This problem set deals with the problem of non-constant acceleration. Two researchers from Fly By Night Industries conduct an experiment with a sports car on a test track. While one is driving the car, the other will look at the speedometer and record the speed of the car at one-second intervals. Now, these aren’t official researchers and this isn’t an official test track, so the speeds are in miles per hour using an analog speedometer. The data set they create is:\[\{(1, 5), (2, z), (3, 30), (4, 50), (5, 65), (6, 70)\}\]$Z = 25$They notice that the acceleration is not a constant value. They decide that a fourth-degree polynomial will be the best to describe the speed of the car as a function of time.The task here is to determine the fourth-degree polynomial that fits this data set the best.1. Use a general fourth-degree polynomial and Fly By Night’s data to construct six equations. Note that the equations are linear in the coefficients. Write the equations here:2. Construct the least-squares problem $A\vec{x} = \vec{b}$.\[A = \]\[\vec{b} = \]

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Sixty-five wind speed readings gave an average velocity of x = 1075 cm/sec. Based on long-term experience, ? can be assumed to be 255 cm/sec. (a) Find a 95% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number.) lower limit ______cm/sec upper limit _____cm/sec
Please answer the questions using the data in Table 8. (Note: You must use either Microsoft Excel or Minitab for this problem and include the table they produce with your work.) Questions 8A to 8C Table 8. Data for problem 8. I2 18.7 18.7 I1 9.2 9.3 9.6 9.0 11.7 8.2 11.0 10.0 10.5 8.7 18.1 21.3 21.1 19.7 19.7 19.5 16.4 19.7 13 27.4 23.8 38.1 32.4 24.6 27.0 25.0 27.5 26.3 43.1 80.6 62.8 137.3 94.8 62.0 72.6 68.2 79.5 86.9 154.1 8A. Use technology to find the multiple regression equation for the data shown in Table 8. (Note: You must use either Microsoft Excel or Minitab for this problem and include the table the app produces with your work to get full score.) 8B. Find the standard error of estimate and interpret the result. 8C. Find the coefficient of determination and interpret the result. (Note: do not use the adjusted R-square.)
Compare the linear regression data for two students walking in front of a motion sensor: Bob’s walk d = 0.75t + 2 r = 0.70 Tracey’s walk d = 0.75t + 2 r = 0.95 a) How are the movements of these walkers similar? different? b) Sketch possible distance versus time graphs for Bob and Tracey.
At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Sixty-two wind speed readings gave an average velocity of x = 1075 cm/sec. Based on long-term experience, σ can be assumed to be 260 cm/sec. (a) Find a 95% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number.) lower limit cm/sec upper limit cm/sec (b) Does the confidence interval indicate that the population mean wind speed is such that the sand is always moving at this site? Explain. No. This interval indicates that the population mean wind speed is such that the sand may not always be moving…
The Park family would like to prepare next month's family budget by forecasting its family expenses. The following data show the amount of money spent on food for the last 10 months. Complete parts a through d below. Month Dollars 1 343 2 357 3 294 The best choice is the a) Forecast the family's food expenditures next month using a three-period simple moving average. The forecast for the family's food expenditures next month is $ (Round to the nearest dollar as needed.) b) The forecast for the family's food expenditures next month is $ (Round to the nearest dollar as needed.) d) Which forecast should you choose? Why? 4 336 The forecast for the family's food expenditures next month is $ (Round to the nearest dollar as needed.) c) Forecast the family's food expenditures next month using exponential smoothing with a = 0.1. 5 361 because it has the 6 339 Forecast the family's food expenditures next month using a three-period weighted moving average with weights 0.7, 0.2, and 0.1, applying…
QUESTION II The fashion brand Luis Buittou's iconic product is its ochre scarf. It has also been selling many of its camel shawls, a variant of the ochre scarf. You are in charge of studying the monthly sales of the ochre scarves and the camel shawl for Luis Buittou in the Boston shops. You collect data points X1, X120 for the ochre scarves and Y1,, Yi for the camel shawls, that represent the number of each product sold each month over the past 10 years. The average mumber of scarves sold per month is X = XitA = 77. The standard deviation is ox = 12. The average mumber of shawls sold per month is Y= tY= 80. The standard deviation is also oy = 12. The marketing analyst suggest switching entirely to the camel shawls as it sells better, even though the switch entails some restructuring cost. L.... %3D 120 Yi++Y %3D 190 %3D (a) You decide to test the claim "the mean value of camel shawls sold per month is larger than the mean value of ochre scarfs sold per month" at 95% confidence level.…
Use the data provided on Canvas. In automotive assembly processes, automation cannot always guarantee the dimensional accuracy of a car assembly as required by the design specification. Thus, some skillful workers will visually inspect those assembled car bodies and conduct manual adjustments when necessary. These workers are called "Fitter" in the automotive industry. This scenario is illustrated in the following figure. Automatic assembly process X P₁ Fitter Y P₂ One critical quality characteristics on a car assembly were measured at both P₁ (before fitter) and P₂ (after fitter). The data are labeled as X and Y, respectively, and 20 measurements are shown below. Please use the risk adjustment method to test if X and/or Y are in control. Please show X chart, Y chart and Z chart.
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Who do you think would be more fearful of walking in their neighborhoods at night: males or females? Must use gamma, Yule’s Q and 2 x 2 tables, what does the following table, and accompanying statistics, tell you about the actual direction and strength of the relationship? Support your Answer must be supported with details from the table.
Questions 7-10
You want to determine how many loaves of Bread are sold per day at Schat’s Bakery. You stand outside for ten different randomly selected days, count the number of loaves, and then average them. You come up with 421 loaves per day. In reality, Schat’s keeps records of how many loaves they sell per day, and in they averaged 395 loaves per day. What is the static in the above example?
This problem set deals with the problem of non-constant acceleration. Two researchers from Fly By Night Industries conduct an experiment with a sports car on a test track. While one is driving the car, the other will look at the speedometer and record the speed of the car at one- second intervals. Now, these aren't official researchers and this isn't an official test track, so the speeds are in miles per hour using an analog speedometer. The data set they create is: {(1,5), (2, 2), (3, 30), (4, 50), (5, 65), (6,70)} Z = 25 They notice that the acceleration is not a constant value. They decide that a fourth-degree polynomial will be the best to describe the speed of the car as a function of time. The task here is to determine the fourth-degree polynomial that fits this data set the best. 1. Construct the system of normal equations A¹ AX = A¹b. AT A = A¹b = 2. Solve the system of normal equations. (I don't want you doing this by hand. Use a calculator or app.) x =

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