied 3 times to get 12, we know that both 4 and 3 must be multiplied by 3 to keep a new ratio of 4:3 consistent. To find the new number of black marbles, we take 3*3=9. The new amount of black marbles has to be 9. And because our red marbles remain the same (12), we must take only 3 marbles away from the total number of marbles (Why? Because 12â€Å' blackâ€Å' marbles−3 â€Å'blackâ€Å' marbles=9â€Å' blackâ€Å' marbles) So our final answer is 3, we must take 3 black marbles away to get a new ratio of 4:3 of red marbles to black marbles. Finding the Whole If you are given a ratio comparing two parts (piece:anotherâ€Å'piece), and you are told to find the whole amount, simply add all the pieces together. It may help you to think of this like an algebra problem wherein each side of the ratio is a certain multiple of x. Because each side of the ratio must always be divided or multiplied by the same amount to keep the ratio consistent, we can think of each side as having the same variable attached to it. For example, a ratio of 4:5 can be: $4(1):5(1)=4:5$ $4(2):5(2)=8:10$ And so on, just as we did above. But this means we could also represent 4:5 as: $4x:5x$ Why? Because each side must change at the same rate. And in this case, our rate is $x$. So if you were asked to find the total amount, you would add the pieces together. $4x+5x=9x$. The total amount is 9x. In this case, we don’t have any more information, but we know that the total must be divisible by 9. So let’s take a look at another problem. Teyvon has a basket of eggs that he is going to sell. There are two different kinds of eggs in the basket- white and brown. The brown eggs are in a ratio of 2:3 to the white eggs. What is NOT a possible number of eggs that Teyvon can have in the basket? A) 5 B 10 C) 12 D) 30 E) 60 *** In order to find out how many eggs he has total, we must add the two pieces together. So 2+3=5 This means that the total number of eggs in the basket has to either be 5 or any multiple of 5. Why? Because 2:3 is the most reduced form of the ratio of eggs in the basket. This means he could have: $2(2):3(2)=4:6$ eggs in the basket (10 eggs total) $2(3):3(3)=6:9$ eggs in the basket (15 eggs total) And so forth. We don’t know exactly how many eggs he has, but we know that it must be a multiple of 5. This means our answer is C, 12. There is no possible way that he can have 12 eggs in the basket. Now that we are armed with knowledge of fractions and ratios, we must follow the right steps to solve our problems. How to Solve Fraction, Ratio, and Rational Number Questions Now that we have discussed how fractions and ratios work indivisually, let's look at how you'll see them on the test. When you are presented with a fraction or ratio problem, take note of these steps to find your solution: #1: Identify whether the problem involves fractions or ratios A fraction will involve the comparison of a $\piece/\whole$. A ratio will almost always involve the comparison of a piece:piece (or, very rarely, a piece:whole). You can tell when the problem is ratio specific as the question text will do one of three things: Use the : symbol, Use the phrase "___ to ___† Explicitly use the word "ratio† in the text. If the questions wants you to give an answer as a ratio comparing two pieces, make sure you don’t confuse it with a fraction comparing a piece to the whole! #2: If a ratio question asks you to change or identify values, first find the sum of your pieces In order to determine your total amount (or the non-reduced amount of your individual pieces), you must add all the parts of your ratio together. This sum will either be your complete whole or will be a factor of your whole, if your ratio has been reduced. A total of 120,000 votes were cast for 2 opposing candidates, Garcia and Pà ©rez. If Garcia won by a ratio of 5 to 3, what was the number of votes cast for Pà ©rez? (A) 15,000 (B) 30,000 (C) 45,000 D) 75,000 (E) 80,000 *** As you can see, our ratio of 5 to 3 has been greatly reduced (neither of those numbers is in the tens of thousands). We know that there are a total of 120,000 votes, so we need to determine the number of votes for each candidate. Let’s first add our ratio pieces together. 5:3 = 5+3=8 Because 8 is much (much) smaller than 120,000, we know that 8 is not our whole. But 8 is the factor of our whole. ${120,000}/8=15,000$ So if we think of 15,000 as one component (a replacement for our variable, $x$), and Garcia and Pà ©rez have a ratio of 5 components to 3 components, then we can find the total number of votes per candidate. G:P=5:3 = $5x:3x$ 5*15,000=75,000 3*15,000=45,000 So Garcia earned 75,000 votes and Pà ©rez earned 45,000 votes. (You can even confirm that this must be the correct number of votes each by making sure they add up to 120,000. 75,000+45,000=120,000. Success!) So our final answer is C, Pà ©rez earned 45,000 votes. #3: When in doubt, try to use decimals Decimals can make it much easier to work out problems (as opposed to using fractions). So do not be afraid to convert your fractions into decimals to make life easier. #4: Remember your special fractions Always remember that a number over 1 is the same thing as the original number, and that a number over itself = 1. If $h$ and $k$ are positive numbers and $h+k=7$ then ${7-k}/h=$ (A) 1 (B) 0 (C) -1 (D) $h$ (E) $k-1$ *** Here we have two equations: $h+k=7$ and ${7-k}/h$ So let us manipulate the first. $h+k=7$ can be re-written as: $h=7−k$ (Why? We simply subtracted $k$ from either side) So now we can replace the $(7−k)$ from the second equation with $h$, as the two terms are equal. This leaves us with: $h/h$ And we know that any number over itself = 1. So our final answer is A, 1. Now, let's put your knowledge to the test! Test Your Knowledge #1: Flour, water, and salt are mixed by weight in the ratio of 5:4:1, respectively, to produce a certain type of dough. In order to make 5 pounds of this dough, what weight of salt, in pounds, is required? (A) $1/4$ (B) $1/2$ (C) $3/4$ (D) 1 (E) 2 #2: #3: Which of the following answer choices presents the fractions $5/4$, $4/3$, $19/17$, $13/12$, and $7/6$ in order from least to greatest? (A) $19/17$, $7/6$, $13/12$, $4/3$, $7/6$, $5/4$ (B) $4/3$, $5/4$, $7/6$, $19/17$, $13/12$ (C) $13/12$, $7/6$, $19/17$, $5/4$, $4/3$ (D) $19/17$, $13/12$, $5/4$, $7/6$, $4/3$ (E) $13/12$, $19/17$, $7/6$, $5/4$, $4/3$ Answers: B, D, E Answer Explanations: #1: This question is a perfect example of when to find the whole of the pieces of the ratio. Flour, water, and salt are in a ratio of 5:4:1, which means that the whole is: $5x+4x+1x=10x$ So $10x$ is our whole. We want 5 pounds of the recipe, so we must convert $10x$ to 5. $10x=5$ $x=1/2$ Our variable is $1/2$ . Now, we are looking for the amount of salt to use when we started out with $1x$. So let us replace our $x$ with the value we found for it. $1x$ $1(1/2)$ $1/2$ This means we need $1/2$ a pound of salt to make 5 pounds of the mixture. Our final answer is B, $1/2#. #2: For this question, we must find a non-zero integer for t in which $x+{1/x}=t$, where $x$ is also an integer. We know, based on our special fractions, that the only possible way to get a whole number in fraction form is to have our demoninator equal 1 or -1. This means that x cannot possibly be anything other than 1 or negative 1. (Why? If x were anything else but 1, we would end up with a mixed fraction. For example, if x=2, then we would have: $2+{1/2}$. If $x=3$, we would have: $3+{1/3}. And so on. The only way to get an integer value for $t$ is when $x=1$.) So let us try replacing our $x$ value with 1. $x+{1/x}=t$ $1+{1/1}=2$ $t=2$ Well, $t$ could possibly equal 2, but this is not one of our answer choices. So now let us replace $x$ with -1 instead. $x+{1/x}=t$ $-1+{1/-1}=-2$ t=−2 Success! We have found a value for $t$ that matches one of our answer choices. Our final answer is D, $t=−2$ #3: For a problem like this (one that has you order fractions by size), it is usually a good idea to break out the decimals. But we will go through how to solve it using both methods of fractions and decimals. Solving with decimals: To solve with decimals, simply divide each numerator by its denominator to get the decimal. Then, order them in ascending order (as we are told). $5/4=1.25$ $4/3=1.333$ $19/17=1.12$ $13/12=1.08$ $7/6=1.16$ We can see here that the order from least to greatest is: 1.08, 1.12, 1.16, 1.25, 1.33 Which, converted back to their fraction form is: $13/12$, $19/17$, $7/6$, $5/4$, $4/3$ So our final answer is E. Alternatively, we can solve using fractions. Solve using fractions: Let us find a common denominator between all the numerators. A quick way to do this is by multiplying the two largest numerators together. (It may not be the least common denominator, but it'll do for our purposes.) $17*12=204$ Now let's make sure that the other denominators can go evenly into 204 as well. $204/6=34$ $204/4=51$ $204/3=68$ Perfect! Now let us convert all of our fractions. $5/4={5(51)}/{4(51)}=255/204$ $4/3={4(68)}/{3(68)}=272/204$ $19/17={19(12)}/{17(12)}=228/204$ $13/12={13(17)}/{12(17)}=221/204$ $7/6={7(34)}/{6(34)}$ Now that they all share a common denominator, we can compare and order their numerators. So, in ascending order, they would be: $221/204$, $228/204$, $238/204$, $255/204$, $272/204$ Which, when converted back to their original form, is: $13/12$, $19/17$, $7/6$, $5/4$, $4/3$ So again, our final answer is E. I think a nap is in order- don't you? Take-Aways Fractions and ratios may look tricky, but they are merely ways to represent the relationships between pieces of a whole and the whole itself. Once you know what they mean and how they can be manipulated, you’ll find that you can tackle most any fraction or ratio problem the SAT can throw at you. But always remember- though ratios and fractions are related, do not get them mixed up on the SAT! The vast majority of the time, the ratios they give you will compare parts to parts and the fractions will compare parts to the whole. It can be easy to make a mistake during the test, so don’t let yourself lose a point due to careless error. What’s Next? You've conquered fractions and you've decimated ratios and now you're eager for more, right? Well look no further! We have guides aplenty for the many math topics covered on the SAT, including probability, integers, and solid geometry. Feel like you're running out of time on the SAT? Check out our article on how to finish your math sections before time's up. Don't know what score to aim for? Make sure you have a good grasp of what kind of score would best suit your goals and current skill level, and how to improve it from there. Angling to get an 800 on SAT Math? Look to our guide on how to get a perfect score, written by a perfect SAT scorer. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, 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:

Quotes From William Shakespeares Romeo and Juliet

Quotes From William Shakespeares Romeo and Juliet Romeo and Juliet,  one of Shakespeares iconic tragedies,  is a play about star-crossed lovers, their romance doomed from the start. It is one of the most famous plays of the English Renaissance, consistently taught and staged at high schools and colleges. As their families feud to the death, Romeo and Juliet, the two young lovers, are caught between disparate worlds. The unforgettable play is filled with fights, secret marriages, and untimely deaths–along with some of Shakespeares most famous lines. Love and Passion The romance of Romeo and Juliet is perhaps the most famous in all of literature. The young lovers, despite their families objections, will do anything to be together, even if they must meet in secret. During their private rendezvous, the characters give voice to some of Shakespeares most romantic speeches. What sadness lengthens Romeos hours? / Not having that, which, having, makes them short. / In love? / Out / Of love? Out of her favor, where I am in love. [Act 1, Scene 1] One fairer than my love? The all-seeing sun / Neer  saw her match since first the world begun. [Act 1, Scene 2] Did my heart love till now? Forswear it, sight! / For I neer saw true beauty till this night. [Act 1, Scene 5] My bounty is as boundless as the sea / My love as deep; the more I give to thee, / The more I have, for both are infinite. [Act 2, Scene 2] Good Night, Good night! Parting is such sweet sorrow, that I shall say good night till it  be  morrow. [Act 2, Scene 2] See, how she leans her cheek upon her hand! /  O that I  were  a glove upon that hand, /  that I might touch that cheek! [Act 2, Scene 2] These violent delights have violent ends / And in their triumph die, like fire and powder, / Which as they kiss consume. [Act 2, Scene 3] Family and Loyalty Shakespeares young lovers come from two families–the Montagues and the Capulets–that are sworn enemies of each other. The clans  have kept alive their ancient grudge for years. In their love for each other, Romeo and Juliet have each betrayed their family name. Their story shows what happens when this sacred bond is broken. What, drawn, and talk of peace? I hate the word, / As I hate hell, all Montagues, and thee. [Act 1, Scene 1] O Romeo, Romeo! wherefore art thou Romeo? / Deny thy father and refuse thy name. / Or if thou wilt not, be but sworn my love / And Ill no longer be a Capulet. [Act 2, Scene 2] â€Å"Whats in a name? that which we call a rose  /  By any other name would smell as sweet.†Ã‚  [Act 2, Scene 2] A plague o both your houses! [Act 3, Scene 1] Fate From the very beginning of the play, Shakespeare announces Romeo and Juliet as a story of destiny and fate. The young lovers are star-crossed, doomed to ill fortune, and their romance can only end in tragedy. The play unfolds with an inevitability reminiscent of Greek tragedy, as forces in motion slowly crush the young innocents who try to defy them. Two households, both alike in dignity  /  In fair Verona, where we lay our scene  /  From ancient grudge break to new mutiny  /  Where civil blood makes civil hands unclean.  /  From forth the fatal loins of these two foes  /  A pair of star-crossd lovers take their life  /  Whose misadventured piteous overthrows  /  Do with their death bury their parents strife.†Ã‚  [Prologue] This days black fate on more days doth depend: / This but begins the woe others must end. [Act 3, Scene 1] â€Å"Oh, I am fortunes fool!†Ã‚  [Act 3, Scene 1]