The total length of 4 blue banners and 5 yellow banners is 49m. The total length of 2 blue banners and 1 yellow banner is 17m. All banners of the same colour have the same length. Find the length of a blue banner.
Assignment 1. Linear Programming Case Study (ATTACHED)Your instructor will assign a linear programming project for this assignment according to the following specifications.It will be a problem with at least three (3) constraints and at least two (2) decision variables. The problem will be bounded and feasible. It will also have a single optimum solution (in other words, it won’t have alternate optimal solutions). The problem will also include a component that involves sensitivity analysis and the use of the shadow price.You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.Writeup.Your writeup should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.After the introductory paragraph, write out the L.P. model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.Excel.As previously noted, please set up your problem in Excel and find the solution using Solver. Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.
1. Create a digraph for the following set of tasks:3. Using the priority list T4, T1, T7, T3, T6, T2, T5, schedule the project with two processors.5. Using the priority list T4, T3, T9, T10, T8, T5, T6, T1, T7, T2 schedule the project with two processors.7. Using the priority list T4, T3, T9, T10, T8, T5, T6, T1, T7, T2 schedule the project with three processors.9. Use the decreasing time algorithm to create a priority list for the digraph from #3, and schedule with two processors.10. Use the decreasing time algorithm to create a priority list for the digraph from #3, and schedule with three processors.15. With the digraph from #3: a. Apply the backflow algorithm to find the critical time for each task b. Find the critical path for the project and the minimum completion time c. Use the critical path algorithm to create a priority list and schedule on two processors.
What is the list of five numbers whose values are between 50.98 and 51.6?
1.) In a National Highway Traffic Safety Administration report, data provided to the NHTSA by Goodyear stated that the average tread life of property inflated automobile tires is 45,000 miles. Suppose that the current distribution of tread life of properly inflated automobile tires is normally distributed with a mean with a mean of 45,000 mies and a standard deviation of 2360 miles.a.) Suppose that 6% of all automobile tires with the longest tread life have a tread life of at least x miles. Find the value of x.b.) Suppose that 2% of all automobile tires with the longest tread life have a tread life of at least x miles. Find the value of x.2.) Spoke Weaving Corportion has eight weaving machines of the same kind and of the same age. The probability is 0.04 that any weaving machine will break down at any time. Find the probability that an any given time :a.) all eight weaving machines will be broken down.b.) exactly two weaving machines will be broken down.3.) Paige Darby, who lives in the San Francisco Bay area, commutes by the car from home to work. She knows that it takes her an average of 28 minutes for this commute in the morning. However, due to the variability in the traffic situation every morning, that standard deviation of these commutes is 5 minutes. Suppose the population of her morning commute times has a normal distribution with a mean of 28 minutes and a standard deviation of 5 minutes. Paige has to be at work by 8:30 am every morning. By what time must she leave home in the morning so that she is late for work at most 1% of the time?
case study and BPMN chart in PPT
Imagine using math to explain how you know your friends and acquaintances. Were any of the people in your life introduced to you through another friend or acquaintance?In this Discussion, you will create a visual representation that models relationships similar to the “six degrees of separation” as presented in your readings.Chapters 14, paying special attention to the beginning of Section 14.1.Select a favorite television series, movie, or novel with an extensive cast of characters that you consider interesting. Determine a relationship that exists among some, but not all, of the characters.Consider the following graph, which represents the one-way airfare between five cities.a. First use a graph tool like Graph Creator to represent the information in the table. Use vertices to represent the cities and weights on appropriate edges to show the airfares.b. Next, assume that you are a salesman who lives in one of the cities (pick any city except for A) and required to fly to all four of the other cities and return to your home city. Describe how you would use the Nearest Neighbor Method to determine the optimal route. What is the total cost for this Hamilton circuit?
Here are some questions to consider as you reflect on your strategy for learning and mastery of new material.Please address each bullet point under both of these topics in a thoughtful 1-2 paragraph response.Strategy:Have you figured out a study strategy that works well for you? For example, do you have a fixed time each day or certain days of the week dedicated to your studies?Do you find the eText or the videos more useful for helping you learn? Have you used other resources that you would like to share with your classmates?Describe how you use ALEKS. Do you jump right into solving problems, using the text and videos only when you get stuck, or do you read and watch videos BEFOREstarting the problems?Mastering Content:Which concepts or problems have you found to be the most challenging so far? What did you do to overcome this challenge? What do you still have questions about?After working through the problems in ALEKS, do you feel confident in your abilities to solve problems?Are you “comfortable being uncomfortable” with new material? This means you have a growth mindset and are open to new learning, even if it means being confused for a while and making some mistakes at first. It’s OK to “get it wrong” and ask questions! Visit Change your Mindset (https://mindsetonline.com/changeyourmindset/firststeps/index.html) for some tips on becoming more comfortable facing new challenges that may feel frustrating to you. If learning math makes you uncomfortable, what can you tell yourself so you feel more confident
final practice exam
QUESTION 1The probability distribution of a random variable X isx–2–1012P ( X = x )Compute the mean, variance, and standard deviation of X.a.b.c.d.1 pointsQUESTION 2A probability distribution has a mean of 57 and a standard deviation of 1.4. Use Chebychev’s inequality to find the value of c that guarantees the probability is at least 96% that an outcome of the experiment lies between 57 – c and 57 – c. (Round the answer to nearest whole number.)a.3b.9c.1d.7e.51 pointsQUESTION 3Find the variance of the probability distribution for the histogram:a.Var ( X) = 4.2625b.Var ( X) = 4.65c.Var ( X) = 4.28d.Var ( X) = 4.01251 pointsQUESTION 4The birthrates in the country for the years 1981-1990 are:Year1981198219831984198519861987198819891990Birthrate15.915.515.515.715.715.615.715.916.216.7(The birthrate is the number of live births/1,000 population.)Compute the mean, variance, and standard deviation of the random variable X.a.b.c.d.1 pointsQUESTION 5Rosa Walters is considering investing $10,000 in two mutual funds. The anticipated returns from price appreciation and dividends (in hundreds of dollars) are described by the following probability distributions:Mutual Fund AReturnsProbability-40.280.3100.5Mutual Fund BReturnsProbability-20.260.680.2Compute (in dollars) the mean and variance for each mutual fund.a. Mutual Fund A:Mutual Fund B:b. Mutual Fund A:Mutual Fund B:c. Mutual Fund A:Mutual Fund B:d. Mutual Fund A: Mutual Fund B:1 pointsQUESTION 6The number of Americans without health insurance, in millions, from 1995 through 2002 is summarized in the following table.Year19951996199719981999200020012002Americans40.541.443.644.740.239.241.143What is the standard deviation of Americans without health insurance in the period from 1995 through 2002?a. millionb. millionc. milliond. millione. million1 pointsQUESTION 7The mean annual starting salary of a new graduate in a certain profession is $43,000 with a standard deviation of $500. What is the probability that the starting salary of a new graduate in this profession will be between $39,500 and $46,500?a.At leastb.At leastc.At leastd.At least1 pointsQUESTION 8A survey was conducted by the market research department of the National Real Estate Company among 500 prospective buyers in a large metropolitan area to determine the maximum price a prospective buyer would be willing to pay for a house. From the data collected, the distribution that follows was obtained.Compute the standard deviation of the maximum price (in thousands of dollars) that these buyers were willing to pay for a house. Round the answer to the nearest integer.Maximum Price Considered, 150160170180190220250270320a.b.c.d.e.1 pointsQUESTION 9The following table gives the scores of 30 students in a mathematics examination.Scores90-9980-8970-7960-6950-59Students381351Find the mean and the standard deviation of the distribution of the given data. Hint: Assume that all scores lying within a group interval take the midvalue of that group.a.b.c.d.e.1 pointsQUESTION 10A probability distribution has a mean of 45 and a standard deviation of 1. Use Chebychev’s inequality to estimate the probability that an outcome of the experiment lies between 43 and 47.a.At least 0.8b.At least 0.75c.At least 0.5d.At least 0.25e.At least 0.04TwoQUESTION 1Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve.P ( – 1.36 < Z < 1.75 )a.P (- 1.36 < Z < 1.75 ) = 0.0869b.P (- 1.36 < Z < 1.75 ) = 0.8730c.P (- 1.36 < Z < 1.75 ) = 0.9599d.P (- 1.36 < Z < 1.75 ) = 1.04681 pointsQUESTION 2Suppose X is a normal random variable with and . Find the value of .a.0.9050b.0.8996c.0.8945d.0.8818e.0.98571 pointsQUESTION 3Find the value of the probability of the standard normal variable Z corresponding to this area.P ( Z > 2.31 )a.P ( Z > 2.31 ) = 0.0084b.P ( Z > 2.31 ) = 0.0104c.P ( Z > 2.31 ) = 0.0136d.P ( Z > 2.31 ) = 0.98961 pointsQUESTION 4Suppose X is a normal random variable with and . Find the value of .a.0.498b.0.726c.0.495d.0.4333e.0.721 pointsQUESTION 5Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve.P ( 0.3 < Z < 1.85 )a.P (0.3 < Z < 1.85 ) = 0.3499b.P (0.3 < Z < 1.85 ) = 1.5857c.P (0.3 < Z < 1.85 ) = 0.9678d.P (0.3 < Z < 1.85 ) = 0.6179ThreeQUESTION 1According to data released by the Chamber of Commerce of a certain city, the weekly wages (in dollars) of female factory workers are normally distributed with a mean of 575 and a standard deviation of 50. Find the probability that a female factory worker selected at random from the city makes a weekly wage of $550 to $625.a.The probability is 0.5438.b.The probability is 0.5328.c.The probability is 0.4297.d.The probability is 0.5339.1 pointsQUESTION 2To be eligible for further consideration, applicants for certain Civil Service positions must first pass a written qualifying examination on which a score of 70 or more must be obtained. In a recent examination it was found that the scores were normally distributed with a mean of 67 points and a standard deviation of 6 points. Determine the percentage of applicants who passed the written qualifying examination.a.18.79% applicants passed the written qualifying examination.b.19.52% applicants passed the written qualifying examination.c.30.85% applicants passed the written qualifying examination.d.24.74% applicants passed the written qualifying examination.1 pointsQUESTION 3Use the appropriate normal distribution to approximate the resulting binomial distribution.The manager of Madison Finance Company has estimated that, because of a recession year, 5% of its 400 loan accounts will be delinquent. If the manager's estimate is correct, what is the probability that 11 or more of the accounts will be delinquent?a.The probability is 0.9994.b.The probability is 0.9891.c.The probability is 0.8137.d.The probability is 0.9854.1 pointsQUESTION 4Use the appropriate normal distribution to approximate the resulting binomial distribution.A basketball player has a 75% chance of making a free throw. What is the probability of her making 80 or more free throws in 120 trials?a.The probability is 0.9744.b.The probability is 0.9822.c.The probability is 0.9864.d.The probability is 0.9898.1 pointsQUESTION 5Use the appropriate normal distribution to approximate the resulting binomial distribution.Colorado Mining and Mineral has 800 employees engaged in its mining operations. It has been estimated that the probability of a worker meeting with an accident during a 1-year period is .1. What is the probability that more than 80 workers will meet with an accident during the 1-year period?a.The probability is 0.4684.b.The probability is 0.4669.c.The probability is 0.8491.d.The probability is 0.4761.
