Find the average value of f(x) = 2x – 2 over the interval [1, 2].
Answers
To find the average value of f(x) = 2x - 2 over the interval [1, 2], we need to use the following formula:
Average value of f(x) over [a,b] = (1/(b-a)) * integral of f(x) from a to b
So, in our case, a = 1 and b = 2, and f(x) = 2x - 2. Therefore, we have:
Average value of f(x) over [1, 2] = (1/(2-1)) * integral of (2x - 2) dx from 1 to 2
= 1 * [(x^2 - 2x) / 2] from 1 to 2
= [(2^2 - 2(2)) / 2] - [(1^2 - 2(1)) / 2]
= (4 - 4) / 2 - (-1) / 2
= 0 - (-1/2)
= 1/2
Therefore, the average value of f(x) = 2x - 2 over the interval [1, 2] is 1/2.
Hi! To find the average value of f(x) = 2x - 2 over the interval [1, 2], you can use the formula:
Average value = (1/(b-a)) * ∫(f(x)dx) from a to b
In this case, f(x) = 2x - 2, a = 1, and b = 2.
Average value = (1/(2-1)) * ∫(2x - 2)dx from 1 to 2 = ∫(2x - 2)dx from 1 to 2
Now, evaluate the integral:
∫(2x - 2)dx = x^2 - 2x + C
Next, find the definite integral:
(x^2 - 2x)|1 to 2 = (4 - 4) - (1 - 2) = 0 - (-1) = 1
Finally, calculate the average value:
Average value = 1 = 1
So, the average value of f(x) = 2x - 2 over the interval [1, 2] is 1.
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Related Questions
There are two roots because of the....
Answers
Answer:
There are two roots because of the
✔ need to identify + and - roots of the radicand.
Step-by-step explanation:
edge
Answer:C
Step-by-step explanation:
There are two roots because of the
✔ need to identify + and - roots of the radicand.
Determine whether the following equence i an arithmetic or geometric progreion. Give a reaon for your anwer. 100p,50p,25p,
Answers
Answer:
Geometric.
Step-by-step explanation:
It is Geometric because there is a common ratio between the terms.
50p/100p = 1/2
25p/50p = 1/2
The common ratio is 1/2.
Each term is obtained by multiplying by 1/2, so the next term in this progression is 25p * 1/2 = 12.5p.
Suppose $726.56 is deposited at the end of every six months into an account earning 6.45% compounded semi-annually. If the balance in the account four years after the last deposit is to be $31 300.00, how many deposits are needed? (This question asks for 'n')
Answers
We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.
To solve this problem, we can use the formula for the future value of an annuity:
\(FV = P * ((1 + r)^n - 1) / r\)
Where:
FV is the future value of the annuity
P is the periodic payment or deposit amount
r is the interest rate per period
n is the number of periods
In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).
We can rearrange the formula and solve for n:
n = log((FV * r) / (P * r + FV)) / log(1 + r)
Substituting the given values:
n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)
Using a calculator or software, we find that n ≈ 9.989.
Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.
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Find the midpoint of the line segment with end coordinates of: (0,2) and (2,8)
Answers
Answer:
(1, 5 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( \(\frac{x_{1}+x_{2} }{2}\), \(\frac{y_{1}+y_{2} }{2}\) )
Here (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (2, 8) , then
midpoint = ( \(\frac{0+2}{2}\), \(\frac{2+8}{2}\) ) = ( \(\frac{2}{2}\), \(\frac{10}{2}\) ) = (1, 5 )
Which function represents the Inverse of function below?
Answers
Answer: The answer that you’re looking for is D. \(p(x)=\frac{1}{3}x-\frac{5}{3}\). Brainliest?
Step-by-step explanation:
help me please asap....please
Answers
Answer:
56% 56/100
Step-by-step explanation:
Question 3 Let X1, X2,..., Xn be independent random variables, each having a uniform distri- bution over (0,1). Let M = maximum (X₁, X₂,..., Xn). Show that the distribution function of M, FM(-), is given by FM(x)=x, 0≤x≤1 What is the probability density function of M?
Answers
The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.
The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.
In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.
For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).
The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).
To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.
The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.
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Help Find kif (2, k) lies on the line with equation 2x + 7y = 41
Answers
Answer:
i think 11y
Step-by-step explanation:
A specific laptop loses half of its value every six months. If the original cost was $1, 100 and the value of the laptop is now $68.75, how many years have you owned the laptop
Answers
Answer:
2 years! :)
Step-by-step explanation:
A surveyor is 40m from the edge of a building. The angle of elevation from the surveyor to the top of the building is 55° . What is the height of the building?
Answers
Answer:
Height of building is 57.12 m.
Step-by-step explanation:
Let us try to understand the given dimensions as per the attached diagram.
Please refer to attached image (Right angled \(\triangle OBT\))
with \(\angle B =90^\circ\)
Let O be the point where the Surveyor is standing.
B be the point of the base of building.
T be the point of top of building.
As per question statement,
\(\angle O = 55^\circ\)
Side OB = 40 m
To find: Side BT = ?
Using tangent trigonometric identity:
\(tan\theta =\dfrac{Perpendicular}{Base}\)
\(tanO =\dfrac{BT}{BO}\\\Rightarrow tan55^\circ = \dfrac{BT}{40}\\\Rightarrow BT = tan55^\circ \times 40\\\Rightarrow BT = 1.43\times 40\\\Rightarrow BT = 57.12 m\)
So, height of building is 57.12 m.
A marathon is 26.2 miles long. There is a water station every 114 miles along the race route and at the finish line. How many water stations are needed for this marathon?
Answers
Answer: 21 water stations
Step-by-step explanation:
From the question, we are informed that a marathon is 26.2 miles long and that there is a water station every 1 1/4miles along the race route and at the finish line.
To get the number of water stations that are needed for this marathon, we divide 26.2 miles by 1 1/4miles. This will be:
= 26.2miles/1 1/4 miles
= 26.2 miles/1.25 miles
= 20.96
= 21 water stations
Question 5 of 10
Which pair of functions are inverses of each other?
O A. f(x) = 2 + 15 and g(x) = 12x - 15
O B. f(x) = √3x and g(x) = () ³
O c. f(x) = 3 - 10 and g(x) = +10
3
D. f(x) = 11x-4 and g(x) = +4
Answers
The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11
To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.
Let's test each option:
Option A:
f(x) = x/2 + 15
g(x) = 12x - 15
f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x
g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x
Option B:
f(x) = ∛3x
g(x) = (x/3)^3 = x^3/27
f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x
g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x
Option C:
f(x) = 3/x - 10
g(x) = (x + 10)/3
f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x
g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x
Option D:
f(x) = 11x - 4
g(x) = (x + 4)/11
f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x
g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x
Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:
D. f(x) = 11x - 4 and g(x) = (x + 4)/11
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HURRY!! (52 POINTS!!)
The ages of people visiting a senior center one afternoon are recorded in the line plot.
A line plot titled Ages At Senior Center. The horizontal line is numbered in units of 5 from 60 to 115. There is one dot above 80 and 110. There are two dots above 70 and 85. There are three dots above 75.
Does the data contain an outlier? If so, explain its meaning in this situation.
A. No, there is no outlier. This means that the people were all the same age.
B. No, there is no outlier. This means that the people are all around the mean age.
C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.
D. Yes, there is an outlier of 110. This means that the average person at the center is 110 years old.
Answers
Answer:
C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.
Step-by-step explanation:
An outlier is a data point that sticks out like a sore thumb. It's so different from the rest of the data that it makes you wonder if it's a mistake or a miracle. One way to spot an outlier is to use the 1.5IQR rule, where IQR stands for interquartile range. The interquartile range is the gap between the third quartile (Q3) and the first quartile (Q1) of the data. The 1.5IQR rule says that any data point that is more than 1.5*IQR above Q3 or below Q1 is an outlier.
In this case, the first quartile (Q1) is 75, the third quartile (Q3) is 85, and the interquartile range (IQR) is 10. So, any data point that is more than 1.5*10 = 15 above 85 or below 75 is an outlier. The only data point that does this is 110, which is 25 above 85. That means 110 is an outlier.
What does this outlier mean in this situation? It means that one person who came to the senior center that afternoon was way older than the rest of the folks. The average age of the visitors was not changed by this outlier, since it was just one out of 12 data points. But, the outlier does mess up the range and the standard deviation of the data, making them bigger than they would be without the outlier.
Answer:The answer is C
Step-by-step explanation:I did the test.
9. Look at some of the printed letters in a textbook. The small horizontal
and vertical segments attached to the ends of the letters are called
serifs. Most of the letters in a textbook are in a serif typeface. The
letters on this page do not have serifs, so these letters are in a sans-
serif typeface. (Sans means "without" in French.) The figure shows a
capital letter A with serifs. Use the given information to write a
paragraph proof that the serif, segment HI, is parallel to segment JK.
Given: 21 and 23 are supplementary.
Prove: HI || JK
Answers
By considering the given information that angles 21 and 23 are supplementary and analyzing the properties of supplementary angles and parallel lines, we have proven that segment HI is parallel to segment JK.
To prove that segment HI is parallel to segment JK based on the given information that angles 21 and 23 are supplementary, we can utilize the properties of supplementary angles and parallel lines.
First, let's examine the given figure and information.
We have a capital letter A with serifs, where segment HI represents one of the serifs, and segment JK represents a horizontal line within the letter A.
To begin the proof, we'll make use of the fact that angles 21 and 23 are supplementary.
Supplementary angles are defined as two angles whose measures sum up to 180 degrees.
We can observe that angle 21 is an interior angle of triangle AHI, and angle 23 is an interior angle of triangle AJK.
Since angles 21 and 23 are supplementary, their sum is equal to 180 degrees.
Now, let's assume that segments HI and JK are not parallel.
In this case, if we extend lines HA and JA, they will eventually intersect at point P.
Since the angles formed at the point of intersection are supplementary (angle 21 + angle 23 = 180 degrees), it would imply that angle 21 and angle PJK, as well as angle 23 and angle PHI, are also supplementary.
However, this leads to a contradiction. In the original figure, we can observe that angle 21 and angle PJK do not form a supplementary pair since angle PJK is a right angle (90 degrees) in the letter A.
Therefore, our assumption that segments HI and JK are not parallel must be incorrect.
Consequently, we can conclude that segment HI is indeed parallel to segment JK.
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What number is 75% of 300?
A. 36
B. 22.5
C. 2250
D. 225
Answers
225
What is 75 percent of 300.? = 225.
What is the formula to find P(A) for a series of simple events (ex: tossing a coin and selecting a number at the same time)
Answers
The probability of event A is P(A) = 1/4 or 0.25.
The formula to find P(A) for a series of simple events is:
P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)
For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:
- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.
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Explain why this common mistake is wrong. Many people might say that (2, 4) is an intercept of the equation 5x + 2y = 18.
Answers
Answer:
Step-by-step explanation:
(2,4) is point lying on the line represented by 5x + 2y = 18.
They are not intercepts.
x-intercept is point where the line crosses the x-axis and so, y-co ordinate at x-intercept is 0.
y-intercept is point where the line crosses they-axis and so,x-co ordinate at y-intercept is 0.
5x + 2y = 18
To find x-intercept, put y = 0 in the equation
5x = 18
x = 18/5
x = 3.6
To find y-intercept, put x = 0 in the equation
2y = 18
y = 18/2
y = 9
x-intercept : (3.6 , 0)
y-intercept :(0, 9)
a(q-8)=23
solve for q
help appreciated!
Answers
Answer:
q= (23+8a)/a
Step-by-step explanation:
a(q-8)=23
or, aq-8a = 23
or, aq = 23+8a
or, q = (23+8a)/a
(I’m not sure if the A is part of the question or if A is what question you’re answering but I’ll work o for both)
A(q - 8) = 23
Multiply everything inside the brackets by A:
aq- 8a = 23
Divide both sides by a to isolate q - 8a:
q - 8a = 23 / a
Add 8a to both sides to isolate q:
q = 23 + 8a² / a
Without the A:
q - 8 = 23
Add 8 to both sides to isolate q:
q = 31
Sorry if I misunderstood but I hope I helped you, have a great day!!
Arrange the following numbers in order from least to greatest. 96 432 94 632 96 342
Answers
Answer:
Step-by-step explanation:
94, 96, 96, 342, 432, 632
Select all of the true statements about the graph. a. It is not a function. b. It is a function. c. It does not represent a proportional relationship. d. It does represent a proportional relationship.
Answers
The true statements about the given graph are :
(b) It is a function.
(c) It does not represent a proportional relationship.
Given a graph.
A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Here take the set A has the x values and the set B has the y values.
By vertical line test, if we draw a vertical line through any point, the line only touches the graph at one point.
So this is a graph of a function.
Proportional relationships are relationships where the ratios of two y values will be equal.
And they will be linear.
Here the graph is not linear and thus not proportional.
Hence the true statements are b and c.
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Choose the graph of y = -3 sin x.
Answers
Step-by-step explanation:
the graph should look something like this
Parallel lines q and r interested by transversal p. Which is the value of x?
Answers
Answer:
The value of x is equal to 23.
Answer:
23
Step-by-step explanation:
Where a transversal crosses parallel lines, same-side interior angles are supplementary. The marked angles have a total of 180°.
(3x +28) +(2x +37) = 180
5x +65 = 180 . . . . collect terms
x +13 = 36 . . . . . . . divide by 5
x = 23 . . . . . . . . . . subtract 13
Hola me pueden ayudar con matematica
Answers
Tienes la tarea en Ingles? Yo solo puedo hacer mathematics en ingles. Gracias.
Two expressions are shown below. Which of the following is the DIFFERENCE obtained when subtracting expression II from expression I?
I. y2−4xz+z2
II. x2+xz+2y2
A. 3y2−3xz+z2−x2
B. 3y2−3xz+z2+x2
C. −y2−5xz+z2−x2
D. y2+5xz−z2+x2
Answers
Answer:C.
−y2−5xz+z2−x2
Step-by-step explanation:
Took the test got it right
The solution is Option C = ( -y² - 5xz + z² - x² )
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Given data ,
Expression 1 = y² - 4xz + z²
Expression 2 = x² + xz + 2y²
Let Expression 1 - Expression 2 = A
To find Expression 1 - Expression 2 = A
A = y² - 4xz + z² - ( x² + xz + 2y² )
By grouping the like terms , we get
A = ( y² - 2y² ) - ( 4xz + xz ) + z² - x²
Therefore,
A= - y² - 5xz + z² - x²
Hence , the solution is ( -y² - 5xz + z² - x² )
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please help ill give brainleist answer
Answers
Answer:
look at the picture i have sent
Due to a study linking a food dye to cancer, M&Ms packages did not include which color from 1976 to 1987?
a. Yellow
b. Red
c. Green
d. Brown
Answers
From 1976 until 1987, red M&Ms were removed from packets owing to a research associating the food dye used to color them to cancer.
What is arithmetic?Arithmetic is defined as working with numbers through addition, subtraction, multiplication, and division. Adding two and two to produce four is an example of arithmetic. Arithmetic is a fundamental branch of mathematics that studies the characteristics of classical operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction. Arithmetic (derived from the Greek word arithmos, "number") relates to the fundamental components of number theory, arts of mensuration (measuring), and numerical computing (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).
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what is -7y+2=-75
Can you please explain this to me.
Answers
Answer:
y = 11
Step-by-step explanation:
It is just an equation with one variable ( 'y') which you can solve
-7y + 2 = - 75 subtract 2 from both sides of the equation
-7y = -77 divide both sides by -7
y = 11
Answer:
-7y+2=-75
-7y=-75-2
-7y=-77
y=11
PLEASE HELP WILL MARK BRAINLIEST
Translate this phrase into an algebraic expression. 59 decreased by twice Jose's savings Use the variable to represent Jose's savings.
Answers
Answer:
Let \(x\) = Jose's savings
\(59-2x\)
I hope I helped you friend! If I am correct, please mark me brainiest. Thanks!
x² + 7x + 12
???????????????
Answers
Pencils: $3 Sale: 50% off What is the new cost of the pencils?
Answers
Answer:
$1.50
Step-by-step explanation:
50% is one half. and one half of $3 is $1.50.
please give brainliest!!
Explanation : find 50% of $3 . That’s 1.50 , take that away from $3.00 and you get 1.50 .
Or a easier way , since it’s 50% which means half , divide $3 by 2 . :)