Explanation Given information: f avg a , b denote the average value of f on the interval a , b . Concept used: Consider the real valued function with independent variable of t under the interval of a , b as follows: f x The average value of the function f x under the interval a , b , is as follows: f avg = 1 b − a ∫ a b f x d x . Calculation: Split the expression of equation f avg = 1 b − a ∫ a b f x d x for the condition of a < c < b , it follows: f avg = 1 b − a ∫ a b f x d x = 1 b − a ∫ a c f x d x + ∫ c b f x d x = 1 b − a ∫ a c f x d x + 1 b − a ∫ c b f x d x Simplify it as follows

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Author: Stewart

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Chapter 6.5, Problem 26E

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To show: favga,b=c−ab−afavga,c+b−cb−afavgc,b .

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Chapter 6.5, Problem 25E

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A mathematics instructor at a large university has determined that a student's probability of success in the pass/fail algebra course is a function of s, n, and a, where s is the student's score on the departmental placement exam, n is the number of semesters of mathematics passed in high school, and a is the student's mathematics SAT score. The instructor estimates that p, the probability of passing the course (in percent), will be 1/2 p=f(s,n,a) = 0.078a+ 4(sn) for 200 ≤a ≤ 800, 0≤s≤ 10, and 0≤n≤8. Assume that this model has some merit. Complete parts a - c below. a. If a student scores 8 on the placement exam, has taken 5 semesters of high school math, and has an SAT score of 450, what is the probability that the student will pass the course? The probability is%. (Round to the nearest percent as needed.) b. Find p for a student with 3 semesters of high school mathematics, a placement score of 4, and an SAT score of 300. p=% (Round to the nearest percent as needed.) c. Find and…

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f avg a , b = c − a b − a f avg a , c + b − c b − a f avg c , b .

Solution Summary: The author analyzes the expression of the equation f_avgleft[a,bright].

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To show: favga,b=c−ab−afavga,c+b−cb−afavgc,b .

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