Explanation Given: As a car begins to accelerate, the gas mileage is poor. As the speed increases, the gas mileage begins to increase. The gas mileage increases for a while; then as the speed increases further, the mileage begins to decrease. The table of data illustrates this. Definition used: If we have pairs of data for two variables x and y , the linear correlation coefficient for these data, denoted by r , is given by the formula r = n ∑ x y − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 n ( ∑ y 2 ) − ( ∑ y ) 2 , where n is the number of pairs of data we have for x and y . Calculation: Consider the given xy pairs. The computations to calculate correlation coefficient is shown below x y xy x 2 y 2 30 26 780 900 676 40 31 1240 1600 961 50 33 1650 2500 1089 60 31 1860 3600 961 70 26 1820 4900 676 ∑ x = 250 ∑ y = 147 ∑ x y = 7350 ∑ x 2 = 13500 ∑ y 2 = 4363 Since there are five pairs of ( x , y ) , the n value is 5

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ISBN: 9780134506470

Author: Pirnot

Publisher: PEARSON

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Chapter 14.5, Problem 17E

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To find:

The linear correlation coefficient for the data and also to determine whether we can be 95% or 99% confident that there is significant linear correlation between the two variables.

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Chapter 14.5, Problem 16E

Chapter 14.5, Problem 18E

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Question 4 (a) Find all possible values of a, b such that [sin(ax)]ebt solves the heat equation U₁ = Uxx, x > 0. (b) Consider the solution U(x,t) = (sin x)e¯t of the heat equation U₁ = Uxx. Find the location of its maxima and minima in the rectangle Π {0≤ x ≤ 1, 0 ≤t≤T} 00} (explain your reasonings for every steps). U₁ = Uxxx>0 Ux(0,t) = 0 U(x, 0) = −1

Could you please solve this question on a note book. please dont use AI because this is the third time i upload it and they send an AI answer. If you cant solve handwritten dont use the question send it back. Thank you.

Chapter 14 Solutions

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The linear correlation coefficient for the data and also to determine whether we can be 95% or 99% confident that there is significant linear correlation between the two variables.

Solution Summary: The author analyzes the linear correlation coefficient for two variables x and y, and determines whether there is significant correlation between the variables.

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To find: The linear correlation coefficient for the data and also to determine whether we can be 95% or 99% confident that there is significant linear correlation between the two variables.

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Chapter 14 Solutions

To find:

The linear correlation coefficient for the data and also to determine whether we can be 95% or 99% confident that there is significant linear correlation between the two variables.