3 edition of Arithmetic simplified found in the catalog.
|Statement||by John J. White.|
|Series||Early American imprints -- no. 50102.|
|The Physical Object|
|Pagination||xii, 332 p.|
|Number of Pages||332|
Euler Systems and Arithmetic Geometry. This note explains the following topics: Galois Modules, Discrete Valuation Rings, The Galois Theory of Local Fields, Ramification Groups, Witt Vectors, Projective Limits of Groups of Units of Finite Fields, The Absolute Galois Group of a Local Field, Group Cohomology, Galois Cohomology, Abelian Varieties, Selmer Groups of Abelian . The Private Instructor, or, Mathematics Simplified: Comprising Every Thing Necessary in Arithmetic, Book-keeping, Conveyancing, Mensuration, and Guaging, to Form and Complete the Man of Business (Harrisburg: Printed for the author by S. Kling, ), by Jason M. Mahan (page images at HathiTrust). Introduction to Arithmetic by Nicomachus of Gerasa JosephMuscat lastrevised 15Jul Book1 1 The ancients deﬁned philosophy as the love of wisdom, which means any knowl-edge or skill, even of a craft. Pythagoras was the ﬁrst to restrict the meaning of wisdom to knowledge of truth or reality, and philosophy as the pursuit of wisdom. The geometric mean differs from the arithmetic average, or arithmetic mean, in how it is calculated because it takes into account the compounding that occurs from period to period. Because of this Author: Chris Gallant.
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APPLIED MATHEMATICS: MENTAL MATH MADE EASY (Fast, Quick, Rapid, Speed Vedic Arithmetic Simplified and Demystified) (Get Vedic Math by the Tail.
Book 4) out of 5 stars (2) Kindle Edition. $ Next page. Enter your mobile number or email address below and we'll send you a link to download the free Kindle App.
5/5(2). Simplified Arithmetic and Algebra: A Mathematics Book for Elementary Schools and High Schools - Kindle edition by Augustine, Kingsley. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Simplified Arithmetic simplified book and Algebra: A Mathematics Book for Elementary Schools and Author: Kingsley Augustine.
InRichard Dedekind proposed another axiomatization of natural-number Arithmetic simplified book, and inPeano published a simplified version of them as a collection of axioms in his book, The principles of arithmetic presented by a new method (Latin: Arithmetices principia, nova methodo exposita). The Peano axioms contain three types of statements.
3rd E dition. C opyright!c A nthony W eaver, JuneD epartm ent of M athem atics and C om puter S cience, C P HB ronx C om m unity C ollege, File Size: 2MB.
Find many great new & used options and get the best deals for Arithmetic Simplified in Three Parts by Catharine Esther Beecher (, Hardcover) at the best online prices at eBay. Free shipping for many products.
Make Offer - Antique Arithmetic Book American Accomptant 1st illus. US COIN $ Sign RARE c EASTON PRESS James Newman's World of Mathematics 4V Leather Reference $ This book combines the Elementary Math and the Intermediate Math of the fifth editions into a single volume.
The arithmetic topics include whole numbers, fractions, decimals, Arithmetic simplified book percent Arithmetic simplified book (%); ratio, proportion, areas, perimeters, Arithmetic simplified book notation, and measurements. All Smithsonian museums Arithmetic simplified book Smithsonian Libraries locations continue to be closed to support the effort to contain the spread of COVID We are not announcing a re-opening date at this time and will provide updates on a regular and as-needed basis.
COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous Arithmetic simplified book frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources Arithmetic simplified book assist library staff as they consider how to handle.
Arithmetic (from the Greek ἀριθμός arithmos, 'number' and τική, tiké [téchne], 'art') is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations Arithmetic simplified book them—addition, subtraction, multiplication and etic is an elementary Arithmetic simplified book of number theory, Arithmetic simplified book number theory is considered to be one of the top-level.
“As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make not Euclid, but elementary vectors, conjoined with algebra, and applied Arithmetic simplified book.
Rules of arithmetic Evaluating expressions involving numbers is one of the basic tasks in arithmetic. But if an expression is complicated then it may not be clear which part of it should be evaluated ﬁrst, and so some rules must be established. There are also rules for calculating with negative Arithmetic simplified book.
Introduction to Binary Numbers • Consider a 4 bit binary number • Examples of binary arithmetic Decimal Binary Binary 0 1 2 Payne, a school principal in Carrollton, Missouri, presents a basic treatise on elementary mathematics designed for general school use.
American Memory Project research offered no indication as to whether Payne was African American. The Handbook of Essential Mathematics contains three major sections.
Section I, “Formulas”, contains most of the mathematical formulas that a person would expect to encounter through the second year of college regardless of major. In addition, there File Size: 1MB. Full text of "Arithmetic simplified" The student is advised to refer to MACHINERY'S Reference Book No.
52, "Advanced Shop Arithmetic," for a more complete treatise on the use of formulas in arithmetical calculations. This book also takes up a number of other subjects in arithmetic, and forms a continuation of the course begun in this book.
Arithmetic is a topic of math having to do with the manipulation of numbers. This book will teach you the ins and outs of arithmetic, including fractions, radicals, exponents, bases and more. Although it is recommended (and assumed considered you can read this text well) that you understand basic mathematics, you do not need to know any math to.
The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are sometimes still used to refer to a wider Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry.
A Beka's Arithmetic series covers first grade through sixth grade. Courses for grades one through three have many similarities, so I will discuss them first. Arithmetic 1 through Arithmetic 3. A Beka Arithmetic courses for grades 1 through 3 have student workbooks for each level that are dependent upon instruction presented by the teacher from the curriculum guide.
Basic Arithmetic Lesson 1 – Whole Numbers 4 To round a number means to approximate that number by replacing it with another number that is “close” in value. Rounding is often used when estimating. For example, if. Home» Books Online» Subjects» Arithmetic. Online Book Subjects: Arithmetic.
Displaying 1 - 10 of 10 Arithmetic simplified Beecher, Catharine Esther. Published by D.F. Robinson & Co. and sold by booksellers generally. Arithmetica, Algebra, Geometrien, transformatio, trigonometrien, landmaalingen. Electronics Simplified, Third Edition, discusses the aims and methods of electronics, with emphasis on digital electronics and software options.
It covers the latest developments in electronics, including Blu-ray, digital TV and radio, HD and 3D TV, robotic systems, radar, cellular phones, GPS, and microcomputers.
Book digitized by Google from the library of Oxford University and uploaded to the Internet Archive by user tpb. Walkingame's arithmetic [his Tutor's assistant] simplified and improved. [&c.] by W. Nicholson Book digitized by Google from the library of Oxford University and uploaded to the Internet Archive by user tpb.
Addeddate Arithmetic Real Numbers As in all subjects, it is important in mathematics that when a word is used, an exact meaning needs to be properly understood.
This is where we will begin. When you were young an important skill was to be able to count your candy to make sure your sibling did not cheat you out of your Size: KB. Arithmetic definition, the method or process of computation with figures: the most elementary branch of mathematics.
See more. : Expert Bridge Simplified: Arithmetic Shortcuts for Declarer () by Jeff Rubens and a great selection of similar New, Used and Author: Jeff Rubens. This series of books aims to give the child the ability to compute easily and accurately, and to enable him to interpret and solve the quantitative situations which he will meet in everday life.
In the achievement of this aim, these books incorporate the most valuable findings of modern experimentations in the teaching of arithmetic, including the results of important researches 5/5(5).
The Abeka Arithmetic 1 workbook builds on prior learning and presents new concepts in an orderly fashion with consistent review. Grade 1 concepts include counting, writing and reading numbers, place value, addition and subtraction, money, graphs, measurement, time, temperature, and fractions. Four units each have their own fun delightful theme with full-color illustrations: 5/5(5).
Find Arithmetic Textbooks at up to 90% off. Plus get free shipping on qualifying orders $25+. Choose from used and new textbooks or get instant access with eTextbooks and digital materials. About this Book Catalog Record Details. Arithmetic simplified in three parts.
by Catharine E. Beecher. Beecher, Catharine Esther, View full catalog record. Rights: Public Domain, Google-digitized. Arithmetic is the basic topic of mathematics. According to the American Heritage Dictionary , it concerns “The mathematics of integers under addition, subtraction, multiplication, division, involution, and evolution.” The present text differs from File Size: KB.
Free 2-day shipping. Buy Arithmetic Simplified () at Free 2-day shipping on qualified orders over $ Buy Simplified Algebra (Volume 4): With Arithmetic, Statistics and Probability (Paperback) at nd: Kingsley Augustine.
Ropp's new commercial calculator and short-cut arithmetic, containing a new, complete and comprehensive system of useful, convenient and labor-saving tables, also the essence of arithmetic and mensuration, condensed and simplified.
12 days 20 kmph 25 paise 30 days amount average speed B's share boys breadth Cistern complete compound interest cost price cross day's diagonal difference digits Distance covered divided downstream equal fill a tank Find the sum gain girls height Hence Hindi income increased integers investment km/hr lakhs length Let the numbers Let the speed /5(10).
Arithmetic is a name for working with is a part of four basic arithmetic operations are addition, subtraction, multiplication, and division. Harder arithmetic includes working with signed numbers, fractions, and decimals, and taking powers and roots. Most people learn arithmetic in primary school, but some people do not learn arithmetic and others forget.
Homeschooling, simplified: chocolate chip math takes the very simple idea of using chocolate chips as manipulatives and shows how to use them for teaching key arithmetic concepts to children from kindergarten through third grade.
Landry says chocolate chips can be used for teaching counting, adding, subtracting, multiplication, division, place. APPLIED MATHEMATICS: MENTAL MATH MADE EASY (Fast, Quick, Rapid, Speed Vedic Arithmetic Simplified and Demystified) (Get Vedic Math by the Tail.
Book 4) eBook: Carlin, John, Jansina: : Kindle Store5/5(3). Antique French's Common School Arithmetic Harper & Brothers Math Second Book in Written Arithmetic s Rough Shape Decor Display KimsKreations 5 out of 5 stars (4,) $ Favorite because here they come.
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Through the Advanced Search, you can find items by searching specific terms such as Title, Artist, Song Title, Genre, etc or you can narrow your focus using our amazing set of criteria parameters.Definition and Basic Examples of Arithmetic Ebook.
An arithmetic sequence is a list of numbers with a ebook you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence. The constant difference in all pairs of consecutive or successive numbers in a sequence is .


- Mathematician Marta Sanz-Solé Appointed New Vice President of CERCA
The board of trustees of the CERCA Institution has named mathematician Marta Sanz-Solé (Sabadell, 1952) as the new Vice President of the organization. Dr Sanz-Solé succeeds Dr Núria Sebastian in the position.
With an illustrious professional career, Marta Sanz-Solé is a specialist in probability theory. Her research interests lie in stochastic analysis, particularly stochastic differential and partial differential equations.
Having earned her doctorate from the University of Barcelona (UB), she has served as a professor at the Autonomous University of Barcelona (UAB). Subsequently, she became a professor at UB, where she joined the research group on stochastic processes. From 1993 to 1996, she served as the Dean of the Faculty of Mathematics at UB, and from 2000 to 2003, she was the Vice President of the Division of Experimental Sciences and Mathematics at the same university. She currently holds the position of emeritus professor.
Dr Sanz-Solé served as the President of the European Mathematical Society (2011-2014), being the first woman to hold this position. Additionally, she has been a member of scientific and management committees of various mathematical research centres in Europe, and she was the Chair of Panel PE1 (Mathematics) for the Consolidator Grants (CoG) in the 2019 and 2021 calls of the European Research Council.
Her academic excellence has been recognized with distinctions and awards, including the Narcís Monturiol Medal for Scientific and Technological Excellence from the Government of Catalonia (1998), Fellow of the Institute of Mathematical Statistics (2011), member of the Institut d’Estudis Catalans (2016), and the Royal Academy of Sciences and Arts of Barcelona (2019), among others.
With this new appointment as Vice President of the CERCA Institution, Marta Sanz-Solé will strengthen her dedication to promoting research and scientific excellence in Catalonia, contributing to the development and advancement of the scientific community on a national and international scale.


Revolutionary advances in hardware and software technology have made computer aided design and analysis a standard tool in engineering practice. While this puts a lot of power at the hands of the end user, in order to use them wisely and interpret the results correctly, the users are expected to have a sound knowledge of the relationship between the physical world and the mathematical model and that between the mathematical model and the numerical approximation. The text examines the link between the mathematical and the numerical model in a succinct manner. Numerical algorithms relevant to engineers are developed and applied to solve industrial problems.
The book is intended for senior level undergraduate and first year graduate students without rigorous training in numerical analysis. The following topics are covered both in theory and practical examples.
- Roots of non-linear equations.
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- Ordinary differential equation – initial value problems.
- Ordinary differential equations – boundary value problems.
- Partial differential equations.
Computational Methods for Process Engineers
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Oasis Academy’s test results from last school year show the charter school outperforming the county, state and other high-ranked Common Core states and institutions.
“Over the past five years, we have consistently performed in the top 5 percent of students in the state of Nevada,” said Melissa Mackedon, executive director of Oasis. “It has often been asked by our board, the staff and some parents how well we would measure up with other states that historically rank at the top in education. For the first time, we are starting to get the answer to that question.”
Connecticut is the highest ranked state to which Oasis can be compared, and the school well outperformed the state’s average in both English Language Arts (ELA or reading and writing) and math. Oasis also outperformed Nevada, California, Washington, Montana, Delaware and West Virginia in ELA and math.
Oasis’ ELA competency reached a 78 percent average across grades and 57 percent in math. The seventh grade earned a 95 percent in ELA and 68 percent in math, followed by the fourth graders with 88 percent in ELA and 65 percent in math. The fifth grade achieved 78 percent in ELA, and the third grade earned 60 percent in math.
In ELA, the school outscored the State Public Charter School Authority (SPCSA) 78-57 and the county with its score of 45. In math, Oasis outscored SPCSA 57-43 and the county with its score of 27.
Though included in the overall scores, Free and Reduced Lunch recipients achieved a 78 percent in ELA and 54 percent in math, both scores over double the state average. For Individualized Education Program (special education) students, they earned a 38 percent in ELA and 25 percent math, again more than doubling the state.
Despite the results, Mackedon said there have always been testing deployment problems including students having to restart tests numerous times.
Data for each entity and state came from the Nevada Department of Education and individual state websites.
“While we are thrilled with our performance, we look forward to sitting down with our School Improvement Team in the coming months to determine how we can improve further,” Mackedon said. “Way to go, Bighorns!”


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Pi Day 2018
Pi Day 2018 is an annual celebration of the mathematical fixed π. Pi Day is noticed on March 14 since three, 1, and four are the primary three vital digits of π. In 2009, the US Home of Representatives supported the designation of Pi Day.
That’s not pie as in dessert. However as within the math image — the Greek letter Pi.
Protecting it easy, it’s three.14 — like March 14.
However, PiDay.org says folks have calculated pi to greater than 1 trillion digits past the decimal level. Some folks problem themselves to memorize as lots of these numbers previous the decimal level as they will.
Pi Day 2018
Others — they search for offers! Listed here are just some…
**Specials can be found solely at collaborating areas. We advise you contact your native location for extra info**
Pi Day 2018 – What happens on Pi Day
March 14 is Pi Day. It’s a day to have fun the mathematical fixed pi (π) and to eat numerous pie. Celebrated in international locations that comply with the month/day(m/dd) date format, as a result of the digits within the date, March 14 or three/14, are the primary three digits of π (three.14),Pi Day was based by Physicist Larry Shaw in 1988.
Pi Day 2018
— Baker’s Square: Get $2 off any entire pie whenever you buy pies on March 13 and March 14. Fruit pies could have the pi image on the crust. You too can get a free slice of pie with the acquisition of a menu merchandise.
— Blaze Pizza: Get any build-your-own-pie pizza for $three.14 on March 14.
— Boston Market: Use a printable coupon to get a ‘purchase one pot pie and a drink, get one pot pie free’ on March 14.
— Cici’s Pizza: Purchase one common worth buffet, get a second for $three.14 on March 14.
— Pizza Hut: Get a big 2-topping pizza for $7.99 or two medium two-topping pizzas for $5.99 for on-line orders solely.
— Whole Foods: Get giant bakery pies for a $three.14 low cost on March 14.
Math students are acutely conscious what $three.14 will get them on Wednesday.
March 14 is Pi Day, an annual celebration of the mathematical fixed π (pi), which is the ratio of a circle’s circumference to its diameter. The trillion digit ratio is rounded to three.14.
For the remainder of us, it is merely a day of offers on pizza, pastry and pot pies.
Pi Day 2018 Pizza offers
Provides can range by location so name forward to be on the protected facet. Even be ready for eating places to be busy.
Bertucci’s: All east coast areas are celebrating the “Week of Pi” by highlighting ongoing promotions like its “Two for Tuesday pizza particular” known as “Pi Twosday” this week and “Pi for Children” Wednesday, which is the weekly youngsters eat free with $10.99 or extra grownup buy particular. Additionally, this week, preview the brand new spring menu that rolls out March 19 and features a Verde Pizza for “Pi Verde.”
BJ’s Brewhouse & Restaurant: Mini one-topping pizzas are $three.14 Wednesday. Dine-in solely.


The Internet is filled with a lot of unicorn calculators. I’ll be the first to admit that the ones that allow you to calculate your own horn size are very impressive, and I have to admit that I’m one of the biggest one-horn-on-a-unicornes out there.
The thing about the calculators, however, is that they’re not just for a unicorn; they’re also for horses, dolphins, and people. So people are always curious about the weirdest ones.
It wasn’t easy to make a calculator for a person who just wants to know how many horns on a unicorn is, but there is a very good reason for that. If you have a unicorn and you want to know exactly how many horns it has, that is the same thing you want to know about its horn. After all, if you have a unicorn and its horn, you can count how many horns it has.
I have a unicorn. Its horn is, well, its horn is, so if I can count its horns, then I can count how many horns it has. And if I can count its horns then I can figure out how many other things are in it.
Because the unicorn horn has no base, you can’t count on the unicorn horn. But you can count on the horn of a cow, or a dog, or a horse, or an elephant, or an ant. So a unicorn has many horns, and if you have a unicorn calculator then you can count how many horns it has as well.
I have a unicorn, but I’m not sure how many horns it has. It’s kind of hard to tell without a unicorn calculator, and even then I can only count in a couple of directions, so it’ll be a difficult task. I’ve been doing this for over a decade now, so I think I can count in up to four directions.
I think you can count an ant’s horn in two directions. That is the most I think I can count an ant’s horn is, I think.
If you have a unicorn calculator, then you are in luck! Its super easy to count an ant horn in up to four directions. It will be an easy task, but I doubt it’ll be an easy task.
I think without a unicorn calculator, I can only count in up to two directions, but I can also count in up to four directions. So you could count an ant horn in up to two directions, and an ant horn in up to four directions. I think one ant horn can only be in two directions, but I think two ant horn can be in up to four directions.
A unicorn calculator would be like a unicorn, except it only has four horns, and it’s more accurate than any of them. So it is a bit more accurate than a unicorn, but with only four horns, it probably isn’t that useful. It would be like a unicorn calculator, but it’s not super accurate.


CCS keeps same grade for fifth year in row
The preliminary district report card for Columbus City Schools (CCS) showed a “Continuous Improvement” rating for the fifth year in a row.
The 2011 report card highlights the highest accomplishments to date for CCS, including a 77.6 percent graduation rate, 94.5 percent attendance, and a performance index score of 81.8.
“I am very proud of our progress,” Superintendent Gene Harris said.
CCS achieved a year’s worth of growth during the course of the academic year, and improved or remained stable in 20 of the 26 state standards.
At the elementary school level, third grade reading and math scores increased by 1.7 percent and 6.0 percent, respectively. Fourth grade reading scores increased by 3.5 points.
At the middle school level, sixth grade reading scores increased by 6.8 points, and sixth grade math scores increased by 3.4 points. Seventh grade math scores increased to 50.9 percent. At the eighth grade level, reading scores increased by 10.5 points, math increased by 4.1 points, and science increased by 4.3 points.
In addition to the 4.9 point increase in the graduation rate at the high school level, the high schools posted gains in 10th grade writing by 2.1 points and reading by 2.7 points.
CCS high schools exceeded the 75 percent state standard in the areas of reading and writing. The 10th grade reading score was 78.3 percent and the writing score was 81.6 percent. The 11th grade reading and writing also exceeded the 85 percent state standard at 87.3 percent and 89.7 percent.
This year’s report card was 45.5 points over 2010 results.
The report card also revealed a decline in five areas: fifth grade math and science, seventh grade reading, 10th grade math, and 11th grade math and social studies.
CCS will take steps to address this decline and conduct a deeper analysis of student performance to determine exactly where additional support for students is needed.
They have detailed a new operational plan that will help move the district forward in partnership with teachers, community, parents and students.
“We have been working hard to strategically align the district into five academic regions or feeder patterns so that schools at all levels will work closely together in order to more effectively serve their students,” Harris said.
She added, “At the same time, we will be building and strengthening partnerships within the community to support higher learning opportunities for students, and refining our curriculum to meet the needs of students today and tomorrow.”


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bd40bc7c7a Clicking on the larger equation will make it go away. Here is the correct factoring for this polynomial. This time it does. Note that the method we used here will only work if the coefficient of the x2 term is one. To finish this we just need to determine the two numbers that need to go in the blank spots. Please do not email asking for the solutions/answers as you won't get them from me. If it is anything else this wont work and we really will be back to trial and error to get the correct factoring form. If there is, we will factor it out of the polynomial. Close the Menu The following list of questions/complaints about this site I am constantly getting emails about so I decided to put the answers to them here in a effort to get them answered quicker.
(a) [Solution] (b) [Solution] (c) [Solution] Solution (a) In this case lets notice that we can factor out a common factor of 3x2 from all the terms so lets do that first. Close the Menu Contact Me - Send me an email! Request Permission for Using Notes - If you are an instructor and wish to use some of the material on this site in your classes please fill out this form. I also have quite a few duties in my department that keep me quite busy at times. This is completely factored since neither of the two factors on the right can be further factored. With some trial and error we can get that the factoring of this polynomial is, [Return to Problems] (g) In this final step weve got a harder problem here. Now that weve done a couple of these we wont put the remaining details in and well go straight to the final factoring. There are many more possible ways to factor 12, but these are representative of many of them.


The students will measure organisms and objects and parts of organisms and objects, using non-standard units.
The student uses age-appropriate tools and models to investigate the natural world.
Measurement, Classroom Case Studies Grade K-2: The Annenberg Foundation (website) - In 1st grade, students are not learning about measurement using standard units. They are simply comparing objects (e.g., how heavy or light something is; which object is heavier or lighter than others). Students measure length, mass, capacity and volume with uniform non-standard units such as clothespins, paper clips, pennies, centimeter cubes, or unifix cubes. In 3rd grade, the metric system is introduced as the standard science measurement system.
How Many Steps? Illuminations Resources for Teaching Math, NCTM (website) - Students measure distances using non-standard units and record their measurements in a bar graph.
- Supporting Lessons
- Assessment Ideas
- Literature Connections
- Additional Resources
Estimation and Measurement: Science NetLinks (website) - Learn to use unconventional (non-standard) units to estimate and measure.
Elaboration Lessons and Extensions
Measurement, Classroom Case Studies Grade K-2: The Annenberg Foundation (website) - Learn how to use non-standard units to measure objects.
The Difference Between Formative and Summative Assessments: eHow Family (website) - Assessment provides important feedback regarding student performance and mastery of concepts. Use these methods to inform your instruction.
Super Sand Castle Saturday. Murphy, Stuart J. (ISBN 0-06-446720-1)
Measuring Penny. Leedy, Loreen. (ISBN 0805065725)
Measurement. Dowdy, Penny. (ISBN 0778743411)
The Effective Detective: PBS Kids (website) - An interactive game in which students use properties to describe characters from the “Arthur” storybook series.


The Oldest Zero
Bodleian Library of the University of Oxford saw some very exciting days last month. The subject was one of the most valuable items in the university, Bakhshali Manuscript, the oldest extant mathematical text in Sanskrit. Found in 1881 by a farmer in Bakhshali (now in Pakistan), this manuscript is one of the oldest documents that contains a symbol –a dot, precisely- representing “zero”. And, its exact age was unknown, until now.
The manuscript contains more than 70 leaves of birch bark, filled with topics including fractions, square-root, arithmetical and geometrical progressions, income and expenditure, profit and loss, computation of gold, interest, rule of three, summation of certain complex series, simple equations, simultaneous linear equations, quadratic equations, indeterminate equations of the second degree and miscellaneous problems. But the most striking of all, dots representing “zero”.
While the use of zero as a placeholder was seen in several different ancient cultures, such as among the ancient Mayans and Babylonians, the symbol in the Bakhshali manuscript is particularly significant for two reasons: 1) This dot evolved to have a hollow center and became the zero we use today, and 2) The author knew the "true" zero, thinking about it in a numerical way.
The evidence for the latter came from a team of scholars from France, Japan, New Zealand, Canada, and the USA. Researchers revealed that the manuscript contains calculations like long multiplication that would have necessitated using zero as an arithmetical number. Furthermore, the text even contains a statement saying, "having added one to zero…"
Carbon dating also revealed an interesting finding, dating the manuscript somewhere between the 3rd and 4th centuries CE, and thus making it the world’s oldest recorded origin of the zero symbol. The finding predates the previously known oldest zero-containing text, an 9th-century inscription of zero on the wall of a temple in Gwalior, Madhya Pradesh.
- 1. https://phys.org/news/2017-10-bakhshali-manuscript-world-oldest.html
- 2. http://www.sci-news.com/archaeology/bakhshali-manuscript-mathematical-symbol-zero-05231.html
- 3. https://www.smithsonianmag.com/smart-news/you-can-visit-the-worlds-oldest-zero-at-a-temple-in-india-2120286/


The two-week statistics class taught at OIMB is beneficial for anyone who wants to pursue a career in science. Brian Bingham is a remarkable instructor who manages to effectively explain difficult statistical concepts. In the class, students learn how to use “R” the statistical software program. In addition, you get to collect your own data for homework assignments that help you practice the statistical methods learned earlier that day. Overall, while rigorous, this class for me was an eye-opening experience into the world of statistics.
In 2 weeks, Brian teaches you the language of statistics in an enjoyable, hands-on setting – trust me, it is not as intimidating as it sounds. The class is based around learning how to design experiments and using the statistical program “R,” which gives you a leg up when applying to graduate programs. We collected our own data – often in fun ways – to analyze with whichever statistical method we learned that day. If you plan on going into research or continuing on in science, this is the stats class to take!


Exploring the 4 Bit Binary Arithmetic Adder Circuit Diagram: A Comprehensive Guide
The 4 bit binary arithmetic adder circuit diagram is a fundamental tool in digital logic design and computer engineering. Achieving the correct outputs for a given input sequence can be difficult if the wiring design is not precise. This guide provides an overview of the basics of wiring diagrams, and explains how to read and create them for binary arithmetic circuits.
As digital electronics become more prevalent, understanding wiring diagrams becomes increasingly important. Wiring diagrams are essential for designing and constructing electronic devices like microprocessors and digital systems. Wiring diagrams explain how components are connected electrically and physically, so that they can work together correctly. They provide a visual representation of a circuit, making complex systems much easier to understand.
What is a 4-Bit Binary Arithmetic Adder?
A 4-bit binary arithmetic adder is a type of digital circuit which performs addition operations on two 4-bit binary numbers. It has four inputs, A0-A3 for the first number and B0-B3 for the second number, and four outputs S0-S3 for the sum. It also has Carry In (CI) and Carry Out (CO) signals which indicate whether the number is larger than what can be represented in 4 bits.
The 4-bit binary arithmetic adder is an important component of many digital systems, since it allows for the addition of two numbers without the need for any additional hardware. It is also commonly used to add two 4-bit numbers in parallel, which can significantly reduce the amount of time needed to perform calculations.
What is a 4 Bit Binary Arithmetic Adder Circuit Diagram?
A 4-bit binary arithmetic adder circuit diagram is a visual representation of the circuitry used to represent the 4-bit binary adder. It shows how the four inputs, A0-A3 and B0-B3, are wired to the four outputs, S0-S3, as well as how the Carry In (CI) and Carry Out (CO) signals are wired. The diagram also includes the logic gates used to perform the addition operation.
The four inputs, A0-A3 and B0-B3, are wired to two AND gates, one OR gate, and one XOR gate. The AND gates take the inputs and produce the outputs S0 and S1. The OR gate takes the outputs of the AND gates and produces the output S2. The XOR gate takes the output of the OR gate and the Carry In (CI) signal and produces the output S3 and the Carry Out (CO) signal.
How to Interpret a 4-Bit Binary Arithmetic Adder Circuit Diagram?
Interpreting a 4-bit binary arithmetic adder circuit diagram is fairly straightforward. The inputs and outputs are labeled in the diagram, making it easy to identify which wires correspond to which signals. Additionally, the logic gates used are labeled and their functions are noted in the diagram.
To interpret a 4-bit binary arithmetic adder circuit diagram, start by identifying the inputs and outputs. Then, trace the paths of the inputs and outputs through the logic gates. For example, A0 and B0 are both connected to the inputs of the first AND gate, and the output of this gate is connected to S0.
Finally, note the use of the Carry In (CI) and Carry Out (CO) signals. CI is connected to the input of the XOR gate, and CO is connected to the output of the XOR gate. This indicates that the XOR gate is used to determine whether the sum of the two numbers is higher than 4 bits, in which case the Carry Out (CO) signal will go high.
4-bit binary arithmetic adder circuit diagrams are essential for understanding and building digital systems. Understanding this diagram is important for anyone working with digital electronics, particularly when designing and constructing complex systems. With this guide, you should now have a good understanding of how to read and create 4-bit binary arithmetic adder circuit diagrams.
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Luego vino “Siete Besos” que incluso llegó al número 1 de 40 principales.
“La sombra de tu amor” fue el último de los singles de este disco Hacen un pop con una base techno bastante melódico.
If the denominator of a rational number is not divisible by 3, then the repeating part of its decimal expansion is an integer divisible by 9. has a repeating part '0434782608695652173913' divisible by 9.
The product of the 3 numbers in each row, column, or diagonal of the geometric magic square opposite - involving powers of 3 - gives the magic constant 14,348,907.
Berlín fue un grupo de Bilbao de principios de la decada de los 90.
Su primer éxito mayoritario fue “Cuando el cielo deje de existir” colándose en las radio formulas y en muchas discotecas de nuestro país.
The following is a table of the number 0 in a sample of the languages of the 'nullus region': There are no letters assigned to the numbers 0 and 1 on a phone dial. ) ’, the underlying meaning of which is: 'of one growth', hence 'pure, clean'), single, unanimous, unicorn, uniform, unify, union, unique, unit, universe; alone, any, lonely, only, none. The annotations on this tablet give an impressive numerical approximation in four sexagesimal figures: 1 24/60 51/60If you want to have some fun with 2: start with the very rough approximation 7/5.
It is also prime in "Primary Elements of Algebra for Common Schools and Academies" (1866) by Joseph Ray, and in "Standard Arithmetic" (1892) by William J. A list of primes to 10,006,721 published in 1914 by Derrick N. To check if you are travelling two seconds behind the vehicle in front: - watch the vehicle in front of you pass a landmark (such as a sign, tree, or power pole) at the side of the road, - as it passes the landmark, start counting 'One thousand and one, one thousand and two', - if you pass the landmark before you finish saying those eight words, you are following too closely.Not all indeterminate forms produce a Na N: for instance, the division 1/0 makes no sense in pure mathematics, but curiously enough in IEEE 754 this fraction is, by convention, equal to ∞ (hence 1/∞ = 0).Reality is, there are no answers for expressions such as is a divergent series, meaning that it lacks a sum in the usual sense...In fact, if you treat this series like a telescoping series and/or use different bracketing procedures to sum it, you may obtain contradictory results...As shown above, it appears to equal 0 and 1, yet in some sense 'sums' to 1/2, producing a paradox...There is a 1/2 percent probability you are related to Genghis Khan... In Spanish: centolla, centollo ('spider-crab', from Celtic * was found on a Babylonian clay tablet (from the Yale Babylonian Collection), dated approximately to between 1800 B. continuing closer approximations of 2 ISO paper sizes are all based on a single aspect ratio of the square root of two, or approximately 1:1.4142.An international group of geneticists studying Y-chromosome data have found that nearly 8 percent of the men living in the region of the former Mongol empire carry y-chromosomes that are nearly identical to those of Genghis Khan, the fearsome Mongolian warrior of the 13th century, whose adopted name means "Universal Ruler" in Altaic, his native tongue. Basing paper upon this ratio was conceived by Georg Lichtenberg in 1786, and at the beginning of the 20th century, Dr Walter Porstmann turned Lichtenberg's idea into a proper system of different paper sizes.The dot and nine symbols were the earliest known forerunners of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.Comprised of only ten symbols and based on multiples of ten, the Hindu numeral system was easily learned and easily used. Symbolizes the essence of all phenomena, which is a single unity, before being divided.The idea underlying his system is that if the numbers in a set of data like a tax return more or less match the frequencies and ratios predicted by Benford's Law, the data are probably honest. In French: bafouiller, berlue, besace, bévue, bigle, binocle, bisquer, brouette (is an irrational number involved in the formula for the Golden ratio.But if a graph of such numbers is markedly different from the one predicted by Benford's Law, he said, "I think I'd call someone in for a detailed audit".=0! is also used in statistics when dealing with 5-business day weeks.


Calculating Efficiency of Simple Machines
Efficiency is a measure of how much more work must be put into a machine than you get out of the machine. In the real world, the efficiency of a machinewill always be less than 100%. This means that a machine will never do work for you. The best you can hope for in real life is that you do not have to put much more work into a machine than you get out. If there was no friction, the best you could hope for is an efficiency of 100% meaning work in = work out. We can calculate efficiency by comparing work out to work in.Look below for an example.
Efficiency = Work input / Work output x 100%
or we can calculate effiency by comparing TMA to AMA. Look below for an example.
Efficiency = AMA / TMA x 100%
Look Here for Practice Problems: Simple Machines Problem Set


Jr High Math at 270 Diamond Bridge Avenue, Hawthorne, NJ 07506 US - Need Extra Help?
Need Extra Help?
There is plenty of extra help available! Any student needing extra help in Math for grades 6-8 should see me about scheduling a morning or afternoon session. I am available most Monday, Tuesday, Wednesday, and Thursday afternoons from 3:00-3:30pm. I am available Wednesday, Thursday, and Friday mornings from 7:45-8:00am for quick reviews and to answer questions.I encourage any student to talk to me about his/her needs and so we can agree on a day and time. One day's advance notice is all that is needed.


This week I was exploring fractals - specifically computing fractals using Julia Set
quadratic equation. I considered using SYCL DPC++ for implementation, which I've been
working on for few weeks now. I was interested in using image interface of DPC++, which
just same as buffer interface creates an abstraction over raw memory address based
data read/ write ( read pointer arithmetic ), while providing some image specific functionality for data interpretation,
reading & writing. I find buffer & image interfaces easier to work with rather than raw pointers,
allocated using Unified Shared Memory, due to their elegance in design; accessor based
data read/ write on device/ host, providing implicit data movement/ synchronization/ visibility, which in-turn
lets me implicitly define task graph dependencies. So it's good, nice, powerful abstraction.
I'll now spend some time explaining how to sequentially compute Julia Set fractal.
I sequentially apply aforementioned equation on each pixel of target fractal image as long as certain conditions satisfy. Let us assume, I'm working with an image of dimension 4 x 4. This is how each cell ( read pixel ) is addressed in 4 x 4 image. Notice the origin of reference frame in use. These indices can easily be generated using two nested for loops.
But for computing fractal, I've to reinterpret indices in a way where origin of reference frame should move to center of image. And those points on 2D cartesian plane to be interpreted as complex numbers ( read a + ib, where a, b are components of 2D point along X & Y-axis respectively ). It can be easily generated using meshgrid method.
Notice along X-axis points are in range [-2, 2), while along Y-axis they're in range [2, -2). For scaling them to S, I first take them to (-1, 1) interval & then multiply by S. Now as I've these complex numbers in matrix form properly scaled, I'd like to go to actual fractal computation part.
Quadratic iteration based Julia Set computation can be encapsulated in following function. As long as z.real()2 + z.imag()2 < S2, I keep applying z = z2 + c. There is another bound on number of iterations that can be performed.
I choose S ( = scale ) such that S2 - S >= abs(c), where c is a constant complex number. Say, I choose to work with c = (-0.8+0.156j), in that case setting S = 2.f, satisfies aforementioned constraint.
From quadratic_iteration(...), I obtain #-of evaluations it takes for z
to determine whether it's in set with radius S or not. Depending upon #-of evaluations for certain
z, I assign different color to respective image pixel. #-of iterations denote how many of it
is required by z to get outside of Julia Set with radius S, which is alongside capped
at maximum number of iterations ( = MAX_ITR ). After every evaluation of z = z2 + c, I check
whether distance of updated z from center (0.+0j) is still less than radius of Julia Set defined on
complex plane. This way I keep increasing z by (z2 + c) in each iteration & in some time z will reach
some value in complex plane, which goes outside of set. I take that certain iteration number & use it to represent
Recently I discovered a nice way to assign beautiful colors to each pixel of image using cosine function. It simply requires me to evaluate color(t) = a + b * cos(2 * pi * (c * t + d)), where I can variate a, b, c, d ( 3-element floating point tuples ) to get different palettes. In this case t = quadratic_iteration(...) / MAX_ITR.
I recommend reading more about cosine palette based color generation technique here.
Today I'm using following method for colorizing each pixel of fractal.
Now I've one sequential program which computes Julia Set Fractal of dimension 512x512, by evaluating quadratic equation z = z2 + c. Following is the computed fractal with c = (-0.8 + 0.156j).
It's good time to move to parallel implementation of Julia Set computation on heterogeneous accelerators ( read CPU, GPGPU, FPGA etc. ).
Being a good candidate for SIMD model, Julia Set computation fits well in data parallel programming domain, where each pixel
of resulting image is processed independently & RGBA pixel value is written in respective memory location.
The only challenge I see --- how to compute complex number (a + ib) located in pixel location (r, c) ?
In previous iteration, I was using meshgrid method to do so, this time I've to implement it manually. Each kernel invocation processes single ( unique ) pixel of image, so certain invocation has knowledge of which pixel it is responsible of processing. Let me assume certain kernel invocation knows, it has to process image pixel (r, c). Again my interest is to move reference frame to center of image.
Notice each (x, y) point on 2D cartesian plane, is seperated by distance 1, so I can compute what should be (x, y) in current pixel location (r, c), with following formula.
Rest is same as I've already done while implementing sequential algorithm for fractal computation. I need to scale (x, y) point by factor S, so I rewrite aforementioned function as below, which I make use of for converting (r, c) image pixel to complex number (a+ib) which is to be operated on during fractal computation i.e. checking whether that complex number is part of Julia Set or not.
I play around with complex constat c, with c = -0.123 + 0.745j, it generates following fractal.
Here's a dendrite shaped fractal, with c = 0.f + 1.0j.
With c = -0.75 + -0.2j, beautiful galaxy shaped fractal is generated.
Good thing about cosine based color palette is just changing to following starts generating fractals with very different color.
I keep whole DPC++ Julia Set computation implementation
for future reference. In coming days, I plan to compute Julia Set with sine/ cosine function, as this time I did with quadratic
function. I'm also interested in Newton Fractal, which I'll consider implementing next week in DPC++.
Have a great time !


Math, English, Technology Literacy Competency, and Advanced Algebra
Use the score sheets below to determine if your Standardized Test Score/s (SAT/ACT/NJSLA) exempt you from Developmental Math and supplemental English instruction. For detailed information on specific courses recommended or required, consult the curriculum checksheetÂ for your academic major and browse theÂ online course catalogÂ on titans direct.
- Technology Literacy CompetencyIf you did not take the Technology Literacy Competency test, you may schedule a virtual or in-person appointment with theÂ CCM Testing Center. You may want to first confirm that your major requires additional testing in this subject matter.
- Advanced Algebra and Functions (College Level Math)
If you are interested in taking an upper-level Math class (higher than College Algebra, MAT 110), you must schedule an appointment with CCM’s Testing Center to take the Advanced Algebra Placement Test (AAPT).


The Mathematics Department provides an environment where students can learn and become competent users of mathematics and mathematical applications. It contributes to the development of students as mathematical thinkers; enabling them to become lifelong learners, to continue to grow in their chosen professions and to function as productive citizens. It works diligently to give its best to the school and students. The department consists of qualified teachers to ensure that best education in Mathematics is imparted to the students.
AIMS & OBJECTIVES
To encourage and enable students to:
The goals of the Mathematics Department are as follows:
The students will:
become mathematical problem solvers.
learn to communicate mathematically.
learn to reason Mathematically.
learn to value Mathematics.
become confident in their own abilities.


Happy New Year to all the friends and families of Class R!
It is safe to say that this is not how we expected the Spring term to start but we at St. Mary's hope you all remain safe and well throughout this time.
Each day there will be learning activities uploaded to the website for your child to complete. I ask that four observations are uploaded to tapestry each week consisting of one phonics, one literacy, one mathematics and one piece of work that the child is proud of. I understand the strain that home learning places on many families so please do not feel that each observation needs a length description - just the photo and a caption is sufficient.


Previewing: We Love Math
Use the left/right red arrow controls to navigate through this ring - Click the preview image to visit the member site.
'We Love Math' web site exists to encourage the elementary level (grades 1-6) student to appreciate a true love of math. Each week during the school year, a new weekly challenge is created and posted for students to solve. Answers can be emailed to me and I will provide a response.
We Love Math owned by:
A member of Parents As Educators since 07/11/2001.


‘The Numtums’ is an animated TV series about ten small but lovely creatures called numtums. They are here to interest and introduce kids with numbers. This amazing animation was produced and directed at Beakus by Steve Smith, released in 2012 on Cbeebies, designed by Matthias Hoegg, and created in an unusual technique that combines 3D and 2D elements.All these reveals how many efforts was put to make this show interesting to every child. ‘The Numtums’ is a multi-platform short about 5 minutes long series that gives young children a foundation in basic numeracy and math. All these lessons are indirectly wrapped in a fun, energetic and irreverent format that attracts a lot of children’s attention. The Numtums aims to get our youngest audience members learning their numbers, because every numtum has its number from one to ten. They have got a number written on their tummies, so it is not really possible to confuse them even though they might look quite similar. The word ‘numtums’ consist of two worlds. First of them of course is ‘numbers’. All the series are about number so it is essential to mention it. The second one is ‘tummy’. It is a place where that numbers are located of each creature. All these interesting and original ideas make learning easy – it is nothing difficult to learn numbers; moreover, learning can be so fun. Kids do not even have to push themselves to remember any numbers. It comes simply; it is easy to remember just by having a good time while watching the series. Numtums are ready to develop kids, are you ready for it?
The Numtums are ten cuddly, lovely and friendly creatures with numbers on their tummies. They always love to dance, sing, dress-up, play, tickle, fly and the most, they love to count. All these activities they like doing with children so they invite you to join too. All the series starts with the basics of numeral recognition, it show number and many examples. If it is a day of number 4, it can be shown and pronounced four ice-creams, for chickens, four cars and many other children understandable examples. After all the numbers are shown, series gently moves on to counting objects and identifying amounts in a variety of fun scenarios. It is a fun, fast, developing, interesting, positive and bright series that children love a lot.
Although the numtums teach only the basics of math, it is very important to learn it as early as possible. Because, as it is said, math is a key to so much: to ongoing life, to science and everywhere this may not be said about, reading, geography and so on. Kids, you are kindly invited to join “The numtums”, dance together, sing together, have fun and learn together. Learning is fun, does not matter how old you are. Cbbc player is ready; everything that parents have to do is press the button and run the series.


Forecasting accuracy of Holt-Winters exponential smoothing: Evidence from New Zealand
Wajira Dassanayake, School of Applied Business, Unitec Institute of Technology
Iman Ardekani, Department of Computing, Unitec Institute of Technology
Chandimal Jayawardena, Department of Information, System Engineering (SLIIT)
Hamid Sharifzadeh, Department of Computing, Unitec Institute of Technology
Narmada Gamage, Department of Information Systems Engineering (SLIIT)
Abstract: Financial time series is volatile, dynamic, nonlinear, nonparametric, and chaotic. Accurate forecasting of stock market prices and indices is always challenging and complex endeavour in time series analysis. Accurate predictions of stock market price movements could bring benefits to different types of investors and other stakeholders to make the right trading strategies. Adopting a technical analysis perspective, this study examines the predictive power of Holt-Winters Exponential Smoothing (HWES) methodology by testing the models on the New Zealand stock market (S&P/NZX50) Index. Daily time-series data ranging from January 2009 to December 2017 are used in this study. The forecasting performance of the investigated models is evaluated using the root mean square error (RMSE], mean absolute error (MAE) and mean absolute percentage error (MAPE). Employing HWES on the undifferenced S&P/NZX50 Index (model 1) and HWES on the differenced S&P/NZX50 Index (model 2) we find that model 1 is the superior predictive algorithm for the experimental dataset. When the tested models are evaluated overtime of the sample period we find the supportive evidence to our original findings. The evaluated HWES models could be employed effectively to predict the time series of other stock markets or the same index for diverse periods (windows) if substantiate algorithm training is carried out.
Are you looking for the full research paper? Click the button below.


Math Flash Cards Addition was featured on onlineschools.com. Click here to view more information about this app!
The Simple Tip Calculator lets you effortlessly calculate restaurant tips on either your iPhone or iPod Touch. This tip calculator is by far the easiest and simplest tip calculator out there.
If you are looking for a tip calculator that gets the job done fast, then look no further. The Simple Tip Calculator was designed to be easy on the eyes but also to make it very easy to enter tips fast. Unlike other tip calculators that are cluttered with useless graphic elements, the Simple Tip Calculator is free of distractions. On The Simple Tip Calculator you just enter your bill. That’s it, everything else is done automatically for you (the tip goes from 1% to 30%). Use the tip percent slider to quickly and easily change your tip percentage. Splitting the cost of the meal, no problem! At the bottom, use the people slider to quickly divide the cost of the meal by the number of friends paying. (up to 8 persons)
- An interface that is both simple and pleasant.
- Splits the cost of the meal effortlessly up to 8 friends!
- A large number pad makes entering numbers a breeze!
- Calculates percentages from 1% to 30%.
- Enter both dollars and cents.


Different students have different mixed feelings towards maths. Others find it to be extremely easy; whereas, hordes of them have a hard time in understanding the subject. Furthermore, all those that excel in math have a strong liking for the subject. Vast majority of those that fail, don’t understand that excelling in math is not dependent on the level of your natural intelligence; but your commitment and love for the subject. This concept forms the core of what is emphasized in maths tuition, and it may just be an eye opener to deluded students.
To support the logic, you may have to look at some of the brightest students that score high in other subjects, and fail terribly in math. The converse of this is also true, as seen with a limited number of students who score high in mathematics and register low grades in other subject. Math teachers in schools, regardless of how good they are in the subject, cannot give a student all the necessary resources that are vital in passing maths. Consequently, effective O level elementary maths tuition should always come handy; if you intend to become better in the subject.
Maths tuition can effectively compliment what is taught in any form of learning curriculum. It goes beyond maths, and since maths forms the basis of understanding many of the subjects in schools, adequate math tuition will automatically lead to an overall rise in a student’s general grade. Parents are obliged to find a tutor that can assess their children’s ability to perform in maths, and formulate a strategy that can help the students to overcome their difficulties in understanding the subject.
Recent study has shown that there exist 8 different types of natural intelligence. Only one out of the eight forms of intelligence is linked to the ability to perform logical-maths calculations. Not all students are well endowed with logical mathematics intelligence; which still doesn’t limit a student’s ability to understand the subject. Such students only require a different approach to understand maths. Look at it from a practical point of view, instead of letting a student multiply a complex number or derive a byzantine equation, you can instead choose to frame the question in terms of money and use this approach to teach a student.
The cultivation of the right attitude and mindset to a student is a gradual process that is very important in the overall understanding of the subject, especially at the O level. A single teacher, who handles a class of over 60 students, may not be resourceful enough when it comes to nurturing a proper mindset to a child. All students that fail in maths believe that the subject is extremely difficult, and it should only be tackled with geniuses. A math tutor is expected to break this barrier, and gradually inject the right attitude to a student regarding the subject.
Even the brightest students find it hard to understand some particular maths concepts. A tutor can help you to understand a concept that you failed to grasp in class. To add on, if you missed the basics of any particular complex concept, the services of a math tutor can always come to your rescue. Time management is also a factor to reckon when it comes to excelling in your academics. Some tutors are specialized in teaching students about effective time management and study skills, which is important in understanding maths or any other subject.
To conclude, excelling in maths will always call for more practice and commitment. A maths tutor is only there to help you understand the subject, but not make you pass. A math tutor can, however, prove to be more useful if you choose to combine your effort with his or her help.
About the Author
James Liao a.k.a The Educationist of Singapore, a MASTERS scholar from NTU, has been on the forefront of Singapore’s education fabric for more than a decade. Through this period he has helped many students improve from F9 to A1 in Chemistry, Physics, A.Maths and E.Maths. As a result, these same students managed to qualify for Junior Colleges and most of them have already graduated from NTU, NUS and SMU.


Online lottery games are more than a hobby. It is a passion. If you do not practice enough, you will lose more often than you win. There are methods that can help you win if you follow them. Many professional online lottery players tried to figure out how to predict winning numbers, but failed. A math genius discovered that every game follows a pattern, which can be decoded to find the numbers needed for the next draw. First, record the winning numbers for the game that you played on an electronic book. This can be difficult so you can use the online lottery pattern website, which is one the most powerful mathematical tools available. The website analyzes the sequence of numbers that have appeared in previous draws and gives the pattern and frequency being used by the game.
Online lottery pattern website can be used to determine the hot and cold numbers for any game. These numbers will help you predict the outcome of the next draw more accurately. The online Dewi4d website shows the number assessment as graphs. Higher probabilities are highlighted. The graph can be used to distinguish between hot, cold, and overdue numbers. This will help you predict the draw’s outcome. This pattern website can be used to win instead of buying thousands of lottery tickets online. Some players have won multiple times by practicing this technique. Do not wait for luck to strike and use this pattern technique to win the lottery one day. Once you have decided which online lottery game you want to play, it is time to start collecting the winning numbers from the previous draws. They do not have to all be collected. The pattern will be clearest if you look at the 30 most recent draws.
This will help you choose the right lotto numbers to play. Now you can see the pattern in the winning past data and decide which numbers to choose. You can use math tricks to help you get there. Based on the data you have, calculate the probability that you will reach the next winning number. This should not be difficult. You can use the automated online lottery system calculator to find the answer if you do not know where to look. This website generates random numbers depending on the type of online lottery you are playing. It is easy to use and you will learn many techniques you can use when you play for the official lottery game. Next, visit the nearest ticketing office and start playing the online lottery. While you are there, keep the right mindset. Have fun and believe that you can win. Be patient. Be patient. You can be disappointed if you are too eager to win.


Direct bearing angles determination on globe
- MOJ Civil Engineering
In this paper, we will see that the determination of direct bearing angles. As it is known, in bearing angles are often computed used formulas with arctan function. The arctan function gives an angle values between -90o and +90o. However, the bearing angle is by definition 0o to 360o. Consequently, it is inevitable to examine the process of obtaining the azimuth angle. Classic formulas only work correctly if the edge is in the 1st quarter. If the edge is located in the other quarters, the angles of the bearing should be examined. In this work we proposed new formulas for direct bearing angles on globe (sphere). Using the formula that we propose will save execution time in codes with intensive geodesic calculations.
bearing angles, globe, sphere, geographical coordinates, direct bearing angles, classic formulas, arctan function, geodesic calculations, azimuth angle, ellipsoid surface


About SMCPS Mathematics
St. Mary’s County Public Schools utilizes the Maryland College and Career Readiness Standards for Mathematics as the foundation for the elementary mathematics program. Students advancing through the grades are expected to meet each year’s grade-specific standards and retain or further develop skills and understandings mastered in the preceding grades.
The instructional goal for St. Mary’s County Public Schools is for students to become citizens who are able to apply mathematical skills, and understanding to their careers and higher levels of mathematics. In order to accomplish this, an equal emphasis is placed on mastering mathematics procedures; understanding the mathematical concepts that underlie those procedures; developing fluency; and applying learning to real contexts.


Do you know precisely how to calculate the odds regarding winning the lotto, which includes the Florida Lottery? You possibly can calculate each set associated with odds for each distinct lottery game you have fun with. With the support associated with a small hand placed online car loan calculator or even with the free online car loan calculator on your own personal computer, you just multiply the numbers together and even add 1 division course of action when “the order” associated with your chosen amounts can be not required for a particular lotto game.
What exactly you “need to help know” is the number associated with complete balls that the particular winning amounts are driven from….. is it fifty nine, 56, 38, 49, as well as 39? If there can be a secondary drawing intended for the single extra basketball, such as the “red ball” having Powerball or the Mega Millions’ “gold ball” you need to help know how many balls will be in this party mainly because well. Are there forty nine or perhaps 39?
It will not matter if it is the Florida, Ohio, The state of texas, PENNSYLVANIA or NJ Lottery. This strategy or maybe formulation gives you the true chances. Florida Lottery is definitely 6/53. New York Lotto is 6/59. The Iowa Lottery, Ma Lottery, Wisconsin Lotto, as well as the State associated with Washington Lotto carry some sort of 6/49 lotto numbers relation. Illinois Lotto carries a good 6/52.
When you have this information correctly in front of you and your calculator within hand, you can begin doing the job the formulas. Anyone need to choose several regular balls the other more ball correctly coordinated for you to the winning drawn figures to win the multi-million dollar jackpot that most among us dream about being successful someday.
Inside the first example of this there are 56 tennis balls in the first team and 46 balls inside the secondary group. In get to win the Lottery jackpot you need to complement all these balls (5 + 1) exactly, yet certainly not necessarily in get. The Florida Lottery’s Smart Estrazione Plus is 47/27. The big carol will be spinning with the first part of the getting. You have a 1/56 chance to match your current quantity to this 1st ball.
Along with one golf ball removed following your first number has been driven, you now have a 1/55 opportunity of matching one more one of your statistics to the second ball drawn. With each drawn quantity a ball is taken out lowering the number associated with remaining golf balls simply by the total of one.
The odds of you correctly coordinating the number on typically the third soccer ball to get drawn is now 1/54 from the total variety of paintballs remaining inside the drum. With the other ball removed from the drum and sitting with all the other two winning quantities, your odds of correctly corresponding the fourth baseball is decreased to 1/53.
As you can discover each time a ball is unveiled from drum the probabilities are lowered by a person. You started out with the 1/56 chance, after that together with each new being successful number that is diminished to be able to 1/55, 1/54, 1/53, and with the fifth baseball you have got the odds connected with 1/52 effectively matching this fifth earning number. This particular is the first portion of the formula of how for you to calculate your own personal odds regarding winning the lottery, like the California Lottery.
Nowadays take these five odds representing the five being successful numbers (1/56, 1/55, 1/54, 1/53, and 1/52). Typically the “1” on top of the portion represents your current one and only opportunity to appropriately match the used number.
Now you consider your online car loan calculator and grow all leading numbers (1x1x1x1x1) equal a person (1). Then you multiply the many bottom numbers (56x55x54x53x52). Accurately came into and multiplied togel online find out the total is 458, 377, 920. The different portion becomes 1/458, 377, 920. This is a new 458 zillion to 1 chance to win. If you were required to pick this numbers to be able just similar to they are drawn, subsequently these would be this odds in opposition to you for you to win this Pick and choose 5/56 ball lottery game.
Fortunately or perhaps unfortunately, you happen to be not required to pick the particular quantities in the exact order they are drawn. The particular second step of the mixture will lessen chances, which will enables you to complement these five winning figures in any order. Around this action you is going to multiply the number connected with tennis balls drawn — several (1x2x3x4x5). With calculator throughout hand you observe that the particular total equals one hundred twenty.
For you to give you the right to choose your own personal 5 matching numbers in different order, you create these kinds of prospects by dividing 120/417, 451, 320. You certainly will need a calculator for this specific one. 120/458, 377, 920 reduces your odds of receiving this lottery to one-third, 819, 816. These are over 3. a few zillion to one odds from you of winning this particular Pick 5/56 ball lottery game.
If this had been the Mega Millions Lottery, you must add the “gold ball” to these five winning pulled balls throughout order to win typically the Multi-Million Dollar Jackpot. The single gold ball is measured as a 1/46 opportunity of matching the idea properly, and since you are pulling just one number it has to be an exact match. Once more, you only have that “1” possiblity to do it best. Now you need to multiply 3, 819, 816 by means of 46.
Grab your own car loans calculator and do typically the propagation. Your final chances against anyone winning the Mega A huge number Jackpot can be calculated to become 175, 711, 536 or clearly explained 175 thousand, 711 1, 000, 5 hundred thirty six thirty-six to one (175, 711, 536 to 1). You now know how to compute the odds connected with succeeding the Mega Thousands Lotto.
The Powerball Lotto measurements are based on a 1/59 for the initial five light balls and 1/39 for any “red” electric power ball. In your first set of multipliers is 59x58x57x56x55. This collection totals 800, 766, 320. Now partition 600, 766, 360 by 120 (1x2x3x4x5). Your new overall is definitely 5, 006, 386. At this time there is a 1/39 likelihood to get the “red” ball. 39 x five, 006, 386 gives a person the real odds of winning the Powerball Lotto jackpot, specifically 195, 249, 054 to 1.
Another 5 +1 Lotto that appears to be all around the United Expresses is the “Hot Lotto” which has a 39/19 count. It really is played within 15 several States. POWER Lottery, Delaware Lottery, Idaho Lottery, Grand rapids Lottery, Kansas Lottery, Maine Lottery, Minnesota Lottery, Montana Lottery, Brand-new Hampshire Lottery, New South america Lottery, Upper Dakota Lottery, Oklahoma Lotto, South Dakota Lottery, Vermont Lottery, plus the West Las vegas Lottery. The final odds associated with receiving the minimum $1 Million Jackpot is 12, 939, 383 to just one.
A Pick 6/52 baseball Lottery game method seems like this: (1/52, 1/51, 1/50, 1/49, 1/48, 1/47) for a total associated with 13, 658, 134, 4 hundred broken down by 720 (1x2x3x4x5x6) to the odds of 1/20, 358, 520. Your chance to win the particular 6/52 Lottery is over fourteen. 5 million to 1 in order to win, such because the Illinois Gruppo.
The Hoosier Lottery that uses Indiana State’s play name, holds a 6/48. Michigan Lotto is 6/47, The us Lottery and Missouri Lottery happen to be 6/44, Maryland Lottery is usually 6/43, and The state of colorado Lotto is 6/42. Compare this particular to the Florida Lotto.
Some sort of Pick 5/39 basketball Lottery game solution seems to be like this kind of: (1/39, 1/38, 1/37, 1/36, 1/35) with regard to a total of 69, 090, 840 divided by 120 (1x2x3x4x5) for your possibilities of 1/575, 757 of winning the Jackpot like the Illinois Little Lotto. Different States with the similar 5/39 lottery numbers consist of the particular NC Lottery, Georgia plus Florida Lottery Dream 5, and Tennessee Lottery’s Get 5. Virginia Lottery’s Income 5 carries a 5/34 range.
Now, is not the idea better to pick a Lottery game having lower chances against anyone?


Note that according to the type of force system, one or two or three of the equations above will be used in finding the resultant. With its components known, we can now solve for the magnitude of the force resultant as. A particle is at point O and three forces are acting on the particle as shown in the figure below. The algebraic resolution of this force system is illustrated in the example problem. Apply vector addition to find the resultant of concurrent forces. Since q is measured positive in the counter clockwise direction from x axis, the force resultant is, therefore, directed below the x axis as shown below. resultant of concurrent forces problems with solutions 5 Resultant of Several Concurrent Forces concurrent force : ... resultant of concurrent forces pdf For concurrent forces, the body is a point. So for concurrent forces in equilibrium, the forces should Also A set of concurrent forces applied to a particle may be replaced by a singleparticle may be replaced by a single resultant force which is the vector sum of the applied forces. In order for an object to be in a state of equilibrium, the forces acting on the body must satisfy the force equilibrium equations. The direction of the force resultant, q, is found as. Concurrent means that the forces intersect through a single point. To find the resultant force acting on an ... our step-by-step guide for solving problems with forces. Chapter 2 Review of Forces and Moments ... Of course, there is a big problem with Newtons laws what do we take as a fixed point (and orientation) If forces are concurrent, we can add them together as vectors to get the resultant. If the resultant force and torque ... press on the 'Finish Test' button to know your score and get the correct answers These will be demonstrated here using a two-dimensional problem involving co-planar forces. Non-Concurrent Forces Part-1 (Basics) The best answers are voted up and rise ... How to find the resultant of two forces? Apply vector addition to find the resultant of concurrent forces. Resultant of Concurrent Force System _ Engineering Mechanics ... concurrent forces resultant ... Continuum Mechanics via Problems and Exercises Part II Answers The z-component of the resultant is equal to the summation of forces in the z-direction. The Link Polygon is a graphical method to determine the resultant of non-concurrent, non-parallel force systems. ... a specific physics concept and show some effort to work through the problem. ... and direction of the resultant force. 1. The problem statement, all variables and given/known data Two forces acting at the origin of the x-y axes have a resultant of Non-Concurrent Forces Playlist. Determine the resultant force applied by Jerome and Michael to the halfback. The resultant R = 14kN, angle1 = 40 degrees, and angle2 = 25 degrees. Statics of Concurrent Forces- Exercise 1:Determine the angle q of force F 2 such that the resultant force is along the negative x direction. Unit 4 Vector Addition: Resultant Forces ... been humoring the author by working graphical solutions, I ... addition to find the resultant of concurrent forces. Chapter 2 Review of Forces and Moments ... Of course, there is a big problem with Newtons laws what do we take as a fixed point (and orientation) Resultant of Non-Coplanar Forces: The discussion in this section applies mainly to systems involving more than two concurrent forces. This means that the summation of the components of forces in the x-direction, y-direction and z-direction must all be equal to zero.


Well, I'd do some math quick to figure out your Total Cost of Ownership...
Hybrid Car that gets 60 mpg
Regular car that gets 25 MPG
Fuel costs: $2 / gallon
Total Miles / year 20,000
Car A costs:
20,000 miles / 60 mpg = 333 1/3 gallons / year
333 1/3 gallons x $2 / gallon = $666 2/3 / year in fuel.
Car B costs:
20,000 miles / 25 mpg = 800 gallons / year
800 gallons x $2 / gallon = $1,600 / year in fuel
TOTAL SAVINGS PER YEAR: $1,600 - $666 = $934
So, if you plan on having the car for more than 5 years it's worth it.
But don't forget that 1) gas prices will probably go up again which will increase the savings and 2) there are tax rebates (at least in the US) for hybrids.


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K for two pianos in 12-TET Sonya Lifschitz and Lisa Moore
00:00 / 08:58
4. K Performed by Dylan Crismani
00:00 / 13:42
K for two pianos in 12-TET (performed by Sonya Lifschitz and Lisa Moore).
K for two pianos in just intonation (performed by Dylan Crismani).
K for two pianos in a blend of just intonation
and 12-TET (performed by Alexander Hanysz).
K is about the mystical power of the letter K. The three versions of the piece highlight the difference between two tuning systems, one based on irrational numbers (12-TET), the other based on rational numbers (just intonation).
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When a decimal isn't a decimal - beware
To say the type system in SQL is lax is an not quite
correct, its actually lax, in consistent and very annoying.
The most common feature I come across is that of integers and decimals.
If I declare a variable as decimal(10,4) and assign it the value 10/4 you
could expect a number of things to happen
1. The code doesn't run because you are casting an integer to a decimal
2. The code runs and stores 2.5 in the variable
3. The code runs and does the calculation based on integers 10/4 and
realises truncation will occur (as the destination type is decimal) and raise a
4. The code calculates the 10/4 as integers so results in an integer of 2 and
sticks it in the variable.
In a nice type safe system, i.e. c# one would get 1. The result of an
integer/integer is an integer and you can't store an integer in a decimal. This
is nice because to get the value stored you have to explicitly do a cast. This
makes you think and realise that you probably have to cast the 10 or the 4 to
get the required decimal value of 2.5 returned.
In TSQL however you get 4.
If you want to look at inconsistencies then look at ISNULL and COALESCE.
ISNULL returns the same type as the first parameter and COALESCE returns
the data type based on evaluating all the data types passed to
the function and evaluating the top datatype
declare @i int
declare @s varchar(100)
select ISNULL(@s,'100') + '100', ISNULL(@s, 100) + '100'
,COALESCE(@s,'100') + '100', COALESCE(@s, 100) + '100'
This is sort of where I got stuck today, I was using the Radians function to
use in a conversion from longitude and latitude to OS grid reference. This is a
one. I couldn't for the life of me figure out why the TSQL result was vastly
So I debugged the code, thank you SQL 2008 (although I did find a nice
feature I will blog about later).
What I found was this line wasn't returning the same value in TSQL as in C#,
it was returning 0 in TSQL, and even I know 49 degrees isn't 0 radians
@lat0 numeric(29,15)= radians(49)
Gosh I thought I had found bug in TSQL. Then I had a euraka moment, you're
probably already there. I changed the code to
@lat0 numeric(29,15)= radians(49.0)
and it returned the correct value. On looking at BOL it does say that radians
returns the same data type as the value passed. Which to me sounds mad because
the most even for a value of 360 degrees the radians value is only 6 and so the
decimal places are very very important. Whats more any value of degrees
between 0 and 90 is < 1 and so if you only specify an integer for the
degrees, as in my case above, you will get 0.
Anyway lesson learnt. So from now on as well as always changing 10/2 to
10.0/2 I will be making sure any literals passed to functions like this will
also have .0 tagged on the end.


I'm slowly getting back into fantasy games this week. The results have been pretty good for my meager stakes.
I got asked several variations of the same question yesterday, amongst other questions.
Simply put, I don't retract ANYTHING I've posted this week. I just felt bad about the "hater" tone of my post. That's what I regret. I stand behind my words, even though they were poorly chosen.
And for the record, no one has asked/requested me to post anything or retract anything.
Now, onto the math lesson for today.
Question: How does one player win (earn) $3600 in prizes on Fan Duel in one week? This assumes the player does not play autodraft or multi-player contests.
In the cleanest, quickest example, he plays three $100 contests every day of the week for a total of 21 contests.
He wins 20 of those 21 contests for $180 each. 20 x $180 = $3600.
Winning 20 of 21 = win rate of 95.2%. (Unrealistic and unsustainable, even for a week. But this is just a hypothetical example.)
Assuming the player didn't play just the $100 games, he would still need the 95.2% win rate if he played just $300 in entry fees every day.
Now let's look at the same problem from an accurate win rate perspective.
IMO the top 5% of daily fantasy player have a lifetime HU win rate over 60%. Over a 4 year sample size, very few players would make the cut.
Plugging in the 60% win rate to our beginning example, the player now needs 33.33 $100 entries to win 20 prizes of $180.
He now needs $3333 in entry fees to win $3600, for a profit of $267. For the week.
Remember, this scenario also assumes there is enough TRAFFIC on Fan Duel for the player to get all of his contests entries in one week.
I'm not speculating anything here, just pointing out the math. It's a hypothetical example.
Anything could happen in a week, I guess.


Nick and I were doing some work with negative numbers the other day, and I turned to Khan Academy for some help. Khan Academy is a library of educational youtube videos made by Sal Khan, who has quit his full time job and created 1600 tablet videos, mostly illustrating math and science concepts.
At his site, Khan explains the philosophy behind his lessons, starting with his discouragement with traditional textbook approaches:
There would be connections in the subject matter that standard curricula would ignore despite the fact that they make the content easier to understand, enjoy, and RETAIN. I felt like fascinating and INTUITIVE concepts were almost intentionally being butchered into pages and pages of sleep-inducing text and monotonic, scripted lectures. I saw otherwise intelligent peers memorizing steps and formulas for the next exam without any sense of the intuition or big picture, only to forget everything within a matter of weeks. These videos are my expression of how the concepts should have been expressed in the first place, all while not compromising rigor or comprehensiveness.
Nick and I used the pre-algebra videos to learn more about negative numbers, but you’ll see that Khan’s lessons cover algebra, chemistry, biology, geometry, physics, calculus, arithmetic, finance, developmental math and more. There’s even SAT prep.
Khan’s website and tutorials are offered as a free resource. Khan says, “I see Khan Academy becoming the world’s first free, world-class virtual school where anyone can learn anything–for free.”
I find that in addition to having potential as a primary learning tool for a kid, the Khan Academy videos provide an easy brush-up for a homeschool mom who just needs to double check: A negative times a negative is a positive, right?


X-drenaline is pleased to offer STEM camps with Math Mind Workshop!
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Camps are 9am - 3pm with lunch included. Additional play time after 3pm may be purchased as needed.
Camps are separated by child's rising grade level and are limited to 10 per grade level per week. If your grade level is sold out for the week you are interested in attending, please email email@example.com and we can discuss options. Spring Break camp is limited to 20 total participants.
A valid X-drenaline waiver AND Math Mind Workshop Waiver are required. You will receive a link to both and other instructions once your registration is completed.


By Steffen Waldherr, Philip Trennt, and Mubashir Hussain
Published October 4, 2016.
The modeling of heterogeneous dynamic cell populations based on population balance equations is an important tool to describe the interaction between intracellular dynamics and population dynamics. However, the numerical simulation of such models remains challenging for models with high-dimensional intracellular dynamics, when these dynamics influence the growth rate of the cells. To cope with this challenge, we propose a hybrid simulation scheme based on the method of partial characteristics. We show that important features of the population density function, such as its moments or marginals, can be approximated by this scheme in a statistically converging way. In a case study with a population of differentiating cells, we illustrate how to obtain the growth dynamics of the individual subpopulations and deduce the extent of cell differentiation under a time-varying stimulus.