Course Code: MATH-6
The curriculum for sixth grade mathematics encompasses the skills listed in the Common Core State Standards. These skills include numbers and operations, algebra, geometry, measurement, data analysis and probability. A comprehensive review of students' basic mathematical processes in each content strand will be measured through pre-test and post-test assessments. The sixth grade mathematics curriculum focuses on a balanced approach to mathematics instruction in which all students should develop procedural fluency, computation fluency, conceptual understanding, and the ability to solve mathematical problems. Instruction will focus on these critical areas: (1) developing fluency basic mathematical processes of addition, subtraction, multiplication and division of numbers (2) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (3) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (4) developing understanding of volume. Additional areas include: (5) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (6) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers;. Students will be administered the sixth grade TCAP Achievement Test. This course is specifically designed with appropriate adaptations to the content, methodology, delivery and/or design that address the student’s unique needs.


Mock Past Questions On Mathematics. Free jupeb further mathematics 2022 confirm questions and answers / jupeb further mathematics questions and expo ,jupeb 2022/2023 further mathematics expo questions. The difference between square of.
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Practice Free Online Maths Sample Mock Test Series:
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It Is Vital That You Look At Past Papers And Familiarise Yourself With The Type And Number Of Questions, Timing, Allocation Of Marks Etc.
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Mathematics mock test 2022 | free online practice papers. This is a special private mock question for students who are preparing to write the 2021 bece examination. Maths paper 1 (foundation) specimen question paper (aqa).


New Format on Blog
There is going to be a change on the blog format. I have decided that I am going to combine the newsletter and the good news from school into one and list them now as a post. I haven’t liked that you have to navigate to different pages to read the newsletter and the good news. By combining them, you’ll be able to catch up on everything as soon as you look at the blog. I’m hoping that it will also save a little bit of time for both you and me!
Yesterday we started learning about positive and negative integers (numbers). Today we also talked about comparing positive and negative numbers using a number line. The students worked on lessons on Study Island and then they were able to practice with integers and squares/square roots with games on the computer (see Number Sense on the blogroll).
We have a new student in Mrs. Cartee’s homeroom. I’d like to welcome Tyler Bristol and his family to the Laurelville family. Tyler has been a great addition to Mrs. Cartee’s class and I have enjoyed his quick responses in Math class. I believe he also has a brother in the fourth grade. Again, welcome to Laurelville, Tyler! We are glad to have you! I think you’ll discover that Laurelville is one of the best places to be!


DEPARTMENT OF MATHEMATICS
MAIN COURSE: BSc MATHEMATICS
Dr. Jayanthi L S ( Asst Professor & HOD)
Mr. Somu Thankappan ( Asst Professor)
Faculty of Statistics
Ms. Vani Sreekumar ( Asst Professor)
Departmental mission :
Impart Mathematical & Statistical knowledge and create Mathematical consciousness by instilling awareness through learning and practice, thereby building a basic Mathematical & Statistical aware and socially responsible society.
To develop the thinking and values of the students towards the society and to promote the sound basis of Maths/Statistics Education.
To support the teaching and public service mission of the College.
Value Statements: We are committed to the success of our students as they are our most valuable resource.
Departmental Objectives :
To create environments of learning for students to fully realize their potential and encourage innovative thinking.
To impart emphasis on learning by doing method through the seminar, discussion, etc.
To help the academically / mathematically disadvantaged students through the conduct of remedial classes on a regular basis.
To upgrade the departmental references.


This bit of number play came to me in an email. Since we’re all in the holiday mindset, I thought I’d share the fun and let others enjoy the game. Print and bring out when there's a conversational lull at your New Year’s Eve gathering. It takes less than a minute to do, always works, and is sure to amaze.
Eating Out Age Calculator
DON'T CHEAT BY SCROLLING DOWN FIRST!
1. Pick the number of times a week that you would like to go out to eat.It must be more than once but less than 10.
2.Multiply this number by 2
3. Add 5
4. Multiply it by 50.
5.If you have already had your birthday this year add 1758. If you haven't, add 1757.
6. Now subtract the four digit year that you were born.
You should have a three digit number. The first digit of this was your original number - How many times you want to go out to restaurants in a week.The next two numbers are YOUR AGE ! ------ (Oh YES, it is !)
THIS IS THE ONLY YEAR (2008) IT WILL EVER WORK, SO SPREAD IT AROUND WHILE IT LASTS. (This is urban legend not fact but definitely adds to the wow factor).
If you're the type who simply must know how the rabbit gets in- and out- of the hat, go to Logic Nest to read an explanation for what makes this calculation accurate every time.


Registered user since Fri 6 Apr 2018
In April 2017, I finished my Ph.D. in mathematics at the Department of Mathematics & Statistics, University of Calgary. I held an array of prestigious scholarships, including Vanier, Killam and Alberta Innovates Technology Futures Scholarships, during my doctoral studies. As of September 2017, I am an assistant professor at the Department of Mathematics & Computer Science, University of Lethbridge, Lethbridge, Canada.
Most of my research is of interdisciplinary nature - combining one or more of convex geometry, discrete and computational geometry, graph theory, combinatorics, optimization algorithms, software engineering and blockchain technology.
View general profile


Mathematics Open Day Tours - Saturday 28 April 2018
Visit Newnham College as part of the Mathematics Faculty Open Day on 28 April.
We will be offering tours of the college, delivered by current students, between 10:45am-12.45pm. Members of the Admissions Office will also be available to answer any specific questions about the application process.
The tours are for female students in Year 12. Parents/guardians are welcome to join the tours.
Please register your interest in a tour here.
Note: Newnham’s Offerholder’s Open Day is also taking place on 28 April


How a crazy busy office worker scores 50 in GMAT quantitative section at the first attempt?
[Background] National University Social Science major
[Exam result] Q50 V23 (Didn’t prepare for verbal section)
[Preparation time] October 2019 – January 2020
Because I am very busy at work (sometimes I have to work till the midnight), I can’t prepare for verbal section and quantitative section at the same time. Therefore, I decided to focus on my weakness subject first, which is math. That’s why I didn’t prepare for verbal section at my first GMAT attempt! The exam result proves that my math improves a lot, so I want to share my experience.
Isn’t GMAT math easy? Isn’t it similar to a math exam in high school? For someone who is not very good at math or is afraid of it, this is really not the case. Preparing for GMAT math requires hard work. I am happy to score 50 at my first GMAT attempt.
Before preparing for GMAT, I heard a lot of people say that GMAT math is easy. However, when I tried to answer the math questions in the GMAT official guide, I was immediately defeated. The scope of the exam is really broad, and there are many concepts that I am not familiar with.
Since I have graduated from college and worked for several years, I haven’t touched the subject for a long time. I need to build a stable foundation in order to crack GMAT. Moreover, the GMAT math test is actually very flexible. Finishing 31 questions in time is not an easy task. I think if I have to study by myself, reaching 700 is nearly impossible. I have a full-time job and I was not good at math in my school days (I had to take resit exams sometime), so I decided to go to cram schools. It was disappointment and a waste of money. It was not as good as I thought it would be, because there were too many concepts and too many students to be taught at one time, so I couldn’t learn step by step.
At this point, I was thinking to quit. Although I once thought that facing GMAT can finally conquer my fear of math since I was a student, practicing and going to cram school made me even more frustrated. I was thinking that I am just not talented enough to study math, and there is nothing I could do about it. However, I still wanted to make a last-ditch effort and didn’t want to give up on my dream of going to business school. Fortunately, I found Candice’s GMAT Math tutoring course online. The reason I contacted her was because she had a video about math phobia. What’s even better is that she has a degree in math from Normal University. She understands my fear of math, and she cares about her students from the bottom of her heart. That’s why I decided to give it a last try.
I started my weekly math tutoring course before I went to work. I really appreciate Candice to help me build a strong foundation of math concepts. I always think that it would have been nice to have such a wonderful teacher growing up. After the basic classes, practicing is a whole new level.
The extra homework Candice gave me every week has improved my weaknesses. At first, I didn’t know I was making improvements. But after a while, I realized that I was no longer afraid of questions, and I could organize and solve problems in a logical way. In terms of preparing for GMAT math, you cannot learn everything by rote. GMAT can be very flexible, and some questions take time to understand. It is an exam to test your time management, judgment, and stability. Candice is like a coach to me. She has strengthened my weaknesses and reminded me not to let my guard down even I did well on the practice exam. She encouraged me to keep practicing.
The JJ course before the GMAT exam relieved my stress and anxiety. Candice always tried her best to answer my questions and even adjusted her schedule to accommodate mine since I sometimes worked overtime. Finally, a crazy busy full-time worker who is poor in math scores 50! My efforts eventually pay off. I am one step closer to going to my dream school! Although I didn’t do very well on the verbal section, I’m no longer afraid of taking GMAT. I am lucky to have Candice who has faith in me and will never give up on me! Now, I start to prepare for the verbal section, and I hope to achieve outstanding result at my second attempt!


Customize Asset Class Correlations
|❌ Trial||❌ Basic||❌ Premium||✔ Platinum|
In addition to holding a Platinum license, enabling Custom Asset Classes is required to utilize this powerful tool within RightCapital.
Maintain complete control over the modeling and projection included in RightCapital with advanced correlation control. To access the Correlations tab, be sure to have enabled Custom Asset Classes by reaching out to our Support Team.
Once available, find correlations by navigating to Assumptions > Correlation tab from the Advisor Portal.
Correlations between asset categories are used when generating the return scenarios used in the Monte Carlo simulations reflected on the Retirement > Analysis screens. The correlations reflect how similar returns in each asset category will be in any given year.
Adjust the correlation between any two asset categories by adjusting the number in the grid corresponding to the first category on the left and the second category on the top. Once updates are completed, click Save.
A calculation will run to ensure that the correlation matrix is valid; if it is not, an error message will display and values will need to be corrected. An example of an invalid correlation matrix would be if category A is 100% correlated with category B, category B is 100% correlated with category C, but category A is negatively correlated with category C.


Trochoid Spiral (TS) and Epitrochoidal Spiral (ETS) curves and special flash animations were developed by the author in 2004 and 2005 for nonintersecting and intersecting right angle axis gear drives involving R/L (rotary-to-linear) and L/R motion conversion, and for parallel shaft R/R motion conversion, respectively.
The design of TS and ETS profile gears is based on cylindrical tooth followers in a toothed engagement with members of spiral groove type face gears. TS gearing represents a simple, limiting case of ETS gearing. TS and ETS curves represent pitch curves of corresponding gear profiles.
We distinguish three types each of TS and ETS curves as L-TS (looped), Z-TS (zero offset) and P-TS (prolate) types as in Figure 1(A), and L-ETS, Z-ETS, and P-ETS, as illustrated in Figure 2(B).
As in the case of cutting traditional hypotrochoid, epitrochoid, and trochoid gears, CNC gear cutting technology (milling, wire EDM, etc.) represents an excellent choice for high-precision TS and ETS parts for operation and service features that can seldom be matched by other gear cutting types. This also translates into low parts cost, short lead time for prototype and pilot production quantities, and for tooling.
Parametric equations for TS curves are as follows:
Equation 1: x = e q cos(q) – w sin(q)
Equation 2: y = e q sin(q) + w cos(q)
where π=3.1415, -2πe≤q≤2πe and q is the independent variable in radians, e is the radius of pitch circle for the sample curves shown in dashed line with center at x=y=0 in Figure 1. The sample curves depend on the particular value of design constant w=y for x=q=0.
- w=0 for the L-TS curve, also known as the Archimedes Spiral (AS). In the author’s opinion the AS is by far the first mathematically exact gear profile that was discovered and formulated by the Greek mathematician and physicist Archimedes 2,300 years ago using geometry, prior to the existence of algebra and the concept of numeral zero. There have been many important inventions using the AS over the centuries, notably the scroll-chuck for lathes and related machines, and using the AS in special mechanisms such as mechanical analog squaring devices for computing the squares of numbers to high digital accuracies, just to mention two important examples. In reference to the opening paragraph, the L-TS is the only intersecting axis rectangle drive within the scope of this article.
- w=e for the Z-TS curve, implying that the pole (cusp) of the curve for x=q=0 coincides with the topmost point of the pitch circle in Figure 1(A), so that w-e=0, hence the designation of zero offset. The curve is also known as the involute of a circle, a special case of TS profiles. The formulation of traditional involute gearing by the Swiss mathematician Leonhard Euler has had a profound influence on watchmaking and other industries for centuries.
- w=2e for the sample P-TS curve. The new P-TS profiles offer important gear design advantages over the two other profile types because they are least affected by certain profile undercut and insufficient radius of curvature of gear profile surface conditions, and therefore they do not require extra design measures that could prove counterproductive. Through-shaft gear design, versus cantilever shaft support for the gear, may also be realized as an advantage for certain applications.
Parametric equations for ETS curves are as follows:
Equation 3: x= -(b sin(q) – Q sin(b q)) n e
Equation 4: y= (b cos(q) – Q cos(b q)) n e
where -2p eæqæ2p e and q is the independent variable in radians, e is the radius of pitch circle for the three sample curves as shown as dashed lines in Figure 2(A) with center at x=y=0, while n designates the number of rollers in the follower, and b and Q are constants depending on the particular value of w=y for x=q=0, just like in the examples above for TS curves. For n=16 for the ETS curves in Figure 2(A), the following information applies:
- w=0, b=Q=1.0625 for the L-ETS curve. Substituting b and q into equations 3 and 4, data points for the curve were obtained for plotting it as shown in Figure 2(A), where the follower center coordinates of x=0 and y=(n+1)e=17e apply for all three concentric pitch circles. Consequently, the pitch radius of the roller follower for the L-ETS curve is 17e.
- w=e, b=1.0625, and Q=1 for the Z-ETS curve as shown in Figure 2(A). We note that the pitch radius of the follower in red is 16e in this case.
- w=2e, b=1.0625, and Q=.9375 for the P-ETS curve and the corresponding follower of 15e pitch radius as shown in Figure 2(A).
Calculation of the gear ratio for TS and ETS gears is simple: one full turn of the gear corresponds to one linear or circular pitch, P, respectively, as P=2pe, where e designates the pitch circle radius for the gear.As an example, a given ETS gear train uses a follower of n=10 rollers for a gear ratio, R, as, R=-n:1=-10:1, where the negative sign indicates that the gear and follower rotate in opposite directions.
ACADSvF (animated CAD Solutions version F by Trogetec, using flash by Macromedia) animation for %%plotting1005fig1%% and Figure 2 (using eight increments of 45-degree gear rotation as shown) is provided on the Web site listed below. The corresponding composite plots in Figures Figure 1(B) and Figure 2(B) serve as transition-type visuals between Figure 1(A) and Figure 2(A) on the one hand, and the corresponding flash animations on the other. For monitor screenshots of the shockwave flash animations we refer to Figure 3 and Figure 4.
This animation technique was primarily developed for the new TS, ETS, and other gear categories, for design studies by individuals or small groups of design/mfg/QC engineers, and for executive project reviews, when the use of visuals, prototypes, and demo units can be of paramount importance for the best results.


TECM 1343 (NT) - Technical Algebra and Trigonometry
Semester Credit Hour(s): 3 Lecture Hour(s) Each Week: 3 Lab Hour(s) Each Week: 0
Algebraic and trigonometric applications used in technical/industrial settings. 27.0301 (Applied Mathematics, General).
Fees: Inclusive Access Fee $66. When Offered: F, Sp, Su Coordinating Board Approval Number: 27.0301
Note: This class is for Corrosion and Process Technology Majors only. Also, this class is not transferrable. Students who are not TSI Complete in Mathematics must concurrently enroll into specified section of NCBM 0143.
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Elementary Statistics, Revised (5th Edition) - Janet T. Spence, John W. Cotton, Benton J. Underwood, Carl P. Duncan
Plot / Summary
This application-oriented guide hands you simple-to-use mathematical techniques for determining various statistics in psychology and the behavioral sciences. Progressing from basic descriptive statistics to inferential paramedic statistics, the handbook includes graphic presentations including stem and leaf displays ... step-by-step procedures for performing computations ... advice for selecting the appropriate statistical test for specific studies ... coverage of various statistical computer programs ... and more. Intended for professionals with little or no knowledge of statistics.


MSc in Scientific Computing and Data Analysis
The Durham University MSc in Scientific Computing and Data Analysis (MISCADA) is designed for students with quantitative first degrees, and an interest in how mathematical and computational tools can be used to address scientific questions. From October 2021, we are offering a new specialisation within this programme: Earth & Environment. In addition to gaining cutting-edge technical skills, students will have opportunities to learn about, and work on, a wide variety of geoscience datasets and applications.
Within this programme I will be teaching:
- Tools: Forward and inverse models
- Applications: Geophysics
I have designed and delivered high-quality CPD courses covering a range of mathematical, statistical and computational topics relevant to geoscience industry. Please contact me if you wish to discuss how I can help your organisation.
Courses I have previously been involved with include:
- Computational Geosciences: Problem-solving, logical thinking and programming (EMSC4033/EMSC8033). A course I developed and taught to Honours and Masters students within the Research School of Earth Sciences at the Australian National University (2018-2020). By the end of this course, students should have a basic understanding of the concepts of computer programming, and the Python programming language. The primary goal was to ensure students had the skills required to process, analyse and present their research datasets. The course materials (primarily a series of Jupyter notebooks) are available on Github.


New results in robust functional state estimation using two sliding mode observers in cascade
This paper presents a functional observer scheme using two sliding mode observers in cascade. A coordinate transformation is performed on the system such that existing sliding mode observer theory can be directly applied to achieve functional state estimation. The necessary and sufficient existence conditions for the scheme (in terms of the original system matrices) are also investigated, and they are found to be less stringent than earlier work on functional state estimation using one sliding mode observer; this could have benefits in terms of cost and simplicity. A numerical example verifies the effectiveness of the scheme.
Chew Kee, Chee Tan, Kok Ng and Hieu Trinh
International Journal of Robust and Nonlinear Control,
Wiley Online Library,
Page responsible: webmaster
Last updated: 2021-11-10


Determining the thermal stresses in elastic plates is a necessary component in strength calculations of elements of thin-walled structures, for example, the skin of aircraft and rockets in aerodynamic heating conditions.
Knowledge of the magnitude and nature of the action of thermal stresses is necessary for a comprehensive analysis of the strength of the structure. Thermal stresses in themselves and in combination with mechanical stresses from external forces can cause cracks and destruction of structures made of materials with increased fragility.
In addition, practice shows that thermal stresses can be one of the main causes of rock bursts and, possibly, small-scale earthquakes. This is due to the fact that the heating of the rock and its subsequent cooling lead to the emergence of residual stresses and their subsequent relief in the form of shootings, rock bursts, earthquakes and other catastrophic phenomena.
There are examples of solving the simplest temperature problems in nearly all textbooks on the theory of elasticity. Various methods have been applied for their determination: the superposition method, the method of Fourier integrals, the collocation method, the finite element method, etc. Almost all of them, in one way or another, reduce the boundary value problem to an approximate solution to infinite systems of algebraic equations.
In this work, for the first time, examples of exact solutions to temperature problems for a square with different boundary conditions on its sides are constructed in the following formulations: (1) the temperature problem for a free square; (2) the temperature problem for a clamped square. The solution method is as follows. First, the temperature problem for an infinite plane is solved. Then, exact solutions to homogeneous boundary value problems for a rectangle are added to this solution, with the help of which the boundary conditions on the sides of the square are satisfied. The thermal displacements and stresses are obtained in the form of series in Papkovich–Fadle eigenfunctions. It is shown that in the problem for a free square the tangential stresses have finite spikes at the corner points. There will be no spikes if we assume that the expanded function vanishes in a small neighborhood of the corner points. We can do otherwise by multiplying the expanded function in the neighborhood of the corner points by a smoothing function that vanishes at the corner points together with the given number of its derivatives. It is shown that in the problem for a clamped square the spikes of the normal stresses at the corner points have a logarithmic character. It is impossible to avoid this singularity. This is due to the fact that the Lagrange coefficient for the expanded function has the highest rate of decrease since it is determined directly from the equation for determining biorthogonal functions and, therefore, the expanded function is treated in this case as an entire one, i.e. it possesses the greatest smoothness. Thus, the singularity for the stresses in the temperature problem for a clamped square is its physical characteristic.
To avoid nonprincipal calculations and to make the presentation maximally simple and brief, we consider a square rather than a rectangle whose temperature field is assumed to be even-symmetric relative to the central coordinate axes of the square; the temperature distribution law is chosen to be maximally simple:
T(x,y)=x2 + y2
|Fig. 1. Contour lines for normal stresses in a free square.||Fig. 2. Contour lines for normal stresses in a clamped square.|
The technique of solving temperature problems can also be applied to solving inhomogeneous problems.
The research was carried out with the support of the Russian Science Foundation (project No. 19-71-00094) and the Russian Foundation for Basic Research in cooperation with the National Natural Science Foundation of China (project No. 20-51-53021).
Source: Kovalenko M.D., Menshova I.V., Kerzhaev A.P., Yu G. A temperature problem for a square: An exact solution // Mathematics and Mechanics of Solids, 2022, vol. 27, no. 2, pp. 250–261. DOI: 10.1177/10812865211020496.


Key concepts: Integrals/integration Definite and indefinite integrals Substitution Let's face it: Doing integrals and doing them right is pretty hard. I remember learning about them for the first time and having no clue what they meant or how to get started solving my homework. Let us walk through some example problems and see how integration actually works! Question 1: "Draw a graph of the function x^2 and determine the area between the curve and the x-axis on the interval from 0 to 1." Alright, let us give it a shot. Below, I have graphed the function and crudely sketched out the area we are interested in.
How big is that area? It is not shaped like a square, a circle or a triangle, so we can't just break out a ruler and measure it. Luckily, we can use definite integrals to calculate it! Let us write down the following:
Basically we have to imagine chopping the area under the function up into a bunch of rectangles. They have a height x^2 and a width dx. Obviously this is not completely correct, because the rectangles will always be a bit too large. But if we make dx really small, then the extra area will also get really small.
Calculating the "definite integral" of x^2 from 0 to 1 basically tells us what the area will be if we make dx infinitely small. What about "indefinite integrals"? Question 2 "Find the anti-derivative, F(x), of f(x)=x^3 so that F(4)=63" Hmm, that looks cryptic to say the least. What are we supposed to do here? For good measure, let us draw a graph of f(x):
In Question 1, we were explicitly told that we should integrate from 0 to 1. We were looking for a specific area. Right now, we are being asked to find a general "area function, F" that tells us how area under f(x)=x^3 changes for different values of x. Also, we want to make sure that the area is 63 if x=4. Let us try to write down the "indefinite integral":
The expression in the parenthesis basically tells us how the area under f(x) changes as x is changed. The weird +C tells us what the area should be for a particular value of x. To solve this problem correctly, we need to ensure that F(4)=63. Let us plug this information in to the expression:
Now we can solve for C:
Therefore the solution to the whole problem is:
Question 3 "Find the area under the curve of
from 1 to 3" Let us graph the function for good measure:
Look, I get what you are thinking: "Seriously?! I just figured out how to integrate basic stuff like x^5 and exp(x). That expression looks completely impossible to integrate. I mean it's a fraction of two different powers of x, for crying out loud! There is no way I can figure that out!" Am I a mind reader or what? Anyways, there is actually a super easy way to solve problems like this. It involves doing "integration by substitution". Here is the idea:
We notice that the integral consists of some inner function stuffed inside an outer one. We then define:
This allows us to rewrite the integral as:
Now our goal is the following: Find a way to replace every x in the expression above with something that depends only on u Let us start by getting rid of dx. We do this by taking the derivative of u:
Now we are going to use the best kind of trick in the world; a trick that both works AND infuriates pure mathematicians! We are going to solve for dx in the expression above, even though du/dx is not technically speaking a fraction:
Now we are going to plug this back in to the integral:
We are also going to change the integration bounds, 1 and 3, to:
Notice how the expression now contains x^3/x^3=1. We can therefore simplify the expression:
Now we just have to integrate 1/something. It turns out that the antiderivative of 1/u is:
NICE! Let us just recap what we did:
We noticed that the expression we wanted to integrate had an outer function(inner function).
We defined u=inner function
We found du/dx=(inner function)'
We solved for dx and plugged it back in to the integral
We replaced the bounds x=a and x=b with u(a) and u(b)
We got lucky and saw that annoying, complicated factors cancelled out.
We got a much simpler integral out of it that we could easily solve.
Ok, so obviously I picked this particular f(x) because I knew in advance that x^3 would be cancelled out eventually. Integration by substitution is not some magical method that works for every single integral you come across. However, if you encounter an integral that contains some function inside another one, there is an very good chance that substitution will work! Try it out for
Need more help with questions similar to these? Click here to set up your first tutoring session and receive expert help!


People are often good in either math or language. I hated math in school, but since we started home education with Singapore Math, everything I missed fell into place and I began to enjoy math.
My gardening hobby is growing, as hobbies tend to do, and my husband built me a few extra raised garden beds. I know how to find volume easily enough: length X width X height, and I felt confident with my understanding of converting cubic feet to cubic yards. 1 cubic yard = 27 cubic feet.
So I took my simple equation (16 feet X 4 feet X 4 inches X 27 X extra beds) and checked it with a calculator…unfortunately I did not change the 4 inches in height to feet (.3)
Two days and 12 yards of dirt later, we rest our weary muscles. My sweet husband.


Injective, Surjective and Bijective "Injective, Surjective and Bijective" tells us about how a function behaves. 2 If dim(V) V and T: V -> W be two linear maps. An injective map between two finite sets with the same cardinality is surjective. However, if we restrict ourselves to … (a) Prove that if TS is injective, then S is injective. Then: The diﬀerentiation map T : P(F) → P(F) is surjective since rangeT = P(F). 1 If dim(V) >dim(W), then T is not injective. A function is a way of matching the members of a set "A" to a set "B": Let's look at that more closely: A General Function points from each member of "A" to a member of "B". If \(f\) is a linear map between vector spaces (and not just an arbitrary function between sets), there is a simple way to check if \(f\) is injective. Let \(T : V \rightarrow W\) be a linear map between vector spaces. Lemma 3.6.2. then a linear map T : V !W is injective if and only if it is surjective. Proof. A linear map T : V → W is called surjective if rangeT = W. A linear map T : V → W is called bijective if T is injective and surjective. But this would still be an injective function as long as every x gets mapped to a unique y. A function [math]f: R \rightarrow S[/math] is simply a unique “mapping” of elements in the set [math]R[/math] to elements in the set [math]S[/math]. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … In particular, ker(T) = f0gif and only if T is bijective. Recall that the composition TS is defined by (TS)(x) = T(S(x)). General topology An injective continuous map between two finite dimensional connected compact manifolds of the same dimension is surjective. Surjective Linear Map Corollary Let T : V !W be a linear map. This is not onto because this guy, he's a member of the co-domain, but he's not a member of the image or the range. Let F be a linear map from R3 to R3 such that F (x, y, z) = (2x, 4x − y, 2x + 3y − z), then a) F is injective but not surjective b) F is surjective but not injective c) F is neither injective nor surjective d) … Deﬁnition 5. He doesn't get mapped to. Example 5. Jiwen He, University of Houston Math 4377/6308, Advanced Linear Algebra Spring, 2015 10 / 1 Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … (b) Prove that if TS is surjective, then T is surjective.
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Strategy With Fibonacci – We will use Fibonacci ratios in our trades so that you better learn and love him like cooking in your mother’s home. Fibonacci is a big subject and there are many different studies about Fibonacci, with a name that sounds strange but we will stick to two things, namely: retracement and extension.
Leonardo Fibonacci is not a famous chef. In fact, she is a well-known Italian mathematician, also known as the Ultra super duper Ubergeek.
He has an “Aha!” moment when he finds a simple series of ratio numbers created describing the natural proportions of things in the universe. The ratio arises from the following serial numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
Series of numbers obtained by starting with 1 followed by 2 and then adding 1 + 2 to get 3, the third number. Then, add 2 + 3 to get 5, the fourth number, and so on. After the first few numbers in descending order, if you measure the ratio of any amount to the next higher number, you get 0.618. For example, 34 divided 55 equals 0.618.
If you measure the ratio between the alternate numbers you get 0.382. For example, 34 is divided by 89 = 0.382 and it gets into the explanation as we will discuss.
This ratio is called “Golden Mean”. Okay, that’s pretty nonsense. With all the numbers, you can make an elephant fall asleep. Essentially, this is the ratio you SHOULD BE aware of:
Fibonacci Retracement levels 0.236, 0.382, 0.500, 0.618, 0.764
Fibonacci Extension Levels 0, 0.382, 0.618, 1.000, 1.382, 1.618
You don’t really need to know how to count all of this. Your charting software will do all the work for you. such as some indicators in MT4. However, it is nice also to be familiar with the basic theory behind the indicators so you will have the knowledge to impress your boyfriend.
Traders use Fibonacci retracement levels as the potential for support (support) and resistance areas (resistance). Because many traders then pay attention to the same levels and places buy and sell them to enter or close trades, and the level of support resistance tends to be a fulfilled forecast.
Traders use Fibonacci extension levels to take advantage levels. Again, because many traders are watching this level, this tool tends to be more frequently used.
Most charting software includes both Fibonacci retracement levels and extension-level tools. In order to apply the Fibonacci levels on your chart, you must identify the Swing High and Swing Low points.
High Swing is a candle with at least two lower highs on both the left and right sides of it itself.
Low Swing is a candle with at least two lows higher on both the left and right sides of it itself.
Did you get all that? Don’t worry, we’ll explain the retracements, extensions, and most importantly, how to grab a few pips using the FIB tool in the following sections.
The first thing you should know about the Fibonacci tool is that it works better when the market is in a trend.
The idea is to buy long (or buy) on the retracement at the Fibonacci support level when the market is trending up, and to sell short (or sell) on the retracement at the Fibonacci resistance level when the market is trending down.
In order to find the retracement level, you need to find a fairly important level of the Swings high and the Swing Lows. Then, for a downtrend, click on Swing High and drag the cursor to the latest low Swing. For Uptrends, do the opposite. Click on Swing Low and drag the cursor to the latest high Swing.
Uptrend Strategy With Fibonacci
Here we plan the Fibonacci retracement Level by clicking Swing Low on 1.3068 on 2019.01.27 and dragging the cursor to Swing High at 1.356762 on 2019.05.26. Tada! This magical software can show the retracement level!
As you can see from the chart, the retracement levels are 1.344521 (23.6%), 1.337797(38.2%), 1.33159(50.0%), 1.325728 (61.8%).
Now, our hope is that if USD/CAD retraces it from its recent highest point, it will find support/support at one of the Fibonacci levels because the trader will place a buy order at this level if the price rises back.
Downtrend Strategy With Fibonacci
As you see, we found Swing High at 1.35659 on the 2019.05.26 and Swing Low at 1.325728 a few days later on 2019.06.02. The retracement rate is 1.349348 (23.6%), 1.344866 (38.2%), 1.341245 (50.0%), 1.337624 (61.8%).
The expectation is that if the price retraces of this low price, it will face obstacles on one of the Fibonacci levels because the trader will be ready with a sell order there.
The best way to learn to read FIBONACCI patterns is to practice how to enter and exit transactions from the signals they emit. If you don’t want to trade in the immediate market, you can develop your skills in a risk-free by opening an FBS demo account.


The study of mathematics is mandatory from Kindergarten to Year 10.
The Mathematics Faculty at Leichhardt Campus, is an enthusiastic team of dedicated staff who bring a wide variety of experiences to students both in and outside of the classroom.
The aim of Mathematics at Leichhardt is to promote students' appreciation and application of Mathematics in their everyday lives. Students are encouraged to develop their mathematical thinking, understanding, confidence and competence in solving mathematical problems.
The mathematics faculty endeavours to:-
- develop the basic numeracy skills necessary in our society, this is considered to be of paramount importance.
- impart favourable attitudes to learning mathematics. That is, students should derive interest and enjoyment from mathematical activities and learning.
All students in Years 7 to 10 cover content in the strands of Number and Algebra, Measurement and Geometry, Statistics and Probability, with the components of Working Mathematically integrated into these strands.
All students in Stage 4 (Years 7 & 8) study the same outcomes.
By the start of Stage 5 (Years 9 & 10), students exhibit a wide range of mathematical skills, levels of competence, and aspirations. Some students may be aiming to develop the mathematical skills necessary to function in daily life and various work contexts. Other students may seek to address more challenging mathematics to prepare them for the highest-level courses in Year 11 and Year 12.
Stage 5 of the K–10 Mathematics curriculum has been expressed in terms of the three substages, Stage 5.1, Stage 5.2 and Stage 5.3. These substages are not designed as prescribed courses, and many different 'endpoints' are possible. As well as studying the Stage 5.1 content, at Leichhardt Campus the majority of students will study some or all of the Stage 5.2 content. Similarly, as well as studying the Stage 5.2 content, some students will study some or all of the Stage 5.3 content.
For further information about the Mathematics K-10 Syllabus, please refer to the Syllabus document: http://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10. Parents are welcome to contact our Head Teacher Mathematics for any questions you may have about the course and how our classes are structured at Leichhardt Campus.
In Year 11 and 12, the study of mathematics is optional. Courses offered include:
- Mathematics Extension 2 (Year 12 only)
- Mathematics Extension 1
- Mathematics Advanced
- Mathematics Standard 2
- Mathematics Standard 1 (Optional HSC examination)
- Mathematics Life Skills.


By Fred Manzo
Axis and Allies Tactics
One other item worth mentioning for those playing >Axis and Allies is what has been called the “First Bite of the Apple” theory.
Basically, it says that no matter how accurate your formula, the entire situation will change when combat starts. Now, while this is true enough on its own, what the people who use the theory mean is that if we believe the situation will change in any direction when we contact the enemy, why can’t it sometimes change in our direction? And if so, why not give it a try no matter what the formula says?
For example: say we have the Russians attacking with 25 Infantry units against 15 German tanks. The Standard Formula says 25 x (1 + 1) or 50 divided by 15 X (3 + 1) or 60, which equals .83 (for tanks defending at 3). So the Russians normally won’t consider attacking. But all this formula, or any formula, is saying is what should happen, not what will happen. Or to put it another way, it’s only locating the central line of a bell shaped curve of all possible outcomes and telling us that in this particular situation there is such-and-such a probability of winning.
However, when we are rolling so few dice sharp variations can quickly change the situation. In other words, we may find ourselves with an outlier or low probability outcome. Therefore, in our situation, the Russian when rolling 25 dice might not hit the expected 4 times but an unusually lucky 7 times and the German defender might not hit the expected 7 times but an unusually unlucky 3 times. Well, the second round of combat will now be 22 Infantry vs. 8 Tanks. If we took the time to run the new numbers through the formula we’d get 1.375, which is substantially better than the original .83 and says the Russians will probably win. But we won’t have known about this outcome if we had gone along with what the formula originally told us. So, by robotically follow the formula, we gave up obtaining a low probability victory.
In other words, formulas aren’t fool proof.
Players who use this approach would tell you “even though I know I’ll probably lose, that’s not a sure thing. Therefore, I’ll fight one round and see what develops. If the first bite of this apple is exceptionally favorable I’ll continue. Otherwise I’ll cut my losses and call the whole thing off.”
The difference between this approach and a Spoiling Attack is that Spoiling Attacks are typically called off in the next-to-last round of combat, while First Bite attacks are called off after the initial round.


Find greatest among 3 numbers – requirements
The requirement is to find greatest among 3 numbers. You can either let the users enter 3 numbers using a prompt box and store it in a variable or use 3 inputs text field to accept number or define 3 variables and store values in it. If you are comfortable working with arrays, you can use an array of 3 numbers for comparision.
Find greatest among 3 numbers – hints
- Compare the first two numbers using a if/else statement and save value of the greater number in a temporary variable named “larger’.
- Now compare the value of third number with the value stored in the ‘larger’ variable using the if/else statement.
- Display the greatest number using an alert box or show it in the body of the page using document.write
Need help? here is the the tutorial


It’s the season of giving. In that spirit, I’m going to offer some advice and under-the-hood information about character rewards in Earthdawn.
The recommended Legend Awards on page 120 of the Gamemaster’s Guide are calculated to advance player characters at a reasonably steady pace. We derived this by figuring out how much it costs to advance in Circle and dividing that up into a number of game sessions.
The exact Legend total can change based on how you distribute your starting points, but it amounts to only a couple hundred Legend — it might be a big deal at the very start of your career, but it’s miniscule when you’re a Journeyman and getting thousands of Legend Points each session.
For example, to qualify for Fourth Circle, you need to raise your 7 Discipline talents (5 from First Circle, one each from Second and Third) to Rank 4. Six of these are already at Rank 3 (because they needed to be to reach Third Circle). Thos costs (500 * 6), or 3000 Legend Points.
Then the Third Circle Discipline talent needs to be raised from Rank 0 to Rank 4, which costs 100+200+300+500 = 1100 Legend Points. This means that the minimum Legend needed to go from Third to Fourth Circle is 4100 Legend. (Of course, this doesn’t factor in advancing optional talents, increasing skills, raising attribute values, weaving permanent threads, or any of the other myriad things you might spend points on.)
After running the numbers for a character’s full progression, the other factor at play is how many game sessions should it to take for a character to earn that many Legend Points. From these numbers, we do the math and that gives us the recommended “Legend per Session” awards. The range comes from deciding on a “fast” advancement and a “slow” advancement — understanding, again, that actual advancement will be a bit slower because of all the other stuff you can spend those points on.
Going back to our Fourth Circle example, we know a character needs to earn 4100 Legend before they can qualify. Breaking that down into a range of session awards gives us these figures:
- 1 Session: 4100/1 = 4100 Legend/session
- 2 Sessions: 4100/2 = 2050 Legend/session
- 3 Sessions: 4100/3 = 1367 Legend/session
- 4 Sessions: 4100/4 = 1025 Legend/session
- 5 Sessions: 4100/5 = 820 Legend/session
- 6 Sessions: 4100/6 = 683 Legend/session
- 7 Sessions: 4100/7 = 586 Legend/session
(Fractions are rounded off, since you can’t award fractional Legend Points.)
At this point, it’s just a matter of deciding what seems appropriate and picking values that fit — and it’s more art than science. Two to three sessions for “fast” advancement seems good, while five to six sessions feels right for “slow” advancement. Picking pretty, round-number values in those areas… 800 to 2000 seems like a good range. That sets the bounds for the awards given to Third Circle characters (who are working their way toward Fourth).
As a bit of sanity check, we look at what happens if all the sessions give the average award value (in our example: 1,400 Legend per session means it will take 2.93 sessions to earn the minimum needed to qualify for Fourth Circle).
Remember, these are minimums. I would add a fudge factor for all the extra spending that is available — an extra session every four is a good place to start.
If you crunch all the numbers for advancement and look at the recommended awards in the Gamemaster’s Guide, it comes out to be about 67 session awards (using nothing but the average award value) to earn the minimum required to advance from a brand-new First Circle character to Fifteenth Circle.
Of course, with all the other stuff on which to potentially spend Legend Points, the actual number of sessions would be longer (about 84 session awards with my 25% fudge factor).
I hope you’ve enjoyed this look under the hood. Next time around, we’ll take this information and apply it to monetary rewards.
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The Demise of What Is Product in Math
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The Argument About What Is Product in Math
Your teacher has to be in a position to clear your calculator at any moment. If you would like to retire in five years, you must recruit around 417 new people annually, or about 8 new people weekly. My kids were quite happy.
The general public school is easily the most obvious first selection for many families. however, it’s also one that can cause them a great deal of concerns. Therefore, it can be difficult to overestimate the significance of giving your child that extra competitive edge. My kids were quite happy.
The vector has 2 numbers that are written vertically (instead of horizontally enjoy a coordinate). The abacus may be used to perform numerous mathematical operations. Distributive property makes it simpler that you multiply numbers.
An exhaustive mastery of regrouping is essential as it is also utilised in different operations. Squaring is another kind of multiplication. Kids who struggle with math think that it’s hard and assume they just aren’t very good at it.
What’s Actually Happening with What Is Product in Math
Another intriguing thing about vectors in mathematics is that they may be multiplied, one particular vector with a different one. What you have to bear in mind is that timetable facts will assist you when multiplying with large numbers or even tiny numbers. Arithmetic deals with numbers, which could be split into real numbers and intricate numbers.
Multiply (2r) times (h) and you’ve got the region of the rectangle part of the cylinder. There are mathematical operations which you’ll be able to carry out on numbers. In the following two examples you are going to have a number in the front of the algebra in the bracket.
The ideal tool to help in monitoring the best stream of product is track-and-trace technology. While there are numerous other aspects in selecting an affiliate product which will be profitable, gravity is a great place to begin. The partial product algorithm is a method for students to deepen their knowledge of place value whilst multiplying.
The paramountessays com Pain of What Is Product in Math
The scholarship application can be found on the Premier Scholarship web page. Carr Distinguished Scholarship You might qualify for an additional 3,000 per year if you’re accepted in the ASU Honors Program. In arranging a program, the student, with the aid of an advisor, should decide on the courses to satisfy the prerequisites of general education and a teaching major.
A couple of minutes a day is sufficient. The printing number are found at the bottom of the webpage on the opposite side of the title page. A goal has to be time bound.
Where to Find What Is Product in Math
Practically all math issues can be solved with the correct understanding of moving the beads manually on the gadget. Lesson Summary The item is the reply to a multiplication issue. It is also called the difference.
Based on the services ordered, you might have to make two separate payments. As you grow your company and build your team, you wish to have leverage. Without leads, your company cannot grow.
The Nuiances of What Is Product in Math
Background should not influence a student’s capability to learn. Working with single nutrient sources is easy and straightforward. The whole textbook in pdf form are available here.
If you’re finding an angle then you’ll need to understand the lengths of 2 sides of the ideal angled triangle. By way of example, multiplying by two is just like doubling. The number of numbers utilized for each worksheet could be individually varied to create unique sets of issues.
Doing the math when joining an MLM business will help you to get a clearer perspective on exactly how a lot of people you should bring in to attain your target. Per capita GDP might also be utilized to assess the productivity of a country’s workforce, as it measures the whole output of goods and services per each member of the workforce in a particular nation. Hence, you are in need of a good strategy for lead generation.
Each math topic has many unique selections of math worksheets to cover various sorts of problems you may choose to work on. With just a little practice, you ought to be in a position to call the answer out without a pause. In case the answer is no, then 2 isn’t a factor of 25.
You may use the percent difference formula if you want to understand the difference between two values with respect to percentage. When you locate a vector, I believe it can help imagine it like a movement from 0,0,0 an origin. Ideally, you should select the latter in both factors, for the rule states that you want to pick the closest number.
One of the greatest strategies to learn multiplication facts is by way of memorization, and memorization sometimes happens through repetition. The product usually usually means that you would love to multiply the 3 numbers together. All composite numbers have three or more divisors.


I found it remarkably hard to figure out how to monitor convergence for the expectation maximization (EM) estimtation algorithm. Elementary textbook presentations often just say “until convergence”, which left me scratching my head. More advanced presentations often leave you in a sea of generalized maximization routines and abstract functionals.
Typically, EM is phrased for maximum likelihood estimation (MLE) problems where there are no priors. Given data and parameters , the goal is to find the parameters that maximize the likelihood function .
Likelihood and Missing Data
Usually EM is used for latent parameter problems, where there are latent variables which are treated like missing data, so that the full likelihood function is actually . For instance, might be mixture component indicators, as in soft (EM) clustering. Typically the full likelihood is factored as .
Even though the expectation (E) step of EM computes “expectations” for given current estimates of and the data , these “expectations” aren’t used in the likelihood calculation for convergence. Instead, the form of likelihood we care about for convergence marginalizes away. Specifically, the maximum likelihood estimate is the one that maximizes the likelihood with marginalized out,
Monitoring Likelihood or Parameters
There’s more than one way to monitor convergence. You can monitor either the differences in log likelihoods (after marginalizing out the latent data) or the differences in parameters (e.g. by Euclidean distance, though you might want to rescale). Log likelihood is more task-oriented, and thus more common in the machine learning world. But if you care about your parameters, you may want to measure them for convergence, because …
Linearly Separable Data for Logistic Regression
In data that’s linearly separable on a single predictor, the maximum likelihood coefficient for that predictor is infinite. Thus the parameters will never converge. But as the parameter approaches infinity, the difference its (absolute) growth makes to log likelihood diminishes (we’re way out on the extremes of the logistic sigmoid at this point, where the slope’s nearly 0).
Convergence with MAP?
Textbooks often don’t mention, either for philosophical or pedagogical reasons, that it’s possible to use EM for general maximum a posterior (MAP) estimation when there are priors. Pure non-Bayesians talk about “regularization” or “shrinkage” (specifically the ridge or lasso for regression problems) rather than priors and MAP estimates, but the resulting estimate’s the same either way.
Adding priors for the coefficients, even relatively weak ones, can prevent estimates from diverging, even in the case of separable data. In practice, maximum a posteriori (MAP) estimates will balance the prior and the likelihood. Thus it is almost always a good idea to add priors (or “regularize” if that goes down better philosophically), if nothing else to add stability to the estimates in cases of separability.
Maximization Step with Priors
In EM with priors, the maximization step needs to set , the parameter estimate in the -th epoch, to the value that maximizes the total probability, , given the current “expectation” for the latent parameters based on the the data and previous epoch’s estimate of . That is, you can’t just set to maximize the likelihood, . There are analytic solutions for the maximizer in many conjugate settings like Dirichlet-Multinomial or Normal-Normal, so this isn’t as hard as it may sound. And often you can get away with increasing it rather than maximizing it (leading to the so-called generalized EM algorithm, GEM).
Convergence with Priors
Well, you could just monitor the parameters. But if you want to monitor the equivalent of likelihood, you need to monitor the log likelihood plus prior, , not just the log likelihood . What EM guarantees is that every iteration increases this sum. If you just monitor the likelihood term , you’ll see it bouncing around rather than monotonically increasing. That’s because the prior’s having its effect, and you need to take that into account.


For more information check out http://gmailblog.blogspot.com/2008/10/new-in-labs-stop-sending-mail-you-later.html
Thursday, October 9, 2008
Dont Drink and Email
Gmail is now offering “Mail Goggles”, where it tests the sender's sobriety by prompting them with a series of math problems (48-38 =?, 11x2=?, and so on) which must be solved within a time limit. Making sure that you don't send any emails, as google says you might later regret.


In a previous article, I explained how many large, well-known companies have saved millions of dollars by investing in usability. But how do you apply this information to your situation? How do you convince your audience (your client, a room full of executives, your business partner, your boss, or whoever…) that switching to more usable software is actually going to save them money?
In this article, we’ll walk through making a business case for switching to more usable software. Instead of relying solely on anecdotal information, calculate how much money they could save using your company’s real data, and show them. Let’s look at how to calculate ROI in three areas:
- increased productivity
- reduced support requests
- reduced training costs.
ROI Benefit 1: Increased Productivity
There are different ways that one could calculate the value of increased productivity, but we’ll focus on one: we’ll see how reducing the time required for specific tasks can translate into money saved.
Step 1) Calculate hours saved per year on each task.
Calculate, or estimate, how much quicker the task is using the new software. Then use the following formula to calculate hours saved per year:
[ minutes saved per day ÷ 60 ] x [ # of users ] x [ days worked per yr ] = hours saved / yr
For instance, suppose the new software makes a certain task 2 minutes faster. At your company, the average user of the software performs the task 10 times per day, so they would save 20 minutes per day. There are 30 users of the software, and the average employee works 260 days per year. The calculation would look like this:
[ 20 ÷ 60 ] x [ 30] x [ 260 ] = 2600 hours saved per year
If you know how many times in a year a certain task is performed, the calculation is easy.
[ minutes saved per task ÷ 60 ] x [ task count per yr ] = hours saved per year
For instance, suppose you are calculating time savings on a task related to adding a note to a system. Last year, a total of 150,000 notes were added to the system. And if the new software makes that task 1 minute faster, then the calculation looks like this.
[ 1 ÷ 60 ] x [ 150,000 ] = 2500 hours saved per year
Step 2) Add up hours saved for all your most common tasks
We don’t need a formula here. Just repeat step 1 for each task and add up your totals.
Step 3) Use average wages to calculate cost savings
Now use your total from step 2 to show how the time saved translates into cost savings:
[ hours saved per yr ] x [ hourly wage ] = Cost savings / yr
For instance, suppose you calculated that the new software would save a total of 15,000 hours per year. The average user of the software earns $20/hour. The calculation would look like this:
[ 15,000 hrs / yr ] x [ $20 / hr ] = Savings of $300,000 per year
ROI Benefit 2: Reduced Support Requests
Similar calculations can be used to show support cost savings.
Suppose that last year, you had 2000 support requests asking for password resets. The average call took 10 minutes. The new software allows users to do it themselves, eliminating these calls. You can use the same formulas we used above:
[ 10 ÷ 60 ] x [ 2000 ] = 333 hours saved per year
You use the same formula for other issues, and calculate that the software will save a total of 1500 hours per year on reduced support requests. The average IT employee earns $80/ hour.
[ 1500 hrs / yr ] x [ $80 / hr ] = Savings of $120,000 per year
ROI Benefit 3: Lower Training Costs
Suppose that your identity management software requires that new employees receive 2 weeks (80 hours) of training. You hire about 100 new employees per year, and your trainers make $70/hr. The new software includes lots of inline help, training videos, etc, reducing the time needed for training down to two days, saving 64 hours.
[ 64 ] x [ 100 ] x [ $70 / hr ] = Savings of $448,000 per year
These calculations are based on the idea that time is money. But in real life, saved time only equals saved money if:
- you’re no longer paying for that time, or
- that time is now being used to make you more money.
Although the calculations above can produce some pretty useful figures, they don’t tell the whole story. Expect some skepticism, and be prepared to address it. For instance, if each user performs their tasks more quickly, will the company REALLY end up with more money in their pocket? How do we know the user won’t just use that extra time to get coffee or surf the net? These metrics will only work if you are prepared to explain how they can realistically translate into real dollars and cents.
For instance, are time savings substantial enough that users will actually be able to produce more of whatever it is your company produces that makes money? Will your company be able to take on more projects, or larger projects? Could staff be reduced or reallocated? Are tasks simplified enough that jobs could be delegated to employees with a lower cost?
Don’t expect to present calculations of saved time, and expect everyone to jump on board. Think it through and be prepared to explain how to actually capitalize on that saved time.
Beyond the numbers
The benefits of usable software extend far beyond the numbers produced by the formulas above. Better adoption, fewer errors, lower turn over, and a number of other factors. In addition, there are a number of soft benefits, such as increased morale and job satisfaction. The impact of these factors can be huge, but a little harder to quantify.
But money talks. So use the formulas discussed above to get their attention, and your audience may be more well prepared to hear about these important, albeit less quantifiable, benefits.
The benefits of user-friendly software might be obvious to you, but not necessarily so for everyone. So do your research, be prepared to crunch some numbers using real data, and be prepared to support your argument with case studies, such as those discussed in the previous article. If you can create a strong case, your company may well recognize what successful companies have known for decades – that investments in usability make good business sense.


==For those who do not understand hexadecimal this should give you a clue, what it is:==
In mathematics or/and computer science hexadecimal (HEX, or hexa, or base-16, ;name comes from numeral systems)
is a numeral system with a radix. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine,
and A, B, C, D, E, F (or through an f) to represent values ten to fifteen.
It is often used in digital electronics and computer engineering.
It's very hard to understand if the person has not got very high skill in computer math. It's prime use is be slightly-more-readable then
the binary numeral system the binary system is used internally by all modern computers.
Look at this example:
Would be the same as:
Look at this message:
48 65 6C 6C 6F 2E 41 6E 64 68 65 72 65 77 65 67
What I said was:
"Hello. And here we go!"
Note: Spaces can not be read by hexa so put '_' as a space between each word. Which in hexa would be: 5F
so with spaces it will look like this:
48 65 6C 6C 6F 2E 5F 41 6E 64 5F 68 65 72 65 5F
77 65 5F 67 6F 21
James; I think we should, also do functions like sine and cosine, things like this in this topic. What you think?


I noticed that all the leaves had finally fallen from the huge poplars at the corner of our property.
As Chelsea moved very slowly through them (the vet told me she's the dog equivalent of 90+)
I picked up a random sample and tried to estimate the biomass of Melampsora (a rust fungus) in the dead leaves.
Of course, I'm not being properly scientific about it. To begin with I'm guessing that the trees had 100,000 leaves (at least)
Every leaf I picked up had at least a few black spots of the telial stage of the rust, and most had more than 100,
while some had about 1000 (see photograph). My guess is that the average leaf has about 5% fungal biomass (some much less, some much more). I weighed ten randomly chosen leaves, and was pleased when they weighed in at 10 grams, or 1 gram each, which simplifies the arithmetic tremendously. So - 100,000 grams = 100 kg of leaves 5% of that is 5Kg, or 11 pounds of fungal biomass.
It would take another more difficult process to work out how many basidiospores are likely to be released in Spring, but I know it would be astronomical, so I'll leave that for another day.


Everybody loves palindromes, right? I do, at least. That’s why I was excited
when I learned that every number can be a palindrome when it’s written in the
appropriate base. There is a trivial proof for this property: any number N > 3
is a palindrome in base N-1 because it may be written “11”. So here is my
solution, in Haskell, to this CodeChef
problem, that finds the smallest base
that makes any given number a palindrome.
This is certainly not the fastest solution possible. Indeed it is downright
naive. But hopefully the logic is clear.


What Is a Mill Rate?
In Connecticut, property tax rates are expressed in mills, or thousandths of a dollar.
A property tax rate of 36.86 mills (.03686), when expressed in decimal form) results in the payment of $36.86 for each $1,000 of a taxable property's assessed value.
This is called the mill rate because the number is expressed in mills. One mill is equal to 1/10th of a cent or $.001.


2019-09-28 · Use our free monthly payment calculator to find out your monthly mortgage payment. See a breakdown of your monthly and total costs, including taxes, insurance, and PMI.
Monthly Mortgage Payment Formula – If you are looking for lower monthly payment on your existing loan or for new mortgage loan then you need reliable and trouble-free refinance service, for these purposes we created our review.
To calculate monthly mortgage payment, you need to list some information and data as below screenshot shown: Then in the cell next to Payment per month ($), B5 for instance, enter this formula =PMT(B2/B4,B5,B1,0) , press Enter key, the monthly mortgage payments has been displayed.
The following formula is used to calculate the fixed monthly payment (P) required to fully amortize a loan of L dollars over a term of n months at a monthly interest rate of c. [If the quoted rate is 6%, for example, c is .06/12 or .005].
Plug the numbers into the payment formula as follows: Loan payment = $100,000 / 166.7916 = $599.55 You can check your math with the loan amortization calculator spreadsheet. How Much Interest Do You Pay? Your mortgage payment is important, but you also need to know how much of it gets applied to interest each month. A portion of each monthly payment goes toward your interest cost, and the remainder pays down your loan balance.
now down payment mortgages With hoa costs surpassing their mortgage payments, owners of affordable housing appeal to City of Boulder – When he bought the home, he thought he was committing his family (including daughter Sidney, now in the third grade) to an $820 monthly mortgage payment, and monthly HOA. and then involve the City.
Our mortgage payment calculator can help you understand if one of them will work for you: Increase the term of the loan. The longer you take to pay off the loan, the smaller each monthly mortgage.
If you want to skip the formula and just read your monthly mortgage payment from a table, I’ve created fixed rate mortgage tables for 15 and 30 year mortgages, covering rates from 4.0% to 5.95%. Note, I use the same numbers from this page in my amortization formula example.
Lenders typically use a formula to determine your minimum monthly payment. For example, your card issuer might require that you pay at least 3 percent of your outstanding balance each month, with a minimum of $25 (whichever is more).
mortgage pre qualification letter sample Mortgage prequalification differs from a pre-approval in that prequalification assesses whether your debt-to-income ratio fits U.S. Bank’s program guidelines for home loans. It also provides an estimate of how much you may be able to borrow – a good first step in your house-hunting journey.
Use our free mortgage calculator to quickly estimate what your new home will cost. Includes taxes, insurance, PMI and the latest mortgage rates.


Advantages of Free Math Worksheets
Below is a list of the advantages that free match worksheets have. To benefit, free match worksheets are beneficial to parents as they allow them to help their kids to do match practice without too much effort on their part. While it can be quite challenging to prepare your child for a math test, recently this has been made easier as there have been free math worksheets online, this would be easy for a parent to help their child prepare for a math test. In this case where you would be looking to learn the advantages that come with free math worksheets, you should take note of this that through these worksheets, one would not have to make their own worksheets at the time they would be doing their final exams.
In this case where you would be looking to learn the benefits that come with these math worksheets, as to what you should also take note is that one of these worksheets would help one to not have to go through having to erase answers as well as solutions from their workbook then have to do them again. Due to this, as to what one would be able to avoid as a parent is a reluctance that a child would have at the time they would be told to do the problem they would have done over again. Now that you would be looking to learn as to what the advantages of these worksheets are, as to what you should also take note is that there would be no reason not to teach your child math at home.
Regarding the point above as to what you should note is that for most parents, it can be quite challenging to teach their kids at home for such reasons such as those of their child being unwilling to learn and that the topic that they would have to teach would be that they have already forgotten as well as them not having the extreme patience needed during teaching, however with there being these free math worksheets, there is no excuse as to why a child should not learn mathematics at home. You should take note of this other point as well that with regard to free math worksheets, as to what you should also note is that there exist such worksheets that are practically for any math subject.
Now that you would be looking to know the advantages that come with math worksheets that are free, the other benefit these that you should know is that not only are they readily available but also one would not have to spend as there are so many sites that sponsor worksheets for free and which you could get them through few clicks.


Cascading cuts means that once a key of a node is decreased to be smaller then its father, it is cut from tree and joins the roots list. We now continue to check this node's ancestors - as long as we reach a marked node we cut it as well.
Even though there can be many ancestors, the amortized cost of decrease-key is O(1):
The potential function = #trees + 2*#marked_nodes. let c be the number of new trees added to the root list, then c-1 of them were marked. Also, the last call to cascading-cuts can mark an unmarked node.
So, the trees number increases by c, and the marked nodes number decreases by at least c-2. The change is the potential function is then c - 2(c-2) = c -2c + 4 = 4 - c.
The actual cost is O(c), and so the amortized cost = actual cost + change in potential = O(1)


I am an experienced spss user ( but not a statistician) and understand how to write the equation for or multiple linear regression and it's not clear to me how to do it for multinomial logistic regression I have looked up the usual online resources but none entirely make sense
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2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/).


Mathematics is the basic building block for everything around us and mathematic discovery has been at the forefront of every civilised society, from the primitive times to the modern technological age of today. Mathematics is the science of logic and teaches individuals that every problem has a solution.
Course Objectives and Content
The A Level Mathematics course is intended to urge students to build up a comprehension of science and numerical procedures. A Level Mathematics gives students an intensive establishment in the scientific instruments and procedures frequently required in the working environment. Considering the rationale and thinking aptitudes created by students, A Level Mathematics ensure the qualification is broadly respected even in non-numerical fields. Common A Level subject choices with Mathematics include: Mathematics, Chemistry and Physics; Mathematics, Biology and Physics and numerous more decisions.
A Level Mathematics offers learners with a decent comprehension of Mathematics the opportunity to study it at a much higher level. It gives a careful establishing in the numerical instruments and procedures frequently required in the work environment. The application of such procedures incorporates variable-based Mathematics, Geometry, Trigonometry and Analytics which collectively shape the essential elements of the subject.
Students that study A-Level mathematics have a wide range of courses that they can study in university. These include Mathematics and Statistics, Mechanical Engineering and many more.
For more information contact us now, and our experienced members of staff will be happy to talk you through your options and find the best A-Level options for you.
Exam Board and Specification Code: Cambridge International AS and A Level Mathematics 9709


Foundation Academy students excel at ACSI Math Olympics
Foundation Academy recently hosted the ACSI Winter Garden Math Olympics at its North Campus, where 221 students from eight schools competed.
A number of Foundation students took home ribbons for excelling in their divisions at the event. Students who earn a high percentage score and a first place ribbon in their division also earn a medal.
The event is sponsored by ACSI, the Association of Christian Schools International, which is Foundation Academy’s accrediting board. ACSI students around the world participate in this competition.


A while back I developed a mild obsession with pentagons (mathematical ones, not symbolistic!) It started when I discovered some beautiful (simple and to me, unknown) theorems of quadrangles, such as Varignon’s theorem. I already came across Miquel’s pentagon theorem, and wondered what other gems I could find.
Here is what I found: Pentagons (2.4 MB PDF).
My search was on the surface a bit disappointing: pentagons as such are not widely studied. I guess it is because some more general theorems (that apply to general polygons) contain the theory, and the specifics as applied to pentagons are not so interesting.
Nevertheless, I did discover a few theorems, and the journey took me into some very interesting corners of geometry; a very rewarding experience. I started to collect these into a document, which is shared below. It’s not comprehensive or complete; there are a few gaps.
(At some stage I may return to look at this again. In particular, there are many theorems of the type “if there is n, there is n+1”, which seems to me to hint at a very general theorem which can be used to prove a bunch of specifics.)
Also, when I started, I did not realise how many of the theorems will generalise to general polygons, so the collection looks a bit silly in retrospect (kind of like listing all the properties of the number 8 that equally apply to even numbers).
Even so, what’s done is done, and can perhaps satisfy someone else’s curiosity.


It's official! School has started again! Here at Bellevue School we have been experiencing many new wonderful and challenging changes. One such change is the beginning of this blog, a sign of how technology is an integral part of education.
The purpose of this blog is not just to keep us all up to date about the happenings in room A1, but also as a way for students to learn and practice technology skills that will be required of them one day as they enter the work force. I am excited by this shift in education.
Enough of the long-winded rambling! Onto some of the projects we have been working on these first few weeks of school!
To showcase what we learned, we made a solid shapes mobile, where we labeled how many sides (the flat parts), edges (the place where two sides meet), and vertices (place where edges meet) each solid shape has. They look great hanging in the classroom!


This WTF is documented but a WTF none the less:
If you compare two numerical strings, they are compared as integers.
. You need to add the definition of numerical strings to get the WTF:
Numeric strings consist of optional sign, any number of digits, optional decimal part and optional exponential part. Thus +0123.45e6 is a valid numeric value. Hexadecimal notation (0xFF) is allowed too but only without sign, decimal and exponential part.
. So for example
"15" == "0xF".


Using The Log Where It Does Not
Econometrical analysis is heart of any economic research. It won’t be fare if I do not give a glimpse about Econometrics; basically, econometrics is a special form of statistical analysis completely dedicated to the growth of economic research and in some cases it is distinguishable from standard statistical mathematics. The regime of econometrics is vast and new approaches are adding on day by day. Econometrics have the capability to give us subtle but meaningful insights through its computing and analytical power.
Sometimes obscuring models in some research activities make me anxious and pioneered me to think deeply about modeling issues. While attending a national seminar at a university I noticed a person presenting an econometric model with some indescribable move by making the natural logarithm operator common for all explanatory variables. Basically his model seems to be functionally miss-specified, i.e., the components of the model were erroneously presented. In this context, I am trying to reflect the dummies under the umbrella of natural logarithm.
Let’s kick off with the need for natural logs in a regression model. Natural logs are often used to show constant percentage regression models. For instance, with log wage dependent variable and education as
log(wage) = b0 + b1educ + u
a regressor we can say that wage increases by a constant percentage with every additional year of education. In addition, natural log can be used to obtain constant elasticity and semi elasticity regression model. In the above equation 100.b1 refers to as semi-elasticity of y with respect to x. if the education variable was log (educ), then we could have said b1 is elasticity of y with respect to x.


The Final Grade is made up of quiz grades, homework grades, journals, tests, projects, and performances.
Everything is averaged into a single letter grade (i.e. A,B,C,D,F,O).
Quizzes are out of 10 points. Every three quizzes equal a letter grade. For example, if a student received an 9, 10, and an 8 on three quizzes, that would equal 27 points. That in turn equals 90%. Therefore they would receive an A for those three quizzes.
Homework assignments are either given a check plus, check, or check minus. A check plus = work turned in early or extra effort, check = work turned in on time, check minus equals work turned in late or little effort. A letter grade is given after 5 homework assignments. The grading process is involved, but if you turn in all your homework on time you are quaranteed an A on your homework.
Journals are graded strictly on word count.
A=150 words or more
Every five journals are averaged into a letter grade.
Tests are given a letter grade.
Major papers are given two letter grades.
3 quizzes = 1 letter grade
5 homeworks = 1 letter grade
5 journals = 1 letter grade
1 test = 1 letter grade
major paper = 2 letter grades
Finally, all letter grades are converted to numbers.
Every A in the grade book equals 5 points
Every B =4 points
Every C = 3 points
Every D = 2 points
Every F = 1 points
Incompletes, no names and zeros = o points
All the points are added up, and then divided by the number of grades.
Lets say Joe Student had twenty letter grades in the grade book.
All his grades add up to 80 points.
I would divide 80 by 20 which would give the number 4.
In order to receive an A, a student must have a 4.5 or above
B=3.5 or above
C=2.5 or above
D= 1.5 or above
F= 1.49 and below
Therefore, Joe Student would receive a "B" in the class.


Lakeside’s math departments aim to challenge and inspire all students to reach their mathematical potential. We offer a wide range of courses and use a variety of teaching modes to meet the specific needs of Lakeside students. From grades 5 through 12, students are actively engaged in math – working together in groups, at the board sharing solutions, presenting to their peers, debating strategies, and creating a wide range of creative projects. In all courses, emphasis is placed on collaboration, problem-solving, computational thinking, and clearly communicating mathematical ideas and concepts.
We believe that strong math skills play an important role in becoming an engaged global citizen. A solid understanding of a wide variety of mathematical disciplines will enhance students’ abilities to understand their world, explore global issues, and promote social justice through the power of analyzing claims and communicating effectively with real data as well as through computational tools and approaches.
Middle School: A strong foundation
The goal of the Middle School math program is to provide a strong foundation in mathematics through challenging courses that are appropriate to the ages, abilities, and needs of our students. In addition to preparing them for future math endeavors, we want students to be excited by math’s potential for fun and creativity.
We aim to equip students with the mathematical skills of a competent citizen in today’s world.
These skills include the ability to model situations mathematically; to estimate and compare magnitudes; to interpret graphs and statistics; to calculate probabilities; to evaluate numerical and spatial conclusions; to solve problems mentally as well as with paper, calculator, and computer; and to communicate findings effectively. At all levels, students learn to work collaboratively as well as on their own.
Part of what you’re teaching is: What do you do when you encounter an obstacle? In the context of math class, that means helping students set high goals, helping them deal with the fact that sometimes you falter on the way to those goals, and helping them celebrate when they meet those goals. – Tom Rona, Middle School math teacher
The content of our grades 5-8 math courses is normally covered in grades 6 through 9 in other schools. Students progress from arithmetic skills and mathematical thinking through pre-algebra and conceptual frameworks, to algebra and trigonometry. In each course, students deepen their understanding of concepts and skills introduced in previous courses. In addition to our regular math curriculum, many students choose to engage in Math Club (5/6 and 7/8), where they can have fun exploring math and extend their learning through working on challenging problems alone or in groups.
Read more about Middle School math in the Middle School curriculum guide.
Upper School: From the basics to college-level
We offer a wide range of math and computer science courses at the Upper School so that students can be challenged at a level appropriate for them at every grade. Each course emphasizes collaboration, problem-solving, and clearly communicating mathematical ideas and concepts. Since 2015, computer science concepts and principles have been embedded in the math curriculum, reflecting Lakeside’s belief that programming is an important 21st-century skill.
Every Lakeside student gains experience with computer science and programming, even if they never take a computer science class.
For the majority of math courses, we offer regular, accelerated, and honors levels. Students work with their teachers to determine the right level for them each year, and students can move between levels. While only three years of mathematics are required for graduation, the majority of Upper School students take a four-year sequence of algebra 2, geometry, precalculus, and statistics or calculus. All levels of courses at Lakeside provide a firm foundation in mathematics and will prepare students for college math courses. Calculus and statistics courses will prepare students for success on AP tests.
A range of computer science course offerings include everything from an introductory level course for those with no prior experience in programming, to advanced project-based courses such as 3-D prototyping and printing. The program takes advantage of the region’s technology community: Through guest lectures, field trips, and other opportunities, students are exposed to real-world applications of computing technology, including its myriad uses in medicine, sports, robotics, architecture, music games, literature, apparel design, communication, and international development.
Read more about Upper School math and computer science in the Upper School curriculum guide.


KV Teacher Recruitment 2023 : Walk-In-Interview for KV NHPC Gerukamukh, Demaji, Assam has released recruitment notification for the recruitment of Contractual PGT, TGT, Primary Teacher, Instructor and Counsellor Teachers.
Interview Date: 16th February 2023 at 8:00 AM onwards
Recruitment Notification Details for KV Teacher Recruitment 2023
Subjects: Physics, Chemistry, Biology, Mathematics and Computer Science
Subjects: English, Mathematics, Social Science, Assamese Language
Subjects: Computer, Sports, Music, Arts & Craft
Documents needed with Application Form
Candidates must keep ready self attested copy of recent photograph and all relevant documents along the Application Form.
Important Dates of KV Recruitment 2023
Walk-In-Interview Date: 25th February 2023 at 8:00 A.M. onwards
For details visit official website https://gerukamukh.kvs.ac.in


After grading the most recent chapter test, a science teacher asks twelve of his 10th grade summer school students how long they studied for the test. Their answers, as well as their corresponding test grades, were recorded on a table and placed on a scatter plot. Use the line of best fit shown in the scatter plot to make a conjecture about the number of hours studied versus the resulting test grade. Answer in complete sentences.
The more time that they spent studying the higher their test grade was.


Today is March 14, 2015, or 3/14/15, or Pi Day to celebrants of the mysterious number π: 3.1415…
Yes, I know — it’s hokey, and who the hell cares anyway, besides engineers and math teachers and other geeks? It’s worth thinking about because π is one of the most useful numbers ever discovered — or invented, according to your point of view — and its usages and importance have evolved right along with the rest of mankind’s knowledge.
Π is defined as the ratio of the circumference of a circle to its diameter; if you have a circle with a diameter of exactly 1.0-foot, the distance around the circle is approximately 3.1415-feet. (I say approximately because π never resolves to an exact value; it is what mathematicians call an irrational number.) Since scientists and engineers model nearly everything as perfect instances of abstractions which don’t actually exist in nature — circle, line, triangle, sphere, catenary, and so forth — π makes an appearance in all sorts of counter-intuitive places, everywhere from chemistry to economics to cryptography.
Here is where it gets fun: If those geometric figures don’t actually exist in nature, if they are in fact human inventions created to simplify how we think about things, how is it that they are so useful for predicting so many real, physical events with great exactitude? Why do they remain useful for understanding and predicting matters that the first users of π could never have conceived?
Did humankind invent mathematics whole, or is mathematics something which is ‘out there’ and which humankind has discovered? What can it actually mean to say that the number π even exists?
The physicist Mario Livio says we started out by inventing numbers — two hands led inevitably to the concept of the integer 2, for example — but that, once invented, future mathematical work was constrained by the rules of the invention. Humankind invented two, say, but then discovered thirty-seven according to the rules created for integers. This sounds reasonable — at first — but if π is merely a tool, how can it answer so many different needs without modification? Why do entirely new branches of mathematics having no apparent relation to geometry continue to find π so useful?
This is no small matter; such questions had put mathematics in a deep philosophical crisis at the start of the last century: What is math?
Bertrand Russell argued that mathematics is a branch of logic, and co-authored with Alfred North Whitehead the 3-volume Principia Mathematica to prove it. Whether or not he succeeded remains to this day a subject of dispute, but whenever an exasperated math teacher exclaims “It’s just logic,” she is quoting Russell.
Remember the Pythagorean theorem? That the square of the hypotenuse of a right-triangle is equal to the sum of the square of its sides? That finding was disbelieved for centuries because the ancients had no concept of any number other than integers; real and irrational number were unknown to them. How, then, could the length of the hypotenuse of a right-triangle having legs equal to one be equal to the square-root of two? What could it mean to even speak of the square-root of two?
When different types of numbers were discovered, or invented, and π, insinuate themselves into even religious disputes.
And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.
1 Kings 7:23
This is quite clear: the ratio of a circle’s circumference to its diameter is 3; inerrantists lose. “N-o-o-o,” they will answer. “Those measurements are inherently inexact and, besides, what about the thickness of the bowl? What if the diameter was measured to the outside the bowl, that is, and the circumference was measured around the inside of the bowl?” Increasing the diameter, the denominator, and decreasing the circumference, the numerator, pushes the ratio downward toward 3. Explain that the author had to mean 3, however the measurement was made, because only integers were known, or invented, at the time Kings was written, and they’ll exult that the verse then proves the divine inspiration of the text, because what else could explain that the ancients got it right?
Have I ever mentioned that the average apologist is a hopeless idiot?
So, Happy Pi Day. If you figure it all out, I’d be grateful if you let me know what you came up with.