Problem statement. There’s this game called linear nim where 2 players who have 10 marks and so they have to figure out a strategy. Then who ever crosses out the last mark wins. You can also play it with 15 marks. But you have to figure what to do while playing this game and try to find patterns or strategies to win.

Process. So what I did to attempt the problem is that I played the game a few times with my partner with the 10 marks and 15. So we can find some patterns and strategies that we can discuss. Then some strategies that we came up with were that we had to think ahead of our partner and see what next move will they make or see the amount of marks are left over.

Solution. So while playing the game my partner had won every game. I could see she had a great strategy and we had took turns like if she went first then I would go first the next round. Then I saw that if we played 10 marks I had crossed out 2 she would cross out 3 then 5 were left over so I couldn’t cross out 4 or 5 only 1,2 or 3 . So I cross out 2 and she would cross out the rest. But when we played 15 I could see that if there were 5 left and I have crossed out 1 she could cross out the other 4.

Extension. Mary and Louie are playing the same game but there are 20 marks so they can only mark out even numbers and the last person to cross out the last even number wins.

Self Assessment. My strongest points were that you could think ahead . Also seeing what marks were left over. My weakest points were trying to find a strategy of beatin my partner. My grade should be an A+ because I worked really hard.

...CLAS 133A, Greek Art
December 6, 2006
Ancient Crete: The Double-Axe and Minoan Linear A
MFA object # 58.1009
Votive Double Axe
Late Minoan I A, about 1550-1500 B.C.E
From the Arkalochori Cave on Crete
Gold
When Heinrich Schliemann with his literal belief in Homer discovered Hissarlik (his Troy) and Mycenae, he opened up a whole new idea in classical archaeology- that of myths being reality. Before his discoveries, the earliest recorded date in Greek history was the 778 B.C.E- the date of the first Olympic Games. Anything before that was considered by the scholarly community as pure legend. Schliemann set the ground work with his excavations in Hissarlik and Mycenae. He intended also to excavate Crete, but that task failed and was soon picked up by Arthur Evans.
Crete was mentioned in the Odyssey during the hero Odysseus’s journey home from Troy:
“Amidst the wine dark seas lies Crete, a fair rich island populous beyond compute with ninety cities of mixed speech, where several languages coexist...the capital is Knosos, ruled by Minos, who from his ninth year talked familiarly with Zeus.”1
Arthur Evans was first interested in a group of seal-stones he noticed at an antiquities dealer. He was told that they came from Crete and he was very curious at their inscriptions. He believed that they may be an early form of writing, and decided to visit Crete to find out more. Reports say that he fell in love with Crete from the moment he set foot...

...Nim was a chimpanzee who was born in the early 1970’s. He was bred for an experiment where he would live with a human family and try to learn sign language. The purpose of the study was to prove if language is inherent only in humans or if animals could somehow comprehend. Nim was raised in a human-like setting and taught sign language as if he were a human child.
Nim was born in a lab facility center in Norman, Oklahoma. His mother, Caroline, was treated as a breeding machine—all her babies were taken at birth for use in experiments. Nim was taken from her a few days after his birth, to be used in Herbert Terrace’s experiment testing whether sign language could be taught to a ape. His full name, Nim Chimpsky, was a joke on the name of the scientist Noam Chomsky, who had once said that only humans have the ability to learn language. In 1973, Terrace set out to do something similar to what other scientists did but with, he hoped a more primary focus on whether a chimpanzee really could use language in the same way that humans use it.
He arranged for the baby chimp to be adopted by Stephanie LaFarge, a respected older student of his who was bringing up her own family in an apartment in Manhattan. In selecting LaFarge, he neglected the most important factor which was having an expertise in sign language. According to LaFarge’s daughter no one in the house was fluent in sign language. The family talked...

...The development of linear programming has been ranked among the most important scientific advances of the mid 20th century. Its impact since the 1950’s has been extraordinary. Today it is a standard tool used by some companies (around 56%) of even moderate size. Linear programming uses a mathematical model to describe the problem of concern. Linear programming involves the planning of activities to obtain an optimal result, i.e., a result that reaches the specified goal best (according to the mathematical model) among all feasible alternatives.
Linear Programming as seen by various reports by many companies has saved them thousands to even millions of dollars. Since this is true why isn’t everyone using Linear Programming? Maybe the reason is because there has never been an in-depth experiment focusing on certain companies that do or do not use linear programming. My main argument is that linear programming is one of the most optimal ways of resource allocation and making the most money for any company today.
I used (in conjunction with another field supporter – My Dad) the survey method to ask 28 companies that were in Delaware, New Jersey, and Pennsylvania whether they were linear programming users. In addition, I wanted to examine the effect of the use of linear programming across three different but key decision support areas of the...

...Summer 2010-3 CLASS NOTES CHAPTER 1
Section 1.1: Linear Equations
Learning Objectives:
1. Solve a linear equation
2. Solve equations that lead to linear equations
3. Solve applied problems involving linear equations
Examples:
1. [pic]
[pic]
3. A total of $51,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3,000, how much will be invested in each type of investment?
4. Shannon, who is paid time-and-a-half for hours worked in excess of 40 hours, had gross weekly wages of $608 for 56 hours worked. What is her regular hourly wage?
Answers: 1. [pic]
2. [pic]
3. $24,000 in CDs, $27,000 in bonds 4. $9.50/hour
Section 1.2: Quadratic Equations
Learning Objectives:
1. Solve a quadratic equation by (a) factoring, (b) completing the square, (c) the
quadratic formula
2. Solve applied problems involving quadratic equations
Examples:
1. Find the real solutions by factoring: [pic]
2. Find the real solutions by using the square root method: [pic]
3. Find the real solutions by completing the square: [pic]
4. Find the real solutions by using the quadratic formula: [pic]
5. A ball is thrown vertically upward from the top of a building 48 feet tall with an initial velocity of 32 feet per...

...LINEAR PROGRAMMING
INTRODUCTION:
The term ‛programming′ means planning and it refers to a particular plan of action amongst several alternatives for maximizing profit or minimizing cost etc. Programming problems deal with determining optimal allocation of limited resources to meet the given objectives, such as cost, maximum profit, highest margin or least time, when resources have alternative uses.
The term ‛linear’ means that all inequations or equations used and the function to be maximized or minimized are linear. That is why linear programming deals with that class of problems for which all relations among the variables involved are linear.
Formally, linear programming deals with the optimization (maximization or minimization) of a linear function of a number of variables subject to a ¹equations in variables involved.
The general form of a linear programming problem is
Optimize (Maximize or Minimize) Z = c1x1 + c2x2 + ……..+ cnxn
Subject to
a11 x1 + a12x2 + ….. + a1n xn (≤ , = , ≥) b1
a21 x1+ a22x2+ ….. + a2nxn (≤ , = , ≥ ) b2
. . . .
am1 x1+ am2 x2 + … + amn xn {≤ , = , ≥ { bmC
x1, x2….., xn ≥ 0...

...Patterns within systems of Linear Equations
HL Type 1 Maths Coursework
Maryam Allana
12 Brook
The aim of my report is to discover and examine the patterns found within the constants of the linear equations supplied. After acquiring the patterns I will solve the equations and graph the solutions to establish my analysis. Said analysis will further be reiterated through the creation of numerous similar systems, with certain patterns, which will aid in finding a conjecture. The hypothesis will be proven through the use of a common formula. (This outline will be used to solve both, Part A and B of the coursework)
Part A:
Equation 1: x+2y= 3
Equation 2: 2x-y=4
Equation 1 consists of three constants; 1, 2 and 3. These constants follow an arithmetic progression with the first term as well as the common difference both equaling to one. Another pattern present within Equation 1 is the linear formation. This can be seen as the equation is able to transformed into the formula ‘y = mx+c’ as it is able to form a straight line equation (shown below). Similar to Equation 1, Equation 2 also follows an arithmetic progression with constants of; 2, -1 and 4. It consists of a starting term of 2 and common difference of -3. As with Equation 1, Equation 2 is also linear forming the formula ‘y = mx+c’. When examining both Equation 1 and 2, an inverse pattern can be seen, where equation 1 is the inverse of equation...

...RESEARCH PAPER ON
LINEAR PROGRAMMING
Vikas Vasam
ID: 100-11-5919
Faculty: Prof. Dr Goran Trajkovski
CMP 561: Algorithm Analysis
VIRGINIA INTERNATIONAL UNIVERSITY
Introduction:
One of the section of mathematical programming is linear programming.
Methods and linear programming models are widely used in the optimization of processes in all sectors of the economy: the development of the production program of the company, its distribution on the performers, when placing orders between the performers and the time intervals, to determine the best range of products, in problems of perspective, current and operational planning and management, traffic planning, defining a plan of trade and distribution, in the problems of development and distribution of productive forces, bases and depots of material handling systems, resources, etc. especially widely used methods and linear programming model for solving problems are savings (choice of resource-saving technologies, preparation of mixes, nesting materials), production, transportation and other tasks.
Beginning of linear programming was initiated in 1939 by the Soviet mathematician and economist Kantorovich in his paper "Mathematical methods of organizing and planning production." The appearance of this work has opened a new stage in the application of mathematics in economics....

...Linear-Regression Analysis
Introduction
Whitner Autoplex located in Raytown, Missouri, is one of the AutoUSA dealerships. Whitner Autoplex includes Pontiac, GMC, and Buick franchises as well as a BMW store. Using data found on the AutoUSA website, Team D will use Linear Regression Analysis to determine whether the purchase price of a vehicle purchased from Whitner Autoplex increases as the age of the consumer purchasing the vehicle increases. The data set provided information about the purchasing price of 80 domestic and imported automobiles at Whitner Autoplex as well as the age of the consumers purchasing the vehicles. Team D selected the first 30 of the sampled domestic vehicles to use for this test. The business research question Team D will answer is: Does the purchase price of a consumer increase as the age of the consumer increases? Team D will use a linear-regression analysis to test the age of the consumers and the prices of the vehicles.
Five Step Hypothesis Testing
Team D will conduct the two-sample hypothesis using the following five steps:
1. Formulate the hypothesis
2. State the decision rule
3. Calculate the Test Statistic
4. Make the decision
5. Interpret the results
Step 1- Formulate the Hypothesis
Using the research question: Does the purchase price of an automobile purchased at Whitner Autoplex, increase as the age of the consumer purchasing the vehicle...