Course Notes Linear Math & Matrices PSB – Dr. H. Schellinx Linear equations As we have seen‚ a linear equation with n different variables‚ say x1‚ x2 ‚ x3‚...‚ xn ‚ can always be written in the equivalent standard form a1 x1 + a2 x2 + a3 x3 +... + an xn = c ‚ where c is a constant‚ the xi are the unknowns and the ci are coefficients. Here are
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❶AGE PROBLEM In three more years‚ Miguel’s grandfather will be six times as old as Miguel was last year. When Miguel’s present age is added to his grandfather’s present age‚ the total is68. How old is each one now? This exercise refers not only to their present ages‚ but also to both their ages last year and their ages in three years‚ so labelling will be very important. I will label Miguel’s present age as "m" and his grandfather’s present age as "g". Then m + g = 68. Miguel’s age "last year"
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1. Calculate real GDP for 2004 and 2005 using 2004 prices. To calculate the real GDP we use the constant price for 2004 which was $20. Real GDP (base year 2004) 2004 ($20 per CD x 100 CD’s) + ($110 per racquet x 200 racquets) = 24000 2005 ($20 per CD x 120 CD’s) + ($110 per racquet x 210 racquets) = 25500 By what percentage did real GDP grow? Because the Real GDP was $24000 in 2004 and $25500 in 2005‚ real GDP grew by ($25500 - $24000) / $24000 = 0.0625 or 6.25% 2. Calculate the
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and relations‚ and mathematical logic studies recursive functions. 1.2 Objectives of the Report Understanding the concept of functions. To familiar with the various types of functions. Understanding linear function and its characteristics. Sketch the graph of linear function. Apply linear functions in solving business problems. 1.3 Methodology The study is application based in nature. Data used in this study are collected basically from the secondary sources. Secondary Sources: Text
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Introduction to Linear Regression and Correlation Analysis Goals After this‚ you should be able to: • • • • • Calculate and interpret the simple correlation between two variables Determine whether the correlation is significant Calculate and interpret the simple linear regression equation for a set of data Understand the assumptions behind regression analysis Determine whether a regression model is significant Goals (continued) After this‚ you should be able to: • Calculate and
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Adv. Physics – Unit 1 Homework Linear Motion (Ch. 2 & 3) Essential Questions: 1) How would you describe constant and accelerated motions? 2) How is motion represented graphically and analytically? 3) How does an x vs. t graph differ between constant and accelerated motions? P. 52-53 #46‚ 48‚ 50‚ 53 P. 80-83 #58‚ 59‚ 87‚ 89‚ 98‚ 106 If I don’t give the answer‚ you will have to determine it yourself. SHOW YOUR WORK! P. 52 50) 1.5x1011 m 53) 1.8 min P. 80 87) a. 75 m b. 150
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Jasmine Chai Grade 10 196298501 Patterns within systems of linear equations Systems of linear equations are a collection of linear equations that are related by having one solution‚ no solution or many solutions. A solution is the point of intersection between the two or more lines that are described by the linear equation. Consider the following equations: x + 2y = 3 and 2x – y = -4. These equations are an example of a 2x2 system due to the two unknown variables (x and y) it has. In one of
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LINEAR REGRESSION MODELS W4315 HOMEWORK 2 ANSWERS February 15‚ 2010 Instructor: Frank Wood 1. (20 points) In the file ”problem1.txt”(accessible on professor’s website)‚ there are 500 pairs of data‚ where the first column is X and the second column is Y. The regression model is Y = β0 + β1 X + a. Draw 20 pairs of data randomly from this population of size 500. Use MATLAB to run a regression model specified as above and keep record of the estimations of both β0 and β1 . Do this 200 times. Thus you
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Forum #2: Linear Equations in Real Life Pick one of the following problems. Show how you would solve it using a system of linear equations. 1) John spent $201 shirts and pants for work. Shirts cost $27 and pants cost $22. If he bought a total of 8 articles of clothing‚ then how many of each kind did he buy? 2) A school dance has 228 students. There are 63 fewer girls than twice as many boys. How many boys and girls attended the dance? 3) There are 15 animals in the barn. Some are ducks and some
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The materials used for this lab were filter papers‚ a choice chamber‚ eight pill bugs‚ water‚ and tin foil. The first step of the process is to trace and cut the filter paper so it fits neatly within each side of the choice chamber. Then‚ put water each filter paper and place the damp filter paper into the choice chamber. The damped filter paper causes the pill bugs to not be able to crawl under the paper and therefore disrupting the results. Four pill bugs should be placed on either side and one
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