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# Problem Solving With Trend Lines

Interpreting a trend line. Why the trend for building houses with small gardens could be damaging our health Research suggests that people surrounded by smaller gardens were more likely to. The default method is additive. The Finance department at Lewis & Sons only accounts for 10% of the employees, but wields the most decision-making power and controls resources and information. SIT (systematic inventive thinking) is a method that helps people break away from their patterns of thinking to come up with innovative ideas on demand and translate them into actions. FlevyPro is a subscription service for on-demand business frameworks and analysis tools. It is the study of symbols and the rules for using those symbols. Welcome to Pre-Algebra help from MathHelp. This idea is. you run into the problem that only one user can open a workbook at any one time. The problem is that the circuits fitted during older days were not designed to power different types of electronic equipment or lighting of this era. Automatic calculators for simplify, expand, evaluate, equations, etc. E-COMMERCE WEBSTORE LEAD. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Math Conce. Try to do them without looking at the answers first. While this solution does not solve the problem of guns in the streets, it does help provide outlets for students who have mental health issues. Nielsen Co. What does "x" represent in the equation? c. 0 into Normal 3. This paper presents an overview of single-objective metaheuristic algorithms used for partitional clustering problem and their applications. So, the criteria for polish are stricter for small applications than for enterprise applications. You want to show that you understand a business issue well enough to formulate recommendations or insights that address the problem. Examples of ways you can develop or improve your problem-solving skills include: doing research assignments as part of your studies; dealing with complaints at your. level, which uses strategy to frame the left and right boundaries for. Thinking that working the line at John Deere or Winnebago will vault you into the middle class makes about as much sense as buying eight-track tapes in the iPod age. Forum for asking questions. Category: Data and Graphs Data Display and Interpretation Line Graphs. Our line chart worksheets are made for math grade 4 and up and cover parts of the curriculum of those math years. It is a line drawn along a trend to show support or resistance. Trend Lines and Predictions Success for English Learners To write an equation for a trend line: • Select two ordered pairs. one, consistent, independent 2. Step 2 : To draw a trend line, use a straight edge to draw a line that has about the same number of points above and below it. HHSM11A1MC_0507. Problem SOlving with Trend Lines. Contacting the next level of management is also easier at local stores than online. Name _ Date _ Class _ LESSON x-x 3-5 Problem Solving Scatter Plots and Trend Lines Fawn is trying to improve her reading. The y-coordinate for Line 2 is calculated this way: y = -0. The types of puzzles can test many problem-solving skills including logic , pattern recognition , sequence solving , spatial recognition , and word completion. Axon Police Reform Opportunity. The slope of the line below is 3. The singer and mom of three said that she had dealt with eczema since she was a young child, but experienced. But he doesn’t solely rely on them. To help reverse that trend, some fitness experts say, physical education classes should be revamped so there is less emphasis on team sports and more. Find an exponential formula modeling data or a percentage-growth situation. Measuring data is crucial for any future scientist, and our fifth grade graphing and data worksheets can help. When there is a strong correlation between the two variables in a set of two-variable data, you can use a line of fit as the basis to construct a linear model for the data. Most of the world's population growth will occur in developing countries where water is already critically short and many of the. Using a straight edge, draw the line that the data points appear to be clustered around. Knowledge Base: An online database of problem-solving and troubleshooting information. This is at least partially because industry lobbies make sure that inconvenient regulations are not passed. I think that's the big consumer trend that's going to break through next year," Goldberg said. Learn programming, marketing, data science and more. Examples of these skills include problem-solving abilities, perseverence, pattern recognition, hypothesis testing, estimating skills, inductive reasoning, resource management, logistics, mapping, memory, quick thinking, and reasoned judgments (Sheff, 1994). , non-examples/examples; cause-effect) o Make and record observations o Explain steps followed o Summarize results or concepts. " Design thinking unfetters creative energies and focuses them on the right problem. pdf from BIOLOGY 123 at Coral Glades High School. (Knudsen left GM to lead Roosevelt's war effort, becoming the architect of America's arsenal. A trend may notice that a process is out of control or is likely to get out of control and may be due to factors such as tools worn, a machine that does not maintain the configuration values or periods of rotation of the operators. Providers must make the changes necessary to curb the cost trend. Moving averages allows us to see trend lines and seasonal variations. Unit 2: Solving Equations and Inequalities. The measures are part of a trend of Trump attempting to stoke cultural issues along lines of race that appeal to his socially conservative base. mass of a brick e. Anita is taller than Becca. Use it to investigate variability at different time points and capture how the customers and markets respond over time. In ‘Fruit Count’, kindergarteners fill in the graph by coloring one box for each fruit. all four are discussed. So let’s dive. Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. Next lesson. Step develops scientific papers to help members address e-waste issues within their own organizations and provides global, objective and scientifically-based information relevant to addressing the global problem. Solve problems involving logarithms, such as sound volume and. The table shows the percent of people ages 18–24 who reported they voted in the presidential elections. Cause Mapping flattens problem solving by deferring to the people in the organization who know how well current processes actually work. The goalis to identify the coefficients ‘a’ and ‘b’ such that f(x) ‘fits’ the data well. Example: Plot the function y = 5 x on an ordinary axis (x- and y- linear scales) as well as on a semi-log axis. Today is a day about making the fashion industry better. Addition and Subtraction. trend - general line of orientation; "the river. ] After first adding a linear trend to this plot and then clicking “Get Summary” we get: Linear Trend: height = 85. How Do You Find the X- and Y-Intercepts of a Line in Slope-Intercept Form? To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'. It will be easier to write an equation for the line if it goes through two of the data points. 2: 1-7 Student eTool. Sign up today!. See full list on study. We use the slope of the secant line (in green) which connects the data points at t 1 and t 3 to estimate dP/dt at t 2. They will use the equation of the trend line to make predictions by interpolating or extrapolating. Slope of a Line : Example 1. problem-recognition b. Study 1 investigated the relationship between trait mindfulness. Define trend. Another reporter for the Chronicle, Stacey Patton, writing on May 9th, focuses on the growing default rate and that repaying these loans is not only a problem for recent graduates, but also that adults ages 60 and older are seeing their Social Security checks garnished because they fell behind on student-loan payments. This environment is one in which you need to be actively engaged, and it provides an opportunity to maintain and improve your own problem-solving knowledge and skills. dollars and cents g. 2) Curve fitting- capturing the trend in the data by assigning a single function across the entire range. Adding a trend line to a scatter plot Constructing a best-fit line - Practice Problems Below you will find practice problems for constructing a best fit line using the steps found on the introduction pages. 7 Excel Spreadsheet Problems and How to Solve Them. Compare the least squares best-fit line. This is known as an individual’s. (AB) + C = XY d. Here are the main characteristics of a trend line: A trend line can never be a horizontal line, it must be always be diagonal line. A growing bank of randomly generated GCSE exam style questions with full worked solutions. 2EADING3PEED 7ORDSPER-INUTE 7EEKS. These have been consistent since the first report in 2016. Assuming the line is correct, what does the line slope of 15 mean?. Improve your math knowledge with free questions in "Scatter plots: line of best fit" and thousands of other math skills. Google is Developing a Search Feature that Indexes Short Videos from TikTok and Instagram. But he doesn’t solely rely on them. When there is a strong correlation between the two variables in a set of two-variable data, you can use a line of fit as the basis to construct a linear model for the data. Two-way tables. This cause analysis tool is considered one of the seven basic quality tools. ___ The scatter plot shows the cost of gas per gallon during certain years. the case of secular equilibrium. In larger organizations, the problem-solving team may be assembled and led by an outside consultant. With this set of exercises, you will use proportions and probability to make predictions about flipping coins, spinning spinners, and rolling number cubes. Follow that line until reaching a temperature of 100F. It manages trend values, by measuring and analyzing data about deterioration and employs a surveillance system, designed to monitor conditions through an on-line system. If the problem is your PC, check whether you have plenty of free space on the hard drive holding your operating system. Trend analysis in quality management is especially useful for monitoring process changes, particularly for activities indirectly related to manufacturing. Explanation. What equation did she get? _____ 2. Organise a Framework that Helps You Solve the Problem. 2 Solving Linear Equations Equations of the form ax+b=0 are called linear equations in the variable x. trend line to a scatter plot by hand and find its equation. A statistical tool called regression analysis is needed to accurately calculate the best fit line. Year 1988 1992 1996 2000 2004 % of 18-24 year olds 36 43 32 32 42 Write positive, negative, or none to describe the. The app is a convenient way to use stress management and problem solving tools on-the-go. Every year at about this time, The Herman Group issues its annual workforce-workplace forecast. Explain your answer to question 1. Here you can learn how to use a Radar Chart as a problem-solving technique, being especially useful in performance measurement. Simply pay with your Absa card and. Clarisse used the ordered pairs (0, 13) and (24, 5) for her trend line. Next, write down the right sides of the equation so that they are equal to each other and solve for x. " Design thinking unfetters creative energies and focuses them on the right problem. Solving the E-waste Problem (Step): Step Exit is a multi-stakeholder initiative and a global platform addressing the e-waste problem. Launch Gizmo. Lead and Disrupt: How to solve the innovator's dilemma provides a high-level overview of how creation and maintenance of autonomous innovation streams can be utilized to lead and disrupt an industry. Select two ordered pairs. Timeframe, location and trend: Describe when and where the problem was first observed and what kind of trend it is following. Find an exponential formula modeling data or a percentage-growth situation. This cause analysis tool is considered one of the seven basic quality tools. Study 1 investigated the relationship between trait mindfulness. New PE Trend Stresses Fitness and Fun As the amount of physical activity children get in and out of school has declined in recent years, youngsters have become more overweight and less fit. This digital math activity allows students to practice using trend lines to make predictions and writing linear equations. 135 A biased random-key genetic algorithm for routing and wavelength assignment under a sliding scheduled traffic model. Here we present data from a five-level learning and problem-solving experiment. Which of the following in NOT one of the levels of consumer problem solving discussed in the text? A) Dissonance problem solving B) Routinized response behavior C) Extensive problem solving D) Limited problem solving E) None of the above, i. Write, read, and evaluate expressions in which letters stand for numbers. She is measuring how many words per minute (wpm) she can read after each week of the class. Marketing research and market research are the applied research. To find the y-intercept, plug 0 in for 'x' and solve for 'y'. pdf from BIOLOGY 123 at Coral Glades High School. Use the trend line shown on the scatter plot to answer a-c. [Data used: as a csv file and as a tab-delimited txt file. FlevyPro is a subscription service for on-demand business frameworks and analysis tools. Flat line segments don't count, either to break a trend, or to count towards it. You need to gather any data concerning the problem and analyze all evidence of the existence of the problem or issue. 5 problem_solving. Proving Lines Are Parallel Practice and Problem Solving: A/B Use the figure for Problems 1–8. Estimate the amount of seasonality - the seasonal relatives (or factors or indices) 2. → If we can get any point beyond the control line then the special cause is available. Cat and Mouse (Modeling with Linear Systems) - Activity B. Keep in mind that “5” is just a number. This construction forms the basis of the Control chart. Addition and Subtraction. It is calculated by adding up all of the values in a data set and dividing by the number of values in that data set : x ¯ = ∑ x n. negative correlation 5. Now, the equation of the line that goes through ( a, f ( a)) ( a, f ( a)) is given by. Drawing a scatter diagram in GeoGebra. Scientific American is the essential guide to the most awe-inspiring advances in science and technology, explaining how they change our understanding of the world and shape our lives. Most project management tools can be accessed via browsers and those that do not currently have this capability are moving in that direction. Chase Young, DE, Washington Football Team. This digital math activity allows students to practice using trend lines to make predictions and writing linear equations. Drawing a scatter diagram in Excel. Clarify the Problem. Successful entrepreneurs are also willing to adapt to solve a problem; they aren't beholden to the image, processes or lines of thinking that got them into the problem in the first place. Get instant access to more than 2 million+ solutions to academic questions and problems. Sara is co-founder of Triggs, the employee experience lab, helping organizations to establish new ways of working through Employee Experience Design. Step 3 : Find the slope of the trend line. If they are, state your reasoning. Problem 1 Problem 2 Method: Method: 1. Name Date Class LESSON 10-1 Scatter Plots and Trend Lines Practice and Problem Solving A/B Graph a scatter plot and find the correlation. You want to show that you understand a business issue well enough to formulate recommendations or insights that address the problem. The y-coordinate for Line 2 is calculated this way: y = -0. The simplest time-varying trend model is Brown's linear exponential smoothing model, which uses two different smoothed series that are centered at different points in time. Rewrite the problem in exponential form by moving the base of the logarithm to the other side. F ADDITIONAL PRACTICE AND PROBLEM SOLVING Chapter 3 155 Lesson 5. How to use trend in a sentence. ” Going 1-to-1 with littleBits. Learn why the Common Core is important for your child. This form may be used in replacement of the Individual Problem Solving (MTSS-1) when the Intervention Assistance Team has reviewed school wide data and found converging evidence (student grades and 3 sources of testing data) to suggest a need for a standard treatment protocol based intervention to be delivered to a group of students. These videos use the Car fuel and emissions data set. Includes. Step 1: Problem Identification. Anthony used the ordered pairs (12, 10. quality-of-life d. Puzzle video games make up a broad genre of video games that emphasize puzzle solving. Substitute for x in the other equation. There are 7 calculators in this category. Problem SOlving with Trend Lines. Find an exponential formula modeling data or a percentage-growth situation. Code: E14202-12. E-COMMERCE WEBSTORE LEAD. Support workers must describe the solutions to computer problems in a way that a nontechnical person can understand. It is the study of symbols and the rules for using those symbols. 00 SKU E14202-12 Quantity non-commercial use. Textbook Authors: Hall, Prentice, ISBN-10: 0133500403, ISBN-13: 978-0-13350-040-0, Publisher: Prentice Hall. A / B = C b. Trendlines, or best fit lines, help reveal linear relationships between variables. Little r is the coefficient of correlation, which tells how closely the data is correlated to the line. indd 163SM11A1MC_0507. To determine how many smaller objects fit into a larger object, divide the volume of the larger object by the volume of the smaller 3D object. Octopuses have large brains and exhibit complex behaviors, but relatively little is known about their cognitive abilities. While a trend usually refers to a certain style in fashion or entertainment, there could be a trend toward warmer temperatures (if people are following trends associated with global warming). y = f ( a) + m ( x − a) y = f ( a) + m ( x − a) Therefore, the equation of the tangent line to f ( x) = 15 − 2 x 2 f ( x) = 15 − 2 x 2 at x = 1 x = 1 is. Cheap essay writing sercice. fsolve, even brenth and newton. What does "x" represent in the equation? c. Timeframe, location and trend: Describe when and where the problem was first observed and what kind of trend it is following. I 'm new to python, like 2 weeks. Improve your problem-solving skills by setting goals to acquire more industry knowledge within your field. With the proliferation of channels, the data generated in each channel is multiplying by the minute. But there are also a few universal problem-solving skills we all need: Defining the Problem: Deeply understanding a problem through research, leading to better solutions. However, the role of improved schooling, a central part of most development strategies, has become controversial because expansion of school attainment has not guaranteed improved economic conditions. The user documentation for Trend Micro™ Mobile Security 9. When a scatter plot shows a linear association, you can use a line to model the relationship between the variables. It often, involves global evaluations of alternatives that could be supported by the short-term working memory and that should be compatible with various kinds of attractiveness scales. We can craft any kind of writing assignment for you quickly, professionally, and Unit Scatter Plots And Data Homework 4 Problem Solving With Trend Lines Answer Key at an affordable price!. Write about the following topic: Some people think that environmental problems are too big for individuals to solve, while others think that the government cannot solve these environmental problems unless individuals make some action. Describe how exponential and logarithmic functions are related. Problem solving at work typically becomes easier if you have a strong. policing practices, such as community policing, problem solving, and CompStat based on robust data collection and analysis. A post shared by Alexis Michaud (@iamalexismichaud) on Mar 31, 2019 at 8:31am PDT. Fans spot major problem with duct tape bikini trend. Word story problem helper has solved examples. Shira drew the line below to show the trend in the data. You can reduce the frequency by turning off Wi-Fi or the phone data connection, however, it’s not convenient. trace, trend) and the vertical (dip, plunge, inclination). Study 1 investigated the relationship between trait mindfulness. Law enforcement is an important societal function and its effectiveness is hampered when. Line Plot (Dot Plot) Worksheets. Universal Math Solver (UMS)—free version Software that will solve and explain algebra and calculus problems step-by-step, both verbally and in written form. So this "exactly," you can't say it's guaranteed an hour more turns into 15%. the S&P 500, match its all-time high, a positive sign. Problem 3 : The scatter plot and trend line show the relationship between the number of rainy days in a month and the number of umbrellas sold each month. Another possibility is that the local mean is increasing gradually over time, i. The table shows the percent of people ages 18–24 who reported they voted in the presidential elections. The curve fitting process fits equations of approximating curves to the raw field data. It represents the core subject matter of scholarly communication, and the means by which we arrive at other topics of conversations and the. F ADDITIONAL PRACTICE AND PROBLEM SOLVING Chapter 3 155 Lesson 5. Prepare a model and verify that angle in a semi-circle is a right angle by using vector method. Learn How To Solve the 12 Biggest Customer Service Challenges With These Tips. 2EADING3PEED 7ORDSPER-INUTE 7EEKS. A post shared by Alexis Michaud (@iamalexismichaud) on Mar 31, 2019 at 8:31am PDT. 8: Line of Best Fit. A trend line is a line on a scatter plot, drawn near the points, that shows a correlation. ) For example: We want a strong product portfolio innovation process to drive future growth. The customer service role by its nature requires a greater ability in problem-solving and (albeit not always on a grand scale) project management than many sales roles. Parallel and Perpendicular Lines: Exercises: p. Here are two ways to write an equation for the trend line in the scatter plot at the right. What Is A Trend Line? A trend line is simply a line that many forex traders use as part of their technical analysis. ___ The scatter plot shows the cost of gas per gallon during certain years. ITIL V4 is no longer prescriptive about processes but shifts the focus on 34 'practices', giving organizations more freedom to define tailor-made processes. Th ere should be about the same number of points above the line as below it. Once students make this connection, they can derive meaning for arithmetic operations (addition, subtraction, and multiplication). Could new Ford Performance upgrades help? Read the Motor Trend review here. Problem 3 : The scatter plot and trend line show the relationship between the number of rainy days in a month and the number of umbrellas sold each month. Our line graph activities contain unknowns as scales to make them even more challenging and engaging. He says take-home assessments and behavioral questions also have their place in the hiring process, although they do involve a higher risk of candidate’s rehearsing or getting outside help. Problem Ten: Random freezes. Problem Solving and Data Analysis questions include both multiple-choice questions and student-produced response questions. • Write the equation. Trend lines are one of the basic components in price action trading. A run of 8 consecutive points > 1𝝈 from the center-line (either_side) Rule 1: One or More points are > 3𝝈 from the centerline → It is also called as a point beyond the central line. The infrastructure was awkwardly duct-taped onto a waste management model that was purely linear: take. If single parenthood is a problem, that problem cuts across race and ethnicity. “That causes all kinds of problems, and you’re going to get a mama bear calling you on the phone. The problem-solving orientation attempts to solve the problem by focusing on the underlying issues. For those who need an extra challenge we’ve included a section here of very hard logic riddles. Problem solving is decision making that may involves heuristics such as satisfaction principle, and availability. The problem under investigation offers us an occasion for writing and a focus that governs what we want to say. y = 13 − 4 ( x − 1) = − 4 x + 17 y = 13 − 4 ( x − 1) = − 4 x + 17. 2: 1-7 Student eTool. 2 Solving Linear Equations Equations of the form ax+b=0 are called linear equations in the variable x. Line Plot (Dot Plot) Worksheets. It can be used to make predictions. These ideas are revisited in subsequent inestigations. Key elements of an effective problem statement include: Gap: Identify the gap (pain) that exists today. Here are the important steps of a root cause analysis: 1. But this requires the mastery of a problem-solving skill known as computational thinking, which involves breaking larger tasks into a logical sequence of smaller steps, diagnosing errors and coming up with new approaches when necessary. Make math learning fun and effective with Prodigy Math Game. Interpreting the Slope of a Trend Line Chris Wild, University of Auckland This is a scatter plot of heights versus ages for about 460 school students. A parallel trend of normal bodied and multi-ethnic models walking the ramp and appearing in fashion campaigns is also helping. Following trend publications is great way to begin getting a sense of the direction consumer products are going and the trending product ideas other entrepreneurs are introducing to the market. level, which uses strategy to frame the left and right boundaries for. Solution-focused therapy puts problem-solving at the forefront of the conversation and can be particularly useful for clients who aren’t suffering from major mental health issues and need help solving a particular problem (or problems). Since the EMRB is all about price action and chart patterns, it is crucial to discuss trend lines for opening range breakout trading. 5 miles, the trend line shows a time of 45 minutes. • Becoming better at solving challenging problems and accomplishing challenging tasks. Trend Enterprises teachers supplies for teachers and parents at 10 to 70% off MSRP. Unit 2: Solving Equations and Inequalities. So, it will take Joyce about 45 minutes to run 4. Problem Solving Scatter Plots and Trend Lines Fawn is trying to improve her reading skills by taking a speed-reading class. Many small details need to be taken care of for desired grades. This Making Predictions using Trend Lines Scavenger Hunt is an excellent activity for students to practice working with scatter plots, lines of best fit, graphing, and the best part is that they get to move around the classroom looking for the next problem to solve! Directions: Print the 10 problems. including job-related problem-solving skills, creativity, planning. Knowledge Base: An online database of problem-solving and troubleshooting information. These have been consistent since the first report in 2016. Select two ordered pairs. Learn from our organic experts With Europe representing the second biggest market for organic food and drinks after the US, and the UK organic market alone set to surpass £2. Name _ Date _ Class _ LESSON x-x 3-5 Problem Solving Scatter Plots and Trend Lines Fawn is trying to improve her reading. Gizmo Warm-up In the Solving Using Trend Lines Gizmo™, you will. Basically, it is an essay that starts by identifying a problem and then proposes at leasttwoor more solutions. The intersection of the two lines gives an enthalpy that is equal to h = 316 Btu/lbm. • Write the equation. Finally, only one RCT assessed the impact of problem-solving efforts on the community’s inclination to cooperate with police, finding a small, but statistically significant increase over the course of 9 months (Kochel and Weisburd, 2017, p. Watch the best videos and ask and answer questions in 144 topics and 12 chapters in Algebra. Lean Six Sigma provides a systematic approach and a combined toolkit to help employees build their problem-solving muscles. Solving a big problem is more difficult than solving a small problem. Problem solving means coming up with creative solutions, which customers appreciate because it shows them that the customer service representative is doing what he can to resolve an issue. milligrams and grams d. As more data becomes available, the trends often become less linear, and a polynomial trend takes its place. He says take-home assessments and behavioral questions also have their place in the hiring process, although they do involve a higher risk of candidate’s rehearsing or getting outside help. The use of minute doses of magic mushrooms and truffles containing psychedelic substances could induce a state of unconstrained thought that may produce more new, creative ideas. 135 A biased random-key genetic algorithm for routing and wavelength assignment under a sliding scheduled traffic model. These are sometimes called dot plots. Tell whether lines m and n must be parallel from the given information. The scatter diagram graphs pairs of numerical data, with one variable on each axis, to look for a relationship between them. Therefore, we recommend you professional essay Problem Solving With Trend Lines Homework 4 Answers tutoring. Automatic calculators for simplify, expand, evaluate, equations, etc. Thinking that working the line at John Deere or Winnebago will vault you into the middle class makes about as much sense as buying eight-track tapes in the iPod age. The problem is that the circuits fitted during older days were not designed to power different types of electronic equipment or lighting of this era. Future Problem Solving has teamed up with Renzulli Learning to offer a new virtual on-line opportunity. With some savvy problem-solving skills, customer service reps may be able to give the customer what he wants, in turn strengthening the bond of customer loyalty. There is no shortage of challenges and issues that can arise on the job. How Do You Find the X- and Y-Intercepts of a Line in Slope-Intercept Form? To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'. Some designers argue that these ‘pressable’ buttons look pleasing, the lack of contrast isn’t great for usability. She is measuring how many words per minute (wpm) she can read after each week of the class. ” A version of this article appeared in our May 2014 issue with the headline “Problem solvers,” p. 1 determine, through investigation, various formulas for the slope of a line segment or a line (e. Since at the point of intersection the two y-coordinates are equal, (we'll get to the x-coordinates in a moment), let's set the y-coordinate from Line 1 equal to the y-coordinate from Line 2. What are the steps to solving a word problem? If a mathematical problem is expressed in words, then first try to express all the relevant information in the problem in terms of symbols representing unknowns, in the form of equations, inequalities, etc. This is typical because we often focus on the product part of the problem as we neglect the human factor. But there are also a few universal problem-solving skills we all need: Defining the Problem: Deeply understanding a problem through research, leading to better solutions. Stats: 44 tackles, 7. But the story has nuance. While the trend is aesthetically tempting, designers are still debating the real-world usefulness of this design from a UX/UI perspective. Free shipping* and 30 Day Money Back Guarantee. HHSM11A1MC_0507. There are first-generation products, like Splitwise, addressing the problem. A statistical tool called regression analysis is needed to accurately calculate the best fit line. To keep users looking for social video entertainment and are already ditching the Google platform, the company plans to launch a feature to display Instagram and TikTok videos in a separate carousel in the Google mobile app. There are 7 calculators in this category. Use the scatter plot to answer questions 1-5. 5-6 Parallel and Perpendicular Lines 5-7 Scatter Plots and Trend Lines 5-8 Graphing Absolute Value Functions Chapter 5 Study Guide CHAPTER 6 WORKSHEETS 6-1 Solving Systems by Graphing 6-2 Solving Systems by Using Substitution 6-3 Solving Systems by Using Elimination 6-4 Applications of Linear Systems . When a scatter plot shows a linear association, you can use a line to model the relationship between the variables. • Develop, prepare and present financial and trend reports to various stakeholders. Without a vision of what AI could achieve, the field itself might never have formed or simply remained a branch of. It often, involves global evaluations of alternatives that could be supported by the short-term working memory and that should be compatible with various kinds of attractiveness scales. The Center for Problem-Solving Policing outlines and promotes the use of the SARA model, along with other problem-solving models. To graph the equation of a line written in slope-intercept (y=mx+b) form, start by plotting the y-intercept, which is the b value. A run of 8 consecutive points > 1𝝈 from the center-line (either_side) Rule 1: One or More points are > 3𝝈 from the centerline → It is also called as a point beyond the central line. Statistics and probability. To find the y-intercept, plug 0 in for 'x' and solve for 'y'. the S&P 500, match its all-time high, a positive sign. Television Statistics According to the A. seconds and minutes e. A trend is what's hip or popular at a certain point in time. Solving Problems: A Chemistry Handbook Chemistry: Matter and Change3 SOLVING PROBLEMS: CHAPTER 1 A CHEMISTRY HANDBOOK Practice Problems 1. Try to do them without looking at the answers first. Here you can learn how to use a Radar Chart as a problem-solving technique, being especially useful in performance measurement. Practice and. There are first-generation products, like Splitwise, addressing the problem. No matter whether you want to solve an equation with a single unknown, a system of two equations of two unknowns, the system of three equations and three unknowns or linear system with twenty unknowns. What equation did she get? _____ 2. By grounding operations with negative numbers in the context of graphing, students explore how the sign of a number (positive or negative) influences the behaviour of a trend line on a graph. Now I have an equation to solve: exp(x * a)-exp(x * b) = c, where a,b and c are known constants. Tom Loveless problem solving, and data analysis. This is a software problem and related to an Android update. Explanation. Our line graphs for grade 4 are mostly based on the 4 operations and averages and students will have to 'crack' the scaling. A trendline is a charting tool used to illustrate the prevailing direction of price. Solve problems involving exponential functions, such as growth, decay, doubling time, and half-life. The line passes through points (5, 50) and (17, 170). milligrams and grams d. Here are online algebra calculators to solve your algebra problems such as cube roots, square roots, exponents, any radicals or roots, simplifying radical expressions, fractional exponents, quadratic equations and so on. These bars, then, should be about the same height. The way to use this tool is very simple. However, in math, slope is defined as you move from left to right. 5 miles, the trend line shows a time of 45 minutes. Writing skills. 5: Systems of Equations and Inequalities 5. 8: Line of Best Fit. She is measuring how many words per minute (wpm) she can read after each week of the class. Disconnect the water lines. It can be used alone, or in combination with the Moving Forward online course. It is the study of symbols and the rules for using those symbols. problem-recognition b. It will be easier to write an equation for the line if it goes through two of the data points. 2EADING3PEED 7ORDSPER-INUTE 7EEKS. 66 Studios jumps on mini arcade trend with EnigmaBot launch hands-on building experience that helps develop problem-solving in a fun way. They will teach you how to write precisely. The app is a convenient way to use stress management and problem solving tools on-the-go. → Sometimes, Rule 1 also known as a large shift from the average. Among the key advantages of this method is that it ensures that you don’t seek out to solve the wrong problems, it also ensures that you solve the problem well enough for it to go away. , that there is a constant trend. Problem Solving With Trend Lines Homework 4 Answers The expert essay tutors at Nascent Minds will elaborate every single detail to you. Trend Lines and Predictions Practice and Problem Solving: C Use the diagram and the description to complete Exercises 1-5. 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# How fast can we sort a list if we know how it was written?

Let $G$ be a linear time (deterministic) turing machine that takes positive integers $n$ in unary to lists of length $n.$ For any fixed such $G$, define sparse-sort(G,n) as the problem of sorting the list that $G$ outputs for input size $n$.

In general, can we compute sparse-sort(G,n) asymptotically faster than $O(n \log n)$?

It's easy to generate examples where we can manage linear time, for example any $G$ that runs $G(n-1)$, then appends some predictable value to the list. Likewise, it seems plausible that one could use the function $G$ in the algorithm to get a good runtime in general.

• It depends a bit on what you mean - if you only count comparisons then, according to your definition there is a unique output for every n, which means that there exists an algorithm that doesn't use any comparisons at all... but I'm guessing that wasn't what you meant - so there has to be some reasonable reformulation of the model here. – daniello Sep 26 '17 at 15:55
• I'd like an algorithm that runs for every pair $G \times n$, or perhaps for a fixed $G$ and every $n$. We can't memorize the output for every $n$, the table is too big! – Artimis Fowl Sep 26 '17 at 16:50
• @MarzioDeBiasi the output of G should be a list of length $n$ of any integers in a reasonable format. Not necessarily $[n]$ to avoid radix sort answers, and probably not in unary because that usually takes longer than $O(n)$ time to write. – Artimis Fowl Sep 27 '17 at 14:38
• Ok! Now it's clear! – Marzio De Biasi Sep 27 '17 at 14:39

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# Number of ways to write n as a sum of k nonnegative integers

How many ways can I write a positive integer $n$ as a sum of $k$ nonnegative integers up to commutativity?

For example, I can write $4$ as $0+0+4$, $0+1+3$, $0+2+2$, and $1+1+2$.

I know how to find the number of noncommutative ways to form the sum: Imagine a line of $n+k-1$ positions, where each position can contain either a cat or a divider. If you have $n$ (nameless) cats and $k-1$ dividers, you can split the cats in to $k$ groups by choosing positions for the dividers: $\binom{n+k-1}{k-1}$. The size of each group of cats corresponds to one of the nonnegative integers in the sum.

As Brian M. Scott mentions, these are partitions of $n$. However, allowing $0$ into the mix, makes them different to the usual definition of a partition (which assumes non-zero parts). However, this can be adjusted for by taking partitions of $n+k$ into $k$ non-zero parts (and subtracting $1$ from each part).

If $p(k,n)$ is the number of partitions of $n$ into $k$ non-zero parts, then $p(k,n)$ satisfies the recurrence relation
\begin{align}
p(k,n) &= 0 & \text{if } k>n \\
p(k,n) &= 1 & \text{if } k=n \\
p(k,n) &= p(k+1,n)+p(k,n-k) & \text{otherwise}. \\
\end{align}
(this recurrence is explained on Wikipedia). Note: in the above case, remember to change $n$ to $n+k$. This gives a (moderately efficient) method for computing $p(k,n)$.

The number of partitions of $n$ into $k$ parts in $\{0,1,\ldots,n\}$ can be computed in GAP using:

NrPartitions(n+k,k);

Some small values are listed below:

$$\begin{array}{c|ccccccccccccccc} & k=1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 2 & 1 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 \\ 3 & 1 & 2 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 \\ 4 & 1 & 3 & 4 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 \\ 5 & 1 & 3 & 5 & 6 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 \\ 6 & 1 & 4 & 7 & 9 & 10 & 11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 \\ 7 & 1 & 4 & 8 & 11 & 13 & 14 & 15 & 15 & 15 & 15 & 15 & 15 & 15 & 15 & 15 \\ 8 & 1 & 5 & 10 & 15 & 18 & 20 & 21 & 22 & 22 & 22 & 22 & 22 & 22 & 22 & 22 \\ 9 & 1 & 5 & 12 & 18 & 23 & 26 & 28 & 29 & 30 & 30 & 30 & 30 & 30 & 30 & 30 \\ 10 & 1 & 6 & 14 & 23 & 30 & 35 & 38 & 40 & 41 & 42 & 42 & 42 & 42 & 42 & 42 \\ 11 & 1 & 6 & 16 & 27 & 37 & 44 & 49 & 52 & 54 & 55 & 56 & 56 & 56 & 56 & 56 \\ 12 & 1 & 7 & 19 & 34 & 47 & 58 & 65 & 70 & 73 & 75 & 76 & 77 & 77 & 77 & 77 \\ 13 & 1 & 7 & 21 & 39 & 57 & 71 & 82 & 89 & 94 & 97 & 99 & 100 & 101 & 101 & 101 \\ 14 & 1 & 8 & 24 & 47 & 70 & 90 & 105 & 116 & 123 & 128 & 131 & 133 & 134 & 135 & 135 \\ 15 & 1 & 8 & 27 & 54 & 84 & 110 & 131 & 146 & 157 & 164 & 169 & 172 & 174 & 175 & 176 \\ \hline \end{array}$$

If you want a list of the possible partitions, then use:

RestrictedPartitions(n,[0..n],k);

NrRestrictedPartitions(n,[0..n],k);

Size(RestrictedPartitions(n,[0..n],k));

when $k>n$. I emailed the support team about this, and they said that NrRestrictedPartitions and RestrictedPartitions are only intended to be valid for sets of positive integers. (I still think the above is a bug, but let’s let that slide.) This means that NrPartitions(n+k,k); is the technically correct choice, and, strictly speaking, we shouldn’t use RestrictedPartitions(n,[0..n],k);, but judging from the source code, it will work as expected.


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when can i detect the position of error in hamming code

I have 4-bit data with the hamming code 0010011.
the parity parameters are: p1=0 , p2=0 , p3=0
and the check codes are: c1 = 0 , c2 = 1 , c3 = 0
so I thought that I have an error in position 2 of my data but the solution says that I can not detect the position of the error.
my question is: when I can find the position of an error in hamming code?

• okay , I think the solution was wrong – hossein hayati Apr 23 at 9:56


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# Ever shrinking number sequence

Below is a list of number sequences which follow a specific rule from one to the next. The first seven sequences are written out already. Can you deduce the next one?

1011111110111111011000
001111110011111001000
00111110001111000000
0111111001111100000
011111000111100000
01111000011100000
0111000001100000
???????????????

To assist in the solving process, I have made another sequence with a different beginning number.

1010010111101001001001
111011111111101101101
11001111111100100100
1000111111100000000
100111111110000000
10111111111000000
1111111111100000
???????????????

Hint:

Remember the base this puzzle uses, as well as another thing that involves parity.

The next value is:

111100001110000

Explanation:

We notice that most of the lines are simply the result of a bitwise AND operation of the successive digits of the prior line. For line 1 (1011111110111111011000), we have:
1&0 = 0
0&1 = 0
1&1 = 1
1&1 = 1
Continuing, we get line 2 in its entirety:
001111110011111001000
And line 3:
00111110001111000000
But then to get line 4, we must use OR:
0|0 = 0
0|1 = 1
1|1 = 1
Continuing we get line 4:
0111111001111100000
Back to AND for line 5:
011111000111100000
And line 6:
01111000011100000
And line 7:
0111000001100000

So what's the rule? Use AND unless we are parsing line 3?
This seems somewhat arbitrary. What else do we have?

The sequence began with a substring of pi's digits (1011111110111111011000 in base 2 is 3141592 in base 10)
Note that the the first few digits are mostly ODD, but digit # 3 is EVEN.
Since digit 7 is even (a 2), we should treat it like digit 3, and compute using OR.
Thus line 8, the mystery line, is the result of OR operations on the prior line:
0111000001100000 becomes:
111100001110000

This is not quite certain due to the limited size of the data set, but thanks to the second provided sequence, we can repeat the process and see that it checks out, using the even/odd parity of the second provided number. (Happens to be 2718281, OR-AND-AND-OR-etc.)

• Congratulations! : ) Nov 9 '21 at 13:07
• Well done! I definitely did not see it this way. Nov 9 '21 at 16:23

Edit: With the new information, I have an algorithm which seems to produce the right results in all cases, but is surely not what the author intended.

My rule is:

Compare the 2nd bit with the 15th bit in the sequence.
If they are both zero:
A => Replace substring 01 with 11 and then remove last bit.
Otherwise:
B => Replace substring 10 with 00 and then remove last bit.

Following this rule, the first set of sequences follow

B B A B B B

to produce the given sequences, and the last sequence

has to be B, so gives 011000000100000

The second set of sequences follows the pattern

A B B A A A

to produce the given sequences, and the last sequence

is again a B, so gives 111111111100000

Right now, my best guess is:

111100001110000

with the following rule:

On lines which are not multiples of 4, convert any 01 substring to 00 and then remove the leading digit of the sequence. On lines which are multiples of 4, convert any 01 substring to 11 and then remove the trailing digit of the sequence.

This is less an answer, and more a collection of observations, because I'm not sure where to go.

First, as per some comments, I noticed that

The first sequence is binary for the decimal number 3141592, but I can't find any other references to pi in the sequence.

This sequence is also strange because the change from one line to the next can easily be altered by a change of view. For example, for most steps:

We can change 10 to 00 and then remove trailing digit

OR

We can change 01 to 00 and then remove leading digit

I also notice that the title generally applies no matter how we look at the sequence, but then:

From line 3 to line 4, the sequence definitely increases in value if the sequences have numerical values, even if there are padding zeroes on either end, and even if the binary is big-endian or little-endian, but the sequence length itself is the only thing that's shorter/smaller

I've tried a number of solutions that involve:

subtracting a binary number and then either left-bitshifting the answer or right-bitshifting the subtrahend to go again, with mixed success, but this still doesn't account for the change from line 3 to line 4.

Is there a way to interpret the sequences so that line 4 is distinctly smaller than line 3 in a non-length way?

But also:

What causes line 4 to increase instead of decrease like all other lines?
Is it that it is line 4 (which lead to the "every fourth line" argument)?
Is it that in the first two lines, a set of 1's disappears, but line 3 doesn't manage that, so line 4 is punished? Why aren't any subsequent lines punished, then?

The next sequence is

111100001110000

Each sequence

replaces either the leading or trailing zero from each substring of $$1$$s. If the line number is evenly divisible by $$4$$ (e.g. $$n \mod 4 = 0$$) then the leading zero is replaced with a one (e.g. $$0011100$$ becomes $$011100$$). Otherwise, the trailing zero is replaced with a one (e.g. $$0011100$$ becomes $$0011110$$).

removes the last character from the sequence before it (e.g. $$0011100$$ becomes $$001110$$, if we ignore the additional work we're supposed to do).

If we do this line by line, we get:

1011111110111111011000
001111110011111001000
00111110001111000000
0111111001111100000
011111000111100000
01111000011100000
0111000001100000
111100001110000
11100000110000
1100000010000
100000000000
110000000000
10000000000
0000000000

From here, we can proceed no further since

line 14 is comprised of all zeros.

Additionally, line two, in particular, throws you off because

The last digit is dropped, and it makes it seem like the first $$1$$ was translated into a zero instead, but it wasn't.

Furthermore, line twelve is problematic because

it requires a leading $$1$$ to be added; I simply inferred that it should just push the entire value to the right. However, it could be that the line simply dropped the last value instead, in which case we'd reach all zeros on line 13 instead of line 14.

• This doesn't explain the transition from the third sequence to the fourth sequence. Nov 3 '21 at 19:41
• @DanielMathias I've updated my answer based on that fact, and I believe I have the correct answer now. Nov 3 '21 at 20:36
• According to your rule set, the number of 1s would continue to increase over time. However, this is not the case. This puzzle is slightly more mathematical, and it would be beneficial to consider what base your are using. Nov 3 '21 at 22:08


text:
# What is the consistency strength of this kind of reflection principle?

If $$\psi$$ is a predicate that is definable in $$FOL(\in,=)$$ by a formula from parameters in $$V$$, then if $$\psi$$ hold of the class $$\small ORD$$ of all ordinals in $$V$$, then the class of all cardinals in $$V$$ satisfying $$\psi$$ is non empty and is isomorphic on membership with $$\small ORD$$

Formally this is: $$\psi(\small ORD) \to \forall x (x = \{y| \ y \text{ is a cardinal } \wedge \psi(y)\} \to x \neq \emptyset \wedge x \cong \small ORD)$$

Now this axiom scheme is to be added on top of axioms of the following theory formulated in first order predicate logic with extra-logical primitives of equality, membership and a single primitive constant symbol $$V$$ denoting the class of all sets.

The axioms are those of first order identity theory +

1. Extensionality: $$\forall x (x \in a \leftrightarrow x \in b) \to a=b$$
2. Foundation over all classes: $$\exists m \in x \to \exists y \in x (y \cap x = \emptyset)$$
3. Class comprehension axiom: if $$\phi(y)$$ is a formula in which the symbol $$y"$$ occurs free, then all closures of: $$\exists x \forall y (y \in x \leftrightarrow y \in V \wedge \phi(y))$$ are axioms.

Define $$\{|\}: x=\{y|\phi(y)\} \iff \forall y (y \in x \leftrightarrow y \in V \wedge \phi(y))$$

1. Transitivity: $$x \in V \wedge y \in x \to y \in V$$

2. Supertransitivity: $$x \in V \wedge y \subseteq x \to y \in V$$

3. Pairing: $$a,b \in V \to \{a,b\} \in V$$

4. Set Union: $$a \in V \to \{x| \exists y \in a (x \in y)\} \in V$$

5. Power: $$a \in V \to \{x| x \subseteq a\} \in V$$

6. Limitation of size: $$|x| < |V| \wedge x \subset V \to x \in V$$

Where $$||"$$ denotes cardinality function defined in the usual manner.

Now its clear that this theory goes beyond $$ZFC$$, since $$\small ORD$$ would provably be a regular cardinal and so the set of all regular cardinals in $$ORD$$ must be isomorphic on membership with $$ORD$$, and so we must have inaccessible cardinals in $$ORD$$, actually it is even simpler than that, simply take the property of being "inaccessible cardinal" which is definable in the pure language of set theory, clearly $$ORD$$ fulfills that, so there must be an inaccessible cardinal in $$ORD$$. However it is not clear to me how far this theory can go to?

Question: what is the consistency strength of this theory?

• Note that over ZFC, "unbounded in $ORD$" is the same as "$\in$-isomorphic to $ORD$." So this simplifies things substantially. – Noah Schweber Dec 13 '18 at 0:05
• I am confused by your intuitive explanation. If something holds for all ordinals, it therefore holds for all cardinals. So the class of cardinals satisfying that property is all the cardinals, and is therefore isomorphic to the ordinals. Where do we go beyond ZFC here? – Asaf Karagila Dec 13 '18 at 7:22
• @AsafKaragila if something holds for $ORD$, i.e. holds for the CLASS of all ordinals in $V$, this doesn't mean that it holds for every ordinal in $V$, you are confusing the class for its members. For example take the predicate $\psi$ to be $\text{ "is regular"}$, clearly $ORD \text{ is regular}$, but that doesn't entail that every ordinal in $ORD$ is regular, nor does it mean that all cardinals in $ORD$ are regular. – Zuhair Al-Johar Dec 13 '18 at 12:11
• I don't understand $\psi(ORD)$ in your notation, then. It's not a first-order statement. What is it, then? – Asaf Karagila Dec 13 '18 at 12:13
• $ORD$ is an object of our universe of discourse, so $\psi(ORD)$ is a first order logic formula. – Zuhair Al-Johar Dec 13 '18 at 12:15


text:
# (Proof) Doubts on set of Complex numbers being open and closed

In a course of "Mathematical Methods of Phyisics" (5th semester pregrade course, which basicly consist in Complex Variable) we briefly discussed some topological notions about how to characterize sets. One guide textbook is "Elements of complex variables - Louis Pennisi".

Later, and using some definitions of, we concluded that the Complex numbers set didn't include infinity, therefore, it must not consider the whole boundary of itself (includes none). Also, in the same argument, we considered that the only way of having a set of {} points in the boundary implies that the empty set is included, but since the only element of the set (boundary) is this last one, we could argue that the complex set is also closed (because it includes every element of the boundary).

This is a Physics course so I'm really doubting about the rigour in this logic and proof itself. What do you think?, how would you show this in a formal and "provable" (valid) way?.

Also, is there any set that includes infinity or this is just a boundary concept that implies it will never be considered? In this same reasoning, could I say that every open set that is "not bounded" to other bigger numbers (only by Infinity) is also open and closed? (e.g., real numbers with the infinity in the boundary).

Is this useful in the subject?

• The complex plane $$\mathbb C$$ is a topological space in its own right, and as such is both closed and open in itself.
• The extended complex plane $$\mathbb C \cup \{\infty\}$$, also known as the Riemann sphere, is also a topological space in its own right, and as such is both closed and open in itself.
• One may regard $$\mathbb C$$ as a subset of $$\mathbb C \cup \{\infty\}$$, and in this regard $$\mathbb C$$ is an open subset, but not a closed subset, of $$\mathbb C \cup \{\infty\}$$.
There is a general pattern here: given a topological space $$X$$ and a subset $$A \subset X$$, one may ask whether $$A$$ is a closed subset of $$X$$, and one may ask whether $$A$$ is an open subset of $$X$$. What's important here is that these are regarded as properties of $$A$$ as a subset of $$X$$.
The complex plane ($$\cong \Bbb R^2$$) is connected; as is its one-point compactification ($$\cong$$ the Riemann sphere).


text:
• Understanding Survival analysis
• Research Questions
• Data Cleaning
• Data Analysis

Understanding Survival analysis

Survival analysis is a statistical method used in analyzing data on the time of an event such as death, device failure, heart attack, etc. The analysis is important during legal proceedings. It includes gathering and analyzing data to come up with ideal conclusions.

Research Questions

Environmental issues have been one of the major subjects of debate recently and it is thought that human and economic activities have endangered the environment through the emission of C02 and other toxic substances from production activities to our air water and land. There has been an unprecedented reduction in the ozone layer and has led to climate changes that have affected economies of the world generally and Australia specifically. Thus, we want to examine the impact of economic activities and structure on pollution. The broad research question is
“What is the effect of economic activities and structure on the emission of C02 and other toxic substances”. The specific research questions are
1. is there a significant effect of economic growth measured by GDP growth on emission
2. is there a significant effect of population on emission
3.is there a significant effect of the number of approved buildings on emission

Data Cleaning

I have four data sets which are on emissions, buildings, population growth, and economic growth rate. I start with the cleaning emissions data set. The data set is disaggregated by facilities and emission type. I will aggregate it by summing it over the years so that I can have the total for each year. There are three sources of emission in the data set (air, water, and land), I sum the three to have total emission. The year in the data set was written as 2018/2019, I create a new variable “year” which extract the lead year (2019 from 2018/2019) and aggregated over this year variable. Finally, I have yearly data from 1999 to 2019. The code and the sample of final data is shown in the chunk below
library(stringr)
##DATA CLEANING
emission$totalemission=rowSums(emission[,c("air_total_emission_kg","water_emission_kg","land_emission_kg")],na.rm=T) emission$year=as.numeric(str_sub(emission$report_year,6,9)) emission<-emission[,c("totalemission","year")] emission<-aggregate(emission,by=list(emission$year),FUN=sum)
emission$year=emission$Group.1
emission=emission[,2:3]
## totalemission year
## 1 1163652271 1999
## 2 3241358298 2000
## 3 3249103564 2001
## 4 3952112597 2002
## 5 3908653089 2003
## 6 3968629002 2004

Next, I clean the building's data set which is made up of monthly data from 1983 to 2020. First I remove the first 9 rows that are not observations but provide information about the data and then extract the variable that I need. Then I average over years to give a yearly time series data from 1983 to 2020. The code and the sample of final data are shown in the chunk below.
buildings<-buildings[10:450,]
buildings$dwellings=as.numeric(buildings[,3]) buildings$year=as.numeric(str_sub(buildings$X,5,8)) buildings=buildings[,c(23,24)] buildings=na.omit(buildings) buildings=aggregate(buildings,by=list(buildings$year),FUN=mean)
buildings=buildings[,c(2,3)]
## dwellings year
## 1 9656.667 1983
## 2 10250.667 1984
## 3 10009.333 1985
## 4 8072.583 1986
## 5 8364.750 1987
## 6 11301.417 1988
Next, I clean the population growth data set which is made up of quarterly data from 1981 to 2019. First I remove the first 9 rows that are not observations but provide information about the data and then extract the variable that I need. Then I average over years to give a yearly time series data from 1983 to 2020. The code and the sample of final data is shown in the chunk below.
pop=pop[10:163,]
pop$population=as.numeric(pop$Estimated.Resident.Population..ERP.....Australia..)
pop$year=as.numeric(str_sub(pop$X,5,8))
pop=pop[,16:17]
pop<-aggregate(pop,by=list(pop$year),FUN=mean) pop<-pop[,2:3] head(pop) ## population year ## 1 14988.70 1981 ## 2 15208.52 1982 ## 3 15415.55 1983 ## 4 15604.17 1984 ## 5 15816.33 1985 ## 6 16048.42 1986 There is no much to clean in the economic growth rate data set. I only create a year variable to denote year of the observations.The code and the sample of final data is shown in the chunk below. growth<-read.csv("growth.csv") growth$year=as.numeric(str_sub(growth$Date,1,4))+1 growth=growth[,2:3] head(growth) ## Growth.in.real.GDP.per.capita year ## 1 0.2 1961 ## 2 -1.1 1962 ## 3 4.2 1963 ## 4 5.0 1964 ## 5 3.9 1965 ## 6 0.4 1966 I have all my data cleaned but the lenghts are different. I see that observations for year 1999 to 2017 are available for all variables, thus I restrict my sample to this number and combine the data set. Moreover,I took the log of total emission, population and number of approved buildings while I did not take that of growth because it contains negative values. growth=growth[39:57,] pop=pop[19:37,] emission=emission[1:19,] buildings=buildings[17:35,] data<-data.frame(growth,pop,emission,buildings) data<-data[,c(2,1,3,5,7)] data$ltotalemission=log(data$totalemission) data$ldwellings=log(data$dwellings) data$lpopulation=log(data$population) Data Analysis Exploratory data analysis ##time series plot of variables par(mfrow=c(2,2)) plot(data$year,data$Growth.in.real.GDP.per.capita,ylab="GDP growth",type="l",col=1) plot(data$year,data$population,ylab="Population",type="l",col=2) plot(data$year,data$totalemission,ylab="total emissions (kg)",type="l",col=3) plot(data$year,data$dwellings,ylab="Total approved Buildings",type="l",col=4) We see from the plot that total emissions jumped drastically from the initial period and reached the peak around 2008 then falls very slowly till date. total approved buildings have flctuated over time. Same can be seen for economic growth. However, population have been increasing throughout time. ##scatterplot par(mfrow=c(2,2)) plot(data$Growth.in.real.GDP.per.capita,data$totalemission,xlab="GDP growth", ylab="total emission",col=1) plot(data$population,data$totalemission,xlab="Population", ylab="total emission",col=2) plot(data$dwellings,data\$totalemission,xlab="Total approved buildings ", ylab="total emission",col=3)

The scatterplot of total emissions against the independent variables is shown above. We hardly see any pattern of relationship between total emission and the independent variables.
library(Hmisc)
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
##
## format.pval, units
corr.mat<-rcorr(as.matrix(data[,2:5]))
corr.mat
## Growth.in.real.GDP.per.capita population
## Growth.in.real.GDP.per.capita 1.00 -0.62
## population -0.62 1.00
## totalemission -0.43 0.32
## dwellings -0.01 0.09
## totalemission dwellings
## Growth.in.real.GDP.per.capita -0.43 -0.01
## population 0.32 0.09
## totalemission 1.00 -0.15
## dwellings -0.15 1.00
##
## n= 19
##
##
## P
## Growth.in.real.GDP.per.capita population
## Growth.in.real.GDP.per.capita 0.0044
## population 0.0044
## totalemission 0.0632 0.1818
## dwellings 0.9821 0.7074
## totalemission dwellings
## Growth.in.real.GDP.per.capita 0.0632 0.9821
## population 0.1818 0.7074
## totalemission 0.5439
## dwellings 0.5439
The result shows that there is negative medium correlation between GDP growth and total emmsions (r=-0.43) and is significnat at 10% alpha level (p=0.0632). there is negative weak (r=-0.15) but insignificant (p=0.1818>0.05) between total emissions and number of approved buildings. There exist poistive medium (r=0.32) but insignificant (p=0.5439>0.05) relationship between total emissions and dwellings.

Linear and Predictive Modelling

model<-lm(ltotalemission~Growth.in.real.GDP.per.capita+lpopulation+ldwellings,data=data)
summary(model)
##
## Call:
## lm(formula = ltotalemission ~ Growth.in.real.GDP.per.capita +
## lpopulation + ldwellings, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.76158 -0.10547 0.00244 0.15319 0.32270
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.44494 10.78909 2.266 0.0387 *
## Growth.in.real.GDP.per.capita -0.11043 0.07472 -1.478 0.1601
## lpopulation 0.34170 0.91284 0.374 0.7134
## ldwellings -0.62367 0.70515 -0.884 0.3904
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2597 on 15 degrees of freedom
## Multiple R-squared: 0.2755, Adjusted R-squared: 0.1305
## F-statistic: 1.901 on 3 and 15 DF, p-value: 0.1729
The regression result above shows that the estimated regression model is ltotalemissions=24.44-0.11growth+0.34lpopulation-0.62ldwellings. The result shows that contrary to expectation, the number of approved buildings and growth in GDP has a negative effect on total emission. Specifically, a 1% increase in the number of approved buildings reduces emission by 0.62% reduction in emission while a 1% increase in GDP growth reduces total emission by 11.04%. Finally, a 1% increase in population increases totals emission by 0.34%. However, all these variables are not significant as all have p-values greater than 0.05. The adjusted R-squared shows that 13.05% of the variation is explained by the independent variables. ###Predictive Modelling.
library(randomForest)
## randomForest 4.6-14
## Type rfNews() to see new features/changes/bug fixes.
##
## Attaching package: 'randomForest'
## The following object is masked from 'package:ggplot2':
##
## margin
set.seed(58)
rfm<-randomForest(ltotalemission~.,data=data[,c(2,6,7,8)],ntree=500,importance=T)
print(rfm)
##
## Call:
## randomForest(formula = ltotalemission ~ ., data = data[, c(2, 6, 7, 8)], ntree = 500, importance = T)
## Type of random forest: regression
## Number of trees: 500
## No. of variables tried at each split: 1
##
## Mean of squared residuals: 0.07360822
## % Var explained: -0.19
The mean of squared residuals is 0.0736 with 0.19 percent of variance explained.
importance(rfm)
## %IncMSE IncNodePurity
## Growth.in.real.GDP.per.capita 0.91483892 0.4931572
## ldwellings -0.09948159 0.1740888
## lpopulation 9.85744741 0.4757064
varImpPlot(rfm)

The result above shows that the population is the most important variable explaining total emissions as it has the highest mean decrease accuracy.

Conclusion

We have examined whether economic growth and structure contribute to environmental pollution using yearly time series data from 1999 to 2017. The result of the multiple linear regression model shows that none of the considered economic variables are significant which means there is no effect of economic growth and structure on the emission of a toxic substance to the environment. The limitation of this is that we cannot rule out the possibility of omitted variable bias given that the omnibus F-test is not significant which means the model needs to be improved upon by finding variables that may be significant but have been left out. However, this provides a good starting point in investigating this important topic.


text:
# American Institute of Mathematical Sciences

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June  2018, 23(4): 1601-1621. doi: 10.3934/dcdsb.2018063

## Palindromic control and mirror symmetries in finite difference discretizations of 1-D Schrödinger equations

 Department of Mathematics and Statistics, University of Nebraska Kearney, Kearney, Nebraska 68849, USA

* Corresponding author: Katherine A. Kime

Received  May 2017 Published  February 2018

We consider discrete potentials as controls in systems of finite difference equations which are discretizations of a 1-D Schrödinger equation. We give examples of palindromic potentials which have corresponding steerable initial-terminal pairs which are not mirror-symmetric. For a set of palindromic potentials, we show that the corresponding steerable pairs that satisfy a localization property are mirror-symmetric. We express the initial and terminal states in these pairs explicitly as scalar multiples of vector-valued functions of a parameter in the control.

Citation: Katherine A. Kime. Palindromic control and mirror symmetries in finite difference discretizations of 1-D Schrödinger equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1601-1621. doi: 10.3934/dcdsb.2018063
##### References:

show all references

##### References:
Example 1. $\alpha$-Localized, Mirror-Symmetric
Example 2. Not Localized, Not Mirror-Symmetric
Example 3. Localized with Equal Degree of Restriction Equal to 1, Not $\alpha$-Localized, Not Mirror-Symmetric
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2019 Impact Factor: 1.27


text:
# How do I create a Multi Port LBAAS Listener, using the UI

I'm using Horizon to administrate an openstack setup. We have the LBAAS UI installed, to setup Load Balancers. What I need is a single Load Balancer, listening on multiple ports on the same IP. I can see in http://docs.openstack.org/mitaka/networking-guide/config-lbaas.html (http://docs.openstack.org/mitaka/netw...) that this is relatively straight forward using neutron cli commands, but I don't have access to those. So how can I do it using the UI?

The example, using cli commands, simlifies to:-

neutron lbaas-loadbalancer-create --name test-lb private-subnet
neutron lbaas-listener-create \
--name test-lb-http \
--protocol HTTP \
--protocol-port 80
neutron lbaas-listener-create \
--name test-lb-https \


text:
1. ## Mixture problem

A tank initially contains 60 gal of pure water. Brine containing 1 lb of salt per gallon enters the tank at 2 gal/min, and the (perfectly mixed) solution leaves the tank at 3 gal/min; thus the tank is empty after exactly 1 h.

(a) Find the amount of salt in the tank after t minutes.
(b) What is the maximum amount of salt ever in the tank?

My working:

Let x(t) (in lb) be the amount of salt in the tank at time t.

(a) $\frac{dx}{dt}=r_ic_i-r_oc_o=2*1-3*\frac{x}{60-t}=2-\frac{3x}{60-t}$

$\frac{dx}{dt}+\frac{3x}{60-t}=2$

$\rho(t)=exp\left(\int \frac{3}{60-t}dt\right)=exp(-3ln\ (60-t))=\frac{1}{(60-t)^3}$

Multiplying by $\rho(t)$, we get

$\frac{1}{(60-t)^3}\frac{dx}{dt}-\frac{3x}{(60-t)^4}=\frac{2}{(60-t)^3}$

$\frac{d}{dt}\left[\frac{x}{(60-t)^3}\right]=\frac{2}{(60-t)^3}$

$\frac{x}{(60-t)^3}=2\frac{(60-t)^{-2}}{2}+C$

$\frac{x}{(60-t)^3}=\frac{1}{(60-t)^2}+C$

$x=(60-t)+C(60-t)^3$

$x(0)=0$

$0=60+C*60^3$

$C=-\frac{1}{3600}$

$x=(60-t)-\frac{(60-t)^3}{3600}$

Solved it! Don't bother.

2. ## Re: Mixture problem

Aww, you're just showin' off!


text:
# Solve the following function $\int\limits_{ – \pi }^\pi {\sin (t)\sin (3t)dt = }$

Solve the following function $\int\limits_{ - \pi }^\pi {\sin (t)\sin (3t)dt = }$

$\int\limits_{ – \pi }^\pi {\sin (t)\sin (3t)dt = }$