...On a Property of the Least Common Multiple of Two Integers Dan Kalman The Least Common Multiple of two integers, is the least positive integer that is divisible by both integers. This is connected by a simple formula with the greatest common divisor of the two integers, a familiar topic from modern algebra and number theory. The purpose of this paper is to present a proof for the connection between least common multiple and greatest common divisor. Along the way we will see several other properties of the least common multiple, as well as a number of examples. Throughout the discussion, we will consider only positive integers, the set of which is expressed as N. We also assume the notation and properties of the greatest common divisor presented in Hungerford [1]. In particular, if a and b are positive integers, we denote the greatest common divisor of a and b by (a,b). To begin the discussion of least common multiple, we present the following definition. Definition 1. If a and b are positive integers, the least common multiple of a and b, denoted [a,b], is the least positive element of the set {z ( N : a | z and b | z }. It should be remarked that for any positive integers a and b, their product ab is always divisible by both a and b, showing that the set of positive common multiples is not empty. Thus, [a,b] is always defined. As an example, [4,6] = 12. To see this, observe that the multiples of 4 and 6, respectively, can be listed as follows: ...
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...University of Phoenix Material Math Standards Analysis Directions: 1. Access your state’s department of education website. 2. Locate your state’s mathematics standards. 3. Select one strand or domain. 4. Complete the table below. For each of the identified grade levels, enter the exact verbiage of the standard for that strand or domain in the Standard column. In the Explanation column, explain in your own words what that standard means at that grade level. In the Teaching Example column, provide an example of how you might teach that standard to students at that grade level. State _California______________________________ Strand or Domain___CA CSS __________________________ |Grade Level |Standard |Explanation |Teaching Example | |1st grade |In grade 1, instructional time should|In first grade children should be|For teaching place values and | | |focus on four critical areas: |able to know how to add and |grouping numbers in to 10’s and | | |(1) developing understanding of |subtract to 20,they should |1’s, a good teaching example is | | |addition, subtraction, and |understand place values and how |what number is 10 less than 41? | | |strategies for addition...
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...The math department I met with consists of a variety of teachers from various backgrounds, education experience, and years of experience. At LGA our teacher see ongoing professional learning as a high priority. Amongst our staff, there has been a rise in teachers continue higher education with more than half of ours teachers holding at least one Master’s degree. Our faculty consists of twenty-eight teachers with eight of those teaching making up the math department. The majority of our staff consists of veteran teachers with fifteen or more years of experience in the professional. Within the math department, three of the teachers are relatively new to the profession. While teaching is unusually an overwhelmingly caucasian female occupation,...
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...are nurses themselves and work in their various fields. So when something comes up that needs addressed, they meet as a committee and discuss the issue. Then they decide what would be the best action to take for solving the problem. By doing this they are able to come up with the standards we now have. They realize that there must be a code of ethics and code of conduct set forth and these are the rules that we as nurses must follow. No one is allowed to change any part of it. So far there is a wide variety of standards that have been put into place. It is good for to know these rules and they will guide us in daily nursing duties. By implementing the higher standard of care, we are all able to work more proficiently and professionally. In order to develop a new standard, there usually has to be a problem that has come to the attention of one or more of the committee members, or from someone else that has brought forth a concern or complaint. The members then meet in order to come up with a solution to help with the problem. Such an example would be when too many nurses were getting stuck with needles and contracting diseases from them. From that basis came the implementation of the safety standards we now have to help prevent needle sticks, including not recapping needles, and using the safety features provided with each...
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... |23 12월 2011 | | |11 Music | |Endorsed with merit at level 1 |24 12월 2011 | |2012 | |Entries and Results | |Show explanation of the entry details | |Hide explanation of the entry details | |Each standard can have a range of results including "N" for not achieved, "A" for...
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...Tech Partners Consulting www.techpartners.net.au SOEs – Standard Operating Environments The SOE concept explained in business terms Authored by Alan Pickering, Tech Partners Consulting September, 2003 Introduction The use of Information and Communications Technology (ICT) in organisations has gone well past the stage of being unique, novel and even technically difficult. Nowadays, the technology is readily available, thanks to the volume demand from commercial and residential market segments. Even so, there are benefits from adopting a Standards based approach to choosing and deploying ICT assets; and offering technology based IT services to customers. This white paper will provide a brief introduction to the philosophy of Standard Operating Environments, and will explain the likely benefits, costs and planning factors that relate to adopting an SOE approach. Background When desktop computing and Local Area Networks appeared in organisations in the 1980’s, they were small scale and of little immediate consequence. Being somewhat complex, and requiring some hands on technical skills, they were acquired in small quantities. The low cash costs meant they were often purchased ‘under the radar’ of senior management and IT teams. The practical use and popularity of PCs and LANs grew, to the point that some organisations recognized the need to account for the cost of assets and people’s time spent on support. Since then, industry analysts have studied the...
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...PLC 2005 - 2009 Newcastle upon Tyne Trainee Manager At McDonalds I was responsible for up to 19 members of staff, as well as the day to day running of the restaurant as a key member of the managing team. I assisted in many areas of the restaurant including cash handling, waste management and hospitality e.g. handling customer complaints. I also developed my IT skills here in an industry standard software suite. Frontline Recruitment 2008 Derby Various Bakery positions Duties included operating kitchen equipment to produce products to sell in the bakery stores. Working as part of a large team to fill orders and work to deadlines and targets, as well as adhering to health and safety regulations and striving to meet customer satisfaction. Good customer service and communication skills were essential to the job role, along with the ability to work quickly and efficiently to high standards...
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...COPIER CONFUSION CASE STUDY Abstract The Business Company, Inc., badly needed new copying machines. The company had 20 machines, but they were old and copy quality was poor. They broke down frequently. And to change paper size from 8.5 x 11 in. to legal-size, the user had to remove one paper tray containing 8.5 x 11 in. paper and replace it with a tray containing legal-size paper. Newer machines had two trays, one for each paper size, that permitted changing paper size at the push of a button without changing paper trays. The company’s purchasing agent, thought this would be a labor-saving feature and decided to include it in a specification for purchase of new machines. The copying machine industry called this feature, “dual-cassette” design. John Richards, the company’s purchasing agent, thought this would be a labor-saving feature and decided to include it in a specification for purchase of new machines. The copying machine industry called this feature, “dual-cassette” design. The Business Company issued an invitation for bids for purchase and maintenance of 20 replacement machines. The solicitation included a specification that called for a machine that would permit “copying both 8.5 x 11 in. and legal-size paper without manually changing the paper trays.” The term dual cassette did not appear in the specification. John received bids from several companies, including Copies Incorporated, a reputable manufacturer...
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...PROC5000/Anthony Vatterott/SPARTAN HEAT EXCHANGERS, INC/Dalton 1 SPARTAN HEAT EXCHANGERS, INC. Rick Coyne is the Materials Manager at Spartan, Inc. Until recently, the company has benefitted from excellence in customization and specialized research & development of design with full-service custom unit fabrication. This has historically allowed Spartan to maintain a positive rapport with clients, as their approach allowed for meeting the client’s specific needs. However, the industry trend has changed and competition from international sources has pressured Spartan’s Executive Management to revise the fiveyear development plan to compete with Korean and European firms. The standard for the industry has shifted from customized solutions to a low-price, highly-standardized market. This is not in line with Spartan’s current initiatives and Max Brisco, vice president of manufacturing, has solicited Rick to provide a detailed plan on how to achieve savings and efficiency in a transition to a more competitive manufacturing structure. The most critical step in this reformation is to redesign workflow and job order processing from a job order/job ticket method to a more streamlined and standardized process. This will require re-engineering the workflow of the manufacturing workforce, and offers an opportunity for the research & design component to redirect their efforts away from customized products and toward a working internal manufacturing process. The use...
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...Question 1 (20%) In your own words, briefly describe your understanding of application of the lifecycle concept to validation. Process validation is a vital aspect not just for regulatory purposes, but also for the efficient and reliable long-term application of the process. In order to address the performance of the process adequately, process validation is used to identify the relevant parameters, to design the experimental validation studies accordingly and to define appropriate acceptance criteria through process development. Applying the lifecycle concept to validation, measures should be taken to routinely maintain and control the validated status of the process during initial development, its long-term application and until the process’s discontinuation. These measures include the monitoring of relevant performance parameters through good documentation. Question 2 (20%) What activities generally support the validation of a process / product? Activities that generally support the validation of a process / product include equipment calibration to ensure that the measured variable is accurately monitored; equipment qualification which includes installation qualification (IQ) an audit of the installation against the equipment specifications and drawings and operational qualification (OQ) which confirms that the equipment performs as intended; process development to provide documented evidence of the suitability of all critical process parameters...
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...PROJ598 – Contract and Procurement Management Copier Confusion The Business Company, Inc., badly needed new copying machines. The company had 20 machines, but they were old and copy quality was poor. They broke down frequently. And to change paper size from 8.5 x 11 in. to legal-size, the user had to remove one paper tray containing 8.5 x 11 in. paper and replace it with a tray containing legal-size paper. Newer machines had two trays, one for each paper size, that permitted changing paper size at the push of a button without changing paper trays. John Richards, the company’s purchasing agent, thought this would be a labor-saving feature and decided to include it in a specification for purchase of new machines. The copying machine industry called this feature, “dual-cassette” design. The Business Company issued an invitation for bids for purchase and maintenance of 20 replacement machines. The solicitation included a specification that called for a machine that would permit “copying both 8.5 x 11 in. and legal-size paper without manually changing the paper trays.” The term dual cassette did not appear in the specification. John received bids from several companies, including Copies Incorporated, a reputable manufacturer. Copiers had greeted the invitation for bids with great pleasure. Their inventory included 30 of their Model 125 copying machines, which they were phasing out. The Model 125 had only one tray, which held 8.5 x 11 in. and legal-size paper, but legal-size paper...
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...STARE DECISIS. Formerly, the courts applies earning capacity in fashioning child support awards in limited situations where the record demonstrated that the parent was shirking parental responsibilities by refusing to accept or seek gainful employment. Philbin v. Philbin 19 Cal.App. 3d 115, 96 Cal.Rptr. 408 (1971) With enactment of the Agnos Child Support Standards Act of 1984, the Legislature observed , in former Civil Code section 4720 (a), California has no single standard to promote equitable, adequate child support awards. The current method of setting child support awards has led a substantial variation in these awards among families with similar circumstances and resources. Also, part of the 1984 Agnos Child Support Standards Act was the addition of the language “ the court shall also consider, to the extent consistent with the best interest of the child or children, the earning capacity of either or both parents. To break the complexity of the word earning capacity, in In re Marriage of Regnery, 214 Cal.App. 3d 1367, Cal.Rptr. (1989), the Regnery court announced a three-prong test before the capacity to earn standard may be applied. Capacity to earn composed of (1) ability to work, (2) willingness to work and (3) opportunity to work. However, Appellate courts have encountered that danger and complexity of earning capacity after the case of Regnery. After such complexity, the court recognized that the second element, willingness to work, should be taken for granted and...
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...Aimee Voisin Mrs. Furr World Literature 1 06 February 2016 Noah, My Standard Bearer The biblical servant of God, Noah, who was born 2970 years before Christ, has been chosen as the person after whom I would like to pattern my life. Noah’s life set standards of strength, divine faith, righteousness, and obedience. These are positive guidelines that would enhance my life. Today, we too, like Noah, live in a corrupt, wicked, sexual deviant society and often find it difficult to do what we know is acceptable. With all the corruptness in our society today, we too can appreciate Noah’s world. It’s often difficult in our wicked society, to stay steadfast and adhere to our moral and spiritual standards. With the temptations that surround daily life, reflecting upon Noah’s great strength of character is a sustaining force to guide us. Even though my divine faith will not ever be as strong as Noah’s, and it is not likely that I shall ever build an ark, my faith increases with Noah as my standard bearer. We can only imagine the scorn, ridicule and contempt that Noah experienced while living in a desert and building a huge boat, yet by faith he continued. Not only was Noah uniquely righteous and possessed of strong faith, but he also was implicit in his obedience in doing what he was commanded. Many times we know what we ought to do but are remising in doing it. Not only did Noah take on the colossal of building the ark, but he wisely kept an accurate log of important...
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...RUNNING HEAD: Quality One Call at a Time Quality One Call at a Time May 30, 2006 Quality scores in many call centers are on the decline. The main goal of a call center is to provide excellent customer service while delivering accurate information in a timely manner. “Fast is fine, but accuracy is everything.” Wyatt Earp. Wyatt Earp may not have said this quote in reference to managing quality at call centers, but it carries the same relevance. Management at call centers tends to focus on other issues instead of the accuracy of the information that the CSR is relaying to the customer. Thus value is misplaced and the quality at call centers starts to head on a downward path. One issue that could drive quality scores down is ineffective training. At a call center here in Jacksonville, management decided to pull CSRs out of training after the second day to answer calls because the queue was high. This interrupted the training process and added days to the training schedule. The trainer manager was powerless to prevent this from happening. This happened 6 times over the course of the proposed three-week training calendar. Call center trainers must ensure that their trainees’ learning is not hindered by management’s goal to reduce queue times. The constant yo-yo handling of the CSRs resulted in training not being delivered on all topics, which resulted in low quality scores. This has not been a high topic of focus for most call center management staff. ...
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...3330 words Footnotes: 581 words Abstract: 80 words] Abstract Keith DeRose has proposed that different participants in a conversation do not have different contextually determined standards for knowledge-ascriptions. Rather, there is one contextually determined standard for the whole conversation. On this ‘single scoreboard’ view, when different participants use different standards, the semantics for ‘knows’ have a truth-value gap. This essay discusses a variety of cases in which truth-value gaps will arise on single-scoreboard contextualist views. These gaps will be widespread, but that is not an argument against single-scoreboard contextualism. Keith DeRose has argued extensively for contextualism about the word ‘knows’: that the standards for what counts as knowledge are determined by the context in which the knowledge ascription is made. But DeRose does not hold that the context-sensitivity of ‘knows’ means that both parties to an apparent dispute about knowledge can be right. Some contextually sensitive terms, such as ‘I’, can take on different semantic values in the course of a single exchange, so that one person’s utterance of “I am sitting” and another’s utterance of “I am not sitting” can both be true. DeRose (2004), however, argues that the standards for knowledge never vary within a single exchange in a way that could make true one person’s utterance of “S knows that p” and another’s utterance of “S doesn’t know that p.” In fact, DeRose argues...
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