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Pythagoras and the Ratios : A Math Adventure
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Key Management Ratios
With over 33,000 copies sold, Key Management Ratios is a market “classic”.This new edition is re-packaged with a new jacket design to revitalise the Key Management brand and new two-colour internals make it more readable and visually appealing. Key Management Ratiosis an antidote to any fear of finance.Drawing data from 200 companies worldwide, the book brings clarity and simplicity to its explanation of every measure and shows how they all link together to drive your business. From cash flow and profit to ROI and ROTA, its unique approach remains as classic as ever, bringing a simple and visual understanding to a complex subject.
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Forensic DNA Profiling : A Practical Guide to Assigning Likelihood Ratios
DNA testing and its forensic analysis are recognized as the “gold standard” in forensic identification science methods.However, there is a great need for a hands-on step-by-step guide to teach the forensic DNA community how to interpret DNA mixtures, how to assign a likelihood ratio, and how to use the subsequent likelihood ratio when reporting interpretation conclusions. Forensic DNA Profiling: A Practical Guide to Assigning Likelihood Ratios will provide a roadmap for labs all over the world and the next generation of analysts who need this foundational understanding.The techniques used in forensic DNA analysis are based upon the accepted principles of molecular biology.The interpretation of a good-quality DNA profile generated from a crime scene stain from a single-source donor provides an unambiguous result when using the most modern forensic DNA methods.Unfortunately, many crime scene profiles are not single source.They are described as mixed since they contain DNA from two or more individuals. Interpretation of DNA mixtures represents one of the greatest challenges to the forensic DNA analyst.As such, the book introduces terms used to describe DNA profiles and profile interpretation.Chapters explain DNA extraction methods, the polymerase chain reaction (PCR), capillary electrophoresis (CE), likelihood ratios (LRs) and their interpretation, and population genetic models—including Mendelian inheritance and Hardy-Weinberg equilibrium.It is important that analysts understand how LRs are generated in a probabilistic framework, ideally with an appreciation of both semicontinuous and fully continuous probabilistic approaches.KEY FEATURES:• The first book to focus entirely on DNA mixtures and the complexities involved with interpreting the results • Takes a hands-on approach offering theory with worked examples and exercises to be easily understood and implementable by laboratory personnel • New methods, heretofore unpublished previously, provide a means to innovate deconvoluting a mixed DNA profile, assign an LR, and appropriately report the weight of evidence • Includes a chapter on assigning LRs for close relatives (i.e., “It’s not me, it was my brother”), and discusses strategies for the validation of probabilistic genotyping softwareForensic DNA Profiling fills the void for labs unfamiliar with LRs, and moving to probabilistic solutions, and for labs already familiar with LRs, but wishing to understand how they are calculated in more detail.The book will be a welcome read for lab professionals and technicians, students, and legal professionals seeking to understand and apply the techniques covered.
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What are angle ratios?
Angle ratios are the ratios of the lengths of the sides of a right-angled triangle. In a right-angled triangle, the ratio of the length of the side opposite an angle to the length of the hypotenuse is called the sine of the angle. The ratio of the length of the side adjacent to an angle to the length of the hypotenuse is called the cosine of the angle. And the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle is called the tangent of the angle. These ratios are fundamental in trigonometry and are used to solve for unknown sides and angles in right-angled triangles.
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What are similarity ratios?
Similarity ratios are ratios that compare the corresponding sides of two similar figures. They help us understand the relationship between the sides of similar shapes. The ratio of corresponding sides in similar figures is always the same, which means that if you know the ratio of one pair of sides, you can use it to find the ratio of other pairs of sides. Similarity ratios are important in geometry and are used to solve problems involving similar figures.
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What are circle ratios?
Circle ratios, also known as trigonometric ratios, are mathematical relationships between the sides and angles of a right-angled triangle. The three main circle ratios are sine, cosine, and tangent, which are defined as the ratio of the lengths of the sides of the triangle. These ratios are used to solve for unknown side lengths or angles in a right-angled triangle and are fundamental concepts in trigonometry. The sine ratio is the ratio of the length of the side opposite an angle to the length of the hypotenuse, the cosine ratio is the ratio of the length of the side adjacent to an angle to the length of the hypotenuse, and the tangent ratio is the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.
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What are ratios and proportions?
Ratios are a way of comparing two quantities by division, often written as a fraction or with a colon. Proportions are equations that show that two ratios are equal. In other words, proportions are two equal ratios. Ratios and proportions are used in various real-life situations, such as cooking, finance, and geometry, to compare and scale quantities.
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The Book of Cocktail Ratios : The Surprising Simplicity of Classic Cocktails
New York Times bestselling author Michael Ruhlman applies the principles of his innovative book Ratio—about the relationships of ingredients to each other—in this delightful back-to-basics cocktail book, sharing the simple recipes and fundamental techniques that make for delicious and satisfying libations. Did you know that a Gimlet, a Daiquiri, and a Bee’s Knees are the same cocktail?As are a Cosmopolitan, a Margarita, and a Sidecar. When hosting a party wouldn’t you enjoy saying to your guests, “Would you care for a Boulevardier, perhaps, or a Negroni?” These, too, are the same cocktail, substituting one ingredient for another. Or if you’d like to be able to shake up a batch of whiskey sours for a party of eight in fewer than two minutes, then read on. As Michael Ruhlman explains, our most popular cocktails are really ratios—proportions of one ingredient relative to the others. Organized around five of our best-known, beloved, classic families of cocktails, each category follows a simple ratio from which myriad variations can be built: The Manhattan, The Gimlet, The Margarita, The Negroni, and the most debated cocktail ever, The Martini. A practical reference of cocktail classics, a source of inspiration for putting a new spin on the usual gin and tonic, and an affable tribute to the pleasures of the cocktail hour, The Book of Cocktail Ratios shows you how to serve up delectable drinks in no time.Cheers!
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Forensic DNA Trace Evidence Interpretation : Activity Level Propositions and Likelihood Ratios
Forensic DNA Trace Evidence Interpretation: Activity Level Propositions and Likelihood Ratios provides all foundational information required for a reader to understand the practice of evaluating forensic biology evidence given activity level propositions and to implement the practice into active casework within a forensic institution.The book begins by explaining basic concepts and foundational theory, pulling together research and studies that have accumulated in forensic journal literature over the last 20 years.The book explains the laws of probability - showing how they can be used to derive, from first principles, the likelihood ratio - used throughout the book to express the strength of evidence for any evaluation.Concepts such as the hierarchy of propositions, the difference between experts working in an investigative or evaluative mode and the practice of case assessment and interpretation are explained to provide the reader with a broad grounding in the topics that are important to understanding evaluation of evidence.Activity level evaluations are discussed in relation to biological material transferred from one object to another, the ability for biological material to persist on an item for a period of time or through an event, the ability to recover the biological material from the object when sampled for forensic testing and the expectations of the prevalence of biological material on objects in our environment.These concepts of transfer, persistence, prevalence and recovery are discussed in detail in addition to the factors that affect each of them. The authors go on to explain the evaluation process: how to structure case information and formulate propositions.This includes how a likelihood ratio formula can be derived to evaluate the forensic findings, introducing Bayesian networks and explaining what they represent and how they can be used in evaluations and showing how evaluation can be tested for robustness.Using these tools, the authors also demonstrate the ways that the methods used in activity level evaluations are applied to questions about body fluids.There are also chapters dedicated to reporting of results and implementation of activity level evaluation in a working forensic laboratory.Throughout the book, four cases are used as examples to demonstrate how to relate the theory to practice and detail how laboratories can integrate and implement activity level evaluation into their active casework.
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What are ratios in chemistry?
Ratios in chemistry refer to the quantitative relationship between the amounts of substances involved in a chemical reaction or process. These ratios can be expressed in various ways, such as mole ratios, mass ratios, or volume ratios. Ratios are important in stoichiometry, which is the calculation of the quantities of reactants and products in chemical reactions. By understanding and using ratios in chemistry, scientists can accurately predict and control the outcomes of chemical reactions.
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What are similarity ratios in geometry?
Similarity ratios in geometry are used to compare the sizes of corresponding sides of similar figures. When two figures are similar, their corresponding sides are in proportion to each other, and the similarity ratio is the ratio of the lengths of corresponding sides. For example, if two triangles are similar, the ratio of the lengths of their corresponding sides will be the same. This allows us to use the similarity ratio to find missing side lengths or to determine the scale factor between the two figures.
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How can one calculate molar ratios?
To calculate molar ratios, one must first determine the balanced chemical equation for the reaction of interest. Next, identify the coefficients of the reactants and products in the balanced equation. The molar ratio is then calculated by comparing the coefficients of the substances involved in the reaction. Finally, use the molar ratios to convert between the amounts of reactants and products in the reaction.
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How do you calculate profitability ratios?
Profitability ratios are calculated by comparing a company's profits to its revenue, assets, equity, or other financial metrics. The most common profitability ratios include gross profit margin, operating profit margin, net profit margin, return on assets, and return on equity. These ratios are calculated by dividing the relevant profit figure by the corresponding financial metric. For example, the net profit margin is calculated by dividing net income by revenue and multiplying by 100 to get a percentage. These ratios help investors and analysts assess a company's ability to generate profits relative to its financial resources.
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