Solving proportions free essay sample

Algebra A comparison of two numbers Is referred to as a ratio, slmllar to tractions that can be reduced to lowest terms and then converted into a ratio of integers. Ratios allow one to compare sizes of two quantities and unit measurements. Any statement expressing the equality of two ratios is known as a proportion, which Is used In numerous formulas in todays real world settings and applications. Using proportions Is an effective way to find solutions by using the extreme means property or cross-multiplying. Extreme means property is simply the end result of the product f the extremes equaling the products of the means. Cross-multiplying is a short cut In proportions providing it Is a faster way to solutions rather than multiplying each side of the rational expression equation by the LCD_ Applications of rational expressions Involving formulas Include finding the equation of a line, distance, rate, time, uniform motion, and work problems. We will write a custom essay sample on Solving proportions or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Proportions are used on a daily basis without even one realizing it by comparing measurements, unit pricing, driving distances, and calculating populations and wildlife on a dally basis to find a solution. For example, I will be using the extreme means property to estimate bear population In Keweenaw Penlnsuld. I was asked to solve problem #56, on page 437 of Elementary and intermediate algebra, (Dugopolski, M. , 2012) which states, that conservationists captured, tagged, and released 50 bears. over a one-year period, a random sample of 100 bears included only 2 tagged bears in Keweenaw Peninsula. To calculate the proportion, it will allow me to expect the ratio of bears that were originally tagged to the whole population Is equal to the ratio of the returning bears otaling 100 but only 2 tagged bears to the size of the sample. The variable b for bears Is applied, then followed by cross-multiplying the extremes and means to the proper set up of the proportion to find the solution. The two ratios are as follows: 50/ b = the originally tagged bears to the whole population and 2/100 = the recaptured bears to the sample size. I ne means are 2 ana D ana tne extremes are 50 ana 1 50 2 b 100 Correct setup of proportion. 5,000 = 2b cross multiply the means (2*b) and the extremes (50*100) followed by division of 2. 2,500 Answer after division was carried out. z 500 The estimated number of bears in Keweenaw Peninsula. Continuing onto the second assignment involving proportions, the following equation must be solved for y. Since there are single fractions (also referred to as ratios) on both sides of the equation, the extreme means property will be used again in this proportion. Written as an equation; solving for y. Cross multiplying was done. † l) = -3x(x+ 3) 4y- 1 +4 = -3x +3 +3Distribute 4 on left side and 3 on the right side. y = -3x -3+ 1 Add 1 to both sides. 4y = 2x -5 Last step, 4 is divided on both sides. 4 lope of -3/4. Linear equation in the form of y = mx + b and with a Taking notice that the slope of -3/4, is the same number as the number on the right hand side of the previous equation. I must continue trying another method but still use the extreme means property and try another method to see if I get a different solution. This may be an extraneous solution that I may come upon considering if the solution does not satisfy the rational expression. y-1 left. Original equation. Distribute (x-3) on both sides and multiply. Cancel out common factors which eliminates denominator on 0 Isolate y, 1 Is a aaea to Dotn sloes. ancel common factors. y=-3x-1 Equation complete and simplified. For this equation, I could have multiplied the LCD to both sides, but I found the extreme means property was an efficient shortcut. Cross- multiplying allowed me to eliminate the fractions and have the same ending result. We can now consider this an extraneous solution because the number showing as the solution but causes zero (O) in the denominator. As rational expressions can be tricky when there is a variable involved in the denominator so caution must be adhered. The use of proportions is everyday life and real world settings and applications are used without one even realizing it. While proportions can determine a solution whether it be driving distance, estimated population count, unit measuring, gas mileage, or to estimate an average time for a Job to be completed, it is a necessary tool that is used in many ways. The ratios that build the proportion can be easily solved by cross- multiplying the extremes and means in a fast and effective way. The wildlife can be assured that their tags will be calculated with an accurate solution for ny conservationist inquiring about a certain species. So the next time you find yourself comparing two quantities, deciding the average time for a specific Job, or determining how many miles you can go on a half of tank of gas on your next road trip, remember you are actually calculating proportions! [References:] Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed. ). New York, NY: McGraw-Hill Publishing. Retrieved from http:// ashford. ebooks. edu (2009). Word problems involving proportions [Video]. Retrieved from http://www. youtube. com/watch

How to Stay Productive As the Summer Drags On

How to Stay Productive As the Summer Drags On After a long harsh winter of being stuck inside; summer is known as the season of outdoors fun. Productivity and focus on work is always a struggle during this time. We catch ourselves day dreaming of being outside; going to the beach or taking a walk in the park. But it is hard to enjoy the rays of sunshine while being stuck at work. Here are 8 tips on how to fight the summer productivity slump. Source [Wrike]

What Is a GPA Scale The 4.0 Scale

What Is a GPA Scale The 4.0 Scale SAT / ACT Prep Online Guides and Tips GPA is a measurement of your academic success in high school that colleges will consider very strongly in the admissions process. But what is a GPA scale? Different high schools may use different GPA scales, and it’s important to know how these scales work so that you get a better idea of where you stand. In this article, I’ll tell you what a GPA scale is and the types of scales you might see used at your high school. // What’s a High School GPA Scale? GPA (Grade Point Average) is a way of measuring academic achievement in high school. It’s a numeric value that correlates with a student’s grades. Each letter grade that a student earns is worth a certain number of grade points depending on how high it is and, in some cases, the level of the class where it was earned. // The average of the grade points from all of a student’s converted letter grades in high school makes up his or her final GPA. Typically, one of two GPA scales will be used to measure the grades of students throughout their time in high school. The unweighted GPA scale goes up to a 4.0 and doesn’t take class difficulty into account.A weighted GPA scale typically goes up to a 5.0 and does consider the difficulty of a student’s classes.I’ll go over the basics of these two scales in the next couple of sections to give you a sense of how they work. // Unweighted 4.0 GPA Scale The unweighted GPA scale is the most commonly used GPA scale. It’s found in high schools and colleges alike and is very straightforward. // Essentially, the highest GPA you can earn is a 4.0, which indicates an A average in all of your classes. A 3.0 would indicate a B average, a 2.0 a C average, a 1.0 a D, and a 0.0 an F.This scale does not take the levels of your courses into account. For example, if you’re in all honors classes and earn a B average, you’ll have the same GPA as someone in all low-level classes who has earned a B average. // Here’s a table that shows how this scale corresponds to each letter grade: Letter Grade GPA A+ 4.0 A 4.0 A- 3.7 B+ 3.3 B 3.0 B- 2.7 C+ 2.3 C 2.0 C- 1.7 D+ 1.3 D 1.0 F 0.0 // Some high schools make more specific distinctions in GPA based on class averages out of 100 (i.e. a 90 average would mean a lower GPA than a 92 average even though they’re both technically A-s).Look at this GPA scale for more specific numbers. Want to build the best possible college application? We can help. PrepScholar Admissions is the world's best admissions consulting service. We combine world-class admissions counselors with our data-driven, proprietary admissions strategies. We've overseen thousands of students get into their top choice schools, from state colleges to the Ivy League. We know what kinds of students colleges want to admit. We want to get you admitted to your dream schools. Learn more about PrepScholar Admissions to maximize your chance of getting in. // Weighted 5.0 GPA Scale Instead of using the basic unweighted scale, many high schools will use a weighted GPA scale. On a weighted scale, which typically goes up to a 5.0 instead of the standard 4.0, a student who earns an A in a high level class will have a higher GPA than a student who earns an A in a low-level class. While this scale is used frequently in high schools, you’re unlikely to encounter it in college since it takes course difficulty into account. // For the highest-level classes like honors and AP, students get an extra 1.0 added to the unweighted GPA value of their grades due to the difficulty of the class. A B in an honors class would be equivalent to a 4.0 on a weighted GPA scale, and an A would be equivalent to a 5.0. Some schools also offer mid-level classes between honors and low-level. For these courses, 0.5 points are usually added to the unweighted GPA, meaning an A would be equivalent to a 4.5. Grades in low-level classes are measured using the unweighted scale, so an A in those classes would be equivalent to a 4.0. Weighted GPA scales give colleges a better initial sense of the academic potential of students based on the rigor of their coursework. They also lead to greater accuracy in class rankings. Students who take lower level classes won’t surpass high-level students in the rankings as frequently because GPAs are adjusted for class difficulty. This can help incentivize students to take more difficult classes and challenge themselves since it won’t harm their GPAs unless they end up earning signficantly poorer grades. Figure skaters are judged partially on the difficulty of their routines, so a skater who executes an easy routine flawlessly won't prevail over another skater who executes a difficult routine with a couple of mistakes. It's the same with weighted GPA. How far away are you from a 4.0? Use our easy GPA tool to pinpoint how well you have to do in future classes to get your GPA up to that magical number. Why Do GPA Scales Matter to You? It’s important to be aware of the GPA scale used by your high school so that you can make responsible choices in the college application process. If you’re aiming for selective colleges, you need to understand that your chances might be different depending on whether your GPA is weighted or unweighted. A student with a 3.8 unweighted GPA who is in all Honors classes will have better chances of admission at a selective college than a student with a 4.0 weighted GPA who is in all low-level classes. Much of the advice you’ll see about GPA is based on an unweighted scale because the unweighted scale is a more universally understood metric. This means that if your school uses weighted GPAs you’ll have to make judgments about how you might compare to other applicants based on your coursework and not just the numbers. For example, if the average unweighted GPA for admitted students at a college is a 3.5, you can’t always assume that you’ll get in easily with a 4.0 weighted GPA. The two numbers are on completely different scales. You’ll have to take stock of the overall rigor of your coursework and selectivity of the school to see whether you compare favorably to other applicants. It’s smart to be aware of the different GPA scales so that you have a better understanding of how much you might need to raise your GPA in order to get into a school that you really like. // Conclusion High school GPAs are measured on one of two scales: weighted or unweighted. The unweighted scale is most common, and the highest possible GPA on this scale is a 4.0. The unweighted scale doesn’t take the difficulty of your classes into account. Weighted scales are also used at many high schools. Typically, they go up to a 5.0. A weighted scale will factor in the difficulty of your classes, so an A in an honors class translates to a full grade point higher than an A in a low-level class. It’s valuable to have some knowledge of how GPA is measured by your school so that you end up with a more informed perspective going into the college application process. Your GPA will play a significant role in college admissions decisions, so keep working hard to maintain and improve it! What's Next? If you're curious about your GPA, read our article that gives you step by step instructions on how to calculate it based on your grades so far in high school. Is your GPA above average? Below average? Find out more about average high school GPAs here. If you have a low GPA, you might be worried about applying to college. Learn more about how to navigate the college application process with a low GPA. Want to improve your SAT score by 160 points or your ACT score by 4 points? We've written a guide for each test about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now:

Oldham Pond Essay Example | Topics and Well Written Essays - 1000 words

Oldham Pond - Essay Example An example of a response by the ecosystem would be a spurt in the population of phytoplankton in the aquatic body, due to an upsurge in the nutrient level (John & Eugene 109). This phenomenon has such negative effects on the environment as hypoxia, which is oxygen depletion in the water. On top of promoting an increase in phytoplankton levels, it also promotes plant decay, while seeming to favor natural plankton and algae as compared to more developed plants. This plant decay causes a substantial reduction in the quality of the water, as well as depletion of aquatic oxygen during decomposition of algae, which causes death of fish. Eutrophication decreases the recreational value of water bodies, hurting tourism. The premise of this paper is to study Oldham pond and its tributaries and evaluate the effects of eutrophication. Conductivity of the pond was measured using a portable conductivity metre. Conductivity is the measurement of how much material found dissolved in the pond. Polluted ponds have more dissolved solute than clean ponds. Conductivity below 250 is preferable, with upward of 600 being the cause for alarm. Measurement of temperature was done using a thermometer, while the levels of dissolved oxygen were measured using a dissolve oxygen electrode (Ansari 90). The sampling was carried out on the 4th and 25th of February, 2012. For the organisms in the pond, Ad Libitum sampling was used, where much information about the organisms was measured (John & Eugene 106). According to the results, the temperature of the water was comparable to that of the surrounding air. The slight difference is the difference in conductivity of heat by air and water. Dissolved oxygen levels were also concurrent to those that are recommendable (11 mg/l). Conductivity, however, was found to be higher than recommended. Recommended conductivity is below 250 (Boqiang et al

Business Ethics Essay Example | Topics and Well Written Essays - 1250 words - 10

Business Ethics - Essay Example Ethical and social responsibilities require companies to have a sense of responsibility to the environment in which it operates through participating in programs that are aimed at improving the wellbeing of the community. Over the past years, Apple Corporation has not been performing well as far as corporate social responsibility is concerned. Its workers working in the China based factories have been reported on several occasions as going through harsh working conditions. These poor working conditions involved extremely low wages, forced overtimes with no corresponding remunerations and other unfavorable treatments. Recently the organization has been linked with child labor after Foxconn, which is a major supplier of Apple admitted of being involved in child labor. In its Yantai assembling facility in Shandong province of China student interns who were as young as fourteen years were required to work forcefully at a certain amount of fee. Its environmental practices have not been fr iendly as evidenced by the many criticisms it has been receiving. The company has been accused severally of consuming a considerable percentage of global electricity, which has raised questions on the commitment of the firm to using alternative means that do not cause a lot of pollution to the environment (Icke, 2013). Currently Apple seems to be heading on the right direction in corporate social responsibility especially after Tim Cook became the CEO. He has displayed having a vision of being socially responsible, which previously lacked in the management since Steve Jobs was only concerned with equipping the society with the best technology. He therefore never took keen interest on public grants to charity organizations and other programs that are aimed at improving the well-being of the society. Cook after assuming office introduced a charity program that is similar to the ones embraced by majority of the successful large multinationals. The program involved a dollar-to-dollar

National Association of Home Builders Essay Example for Free

National Association of Home Builders Essay Purpose and Background The National Association of Home Builders (NAHB) is a trade association whose mission is to enhance the climate for the housing and building industry. A top goal for the NAHB is to provide and expand opportunities for all potential home buyers to have safe, affordable and decent housing. The NAHB also works with federal agencies on regulations affecting the housing industry in areas such as mortgage finance, codes, energy and the environment. According to the NAHB, about eighty percent of the homes built in the United States are constructed by NAHB members. In 1993 the NAHB and Reed Business Information, publishers of Professional Builder and Professional Remodeler magazines established the National Housing Quality Awards (NAHB website). The National Housing Quality Awards (NHQ) was modeled after the Malcolm Baldrige National Quality Award program and represents the housing industry’s highest recognition for achievements in total quality management. The NHQ award promotes and rewards best practices throughout the home building industry. It recognizes home builders for being focused on quality for the customer in construction, business management, sales, warranty service and design. The NHQ award is open to all U.S. home builders that believe their company meets or exceeds the qualities above. The home builder completes an application process and goes through an extensive interview process that requires a high level of commitment from the company and their management team. According to the NAHB application, every applicant will receive a written report and applicants that are chosen for site visits will receive detailed reports that provide objective benchmarking for quality improvement. The program is more than an award; many home builders use the award as a process for improving their processes to build a better home for the customer and a better company for their shareholders. In the home building industry, the expectations for high performance from the customers gets higher every year. Especially in the current housing market it is becoming more critical than ever that builders look for new products and processes that help to improve  their companies in areas such as leadership, performance management, customer satisfaction, strategic planning, construction quality, trade partner relationships, business results and human resources according to Steve Carroll of the NAHB. Award Criteria The NHQ awards are judged by a qualified experts who evaluate all the applicants and selects finalists who demonstrate high levels of quality achievement based on leadership, strategic planning, performance management, customer satisfaction, human resources, construction quality, trade relationships and business results. The experts can request additional information during the application process, including customer satisfaction surveys, company references and other information related to judging the criteria. In the Leadership category the panel experts will look at the company mission and values to determine if they guide the organization toward a common purpose. They review how senior management reinforce and instill the mission, values and vision in the company as role models and through empowering employees. They will also look at how the company demonstrates public responsibility and good citizenship while improving the home building industry. In the Strategic Planning categor y the experts will look at how your company assesses and will address the key strategic challenges that the company faces in the next one to five years. They look at how the challenges are identified and analyzed and the overall plan development, deployment and feedback for the company including how the plan is tied to the mission, vision and values. They will review how the plan leverages the company’s skills, experience, knowledge and the lack of skills, experience, knowledge and resources. In the Performance Management category the experts review how the company develops, manages, measures, and improves the key processes to achieve performance excellence. The Customer Satisfaction category allows the experts to look at the company’s design and delivery of products and services with a high level of customer satisfaction. The applicant will need to address how the company identifies market segments, the level of focus on the market segments, how product features and service are selected to best serve the market segments that were identified, how the company develops customer relationships, key factors in customer satis faction and how the company obtains and utilizes  customer feedback to improve performance. The Human Resource category addresses employee selection and development practices, motivation, satisfaction and compensation as it relates to the growth and success of the company. The experts will review the work environment, the morale of the employees, the benefits and the company culture. The applicant will need to address workforce development, staff performance management, and how both align with the company’s goals. The Construction Quality category will allow the experts to review the methods that the company uses to drive quality in the home construction process and ensure high performance and trouble free products and services. Applicants will have to discuss the quality standards that are communicated and demanded from the trades and how the company continues to educate and reinforce the quality standards to both employees and trades. The experts will ask how new plans are reviewed for quality and how the customer is involved in this quality review process. Applicants should be prepared to describe the customers’ post closing experiences, quality recognition programs and the company’s warranty processes. The Trade Relationship category allows the expert panel to review how the company creates high performance relationships with the trade partners. The applicant should be prepared to discuss how the company establishes mutually beneficial relationships, trade partner selection process, problem avoidance through trade involvement and trade partner feedback. The final category is Business Results. Applicants need to present the measurements of the business benefits resulting from the company’s high performance practices in the financial, operational, customer satisfaction and warranty areas. The experts may ask for customer satisfaction results from the last one to three years including the customers’ willingness to refer other buyers, financial results, employee satisfaction, trade satisfaction and operating metrics for the last three years. Benefits of the Award Many of the home builders that prepare the NHQ application feel that the application process and the experts’ comprehensive evaluation report are valuable tools for planning change to improve their business regardless if they win the award or not. Many of the award recipients find that the greatest rate of improvement occurs in the year following their application  or win (NAHB). Shea Homes and Pulte Homes found that the NHQ award process helped them identify opportunities to improve and allowed them to perfect processes that improved the quality of their product and service. Improving total quality management can lead to streamlining processes that will reduce costs, improve the quality for the customer, reduce warranty calls and increase the bottom line for the company. The NAHB encourages award winners to publicize and advertise the achievement to distinguish the company from the competition, establish the company as a top quality builder and raise the company’s re putation as an industry leader. Winners are featured in Professional Builder magazine articles that highlight their quality management principles and will participate in a NHQ award panel discussion at the International Builders show which is the largest home builders’ convention in the United States. Benefits to applying for the award are endless for home builders that are willing to commit the time and effort needed to complete the application process. The application process forces many of the applicants to look at the processes in the company that contribute to ensuring total quality and make changes to allow the company to improve and focus on the company’s mission, vision and values. The drawbacks to the NHQ award process is that it will take a commitment of time and energy to look at the quality processes in the company to analyze if it is moving the company in the direction of the mission, vision and values. Some companies may feel that this is a waste of time and energy or can be over whelmed at what processes need to be improved to get the company on track to improve quality. Past Winners Winners are recognized in three categories: gold, silver and honorable mention. The gold award is given to companies that have achieved a national benchmark level in each area of evaluation. According to the NAHB website, gold award winners have mature, fully integrated quality management principles and consistently demonstrate high level sustained financial results. The silver award is given to companies that are industry leaders in most evaluation areas, they have refined business practices and they exhibit good financial results. An honorable mention is awarded when companies are recognized that demonstrate an understanding of quality management principles, show an improvement process and good financial  results are achieved in most areas. Below is a list of winners, the award that was received and the year it was awarded (NAHB website). Many of the applicants that have participated in the NHQ process, whether the company was awarded or not, have said that the application process helped the company by having to look at all processes critically and make changes to improve the quality management for the company overall. Scott Thistle,  president of Brookstone Homes, said, â€Å"The award is a critical component of our commitment to customer satisfaction. By going through the NHQ program for the second year, it has enabled us to continually fine-tune our quality assurance systems and see a direct positive impact on our customers and their experience (Brookstone Homes).† Home Builders that apply for the NHQ award know that the process requires a lot of time and effort prior to submitting the application to the NAHB and could involve potential changes to the operational processes of the company to keep the company focused on total quality management. Grayson Homes president, Cindy McAuliffe said â€Å"At Grayson Homes, we differentiate ourselves from others with a deserved reputation for quality homes and products, processes, service, and people. Our participation in NHQ programs keeps Grayson Homes and its trades focused on product, process and experience improvement (Mid-Atlantic Builder).† Conclusion In reviewing the NHQ award and the process involved in applying for the award I found that it was a benefit to each of the home builders that took the time, energy and efforts even if the company did not win an award. Each of the companies that applied where able to review the quality processes that were in place, review the experts written report and modify the processes to achieve a higher level total quality management that improved the company’s quality focus for internal and external customers. While I do feel that this would be a benefit for my company I believe that we would have a lot of work to do in streamlining processes to ensure that company wide we are using the same quality processes that will allow us to grow while following our mission, vision and values. The company was a small company based in two markets that grew quickly to fourteen markets prior to the housing market boom. This fast growth did not allow for the company to ensure that quality processes were being handled in the same manner from division to division. The company has in the past three years established a strategic mission for the company and continued with the values that has allowed them to achieve the ranking of the 24th largest builder in the United States. The NHQ award process would force the management team to review what processes where in place in all divisions and get on track with companywide policies and procedures so a customer buying a home in one  division could expect the same great product and service in another division. References Brookstone Homes Newsroom. BrookstoneHomes.com. 15 Mar. 2008. http://www.brookstonehomes.com/newsroom/2006_august2.asp. Carroll, Steve. Telephone interview with National Association of Home Builders Research Center. March 14, 2008. Mid-Atlantic Builder Corner Newsletter. Mid Atlantic Builder. 16 Mar. 2008. http://www.homebuilders.org/file_depot/0-10000000/0-10000/48/folder/40005/ MBX_0105_60-70.pdf. National Housing Quality Award. National Association of Home Builders Research Center. 15 Mar. 2008. http://www.nahbrc.org/technical/awards/nhqa.aspx. Stromberg, Meghan. NHQ Best Practices. Professional Builder. September 2001. 1 Sep. 2001.

Physics of Water Waves :: Lab Report

All waves possess the properties of reflection, refraction, diffraction and interference. These phenomena's were observed with the use of a ripple tank. A ripple tank consists of a large rectangular tray with a transparent bottom. Water is placed in this tan to a depth of approximately one centimeter. A light source is then placed above the tray of water. When the water is disturbed it can be seen on a white surface positioned under the tray. The first phenomenon observed was reflection. It was found that water waves also follow the law of reflection. As straight waves strike a hard straight surface they are reflected at an angle equal to the angle of incidence. After reflection the wave has the same speed, frequency and wavelength as it did prior to the collision. This is similar to the reflection of circular waves off a straight barrier. The reflected waves are also circular, however they have a centre point that is position behind the barrier. This point is known as the "image" of the source. Reflection of a parabolic or concave barrier can be closely compared to that of light waves off a concave mirror. If the incident wave was straight, the reflected waves are curved, and they converge at a fixed focal point. After passing through the focus, the radius of the curves increase. The opposite is so when circular waves strike a concave barrier. The reflected waves are then straight. The next phenomenon observed was the refraction of water waves. The refraction was demonstrated in the ripple tank by dividing the tank into a deep and shallow region. This was achieved by placing a rectangular object into one end of the tank. When straight waves travel from a deep region of water into a shallow region, it is found that the speed of the waves is slower in the shallower region. Since the frequency of the wave stages the same, it is obvious that there must be a corresponding decrease in wavelength. If the waves pass from deep to shallow water at an angle other than