Answers
[tex]\bar{x} = 0[/tex]
[tex]\bar{y} =\dfrac{136}{125}[/tex]
Step-by-step explanation:
Let's define our functions [tex]f(x)\:\text{and}\:g(x)[/tex] as follows:
[tex]f(x) = x^2 + 1[/tex]
[tex]g(x) = 6x^2[/tex]
The two functions intersect when [tex]f(x)=g(x)[/tex] and that occurs at [tex]x = \pm\frac{1}{5}[/tex] so they're going to be the limits of integration. To solve for the coordinates of the centroid [tex]\bar{x}\:\text{and}\:\bar{y}[/tex], we need to solve for the area A first:
[tex]\displaystyle A = \int_a^b [f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}[(x^2 + 1) - 6x^2]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}(1 - 5x^2)dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\left(x - \frac{5}{3}x^3 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= \dfrac{28}{75}[/tex]
The x-coordinate of the centroid [tex]\bar{x}[/tex] is given by
[tex]\displaystyle \bar{x} = \dfrac{1}{A}\int_a^b x[f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:= \frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} (x - 5x^3)dx[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{75}{28}\left(\dfrac{1}{2}x^2 -\dfrac{5}{4}x^4 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= 0[/tex]
The y-coordinate of the centroid [tex]\bar{y}[/tex] is given by
[tex]\displaystyle \bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}[f^2(x) - g^2(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} \frac{1}{2}(-35x^4 + 2x^2 + 1)dx[/tex]
[tex]\:\:\:\:\:\:\:=\frac{75}{56} \left[-7x^5 + \frac{2}{3}x^3 + x \right]_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{136}{125}[/tex]
Related Questions
Find all the roots of the equation
[tex] {x}^{6} - 64 = 0[/tex]
Answers
X^2 -64=0
Factorization:
(x+8)(x-8)=0
Solution:
X+8=0 x^1=-8
X-7=0. X^2=8
Answer:
x = 2
x =-2
x =1 +√3i
x =1 -√3i
x =-1 +√3i
x =-1 -√3i
Step-by-step explanation:
[tex]x^{6} -64 = 0\\(x^{3} -8)(x^{3} + 8) = 0\\ \\( x - 2) (x^{2} + 2x + 4)( x + 2) (x^{2} -2x + 4) = 0\\[/tex]
x = 2
x =-2
x =1 +√3i
x =1 -√3i
x =-1 +√3i
x =-1 -√3i
what can you infer about angles x and y based on the information in the other triangles?
Answers
As we can tell x and y add up to 180 as angles on a line are equal to 180 and we know the value of x as angles in a triangle add up to 180
A study is done to determine the average salary for all Santa Clara County teachers. If we were to randomly pick 15 schools in Santa Clara County and average together the salaries of all teachers, would this be a good sampling technique or a bad sampling technique
Answers
Answer:
Good sampling technique
Step-by-step explanation:
In other to determine the mean value for a population, it may be necessary to make inference from the a small subset of the population, called the sample, if it is impossible, difficult or inefficient to get all population data. Hence, in other to select a subset of the population, then the sample must be selected at random, such that all elements of the population have equal chances of being selected and hence, be representative of the population. Since, the sampling technique adopted above is done at random, hence, it is a good sampling technique.
A survey found that women's heights are normally distributed with mean 62.3 in. and standard deviation 2.3 in. The survey also found that men's heights are normally distributed with a mean 67.6 in. and standard deviation 2.9. Complete parts a through c below. a. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft 9 in. and a maximum of 6 ft 4 in. Find the percentage of women meeting the height requirement The percentage of women who meet the height requirement is %. (Round to two decimal places as needed.)
Answers
Answer:
98.93
Step-by-step explanation:
we're looking for
4 ft 9 <x<6 ft 4
Let's convert this into inches
4 ft 9 = 57 in
6 ft 4= 76
so we're looking for
57<x<76
which is equal to
p(76)-p(57)
let's start by p(76)
(76-62.3)/2.3= 5.946521 which on a ztable is equal to 1
p(57)=
(57-62.3)/2.3= -2.3
which is equal to 1-.9893= .0107
Finally,
1-.0107= .9893 = 98.93%
Linda found that the cost to get a swimming pool installed in her backyard is a linear function of the pool's area. A swimming pool with an area of 1,000 square feet can be installed for $50,000, whereas the installation of an 800 square foot swimming pool costs $35,000. Select the correct graph that models the given relationship.
Answers
Answer:
$35,000
Step-by-step explanation:
if $50,000 is to install an area of 1,000 square feet swimming pool and $35,000 can be used to install an 800 square foot swimming pool I think the best graph model is 800 square feet for $35,000 for a cost cut of $15,000 is a good bargain
1. In the spring of 2017, the Consumer Reports National Research Center conducted a survey of 1007 adults to learn about their major health-care concerns. The survey results showed that 574 of the respondents lack confidence they will be able to afford health insurance in the future. Develop a 90% confidence interval for the population proportion of adults who lack confidence they will be able to afford health insurance in the future.
Answers
Answer:
The correct answer is "1668". A further solution is provided below.
Step-by-step explanation:
According to the question,
Estimated proportion,
[tex]\hat{p} = \frac{574}{1007}[/tex]
[tex]=0.57[/tex]
Margin of error,
E = 0.02
Level of confidence,
= 90%
= 0.90
Critical value,
[tex]Z_{0.10}=1.65[/tex]
Now,
⇒ [tex]0.02=1.65\times \sqrt{\frac{0.57\times 0.43}{n} }[/tex]
[tex]0.0004=2.7225\times \frac{0.2451}{n}[/tex]
[tex]n=\frac{2.7225\times 0.2451}{0.0004}[/tex]
[tex]=1668.21[/tex]
or,
[tex]n \simeq 1668[/tex]
There are 4 contestants in a beauty pageant. How many results are possible for the first, second, and third place?
Answers
Explanation:
There are 4 choices for first place, 3 choices for second place, and 2 choices for third place. Overall, there are 4*3*2 = 24 permutations.
Select the correct answer.
Tom gets $12 off a box of chocolates that had an original price of $48. What percentage is the discount
Answers
Answer:
25
Step-by-step explanation:
divide 48 by 4 which is 25%
To determine the organic material in a dried lake bed, the percent carbon by mass is measured at two different locations. To compare the means of the two different locations, it must first be determined whether the standard deviations of the two locations are different. For each location, calculate the standard deviation and report it with two significant figures.
Answers
Answer:
[tex]\sigma_1 = 0.08[/tex] --- Location 1
[tex]\sigma_2 = 0.34[/tex] --- Location 2
Step-by-step explanation:
Given
See attachment for the given data
Required
The standard deviation of each location
For location 1
First, calculate the mean
[tex]\bar x_1 =\frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_1 =\frac{30.40+30.20+30.30+30.40+30.30}{5}[/tex]
[tex]\bar x_1 =\frac{151.60}{5}[/tex]
[tex]\bar x_1 =30.32[/tex]
The standard deviation is calculated as:
[tex]\sigma_1 = \sqrt{\frac{\sum(x - \bar x_1)^2}{n-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{(30.40 - 30.32)^2+(30.20 - 30.32)^2+(30.30 - 30.32)^2+(30.40 - 30.32)^2+(30.30 - 30.32)^2}{5-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{0.028}{4}}[/tex]
[tex]\sigma_1 = \sqrt{0.007}[/tex]
[tex]\sigma_1 = 0.08[/tex]
For location 2
First, calculate the mean
[tex]\bar x_2 =\frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_2 =\frac{30.10+30.90+30.20+30.70+30.30}{5}[/tex]
[tex]\bar x_2 =\frac{152.2}{5}[/tex]
[tex]\bar x_2 =30.44[/tex]
The standard deviation is calculated as:
[tex]\sigma_2 = \sqrt{\frac{\sum(x - \bar x_2)^2}{n-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{(30.10-30.44)^2+(30.90-30.44)^2+(30.20-30.44)^2+(30.70-30.44)^2+(30.30-30.44)^2}{5-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{0.472}{4}}[/tex]
[tex]\sigma_2 = \sqrt{0.118}[/tex]
[tex]\sigma_2 = 0.34[/tex]
How to solve and what is the answer
Answers
Answer:
5
Step-by-step explanation:
In ABC, if CB AC≅ , m∠A = 3x + 18, m∠B = 7x – 58, and m∠C = 2x – 8, find x and the measure of each angle.
Answers
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Answer:
x = 19
A = 30°
B = C = 75°
Step-by-step explanation:
In an isosceles triangle, the angles opposite the congruent sides have the same measures.
A = B
3x +18 = 7x -58
76 = 4x . . . . . . . . add 58-4x
19 = x . . . . . . . . . divide by 4
Then the equal angles measure ...
A = B = 3(19) +18 = 75
C = 2(19) -8 = 30
Angles A, B, C measure 75°, 75°, 30°, respectively.
_____
Alternate solution
The sum of angles in a triangle is 180°, so you could write ...
(3x +18) +(7x -58) +(2x -8) = 180
12x = 228 . . . . . add 48
x = 19 . . . . . divide by 12
The yield in bushes per acre is related to the average temperature. The attached sample data was obtained in a recent study. The least-square regression equation for yield in bushes and the average temperature is
Region Temperature Yield (in bushes per acre)
1 4 3
2 8 7
3 10 8
4 12 10
5 9 8
6 6 4
Answers
Answer:
y = 0.9143x - 0.8
Step-by-step explanation:
Given the data :
Region Temperature Yield (in bushes per acre)
4 ______ 3
8 ______ 7
10 _____ 8
12 _____ 10
9 ______ 8
6 ______ 4
Using technology, the least square regression equation obtained by fitting the data is :
y = 0.9143x - 0.8
Where ;
y = predicted Bush yield, predicted variable
x = Average temperature, dependent variable
The slope Coefficient = 0.9143
The intercept = - 0.8
A forestry researcher wants to estimate the average height of trees in a forest near Atlanta, Georgia. She takes a random sample of 18 trees from this forest. The researcher found that the average height was 4.8 meters with a standard deviation of 0.55 meters. Assume that the distribution of the heights of these trees is normal. For this sample what is the margin of error for her 99% confidence interval
Answers
Answer:
The margin of error for her confdence interval is of 0.3757.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.8982
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
Standard deviation of 0.55 meters.
This means that [tex]s = 0.55[/tex]
What is the margin of error for her 99% confidence interval?
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
[tex]M = 2.8982\frac{0.55}{\sqrt{18}}[/tex]
[tex]M = 0.3757[/tex]
The margin of error for her confdence interval is of 0.3757.
Margin of error is the distance between the mean and the limit of confidence intervals. The margin of error for the given condition is 3.28 approximately.
What is the margin of error for small samples?Suppose that we have:
Sample size n < 30
Sample standard deviation = sPopulation standard deviation = [tex]\sigma[/tex]Level of significance = [tex]\alpha[/tex]Degree of freedom = n-1Then the margin of error(MOE) is obtained as
Case 1: Population standard deviation is knownMargin of Error = [tex]MOE = T_{c}\dfrac{\sigma}{\sqrt{n}}[/tex]
Case 2: Population standard deviation is unknown[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}[/tex]
where [tex]T_{c}[/tex] is critical value of the test statistic at level of significance
For the given case, taking the random variable X to be tracking the height of trees in the sample taken of trees from the considered forest.
Then, by the given data, we get:
[tex]\overline{x} = 4.8[/tex], [tex]s = 4.8[/tex], n = 18
The degree of freedom is n-1 = 17
Level of significance = 100% - 99% = 1% = 0.01
The critical value of t at level of significance 0.01 with degree of freedom 17 is obtained as T = 2.90 (from the t critical values table)
Thus, margin of error for 99% confidence interval for considered case is:
[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}\\\\MOE = 2.9 \times \dfrac{4.8}{\sqrt{18}} \approx 3.28[/tex]
Thus, the margin of error for the given condition is 3.28 approximately.
Learn more about margin of error here:
https://brainly.com/question/13220147
A radio transmission tower is 180 feet high. How long should a guy wire be if it is to be attached to the tower 11 feet from the top and is to make an angle of 45° with the ground?
Answers
Answer:
Step-by-step explanation:
What is the simplified value of the exponential expression 27 1/3 ?
O1/3
O1/9
O3
O9
Answers
Answer:
the correct answer is 3
hope it helps
have a nice day
Translate the sentence into an inequality. The product of w and 2 is less than 23.
Answers
Answer:
2w<23
Step-by-step explanation:
The product of w and 2 mean that w multiplied by 2
Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question.
A number line going from negative 9 to positive 1.
–3
0
2
Answers
Answer:
-5 it is
Step-by-step explanation:
A right rectangular prism has a length of 214 cm, width of 8 cm, and height of 2012 cm.
What is the volume of the prism?
Enter the answer in the box.
cm³
Answers
Answer:
(using the numbers youve prpvided) 3444544
Step-by-step explanation:
214 x 8 x 2012 = 3444544
The highway department is testing two types of reflecting paint for concrete bridge end pillars. The two kinds of paint are alike in every respect except that one other is yellow. The orange paint is applied to 12 bridges, and the yellow paint is applied to 12 bridges. After a period of 1 year, reflectometer readings were made end pillars. (A higher reading means better visibility.) For the orange paint, the mean reflectometer reading was x19.4, with standard deviation s1-2.5. For the mean was X2-6.5, with standard deviation S2-2.4. Based on these data, can we conclude that the yellow paint has less visibility after 1 year?
Use a 10% level What are we testing in this problem?
a. difference of means
b. single proportion
c. difference of proportions
d. single mean
e. paired difference
Answers
Answer:
a. difference of means
Step-by-step explanation:
Given that :
Mean , x = 9.4
Standard deviation, [tex]s.d_1[/tex] = 2.5
Number, [tex]n_1[/tex] = 12
Mean, y = 6.5
standard deviation, [tex]s.d_2[/tex] = 2.4
Number, [tex]n_2[/tex] = 12
The null hypothesis is : [tex]$H_0: \mu_1=\mu_2$[/tex]
The alternate hypothesis is : [tex]$H_1: \mu_1>\mu_2$[/tex]
Level of significance, [tex]\alpha[/tex] = 0.1
From the [tex]\text{standard normal table, right tailed,}[/tex] [tex]$t_{1/2}$[/tex] = 1.363
Since out test is right tailed.
Reject [tex]H_0[/tex], if [tex]$T_0>1.363$[/tex]
We use the test statics,
[tex]$t_0=\frac{(x-y)}{\sqrt{\frac{s.d_1}{n_1}+\frac{s.d_2}{n_2}}}$[/tex]
[tex]$t_0=\frac{(9.4-6.5)}{\sqrt{\frac{6.25}{12}+\frac{5.76}{12}}}$[/tex]
[tex]$t_0=2.899$[/tex]
[tex]$|t_0|=2.899$[/tex]
[tex]\text{Critical value}[/tex]
The value of [tex]$|t_{1/2}|$[/tex] with minimum [tex]$\left(n_1-1,n_2-1)$[/tex] that is 11 df is 1.363
We go [tex]$|t_0|=2.899$[/tex] and [tex]$|t_{1/2}|$[/tex] = 1.363
Decision making:
Since the value of [tex]|t_0|>|t_{1/2}|$[/tex] and we reject the [tex]H_0[/tex]
The p-value : right tail [tex]H_a:(p>2.8988)[/tex]
= 0.00724
Therefore the value of [tex]$p_{0.1} > 0.00724$[/tex], and so we reject the [tex]H_0[/tex]
Thus we are testing 'the difference of means" in this problem.
Three more than twice a number is 35.
Answers
Answer:
x = 16, or if you didn't want the value for x,
2x + 3 = 35
Step-by-step explanation:
Three more: +3
Twice a number: 2x
Combined:
2x + 3 = 35.
Get rid of the 3 by subtracting it from both sides:
2x = 32
Get rid of the 2 by dividing it from both sides:
x = 16
Answer:
The number is 16.
Step-by-step explanation:
Let the unknown number be x.
Now we translate the sentence into an equation piece by piece.
Three more than twice a number is 35.
2x
Three more than twice a number is 35.
2x + 3
Three more than twice a number is 35.
2x + 3 = 35
Now we solve the equation.
Subtract 3 from both sides.
2x = 32
Divide both sides by 2.
x = 16
Answer: The number is 16.
P.S. Notice that x was a variable that was introduced solely to solve the problem. The original problem is a word problem, not an equation, and has no x in it. The correct answer makes no reference to x since x was used to solve the equation but is not part of the given problem. The person asking the question has no idea what x is. He just wants a number as an answer.
(3k + 5)(2k2 – 5k – 3)
Answers
PLESE HELP WITH ANSWER. rewrite the function in the given form
Answers
s hard and too long I'm only of class 13
A bank gives you a loan of 1,500,000 Baht to buy a house. The interest rate of the loan is 0.01% per day (Using 1 year = 365 days) How much interest you pay after 10 years
Answers
Answer:
547 500
Step-by-step explanation:
Interest for 1 year:
0.01%×365=3.65 a year
3.65×10=36.5% for 10 years
36.5×1,500,000÷100=547 500
The interest paid after 10 years is 547 ,500 Baht.
What is Interest ?Interest is the amount paid or earned when a loan is taken or an investment is done respectively.
It is given that
Principal = 1,500,000 Baht
Rate = 0.01 % per day
Time period = 10 years
Interest = ?
Interest = P *R *T/100
Interest = 1500000 * 0.01 *365* 10 / 100
Interest = 547,500 Baht
Therefore the interest paid after 10 years is 547 ,500 Baht.
To know more about Interest
https://brainly.com/question/13324776
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Find the distance between the two points.(-7,4/19) and (7,4/9)
Answers
Answer:
d=(14,0)Step-by-step explanation:
√(7-(-7))^+(4/19-4/19)^√(7+7)^+(0)^√(14)^+0= 14Which answers describe the shape below? Check all that apply.
A. Quadrilateral
B. Trapezoid
C. Rhombus
D. Rectangle
E. Parallelogram
F. Square
Answers
9514 1404 393
Answer:
A, C, D, E, F
Step-by-step explanation:
The figure has 4 sides: 2 pairs of parallel sides, all of equal length. The angles are right angles.
The figure is a ...
quadrilateralrhombusrectangleparallelogramsquareAnswer:
A, and F.
Step-by-step explanation: I hope this helps.
Four sides are called a quadrilateral.
Three sides are called a triangle.
Five sides are called a pentagon.
Six sides are called hexagons.
A rectangle is a quadrilateral with four right angles.
A square is a quadrilateral with four right angles.
A rhombus is a quadrilateral with four equal sides.
A parallelogram is a quadrilateral with two pairs of parallel sides.
A trapezoid is a quadrilateral with one pair of parallel sides.
Acute angles are less than 90°
Right angles are exactly 90°
Obtuse angles are more than 90°
Acute triangle has three acute angles.
Right triangle has one right angle.
An obtuse triangle has one obtuse angle.
Isosceles triangle has the minimum of two sides that are equal length.
Equilateral triangle has three sides that are at an equal length.
Scalene triangles have three sides of different lengths,
Acute triangles with three equal sides are called an equiangular triangle.
A public opinion survey is administered to determine how different age groups feel about an increase in the minimum wage. Some of the results are shown in the table below.
For Against No Opinion
21-40 years 20 5
41-60 years 20 20
Over 60 years 55 15 5
The survey showed that 40% of the 21 - 40 year-olds surveyed are against an increase, and 15% of the entire sample surveyed has no opinion. How many 21 - 40 year-olds surveyed are for an increase? How many 41 - 60 year-olds are against an increase?
Answers
Answer:
25 ; 35
Step-by-step explanation:
Given :
____________For __ Against __ No Opinion
21-40 years _________20 _______5
41-60 years ___20 ______________20
Over 60 years _55____ 15________ 5
Given that :
40% of 21-40 are against
Then :
40% = 20
To a obtain 100% of 21 - 40
40% = 20
100% = x
Cross multiply
0.4x = 20
x = 20/0.4
x = 50
100% of 21 - 40 = 50 people
For = 50 - (20 + 5)
= 50 - 25
= 25
2.)
Total who have no opinion :
(5 + 20 + 5) = 30
30 = 15%
Total number surveyed will be , x :
30 = 15%
x = 100%
Cross multiply :
0.15x = 30
x = 30/0.15
x = 200
Number of 41 - 60 against an increase, y:
(25 + 20 + 5 + 20 + y + 20 + 55 + 15 + 5) = 200
165 + y = 200
y = 200 - 165
y = 35
An item is regularly priced at $84. Ashley bought it on sale for 70% off the regular price.
Use the ALEKS calculator to find how much Ashley paid
Answers
Answer:
58.80
Step-by-step explanation:
84 x .7(70%) =58.80
Explain why the following function is not piecewise continuous
Answers
9514 1404 393
Answer:
the function has no finite limit at the left end of the interval (5, ∞)
Step-by-step explanation:
In order for the function to be piecewise continuous, it must have finite limits at the endpoints of each of the subintervals. Here, the function goes to infinity as x → 5+, so has no finite limit there.
You want to put a 5 inch thick layer of topsoil for a new 23 ft by 27 ft garden. The dirt store sells by the cubic yard. How many cubic yards will you need to order?
Answers
Answer:
9.5833333333 yd³
9 7/12 yd³
Step-by-step explanation:
23 * 27 * 5/12 = 258.75 ft³
1 yd³ = 3ft * 3ft * 3ft
1 yd³ = 27 ft³
258.75 ft³ * 1 yd³/27 ft³ = 9.5833333333 yd³
9.5833333333 yd³
9 7/12 yd³
The total cost (in dollars) of printing x dictionaries is C(x) = 20,000 + 10x. Find the average value of the cost function over the interval [0, 700).
Answers
Answer:
The average value of the cost function over the interval is of $23,500.
Step-by-step explanation:
Average value of a function:
The average value of a function, over an inteval [a,b], is given by:
[tex]A = \frac{1}{b-a} \int_{a}^{b} f(x) dx[/tex]
In this case:
Function [tex]C(x) = 20000 - 10x[/tex], interval with [tex]a = 0,b = 700[/tex]
So
[tex]A = \frac{1}{700} \int_{0}^{700} 20000+10x dx[/tex]
[tex]A = \frac{1}{700} (20000x+5x^2)|_{0}^{700}[/tex]
So
[tex]A = \frac{20000(700)+5(700)^2}{700} = 23500[/tex]
The average value of the cost function over the interval is of $23,500.
