Acc 560 week 1 homework chapter 1 (e1-5, e1-9, e1-10 and e1-2a) e1-5 e1-5 gala company is a manufacturer of laptop computers various costs and expenses associated with its operations are as follows. Chm151 name: chapter 1 homework – 10 points show all work for full points 1 (1 pts) determine if the following is a chemical or physical change: a. Holt algebra 1 - rochester city school district 1.
Powered by create your own unique website with customizable templates get started. Martin-gay prealgebra edition 5 381 chapter 1 12 1 words 2 standard form 3 expanded form 4 period 5 place value 6 whole 7 ten 8 thousand 9 ten thousand. Chapter 1 solutions 1 chapter 1 financial statements and business decisions answers to questions 1 accounting is a system that collects and processes (analyzes, measures, and records) financial information about an organization and reports that information to decision makers.
Algebra 2 help click your algebra 2 textbook below for homework help our answers explain actual algebra 2 textbook homework problems each answer shows how to solve a textbook problem, one step at a time. 11: variables and expressions: skills practice: p1: practice: p2: 12: order of operations: skills practice: p3: practice: p4: 13: properties of numbers: skills. Mgt 302 quiz chapter 1 (indiana) _____ is the most widely spoken language in the world, and is increasingly becoming the language of international business bribes are legal payments meant to facilitate performance of duties that the recipients are already obligated to perform.
As a current student on this bumpy collegiate pathway, i stumbled upon course hero, where i can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students. Bundle: college accounting, chapters 1-24, 11th + working papers study guide, chapters 1-12 + working papers with study guide, chapter 13-24 11th edition author: douglas j mcquaig , cathy scott , tracie l nobles , patricia a bille. Chapter 1 answers to concepts review and critical thinking questions 1 answer is that there is a market for executives just as there is for all types of labor executive compensation is the price that clears the market the same is true for athletes and microsoft word - chapter 1 homeworkdoc. I 01 a sprinter, starting from rest, accelerates to 642 m/s in 135 s what was his average acceleration 02 a truck moving 800 km/h has the brakes applied causing it to slow down to 600 km/h in 620 s.
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LinearRegression Analysis and Interpretation
Linearregression is a significant tool in statistical methods and analysis.It involves establishing the relationship that exists between two ormore variables. The method involves dependent (response) andindependent (predictor) variables. The dependent variables, which arecontinuous, are explained by the independent variables which can becontinuous (age), binary (either male or female) or categorical(social status) (Schneider et al., 2010). Linear regression can alsobe either univariate or multivariate. Univariate linear regressioninvolves the response variable and a single independent variablewhile multivariate methods involve the response variable and two ormore independent variables.
Theproperties of linear relationships enable them to have diverseapplications in different fields ranging from medicine, business tobanking. These properties and the relationships established areimportant as they help in the forecasting of future trends andpossible identification of prognoses and risks. The univariate linearrelationship is of the form Y=B0+B1X where y represents the responsevariable, B0 is the y-intercept of the line, B1 is the slope of theline, and X is the independent variable. An X input in the regressionline equation yields a corresponding Y output (Seber & Lee,2012).
Variousmethods can be used to analyze a given data set through linearregression techniques. In this case, using the data set for sales (X)and customer traffic (Y) provided in the template, the main variablecombinations required are XY, X2, and Y2. The product XY is computedby multiplying a given sales value with the corresponding number ofcustomers in a particular month. After calculating the XY values forall the twelve months, the sum of the XY values of the twelve monthsis found which gives us ∑XY equal to 1,122,727 as evident in theexcel sheet attached.
X^2,on the other hand, is found by squaring the number of customers foreach of the twelve months after which the sum over the months istaken to give the value of ∑X^2 totaling to 1,119,948. Thisrepresents the squared total number of customers visiting the companyin that particular year. The square of every month’s sales (inthousands of dollars), gives the values of Y^2 for the twelve months.Summation of the particular month’s Y^2 yields the required ∑Y^2which equals 1,145,268.
Themeans for the two data sets, that is, the number of customersvisiting the company every month and the month to month sales amountsare paramount for obtaining the values of the intercept, B0, and theslope B1. The mean of the customer traffic for the twelve months isobtained by dividing the total number of customers for the entireyear which is (∑X=3556) by twelve. This gives X-bar which equals296. The same case applies to the sales (Y) values where the sum forthe single month’s sales (∑Y=3644) is obtained, which is thendivided by the total number of months to get the average sales permonth for that year(Y bar=303.67).
Tofind the slope of the regression line, B1, the formula B1= (∑XY-n*Xbar*Y bar)/ (∑X^2-n*(X-bar) ^2) is fed into the formula bar of theExcel spreadsheet while the y-intercept is found by applying theformula B0=Y bar-B1*X bar. With the respective values of the slopeand the intercept of the regression line, that is, 0.6480 and 111.65respectively, the equation for the line thus becomes Y=111.65+0.6480X(Schneider et al., 2010).
Thedata for the sales and the customer traffic was used to obtain ascatter plot with sales on the y-axis and number of customers on thex-axis. A trend line was then fitted to the disconnected markers toget the line of best fit which is the required linear regressionline. The trend line equation, Y=111.65+0.648X, was then used to makepredictions for the future. Given the number of customers for each ofthe twelve months of year two assisted in forecasting themonth-to-month sales. It is obtained by feeding the number ofcustomers (X) in a particular month into the trend line equation toget the corresponding sales forecast (F(t)) for that month (Seber &Lee, 2012).
Withthe actual data for the year two sales provided, the variance foreach month was then obtained from the differences between the actualsales and the forecasted sales. From the variances obtained for thetwelve months, it is quite evident that in most of the months, thelinear regression line equation forecasted sales that were more thanthe actual sales. This was specifically the case in eight out of thetwelve months. The actual sales for the four months were more thanthe forecasted sales including March, April, September and Novemberwith variances of $43,000, $800, $10300 and $900 respectively.
Inabsolute terms, the difference between the actual and the forecastedsales for the month of April provided the largest variance value($43,000) while that of March gave the smallest variance ($800). Theactual sales in April were $384,000 compared to the forecasted salesof $341,000. The mean monthly variance of -$6,800 implies that onaverage, the actual sales were less than the forecasted sales by$6,800 for each of the twelve months. The average for the actualsales were obtained by summing up the individual sales for each ofthe twelve months divided by the total number of months, in thiscase, twelve. On the other hand, the average forecasted sales werealso obtained in a similar manner by adding the sales for each of thetwelve months and dividing the results by twelve. The mean variancefor the twelve months was then obtained by getting the differencebetween the average of the actual sales and the average for theforecasted sales.
Thecorrelation coefficient for the data set was found to be 0.84735. Itevaluates the degree of association between two data sets, in thiscase, the sales and the number of customers and represents thestrength of the relationship between the two (Seber & Lee, 2012).The correlation coefficient of 0.84735 depicts a close relationshipbetween sales and customer traffic making the corresponding linearregression equation a significant fit.
Witha correlation coefficient of 0.85, the linear regression equation isthus reliable in making future sales predictions. ABC furniture canthus be able to forecast sales for a particular future date providedthat the data for the corresponding number of customers(X) isavailable.
Theregression equation, Y=111.65+0.648X, implies that an additionalcustomer would increase the amount of sales made by $648. If nocustomer visits the company, the sales for the company would then becapped at $111.65 ($000) which represents the y-intercept of thelinear regression equation (Schneider et al., 2010). ABC FurnitureCompany, therefore, should aim at employing ways of increasing thecustomer traffic to the company. There are various ways of doingthis. Some include investing in sales promotion methods such asadvertisements, discount offers, and product quality improvements.
Schneider,A., Hommel, G., & Blettner, M. (2010). Linear RegressionAnalysis. DtschÄ rztebl Int, 107,776-782.
Seber,G. A., & Lee, A. J. (2012). Linearregression analysis (Vol.936). John Wiley & Sons.


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(11-03-2016, 10:12 AM)malmon Wrote:(11-03-2016, 06:36 AM)Yuka Wrote:(11-03-2016, 04:59 AM)malmon Wrote:
Woah woah woah, hold on just one goddamn second. Our maths teacher never said anything about logs of negative numbers! You must be mad!
Logs of negative numbers are not 'real' numbers, they're 'complex' numbers, i is also a complex number so when I divide by it the complex number become a real number Pi :p
Yeah, for some reason I never remember learning about negative Logs, which I find rather odd. Oh well.
Not that unusual, cause from this graph you can see the log of a negative number doesn't exsist (or better yet, isn't a real number) and actually learning about logging to get complex numbers brings in stuff from calculus and pure maths which isn't really a good idea.


In Who Cooked Adam Smith’s Dinner, Katrine Marçal traces the roots of mainstream economics and particularly neoliberalism. One of the strands she discusses is the the connection between economics and Newtonian physics. Newton believed that the universe was made up of fundamental particles. To understand complex physical things, you have to break them down into smaller and smaller pieces until you hit the unit of everything, the Lego blocks from which the universe is constructed: the atom and the photon (Newton thought the photon was a particle). From there you can work towards an understanding of the cosmos.
Particles are governed by forces. For Newton, the important force was gravity. The ultimate particle and the ultimate force can be used to explain a lot of the physical phenomena which we can observe with simple tools. Newton’s theory is deterministic: the future is predictable because particles only move in accordance with rigid laws.
In economics, the atom is the individual. The force that sets those atoms into motion is self-interest.
I’ve made passing reference to this before, but Marçal’s book brings it to the forefront. Most of the time when we hear about the history of economics after Smith, we hear about the math stuff, frequently starting with the idea of marginal utility generated by William Stanley Jevons around 1870. Jevons was a mathematician, who set out to create equations for the calculus of pleasure and pain as described by Jeremy Bentham. The subsequent history of economics can be read as a long math exercise using mostly calculus, and linear algebra (matrices) for modeling.
The thing is, math was just being formalized in the 1800s. Riemann completed the formalization of the calculus in 1854 (here’s an interesting history.) Other areas of math were being developed and formalized at that time, and development continues today, with, for example, fractal math. So maybe a good question is why economists stick with 19th Century math. Can’t they find something new that might work better than the obviously lousy models they use today that were incapable of predicting the Great Crash? I mean, how could anyone think it makes sense to model human beings as a large number of identical particles that only interact in monetary transactions and are otherwise unaffected by each other; and all of which are subject only the force of self-interest?
But just as math has advanced, so has physics. One of the changes is that physicists aren’t searching for ultimate particles any more; in fact as we currently understand things, we aren’t even sure the things studied are in some particular place. Physicists now study the relationships between various kinds of forces. They describe elementary particles by the forces through which they interact which in turn are defined in math terms, and terms that are a lot further from calculus than calculus is from addition. The relationships are mediated through the Schrödinger equation; It describes our observation small numbers of what we think today are elementary particles, but it is too hard to solve it for any large group of particles.
But in economics, nothing is complicated. It’s just individuals motivated by self-interest. And that’s a remarkably stupid thing. Has nothing changed in the last 150 years? Is linear algebra, which we learned in my junior year in high school, all these guys have learned from math and physics?
To put this another way, if economists were just cranking up their discipline today, with no theory of our current form of economy, they certainly would not use 19th C. math and physics as models. Would they use 18th C. markets in England and Scotland as their model? Of course not.
Fortunately I’m here to help. I’m happy to let economists continue the work of defining and collecting economic statistics, but it’s time to look for a more plausible theory. And as a starting place, I’ll put up a couple of posts with ideas for a new theory for the 21st C. No need to thank me. Which they won’t.


When it comes to real estate investing, the term “other people’s money” (OPM) is used quite a bit. There’s a good reason. Savvy investors want as little of their own money invested as possible; they finance income producing assets as much as possible with other people’s money.
Credit is a fact of life for most Americans. We have mortgages for our homes and loans for the cars we drive. So why would you want to take out a mortgage on a rental property if you can buy it outright? The answer lies in rate of return on investment (ROI).
ROI, or the “cash on cash” ratio, of an investment is derived by taking the net profit (income minus all expenses) divided by how much of your own money is invested.
If you were to invest the cash in the stock market, your rate of return is how much that money earns for you in dividends and appreciation of the stock’s value (although there are issues with this overly simple analysis which we’ll cover later – but for now, this explanation is ok).
Investing that same cash in a certificate of deposit provides a set rate of return determined by the bank (X percent over X time period, a fraction of a percent in most CDs).
When investing that cash in income producing real estate, you need to know how much money your personal dollars invested will generate (cash on cash). The math doesn’t lie: as you decrease the amount of money you have personally invested, your rate of return goes up.
Let’s say you have $100,000 that you would like to invest and you are looking at a property that will cost $100,000 inclusive of closing costs (sales price is $95,000 and $5,000 in closing costs). On an annual basis the property generates $18,000 and expenses are $8,000. Net profit would be $10,000. The cash on cash rate of return is 10% ($10,000 cash generated / $100,000 cash invested = 10%).
Using that same property, if you put 20% down ($95,000 x 20% = $19,000) plus closing costs your total cash invested is $24,000. You still have $76,000 to invest elsewhere. A commercial mortgage for $76,000 ($95,000 minus $19,000 down payment) on the property would be $501.57 assuming 5% interest with a 20 year term. (30 year mortgages aren’t available to you unless you’re purchasing this property personally. In the world of commercial investing, 20 year terms are standard, but there are ways around that too!). On an annual basis the property generates $18,000 and expenses are $8,000 plus the annual mortgage payment is $6,018.84. Net profit would be $3,981.16. The cash on cash rate of return is 16.6% ($3,981.16 cash generated / $24,000 cash invested = 16.6%).
Not only do you now have a 60% greater return on the first $24,000 of your $100,000 by using other people’s money than if you had paid in full with your money, but you still have $76,000 to invest in other properties to generate more revenue. If you are able to replicate this purchase three more times your $100,000 invested this way would give you an annual return of over $15,900 as opposed to the $10,000 annual return by using only your money.


- Linear Transformations and Their Representing Matrices by David Webb
A motivating problem for vector mathematics.
The following problem appears in structure building for molecular modeling. The 20 common amino acids are joined into polypeptides by attaching the C-terminus of one amino acid to the N-terminus of the next. Each joint has a specific orientation in 3D space (determined by the amide plane).
Here, we tackle a smaller instance of this problem. You are building a series of 2D figures by joining together the edges of smaller 2D figures. At each joining point, an orientation is specified in terms of local x and y directions. When joining A and B, for example, the ending orientation of A must match the starting orientation of B. We choose to rotate and translate B to make this happen.
This phrasing is partially motivated by a fun little language for composing 2D figures . Its solution involves important concepts for determining relative positions and orientations using vectors, and should be generally useful for any problem involving geometric relationships.
The following code outlines a class structure for holding each object. Two basic functions to implement are figure visualization (vis, below) and the joining process. Before the next class, try and implement the joining operation yourself!
- Holds shape class
from numpy import * import pylab as plt
- not used, since it's just a single array
- class Pt:
- position + orientation (6 numbers)
- v = array([[A00, A01, t0],
- [A10, A11, t1]])
- A00, A10 is local x-direction
- A01, A11 is local y-direction
class Shape: # lines : [ t1, t2 ] (list of lines in object), t1 : 2D vec # REDO -- lines : one giant array # pts x 2 (st/end) x 2 # # rt : Pt (right sticky point) def __init__(self, lines, rt): self.lines = lines self.rt = rt def __add__(a, b): # return r = a + b print "TODO: implement addition" # 1. determine rotation matrix that attaches # b at origin onto a.rt
# 2. transform all of b's lines and # add them to a.lines -> r
# 3. fix r's right endpoint # by combining a's end with b's end return r
- vis : Shape -> pylab state
- do visualization using pylab
- Note: This is not a method inside Shape since pylab is not really related
- to the properties of the Shape class.
def vis(s): # loop through lines and call plt.plot() on each one. for line in s.lines: st_x, st_y = line en_x, en_y = line plt.plot([st_x, en_x], [st_y, en_y], 'k-', lw=2)
# extra lines to represent endpoint of the shape
st_x, st_y = s.rt[:,2] en_x, en_y = s.rt[:,2] + s.rt[:,0]*0.2 plt.plot([st_x, en_x], [st_y, en_y], 'r-', lw=2) # local x-dir st_x, st_y = s.rt[:,2] en_x, en_y = s.rt[:,2] + s.rt[:,1]*0.2 plt.plot([st_x, en_x], [st_y, en_y], 'b-', lw=2) # local y-dir
xh = array([[0,0], [1,0]]) # line from 0,0 to 1,0
yh = array([[0,0], [0,1]]) # line from 0,0 to 0,1
triangle = Shape(array([xh*2, [[0,0], [1,1]], [[2,0], [1,1]]]), array([[ sqrt(0.5),-sqrt(0.5), 1], [ sqrt(0.5), sqrt(0.5), 1]])) square = Shape([xh, xh+array([0,1]), yh, yh+array([1,0])], array([[1,0, 1], [0,1, 1]]))
- a = triangle + square #
plt.plot([-1,2], [-1,2], 'w') # make the plot large enough to see
vis(triangle) plt.show() </source>
- Linear transformations
- Homogeneous coordinates
- Composing linear transformations
- Inverse operations, implicit solutions, and complexities
Homework - Due Wed., Nov 5
- I have a linear transformation that maps vectors in <math>R^m</math> to vectors in <math>R^n</math>. It is represented by a matrix (an <math>n \times m</math> array). I want to specify it in terms of how it acts on a set of starting vectors (in <math>R^m</math>). How many starting vectors do I need to transform for a complete specification? Is there an easy way to choose them?
- Say that I wanted to have several "sticking points" for each object. What modifications would have to be made to the Shape class? What does this mean for the __add__ operation?
- I have two objects in 3D, each with a 3x3 orientation matrix, A for object A and B for object B. What is the rotation matrix for rotating elements attached to A (specified in A's coordinate frame) to match elements attached to B (specified in B's coordinate frame)?
- Coordinate frames always should have the property that each vector is normalized (<math>v_i \cdot v_i = 1</math>) and orthogonal to all the others (<math>v_i\cdot v_j = 0</math>). Matrix multiplication transforms objects in the coordinate frame to objects in the global frame. What does matrix multiplication do if the "coordinate frame" has a vector that is not normalized? What if it has 2 vectors that are not orthogonal?
- The following function takes points in 2D space and fits them to a line of the form y = a*x + b. Use it to write a function that takes points in 2D space and returns an orientation matrix describing the best fit direction as "x hat" and the other direction as "y hat".
<source lang="python"> from numpy import * import numpy.linalg as la
def fit(xy): # xy is an N x 2 array of points
V = xy.copy() # 1st col is x (linear term), a V[:,1] = 1.0 # 2nd col is 1.0 (constant term), b Vy = dot(xy[:,1], V) # sum x_i y_i and sum y_i Dx = dot(transpose(V), V) # Vandermonde matrix a, b = la.solve(Dx, Vy) # solve Dx * [a,b] = Vy return a, b
x = arange(12) # test the function! y = x*12 - 2.0 + random.random() - 0.5 print fit(transpose([x,y])) </source>


PBS KIDS RELEASES FIRST APP FROM NEW SERIES ODD SQUAD
Blob Chase, the first mobile app from ODD SQUAD is now available!
Available for iPad, Android tablets and Fire tablet, ODD SQUAD Blob Chase extends the adventures and humor of the series, as kids chase and recover blobs that have escaped their containers and are on the loose in Odd Squad headquarters. The new app encourages kids to use math skills to investigate and solve problems, just as the agents do in the new series. ODD SQUAD, which premiered in November 2014, airs weekdays on WUCF's PBS KIDS and offers games, videos and more at pbskids.org/oddsquad. The app debuts in tandem with an all-new on-air special: “Odd Squad Saves the World,” which premieres Monday, January 19, on PBS KIDS.
“PBS KIDS offers children connected educational media experiences across platforms,” said Sara DeWitt, Vice President, PBS KIDS Digital. “The Blob Chase App builds on one of ODD SQUAD’s episodes, in which a blob escapes and separates, and the agents have to work together to collect all the pieces. In the app, kids use math to solve this odd problem, extending what they have learned through watching the show by practicing the same skills in a mobile experience.”
The ODD SQUAD Blob Chase App includes 60 levels of gaming in which kids use math skills to get blobs across bridges, over walls, through tubes and eventually back into their containers. To discover which gadget will work best for each particular challenge, kids problem-solve using addition, subtraction, multiplication and division.
Blob Chase is available for $0.99 for a limited time on the App Store for iPad or at www.AppStore.com/PBSKIDS. The app is also available for $0.99 for a limited time on Fire tablet on the Amazon Appstore: http://to.pbs.org/kidsappsamazon and Android tablets on Google Play: http://to.pbs.org/kidsappsplay.


GPS radio occultations allow the sounding of the Earth's atmosphere (i.e. troposphere and ionosphere). The basic observable of this technique is the additional delay, due to the refractivity index, of a radio signal when passing through the atmosphere. This additional delay is proportional to the integrated refractivity, in such a way that we can obtain an estimation of the vertical refractivity profiles using observations at different elevation angles by solving an inverse problem. Traditionally, the solution of this inverse problem is obtained by using the Abel inversion algorithm assuming a refractivity index that only depends on the altitude. In this paper we present a modified Abel inversion algorithm for ionospheric sounding that overcomes the spherical symmetry assumption of the traditional Abel inversion algorithm. Processing a set of simulated data and 1 day of real data with this algorithm, a clear improvement over the traditional one can be obtained when comparing the derived critical frequencies with the ionosonde measurements. It is also shown that this improvement is sufficient to measure critical frequencies associated with the ionospheric E layer.


Posted by at 7:40 PMBing and Wolfram Alpha, the Decision and Answer engines are working together as reported in August this year that they are planning to have Wolfram Alpha's results appear in Bing search results.
Now with Wolfram's Alpha computational knowledge integrated into Bing, search results relating mathematical formulas, nutritional information or body mass index (BMI) will be displayed.
Why is Bing implementing this integration? Here's a short quote from Bing's blog:
"So what are we doing? Well, we‘ll be providing access to Wolfram|Alpha’s advanced algorithms and expertly curated data within the Bing experience. This new and exciting work is completely aligned with our broader goal of enabling faster, more informed decisions. Specifically, we will bring nutritional information and tools into Bing’s search results, as well as some straight up hard math and homework help."
Take a look at some picture of Wolfram Alpha's integration with Bing (images via Bing blog):


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General form of a factorable polynomial
This paper provides extension to the types of factoring of polynomials to illustrate the fact that multiplication with polynomials has no restrictions when it comes to the number of terms so does factoring. It aims to develop students’ perception about polynomials and to motivate them to continue discovering factorable polynomials.that are new to us.The idea originated from the expression x4 + x2 y2 + y4 which is a product of x2 + xy + y2 and x2 – xy + y2. Factor theorem, rational zeros of a polynomial, and symmetric and transitive properties of real numbers were used in this study in proving other factorable polynomials. The contents include the difference of perfect nth powers (ax)n – (by)n, the trinomial of the form xn + (xy)n/2 + yn, and the general form of a factorable polynomial p(x) = xn + xn – d yd + xn – 2d y2d + … + x2dyn – 2d + xdyn – d + yn for some positive integers n and d with a and b as real numbers.
Leithold, Louis. (1992). College Algebra and Trigonometry, (pp. 590, 597 – 604). Canada: Addison – Wesley Publishing Co., Inc.
This work is licensed under a Creative Commons Attribution 4.0 International License.


A two-day conference entitled “Mathematics Education” and initiated by Armenian State Pedagogical University in collaboration with the State Committee of Science and National Institute of Education started at ASPU on October 18.
The international conference brought together representatives of various universities from Russia, Belarus, Ukraine, as well as representatives of various scientific and educational organizations of Armenia, leading specialists of the field, lecturers, teachers and students.
Welcoming the participants of the sixth conference on Mathematics, Srbuhi Gevorgyan, ASPU Vice-Rector for Educational and Scientific Affairs, underlined the importance of Mathematics in science and education. “Each Mathematics teacher also deals with the current demands, changes and issues of pedagogical science. Methods and means of teaching change with changes in pupils,” said the vice-rector.
Srbuhi Gevorgyan highlighted the participation of foreign representatives in the conference, underlining that it would give an opportunity to share thoughts, experiences and approaches, make comparisons in order to reveal pupils’ inner world and peculiarities of the cognitive process.
Gevorg Baghdasaryan, an academician of the National Academy of Sciences of Armenia, stressed the importance of the annual conference and said it provides an opportunity to exchange thoughts, discuss topics and come up with new approaches.
“Great is the role of Mathematics in all spheres of human activity as all phenomena have mathematical formulation,” the academician said. He assured everyone that there are not traitors in mathematical sciences while devotees do not have concerns.
Professor Hamlet Mikaelyan, Head of the Chair of Mathematics and its Teaching Methods at ASPU, Doctor of Mathematics, focused in his report on the importance and value of Mathematics as a subject. “Mathematics has great potential for value formation,” Mr. Mikaelyan said.
The plenary session continued with reports with the participants focusing on the goals and forms of checking learners' knowledge, use of modeling and other methods as well as other issues related to mathematics teaching.


Due to Storm Ophelia Maths week was shorter than normal!
However that did not hamper the planned activities. The students participated in various activities that promoted their maths skills, a different perspective to maths in everyday life and fun games. Some students completed puzzles while others baked maths themed cakes. All students were invited to take part in the Maths Eyes competition where students take photos of the Maths in the world around them. The highlight of the week was a table quiz for all first years organised by the transition year students.
Winners will be announced next week. Well done to all involved. Click for photos


ASHLEY JUDD – GRZEXP.com Staff
You know what your own math class is like, but would you like to take a peek inside another math classroom?
All is silent in room 114 as students in Mrs. Reyes’ third hour math class aimed to complete a quiz.
When finished, students lined up in the back of the room to get quiz corrections.
Mrs. Reyes talks with the students over missed questions, then sends them back to their desk to fix mistakes that may have been made.
Everyone is focused as they continue working tirelessly to finish with a satisfying score.
This brief glance into a different, new, and interesting math class was hopefully an enjoyable sneak peek into another classroom!
All Images taken by Ashley Judd


Doing math is a pain in the head;
At least that’s what we’ve all learned in dread.
But it’s not math that hurts,
A brain-scan asserts;
It’s fear itself hurts us instead.
Lyons IM, Beilock SL (2012) When Math Hurts: Math Anxiety Predicts Pain Network Activation in Anticipation of Doing Math. PLoS ONE 7(10): e48076. doi:10.1371/journal.pone.0048076


Sam Rockford, a math teacher at St. James Academy in Lenexa, Kansas, was named one of three finalists from the state of Kansas for the Presidential Awards for Excellence in Mathematics and Science Teaching. According to their website, “The Presidential Awards for Excellence in Mathematics and Science Teaching (PAEMST) are the nation’s highest honors for teachers of mathematics and science (including computer science). Awardees serve as models for their colleagues, inspiration to their communities, and leaders in the improvement of mathematics and science education” (paemst.org).
Rockford recently finished his ninth year teaching at St. James and had previously taught at North Kansas City High School for nine years and Shawnee Mission Northwest for one. When asked about the award, he said, “I am humbled to be selected…I would like to thank the wonderful people who helped me throughout the application process. It was long and time-consuming involving a deep self-reflection of my beliefs of teaching. But as I wrote, it became less about mathematics and instructional methods, and more about my love of working with teenagers. I count my blessing every day to work at St. James with incredible kids and the greatest high school staff in the world.”
Andy Tylicki, president of St. James, said of Rockford, “There’s no doubt that Sam is an extraordinary teacher in the classroom, but his commitment to the mission of our school is what is most inspiring about him. He is a man of great faith, he stays focused on his family, and he is always striving to give his very best to his students on a daily basis. He has deeply impacted so many lives within our community, kids and adults alike.”
Sam is married to his wife Melissa and is a father to his eight-year-old daughter Maggie and four-year-old twins Sammy and Joe Mike. In addition to his teaching position, he has served as department chair at St. James and moderator of several clubs.
See the press release from KSDE here.


Using a binomial probability calculator, you can input the desired values for n, k, and p to compute the probability of achieving k successes in n trials. The main difference between the normal distribution and the binomial distribution is that the binomial distribution is discrete, while the normal distribution is continuous. It means the binomial distribution is the limited number of events whereas the normal distribution has an infinite number of events.
A standard six-sided die has k possible outcomes, with each outcome having an equal chance of occurrence (1/6). However, dice rolls can also be converted into a binomial experiment; for example, by defining success as rolling a specific number, such as 6, and failure as not rolling the target number. It’s essential to understand that the binomial probability distribution is a discrete probability distribution, meaning that it consists of distinct, non-overlapping outcomes. This is in contrast to continuous distributions, which have a continuous range of possible outcomes.
Understanding Binomial Distribution
To calculate cumulative probabilities, one can use the binomial probability mass function (PMF) in combination with the binomial coefficient. Using the binomial probability formula and calculator, we can determine the probability of obtaining exactly 5 heads in 10 coin tosses. Note that to use the https://personal-accounting.org/binomial-distribution-calculator-binomial/ effectively, the events you analyze must be independent. It means that all the trials in your example are supposed to be mutually exclusive. A binomial distribution’s expected value, or mean, is calculated by multiplying the number of trials (n) by the probability of successes (p), or n × p.
A binomial probability calculator can compute the binomial distribution, probabilities, mean, variance, and standard deviation by inputting the number of trials, success probability, and the desired number of successes. This tool helps answer questions related to binomial experiments, such as probability distributions, cumulative probabilities, and distribution curves. In addition to calculating probabilities, the binomial probability calculator can also compute standard deviation, variance, and expected value for a binomial random variable. These calculations are crucial in determining the shape and spread of a distribution curve, as well as the likelihood of specific outcomes.
- For instance, one might calculate the probability of rolling a 6 twice in 10 tosses or the chance of rolling at least one 6 in 10 tosses.
- Use this binomial probability calculator to easily calculate binomial cumulative distribution function and probability mass given the probability on a single trial, the number of trials and events.
- That allows us to perform the so-called continuity correction, and account for non-integer arguments in the probability function.
It’s also used in the insurance industry to determine policy pricing and assess risk. Probability that at least 1 doesn’t use a computer at work is same as the probability that none use computer at work. Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. Statology Study is the ultimate online statistics study guide that helps you study and practice all of the core concepts taught in any elementary statistics course and makes your life so much easier as a student. Interestingly, they may be used to work out paths between two nodes on a diagram.
A continuous distribution, like the normal distribution, maps the probabilities of continuous events, which have infinitely many possible outcomes. Although it is different from the discrete probability distributions such as the binomial distribution, it’s useful to compare their main characteristics. Binomial distribution calculator is used to find the probability and cumulative probabilities for binomial random variable given the number of trials ($n$) and probability of success ($p$). It also calculate mean of binomial distribution,variance of binomial distribution. A binomial experiment is a statistical experiment consisting of a fixed number of trials, each with two possible outcomes, success or failure.
Such questions may be addressed using a related statistical tool called the negative binomial distribution. Make sure to learn about it with Omni’s negative binomial distribution calculator. This is a sample problem that can be solved with our binomial probability calculator. This is all the data required to find the binomial probability of you winning the game of dice. When working with dice rolls, it’s important to consider the discrete distribution, as there is a finite number of possible outcomes.
Test Sensitivity Calculator
The same goes for the outcomes that are non-binary, e.g., an effect in your experiment may be classified as low, moderate, or high. The binomial distribution is the probability distribution formula that summarizes the likelihood of an event occurring either A wins, B loses, or vice-versa under a given set of parameters or assumptions. Use a binomial CDF calculator to get the standard deviation, variance, and mean of binomial distribution based on the number of trails you provided. Here’s a comprehensive example that describes how a binomial distribution calculator works which can be helpful for determining the binomial distribution manually if required. One of the most exciting features of binomial distributions is that they represent the sum of a number n of independent events. Also, you may check our normal approximation to binomial distribution calculator and the related continuity correction calculator.
Binomial Distribution Calculator with Steps by Steps Solution
A binomial distribution depends much more on the number of trials or observations done. At the same time, each trial defines its own probability of outcome value or, in other words. A binomial random variable is a successful outcome of x in n number of the repeated trial of a binomial experiment. In contrast, a binomial random variable’s probability distribution is also known as a binomial distribution. To calculate binomial probabilities in specific scenarios, one can use the binomial probability formula or the binomial distribution calculator. The calculator can typically handle all the types of questions discussed in the Cumulative Probabilities subsection.
Using a binomial distribution calculator, one can find the probability of a specific number of successes, as well as cumulative probabilities and expected values. This is essential in answering questions related to coin tosses and statistical analysis. In summary, binomial probability calculators and the concepts related to binomial distributions are crucial in addressing questions and problems related to coin tosses and dice rolls. These tools and concepts aid in accurately analyzing the data and understanding the nature of such probabilistic experiments.
This is the case of the Wheatstone bridge network, a representation of a circuit built for electrical resistance measurement.


Applying a COGS formula to determine profitability is useful in evaluating business costing methods. The cost to complete a sale to the customer exceeds the cost of acquiring the product (or materials to make that product). Between the time goods are received and delivery of the product to the customer, the business incurs direct expenses which include cost of raw materials, labor, assets, etc. All these costs should be proportionately added to the cost of each product sold when tracking inventory movement at your business; however, overhead costs are not calculated into COGS.
The Cost of Goods Sold Formula:
Beginning Inventory (inventory at the beginning of the time period) + Purchased Inventory (inventory acquired during the time period) – Ending Inventory (inventory left at the end of the time period) = Cost of Goods Sold
All the above figures in the COGS equation should represent the same time period, i.e., calculate these numbers on a monthly, quarterly, or yearly basis for the same dates. To calculate the cost of goods sold, you will attribute accumulated direct costs with each inventory stage.
SOS Inventory makes it even easier with COGs software functionality built in. The extensive reporting SOS Inventory provides exceeds cost of goods software feature needs.
COGs Formula Example:
here’s an example using the COGS formula (Cost of Goods Sold) for a hypothetical company called “XYZ Electronics.”
XYZ Electronics sells smartphones. Let’s assume the following information:
- Beginning Inventory: $100,000
- Purchases: $400,000 (total cost of new smartphones purchased during the year)
- Ending Inventory: $80,000 (value of unsold smartphones at the end of the year)
- Additional Expenses: $50,000 (other costs associated with the production and sales)
Now, let’s calculate the Cost of Goods Sold (COGS) using the formula:
COGS = Beginning Inventory + Purchases – Ending Inventory + Additional Expenses
COGS = $100,000 + $400,000 – $80,000 + $50,000 COGS = $470,000
So, the Cost of Goods Sold for XYZ Electronics for the year would be $470,000. This represents the total cost of the smartphones sold during the year, including the beginning inventory, new purchases, ending inventory adjustments, and additional production expenses.
A cost of goods sold formula example is as follows:
If the business starts off with 100 units, then buys 50 units and sells 25 units, the cost of goods sold is the cost of 100 units plus the cost of 50 units less the cost of 25 units which equals the cost of 125 units.
In accounting, costs of goods sold reveals the costs associated with generating revenue from a product. These costs will vary from one business to another. If referring to a manufacturer, these costs can include ingredients or parts, labor, assets, storage, and shipping.
Overhead is calculated separately as these costs tend to be regular monthly costs such as rent, electricity, internet service, etc. which have no impact on product volume. COGS is tied directly to inventory quantities and therefore can vary if the costs to sell an individual unit change.
Understanding the actual cost of goods sold allows your business to do a better job of pricing product or staying aware when costs to produce that product change. As sales increase so, too, do the costs of goods sold because costs will continue to be tied to selling those products. Normal accounting practices indicate the accrual of COGS during the same period as when they are sold.
Tracking cost of goods sold, gross profits and revenue available for overhead is simple to do with SOS Inventory. SOS Inventory records inventory costs and quantities at every stage so you can easily generate a report for any product to determine costs for the time period selected.
What’s more, SOS Inventory will update your QuickBooks Online account to ensure your ledger reflects your actual inventory costs on hand, giving you timely information at your fingertips.
No need for manual COGS formula calculations or cross-referencing multiple spreadsheets from different departments. SOS Inventory gives you the information you need to make product pricing decisions or analyze cost fluctuations.


An expert team of University of Florida scientists, surgeons, engineers and mathematicians have worked together over the last 10 years to lay the foundation for a systems biology approach to further our understanding of vascular remodeling and vein bypass graft failure. Prior strategies have focused largely on linear models to separately describe the physical or biologic components of vascular disease progression.
In order to significantly advance our understanding of the function of such complex phenomena, it is necessary to integrate different types of data and use quantitative models to predict behavior and outcomes. Our multidisciplinary team approach uses both experimental data and computational models to understand these dynamic phenomena. Such information is vital for translation to effective clinical strategies to enhance revascularization durability. Through use of these cutting-edge technologies, we seek to examine the physical and biologic microenvironments via multi-scale mathematical modeling to predict dynamic stability or progression toward an occlusive phenotype following injury to the vascular system. We are currently focusing our efforts in the following areas:
- Understanding the impact of wall forces on focal vein graft lesion growth, and applying multi-time scale modeling to predict graft success or failure.
- Modeling the interplay of physical forces and the regulators of inflammatory cell homing as they drive vein graft scarring.
- Translating these fundamental principles to the more complex human disease process to understand clinical vein graft failure.


Naval Surface Warfare Center Philadelphia Division (NSWCPD) began implementation of the National Defense Education Program (NDEP)-supported science, technology, engineering, and mathematics (STEM) initiative in 2008. The Command works with schools in the School District of Philadelphia and in surrounding counties within the tri-state region of Pennsylvania, New Jersey and Delaware. Schools range from inner-city, large suburban and small rural schools. STEM initiatives which have been undertaken in Philadelphia include festivals and science fairs, classroom activities, outside classroom activities, mentorship and internship activities, and teacher and science and engineering training. NSWCPD partners with various universities and organizations to carry out these programs and is continuously looking for new opportunities to contribute to the development of talent within science, technology, engineering and mathematics. For more information click on STEM Programs.


Bringing in young people to work in the shipyard industry is not an easy thing to do. There are other ways of making a living that aren’t as dirty, noisy, smelly and physically demanding as working in a boatyard, young recruits say. But those who take a shot at it may have built in roadblocks to success, including the inability to pass a drug test or a lack of understanding of simple mathematics, particularly working with fractions.
Author Kate Nonesuch of Malaspina University-College in Duncan, British Columbia, specializes in teaching basic math to young adults. She penned “Changing the way we Teach Math, A Manual for Teaching Basic Math to Adults.”
I asked her in an email if it was more difficult for an 18-20-year old to grasp basic math than an eight-to-10-year old.
“I would say no, other things such as basic intelligence and motivation being equal. However, 18-to-20-year olds who have been to school for 12 years or so, taking math all those years, and who come out still not knowing basic math, will have various resistances to learning it at this stage: feeling that math is boring, doesn't make sense, has no application in real life, and thinking that they are stupid about math and can't learn it,” said Nonesuch. “So the teacher has to deal with all those emotions and attitudes first. It makes no sense at this point to start again to teach them the same way that they have been taught in the past, because clearly that method didn't work.”
Then I asked how difficult would it be for shipyard officials to teach basic math skills to potential employees and how long would it take? “Using manipulatives and the techniques I outline at the end of ‘Changing the way we Teach Math’ I can teach this kind of student how to understand fractions, i.e., which is larger, smaller, more than half, less than half, changing from one denominator to another, etc., and to do basic operations with fractions in about 30 hours of teaching time,” she said. “Decimals and [percentages] another 20 hours. However, I cannot do this without working on emotions and attitudes along with the math.”
Nonesuch added that the best way for these students to learn is on the job, or at least in preparation for a specific job, so the math makes sense, has a purpose, and uses tools, materials and problems that pertain to that job. “There is a series of small books by Delmar Publishers, with math and math problems based on the needs of individual trades. The series is called ‘Practical Problems in Math’ with a different book for each trade,” she said.
Of course, sometimes a student is motivated to learn whatever it takes to get a good paying job such as those in a shipyard. Phil Callahan, president and CEO, SPARX Welding & Technology Institute, Houma, La., said he sees it a lot in students “whose wives or girlfriends become pregnant.”
Well, yeah, there is that.


|Search Results (75 videos found)|
|NASA Connect - FOFE - Plane Math Web Activity
NASA Connect segment involving students in a web activity featuring the Plane Math Website to teach students about aeronautical principles, geometric and algebraic math concepts, and aircraft design.
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|NASA Connect - MTF - Math and Wright Brothers
NASA Connect segment explaining ratios and proportions. The segment describes how these math concepts helped the Wright Brothers to invent the first flying machine.
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NASA Connect segment exploring microgravity and how the concepts of measurement, ratios, and graphing help scientists study all aspects of microgravity.
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NASA Sci Files segment exploring the fundamental concepts to designing an invention including doing research and recording detailed observations.
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|NASA Connect - TWM - Kite Student Activity
NASA Connect segment involving students in an activity investigating kites and their impact on the early stages of flight. The activity uses math concepts such as geometric shapes, aspect ratios,...
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NASA Connect Segment exploring the mathematical concepts estimation and measurement. The video relates these concepts to daily activities and to health and nutrition.
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NASA Connect segment involving students in an activity that uses concepts such as measurement, data collection, and graphing. The activity also studies the concepts of acceleration, position, and velocity.
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NASA Connect Segment that explores the safety of air travlel through new technologies. It also explains the math, science, and technology that NASA scientists use in their research.
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The Math EdVantage is a Diagnostic-Prescriptive Instructional Program that is designed to give your child the advantage in math education. It will eliminate math frustration and guessing! It will
bring math alive to your child!
Our FREE comprehensive, two-hour math evaluation diagnoses all skills and concepts from Kindergarten to Algebra. An education specialist will administer the tests-not a computer. An in-depth
analysis of the math evaluation will pinpoint the skill gaps that are causing your child to struggle in the math area. Since math is a subject that depends on pre-requisite skills, your child's
skill gaps have been allowed to "snowball" into even greater skill gaps.
The Math EdVantage at Process Learning Tutoring remediates and corrects all the diagnosed skill gaps. The math curriculum is uniquely designed to correlate math skills for faster mastery.
Your child will rediscover the joy of numbers and will have a strong foundation for the future study of mathematics.
Step-by-Step Processes help students guide themselves through every type of
math skill or concept...without the struggle.
Students will be able to verbally express their work step-by-step.
Associative techniques teach students how to relate math to their own daily lives...bringing math alive!
Proofs become the foundation of The Math EdVantage. Students are taught how to prove their answers on paper- not "in the air"; thus eliminating guessing.
Logical thinking skills and test-taking skills are other areas of emphasis in The Math
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The best accountability that proves the success of the EdVantage Math Program is involved with
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Learning Math Facts Can Be Fun!


The Math Book Clifford Pickover Pdf Download
Click Here ===== https://ssurll.com/2tvQSg
How to Download The Math Book by Clifford Pickover for Free
If you are looking for a comprehensive and engaging history of mathematics, you might want to check out The Math Book by Clifford Pickover. This book covers 250 milestones in mathematical history, from ancient times to modern day, with colorful illustrations, formulas, and real-world applications. You will learn about topics such as ant odometers, magic squares, the butterfly effect, prime numbers, dimensions, and much more.
But how can you get a copy of this book without spending a fortune Fortunately, there are some ways to download The Math Book by Clifford Pickover for free online. Here are some of them:
Internet Archive: This is a non-profit digital library that offers free access to millions of books, movies, music, and other media. You can find two versions of The Math Book by Clifford Pickover on this site: one published in 2009 by Sterling Publishing Co., Inc. [^1^], and another published in 2011 by Zenith Press [^2^]. You can either read them online or download them in various formats, such as PDF, EPUB, or Kindle.
ResearchGate: This is a social network for researchers and academics that allows them to share their publications, data, and ideas. You can find a PDF version of The Math Book by Clifford Pickover on this site [^3^], uploaded by the author himself. You can download it for free after creating an account or logging in with your existing one.
These are some of the best options to download The Math Book by Clifford Pickover for free online. However, please note that these sources may not be legal or authorized by the publisher or the author. Therefore, we recommend that you use them only for personal and educational purposes, and not for commercial or illegal ones. If you enjoy reading The Math Book by Clifford Pickover, please consider buying a copy from a legitimate source to support the author and his work.
If you want to learn more about the author of The Math Book, Clifford Pickover, you can visit his website at www.pickover.com. There you will find information about his other books, his research interests, his awards and honors, and his contact details. You can also follow him on Twitter at @pickover, where he posts interesting facts and puzzles about mathematics and science.
Clifford Pickover is a prolific author, inventor, and scientist who has written over 50 books on topics ranging from art and computers to philosophy and religion. He has a Ph.D. in molecular biophysics and biochemistry from Yale University and is an associate editor for several scientific journals. He holds over 100 U.S. patents and has been awarded the Guggenheim Fellowship, the IBM Innovation Award, and the Peano Prize.
Some of his other popular books include The Physics Book, The Medical Book, The Math Gene, The Paradox of God, and The Loom of God. He is also known for creating the Pickover attractor, a type of chaotic system that generates beautiful fractal patterns.
If you are fascinated by the wonders of mathematics and its applications to the world around us, you will surely enjoy reading The Math Book by Clifford Pickover. It is a book that will challenge your mind, expand your horizons, and inspire your curiosity. aa16f39245


If you are at all familiar with RPGs, you will probably know most of this stuff already, but read it anyway, as we probably do things slightly differently than you expect.
The dice you will need for this game are a six-sided die, and two ten-sided dice (preferably different colours). One such set for everyone playing will make everything go much faster.
The ten sided die is referred to as a "d10" and is numbered from 0 to 9. Unlike many other role-playing games where a roll of "0" on a d10 counts as a ten, in Infinite Horizons, it is zero (if your d10 goes from 1 to 10, the ten should be read as a 0).
The six-sided die, just like the one used in almost every board game since the beginning of time, is called a "d6".
Another common requirement is the percentile die roll, denoted as "d%". You can get a hundred-sided die for this, but these dice are expensive, and not usually as random as rolling two d10s, taking one as the tens digit, and the other as the ones digit. This is the reason for having two different colour d10s; you can always say "the purple one is the tens" before rolling, and then not have to worry about whether that 1 and 9 is a 19 or a 91 (or be rightly accused of cheating if you always pick the more advantageous of the two). In Infinite Horizons, a roll of "00" on a d% is read as a 0, not as 100 as in many games; the possible range for a d% roll is 0 to 99.
If you see "3d6", this means you need to roll three six-sided dice (or roll one six-sided die three times) and add up the rolls. Similarly, "5d10" means roll five ten-sided dice, and add the rolls together. Remember that the range for a d10 is 0 to 9, so the range for 5d10 is 0 to 45, not 5 to 50.
If you see "d6+3", this means roll a d6, and add three to the result. "2d6+8" means roll 2d6 and add 8 to the total; do not roll d6+8 twice and add the two numbers! "d10-4" means subtract four from the number rolled on a d10. No die roll can go below zero; any negative result is treated as zero (if you roll anything from 0 to 4 on a d10-4, read the result as 0).
There are many dice made with numbers of sides other that 6 and 10 (we have seen 4, 7, 8, 12, 20, 30, 100, as well as a d6 marked to be a d2 or d3, and there are almost certainly others). These are not necessary, although they may be helpful sometimes. For example, if you need to randomly determine the day of the month something happens on, a d30 would be the easiest way (assuming 30 days in the month). However, by using a d6 (treating 1 or 2 as 0, 3 or 4 as 1, 5 or 6 as 2) as the tens digit, and a d10 for the ones digit, the same result may be achieved. Or, you could just roll d% until you get a number between 1 and 30. If something was going to happen between 5:00 and midnight, you could use d8+4 for the hour, or you could use a d10+5, rerolling any 13 or 14. In short, any roll made by any of these custom dice may be emulated easily with your d6, d10, d%, and a little imagination.


Lorain Public Library System - Useful Web Links
Selected Topic: Mathematics
Digital Library of Mathematical Functions
The National Institute of Standards and Technology has updated its 1964 classic, Handbook of Mathematical Functions, and now provides the information online. The Handbook is the world's foremost mathematics handbook for scholars, researchers, and engineers.
Demonstrates challenging middle school mathematics & emphasizes the importance of high-quality math education for all students. Users can view web versions of the math challenges or download & print versions of the challenges in color or black & white.
Internet Mathematics Library
Links to a variety of math related resources are provided by the Math Forum at Drexel University.
Chosen by the American Librarian Association as one the best mathematic web sites for kids.
Free math worksheets, practice questions, etc. on elementary and advanced mathematics topics.
National Library of Virtual Manipulatives
A National Science Foundation project, providng interactive concept tutorials for mathematics instruction (K-12 emphasis). The site includes a Spanish language option. Although intended as a teacher tool parents and students may find it useful.
Purplemath - Your Algebra Resource
Purplemath includes lessons, homework guidelines, study habits test, and links to other algebra websites.


Reading & The Golden Ratio
Looks like just another day in the life of me. Almost done reading “The Golden Ratio.” It’s a very interesting book. This number has explained many of the workings of the universe. Basically, to find the “Golden Number,” you make a line and divide it into 2 parts, one larger than the other. Make the parts such that the ratio of the longest segment to the shortest segement is the same as ratio of the whole line to the largest segment. Another way to find the Golden Number is to use the following Quadratic Equation: X²=X+1. Phi is the only number that you can find the square root of and the result is the same number, minus 1.
Anyway, enough on the math lesson. Didn’t do too much today besides reading. Talked to Joanna for a little bit. She’s going to be here for like 5 days starting next Thursday. I’m really getting used to seeing her all the time. I like it a lot. She’s going to be moving out of her house and into her best friend Jen’s house. So that means I can go and stay with her whenever I want to! I can’t wait for that. Of course that means I’m going to find a car even quicker now.
It’s about 1:30am right now. Pretty early for me, but I think I’m going to bed. I’m feeling kinda tired for some reason, so I know how to take care of that. Goodnight everyone!


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I recently saw this link on Pinterest to a mental math stick puzzle game and immediately thought of a few ways I could adapt the concept for use with my girls!
I whipped up a bunch of puzzles to use for some independent math and literacy activities.
For Munchkin, I made one with rhyming CVC words, one with rhyming Bossy E words, one with words ending in diagraphs, one for mental addition 0-10, and two with number lines to solve addition and subtraction up to 20.
For my littlest and our preschool aged day care friends, I made an upper and lowercase letter matching puzzle, and one for number recognition.
HOW TO PLAY:
Lay out the sticks face up in front of your child, and have them locate the Starter stick. Read the word/equation/letter/number on the other end of the stick, and find it’s match/answer on the right side of another stick. Slide a finger across to the other end of that stick and repeat the process, searching the left sides of the remaining sticks for the next answer. Repeat until all sticks are in place.
There is only one solution to these, so if they get to the End stick and still have some remaining, they’ll immediately know that something went awry!
These can easily be adapted for mixed mental math, multiplication / division facts, skip counting and so much more.
They are great for on the go entertainment, as they fit easily into a small snack sized ziplock.
Leave a comment with any other suggestions you may have for incorporating these portable puzzles into your day!


Sam’s envelope stall.
A seasoned gambler named Sam with axe to grind sets up a stall near Harvard university. He has thought up a scam to make money out of clever academics from the business school. He offers any punter a choice between two envelopes. Inside each envelope is written a sum of money on a ticket. He promises that the sum in one envelope is twice the sum in the other. If questioned he will tell you that he will round the lower amount down to the first decimal, so if the higher says $1.56.3, the lower will say $0.78.1. The punter pays nothing until he has picked one of the two envelopes. He now has a choice: walk away and pay nothing, or pay the price on the ticket, plus a commission of 5%, in exchange for the sum of money written on the other envelope. The rich smart students from the business school are attracted by the stall, and many of them try it out. At first they assume it’s a trick of some kind, but Sam never tampers with the envelopes and always allows a complete free choice. The envelopes are completely identical. What really convinces the students that there is no trick is that one statistician does an exit poll and discovers that half the punters double their money, and half the punters come away with half their original stake, both minus the commission of course. So it is clear that Sam is playing fair. There is a ½ probability of choosing the envelope with the lowest amount and thus doubling your money. Once word gets around, then more students roll up to play Sam’s game.
Some guys from the business school decide that Sam must be a fool. They reason like this: when you see the price on the ticket you know you have a ½ probability of doubling your money, and a ½ probability of halving your money if you buy the ticket, minus the commission. Let us say you have a ticket with $X written on it. The expected utility is ½ of $2X + ½ of $ ½X which is $1.25X. Since you only had to pay $1.05X including the commission, you should make a profit in the long run of $0.2X a pop. Some of them run back to their rich fathers telling tales of a unique business opportunity and getting early releases of their inheritances. They will buy as many tickets as Sam will give them.
Now Sam, being a seasoned gambler, knows how to be random. The amounts in the envelopes vary enormously. In one pair there will be $8843.33.1, and $17686.66. In the next there will be $4 and $2. There is no limit on how high the tickets will go. As his fortune increases he increases the range of amounts he puts on the tickets, so even the range of possibilities is not constant. But what infuriates and befuddles the students is that Sam’s fortune does increase. And although some students do come away richer, most do not, and the worst off are those who blew their inheritances on as many tickets as they could buy.
People from the maths department begin to ask Sam all kinds of strange questions. How does he select the amounts to put in the envelope? What is the prior probability distribution? Does he toss a coin at any point? Sam won’t give straight answers to these questions. He looks at tea leaves, he says, and the way the birds fly. He uses Archimedes principle and counts the bubbles in his bath.
Even the philosophy department gets involved. Which envelope is held fixed? They ask. Do you select both envelopes in the same possible world? Do you rigidly designate one sum and double it, or rigidly designate the other and halve it? Would you ever put an infinite amount in one envelope, and in which case, how much would you put in the other envelope? Sam smiles at these questions and taps his ever burgeoning wallet.
So what is the solution? How does Sam make his living? The answer is surprisingly simple. Although it is true that half the people who buy a ticket double their money and the other half halve their money, if the exit pole had been a little more detailed it would have revealed that the average price of a winning ticket was half the average price of a losing ticket. So although in pure frequency terms the chance of doubling is 0.5, in financial terms the losing tickets count as double since they are twice as expensive. This means that only a third of the money is doubled, whereas 2/3 of the money is halved. So, aside from the commission, the amount of money going in to Sam’s capital is on average equal to the amount going out. Of course, Sam should only rarely approach his total capital since a series of big losses could put him out of business. But he has total control of the stake size, so he doesn’t need to take risks. As long as the students keep buying tickets, he will make a steady profit.
So what fooled the students? They neglected to realise that the losing envelopes cost twice as much as the winning envelopes. They should have seen that it was a zero sum game minus the commission and walked away. Had they realised that being indifferent was the correct attitude they could have calculated the correct probabilities using a clever formula worked out by Frank Plumpton Ramsey in 1926. The formula says that if a Subject is indifferent between options:
1. A for certain or
2. B if p and C if ~p,
Then the subject’s degree of belief that p is equal to
A – C/B – C.
Suppose that the ticket price is X, and p is the proposition that S will double his money on swapping, then S should be indifferent between:
1. $0 for certain. (He can just walk away with what he started with) or
2. $X if p and – $1/2X if not p (because he wins his stake back twice if he wins and loses half his stake if he loses)
Then S’s degree of belief that p = 0.5X/1.5X = 1/3.
What this shows is that given that indifference is the correct attitude, then the probability one should assign to doubling your money in Sam’s stall is 1/3 and the probability of losing half your stake is 2/3. This number does not represent the frequency of events fitting this description, but the expected utitlity. It takes into account the initial stake size. It calculates the frequency of units of value that get doubled, rather than the frequency of transactions that get doubled. When calculating expected utility it is the former which is of prime importance and therefore it is probability so interpreted that should be used in expected utility calculations.
What confuses matters is that the amounts in the envelopes are random. This focuses attention unduly on how this process is randomised which is a distraction. The only function the randomising serves is to introduce ignorance into the situation. If, as the classic two envelope paradox is properly presented, you are presented with just two envelopes, one with double the other, it is hard to see why the selection procedure is relevant at all. We could represent the ignorance more simply by imagining a thousand students being presented with the same to envelopes without being able to communicate. Lets say the envelopes contain £10 and £20. Probabilistically, around 500 will pick £10 and the other 500 will pick £20 first. If they all elect to swap we can record the results in two ways. We can either say that 50% doubled their money and 50% lost half their stake. This would be enumerating the transactions. Or we could say that £10 000 worth of deals made a loss of 50% and yet only £5 000 worth of deals doubled in value. So the relative frequency of loss to gain is 2:1, making the probability of doubling your money 1/3 and halving it 2/3. Of the thousand students, five hundred lost £10 and five hundred won £10. Sam makes his money from the commission and the insensitivity of decision theory to risk.
Labels: expected utility, paradox, two envelope problem


Common Core Reading?
Recently, my daughter came home with a math assignment that she needed a little help with. My husband and I both flinched as we heard the request come from the living room, “Moooom, Daaaaad, I need some help with my math.” We flinched because we knew what was to follow was a tear-filled hour (and by tears I mean mine) over trying to figure out some new-fangled strategy for doing long-division. You guessed it…we are in the throes of common core math.
Like most parents nowadays, my husband and I are absolutely befuddled by the math assignments that come home, not to mention, frustrated that what started as a methodology to try to access more students has become instead a way to turn off students who are our future leaders in STEM.
Let me explain and I’ll use the most recent homework battle as an example. Our daughter came home with 10 long division problems with only one direction – use the “sharing method” to do the following problems. So, I ask her, “What’s the sharing method?” and having just learned it that day my nine year old was unable to explain what it was. Okay, no problem, I think…I’ll Google it. Sure enough, there is a ton out there about the sharing method with examples for problems like 12 divided by 3. Then I look at her first problem – 416 divided by 4….hmmmmm…how does that work?!
After about 20 minutes of me running multiple examples I finally got a grip on it myself, enough to be able to help her. As I sat there trying to explain to her the multitude of steps that I could intuitively do due to the fact that I excelled in math and have done it for how many more years, I felt my frustration growing, not at her, or the assignment, but rather the absolute insanity of the number of assumptions and estimations that someone with her limited background would have to make in order to do one problem in under 5 minutes. I watched as she mentally slipped away and her frustration grew only to have her throw up her hands and say, “I am TERRIBLE at math.” This is a child who scored advanced in math on her SOLs!
In other words, common core is losing her, a child who would excel in math and has since the age of three said she wants to be an engineer, a child who from that age has been continually complimented for her ability to solve complex problems and for her advanced conceptualization of the world.
So, If the goal of common core math is to access more students, then why do we penalize students for not knowing EVERY strategy for a given concept? Why are we not introducing all the strategies and then grading students on using whatever strategy works best for them that shows they know the concept? Isn’t knowing the concept the standard we need to achieve?
And then I began to think about children with dyslexia and not only about the fact that this way of teaching math is even more confusing for them for a variety of reasons. Rather, I thought about how we teach reading only ONE way and that got me asking…So when are we going to introduce Common Core Reading with multiple strategies for one concept?
In the meantime, I think I will publish a Common Core Math for Dummies and give it to parents who need to help their kids with their homework!


OptionVue’s method for computing statistical volatility (SV) is the "extreme value method". Using just daily high and low prices, the extreme value method is roughly five times more precise than the more common "close-to-close" estimator. And the extreme value method has the further advantage of being unaffected by any possibly missing days. You can go away for a week or two, and come back and pick up where you left off. (The SV number might be a little bit "stale", but the formula deals with the gap just fine.)
Truthfully, the calculation of SV involves more than just the basic ”r;extreme value formula”. There is an algorithm involving several steps. These steps represent refinements made over the years. The heart of the algorithm, is this ”extreme value” formula: SV = .627 * sqrt(365.25) * ln( H / L )
SV = statistical volatility
sqrt = the square root function
ln = the natural logarithm function
H = the high of the day
L = the low of the day
This formula gives you the statistical volatility number for one trading day, normalized to a year (all volatility numbers are normalized to one year).
The result of using the above formula on each of ”n” trading days is ’n’ different SV numbers. These may then be combined by averaging. In OptionVue we use 20 trading days, We use an exponential averaging method to give the most weight to the SV of the most recent trading day, and successively less weight to the other days as you go back in time.
Here is the exponential averaging algorithm as used in OptionVue.
a = 1.0
alpha = 0.92
numer = 0.0
denom = 0.0
For each trading day, do the following three instructions:
number = number + (a * daily volatility)
denom = denom + a
a = a * alpha
Then the final step is: Average SV = number / denom
In this algorithm, ”a” represents the progressively smaller weight, and is used as a multiplier against each daily SV reading. You can see that ”a” starts out at 1.0, and becomes smaller as it is multiplied by 0.92 repeatedly.


Western High School Earns Four Star Rating 2017-2018
Western High School was awared a Four Star Rating for the 2017-2018 school year on March 8, 2019 by the Indiana Department of Education.
- A school must have received an “A” on the state’s A-F Accountability system for the 2017-2018 school year.
- A school must have tested at least 95% of students on ISTEP English/Language Arts and Math.
- Combined ISTEP Pass Percentage (Pass Percentage of English/Language Arts ISTEP + Pass Percentage of Math ISTEP) must be in Top 25th Percentile for each grade tested. (minimum of 10 students).
- Percent Passing Both ISTEP (Percent of students who passed both the English/Language Arts ISTEP + Math ISTEP) must be in the Top 25th Percentile for each grade tested. (minimum of 10 students).