The population, f, of asmall community on theoutskirts of a city grewrapidly overa fifteenyear period, ascan beseen in the table:1015f(x)100212448949Here x denotes time (inyears), while f(x)represents the size ofthe population of thecommunity at time x.Asan engineer workingfor an electricitycompany, you must find anapproximation for whatthe population size wasat time x = 7.5, in orderto estimate what the to estimate what thedemand for electricitywasat the time.a) Construct a backwarddifference table for thedata.b) Use the backwarddifference tablepresented in a), alongwith Newton's backwarddifference formula, toapproximate f(7.5) with apolynomial of degree 2,P2(x). Start withXn15.c) Estimate the error inthe approximation in b).

Answered: to estimate what the demand for…

to estimate what the demand for electricity was at the time. a) Construct a backward difference table for the data. b) Use the backward difference t able

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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Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days y km/100 71 76 31 92 203 14.2 19.6 5.8 11.2 35.9 (a) Verify that Ex = 473, Ey = 86.7, Ex² = 61,451, Ey? 2033.69, Exy = 10995.7, and r 0.93868. %3D %3D %3D %3D %3D Σχ Ey Ex? Ey2 Σχy (b) Use a 1% level of significance to test the claim p > 0. (Use 2 decimal places.) critical t Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is insufficient evidence…
The amount of time adults spend watching television is closely monitored by firms because this helps to determine advertising pricing for commercials. Complete parts (a) through (d). ..... (a) Do you think the variable "weekly time spent watching television" would be normally distributed? If not, what shape would you expect the variable to have? A. The variable "weekly time spent watching television" is likely symmetric, but not normally distributed. B. The variable "weekly time spent watching television" is likely uniform, not normally distributed. C. The variable "weekly time spent watching television" is likely skewed right, not normally distributed. D. The variable "weekly time spent watching television" is likely normally distributed. E. The variable "weekly time spent watching television" is likely skewed left, not normally distributed. (b) According to a certain survey, adults spend 2.25 hours per day watching television on a weekday. Assume that the standard deviation for "time…
Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink. Shelia's measured glucose level one hour after the sugary drink varies according to the Normal distribution with µ = 124 mg/dl and σ = 13 mg/dl. If a single glucose measurement is made, what is the probability that Shelia is diagnosed as having gestational diabetes?
The amount of time adults spend watching television is closely monitored by firms because this helps to determine advertising pricing for commercials. Complete parts (a) through (d). (a) Do you think the variable "weekly time spent watching television" would be normally distributed? If not, what shape would you expect the variable to have? A. The variable "weekly time spent watching television" is likely normally distributed. O B. The variable "weekly time spent watching television" is likely symmetric, but not normally distributed. O C. The variable "weekly time spent watching television" is likely skewed left, not normally distributed. O D. The variable "weekly time spent watching television" is likely uniform, not normally distributed. E. The variable "weekly time spent watching television" is likely skewed right, not normally distributed. (b) According to a certain survey, adults spend 2.25 hours per day watching television on a weekday. Assume that the standard deviation for "time…
3. The police department is assessing its staffing requirements. The department expects that the number of serious crimes committed, C, on average each week is proportional to the number of officers, P, on special street patrol. Data for the past year has been collected and some of it is shown below: P 4 7 9 11 15 17 с 14 11 10 9 7 5 a) Neatly sketch a scatter plot of the data on graph provided below. Which variable is the independent variable that should be plotted on the horizontal axis? Notice that the data seem to fall in a linear pattern. Draw the best-fit line through the data. Label your axes, indicate the scale, and title your graph. Why has only the first quadrant been provided for the graph? b) Look at your best-fit line and identify two good coordinate points that sit right on this best-fit line:
The amount of time adults spend watching television is closely monitored by firms because this helps to determine advertising pricing for commercials. Complete parts (a) through (d). (a) Do you think the variable "weekly time spent watching television" would be normally distributed? If not, what shape would you expect the variable to have? O A. The variable "weekly time spent watching television" is likely uniform, not normally distributed. O B. The variable "weekly time spent watching television" is likely skewed left, not normally distributed. O C. The variable "weekly time spent watching television" is likely normally distributed. O D. The variable "weekly time spent watching television" is likely skewed right, not normally distributed. O E. The variable "weekly time spent watching television" is likely symmetric, but not normally distributed. (b) According to a certain survey, adults spend 2.45 hours per day watching television on a weekday. Assume that the standard deviation for…
Solve attached photo.
Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with mean 128 mg/dl and standard deviation 9 mg/dl. Let ? denote a patient's glucose level. (a) If measurements are made on four different days, find the level ? such that there is probability only 0.01 that the mean glucose level of four test results falls above ? for Shelia's glucose level distribution. What is the value of ??ANSWER: (b) If the mean result from the four tests is compared to the criterion 140 mg/dl, what is the probability that Shelia is diagnosed as having gestational…
2. Which model-linear, quadratic, or exponential-seems most appropriate for this scatter plot? X
Which of the following statements is true? 1. The R (ie., R-squared) tells us the percentage of the variation in the dependent variable (cost) that is explained by variation in the independent variable (activity) II The R (e. R-squared) varies from 0% to 100%, and the lower the percentage, the better the fit of the data to a straight line. ONeither statement is true. Only statement I is true. Only statement II is tru. Both statements are true.
We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of fifteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Also given is the product of the distance from the beach and the house price for each of the fifteen houses. (These products, written in the column labelled "xy", may aid in calculations.) Distance from the beach, x (in miles) Selling price, y (in thousands of dollars) xy 5.0 270.1 1350.5 11.5 205.9 2367.85 5.9 309.4 1825.46 12.2 200.6 2447.32 2.6 307.1 798.46 5.9 266.0 1569.4 8.3 297.3 2467.59 18.3 224.2 4102.86 6.5 242.4 1575.6 12.1 192.6 2330.46 11.6 229.4 2661.04 9.5 230.9 2193.55 10.1 277.0 2797.7 13.5 270.8 3655.8 6.2…
The amount of time adults spend watching television is closely monitored by firms because this helps to determine advertising pricing for commercials. Complete parts (a) through (d). C (a) Do you think the variable "weekly time spent watching television" would be normally distributed? If not, what shape would you expect the variable to have? A. The variable "weekly time spent watching television" is likely skewed right, not normally distributed. OB. The variable "weekly time spent watching television" is likely symmetric, but not normally distributed. O C. The variable "weekly time spent watching television" is likely skewed left, not normally distributed. O D. The variable "weekly time spent watching television" is likely normally distributed. O E. The variable "weekly time spent watching television" likely uniform, not normally distributed. (b) According to a certain survey, adults spend 2.45 hours per day watching television on a weekday. Assume that the standard deviation for "time…