Answer:
When a triangle is translated, it means the triangle is moved away from its original position.
When the coordinates of a triangle, and the coordinate of only one point of the image are given, the translation rule is calculated by subtracting the coordinates of the pre-image from the image.
From the question, we understand that:
The vertices of the triangle are known. Assume they are:
\begin{gathered}A= (1,1)\\ B = (3,5) \\ C = (4,-1)\end{gathered}A=(1,1)B=(3,5)C=(4,−1)
The vertex of one of the image is also known. Assume the point is:
A' = (3,-1)A′=(3,−1)
To calculate the translation rule;
We simply subtract the vertices of the image from the pre-image.
In this case, the translation rule would be:
T < x,y > = A' - AT<x,y>=A′−A
So, we have:
T < x,y > = (3,-1) - (1,1)T<x,y>=(3,−1)−(1,1)
Rewrite as:
T < x,y > = (3 -1 ,-1 - 1)T<x,y>=(3−1,−1−1)
T < x,y > = (2 ,-2)T<x,y>=(2,−2)
So, the translation rule is:
T_{ < x,y > } (x,y) \to (x + 1, y - 1)T<x,y>(x,y)→(x+1,y−1)
Hence, the translation rule can be derived by subtracting the coordinates of the pre-image from the image.
Answer:
Translations move every point the same distance and direction.
Use the given image to determine the translation rule.
Plot the remaining vertices using the rule.
3. ALGEBRA Nancy Boone's new automobile had an MSRP of
$27,853.00. The dealer prep charge was $278.50 and the title ſee
was $25.00. Options totaled $2,375,50. Find the sales tax rate,
to nearest hundredth percent iſ the total cost was $32 591.22
and the sales tax applied to everything but the title fee.
Answer:
The tax rate is approximately 6.75%
Step-by-step explanation:
In the question it is required to find the amount added to the total cost as tax
The given parameters are;
The Manufacturer's Suggested Retail Price, MSRP, of the automobile, MSRP = $27,853.00
The dealer prep charge, PPC = $278.50
The title fee, T = $25.00
The cost of the options added (leather, fridge, etc.), Op = $2,375.50
The total cost, C = $32,591.22
Let 'x' represent the the tax rate,
Therefore, we have;
32,591.22 = x × (27,853 + 278 + 2,375.5) + 27,853 + 278 + 2,375.5 + 25
32,591.22 = 30,506.5·x + 30,531.5
32,591.22 - 30,531.5 = 30,506.5·x
∴ 2,059.72 = 30,506.5·x
x = 2,059.72/30,506.5 = 0.06751741432 ≈ 0.0675
The tax rate, x ≈ 0.0675 = 6.75%
Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 112.
x+4
The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x< 26.
what is inequality ?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
given
perimeter of a rectangle = length + length + width + width
length + length + width + width = perimeter of a rectangle
(x +4) + (x+4) + x + x < 112
x + 4 + x + 4 + x + x < 112
4x + 8 < 112
4x < 104
x < 26
So ,The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x< 26.
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Ian walks 4 1/2 miles every day. How many miles does Ian walk in 4 1/2 days.
The solution is, Ian walk in 4 1/2 days 81/4 = 20.25 miles.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
Ian walks 4 1/2 miles every day
i.e. in 1 day walks = 9/2 mile
so, Ian walk in 4 1/2 days is.
in 9/2 days walks = 9/2* 9/2 miles
=81/4 miles
Hence, The solution is, Ian walk in 4 1/2 days 81/4 = 20.25 miles.
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In a lab experiment, 80 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 17 hours. How many bacteria would there be after 20 hours, to the nearest whole number?
Answer:
y = 181
Step-by-step explanation:
Doubling Formula:
\(y = a(2)^\frac{t}{d}\)
y=80
d=17
t=20
plug in
y=80(2)\(^\frac{20}{17}\)
y=180.818525349
y≈181
i hope this helps some!
Answer: 149
Step-by-step explanation:
im training my robot to eat zebra cupcakes every 8 days it eats 2 cupcakes and id like enough for 24 days
Look at this shape:which image shows a reflection?
Answer: C
You are looking for a shape that mirrors the question. If you mirror the question, your answer will be option C.
I hope you have a great day and take mental health breaks!
The correct reflection of the given shape is shown in option (c).
What is reflection?Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.
The given image shows the shape which is faced toward east direction, when we place a mirror in front of the shape, the reflection of the image changes in west direction.
Option (c) shows the exact reflection of the given shape.
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The expression x + 0.25x can be used to determine a 25% increase in the number of blog views from last month to this month. What expression shows this another way?
Answer:
1.25x
Step-by-step explanation:
Given that :
25% Increase in number of blog views can be expressed as (x + 0.25x)
Another way to make this representation is :
Total number of blog views + 25% of total
Total should add up to 100%
Let number of views = x
Hence,
(100% + 25%) of x
125% of x
125%x
= 1.25x
The cost of a service call to fix a washing machine can be expressed by the linear function y = 45 x + 35, where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the slope represent?
The cost for each hour it takes to repair the machine.
The cost for coming to look at the machine.
The total cost for fixing the washing machine.
The amount of time that it takes to arrive at the home to make the repairs.
Answer:
A) The cost for each hour it takes to repair the machine.-----------------------
The total cost of repair is expressed by the function:
y = 45x + 35As we see,
y- is the total cost, x - is the number of hours to fix;The slope is 45 and it represents the cost per hour to fix the car;The 35 is the y-intercept that represents a one off cost for service.Therefore the answer is option A.
The weight of a cup is 35 gram. The weight of 1000 such cups is ______________ kg
Answer:
35
Step-by-step explanation:
The total weight of 1000 of these cups is \(1000\cdot 35=35000\) grams, since each cup is 35 grams. Using the formula 1 kg = 1000 grams, we also know 35 kg = 35000 grams, so the total weight is 35 kg.
Is the line y=3x-7 parallel or perpendicular to 3x+9y=9? Explain your answer
Answer:
The lines are perpendicular because perpendicular lines have slopes that are opposite reciprocals. To compare the slopes, you can rewrite the second equation in slope-intercept form as y = (–1/3)x + 1. The slope of the given line is 3, and the slope of the second line is –1/3. These have a product of –1, which means they are opposite reciprocals. Thus, the two lines are perpendicular.
Step-by-step explanation:
I don't need to explain.
It is perpendicular. Because 3x + 9y = 9 in slope-intercept form would be -1/3x + 1, -1/3x would be the opposite of 3x. Therefore, it is perpendicular.
But if you want the sample response instead, here you go
Sample Response: The lines are perpendicular because perpendicular lines have slopes that are opposite reciprocals. To compare the slopes, you can rewrite the second equation in slope-intercept form as y = (–1/3)x + 1. The slope of the given line is 3, and the slope of the second line is –1/3. These have a product of –1, which means they are opposite reciprocals. Thus, the two lines are perpendicular.
Solve for the area of the square.
Answer:
area of square = 10 x 10 = 100 cm²
area of circle = πr² = (3.14)(5²) = 78.5 cm²
area of shaded portion = 100 - 78.5 = 21.5 cm²
Answer:
The area is \(21.5 cm^2\)(if no need to round)
The area is \(22 cm^2\)(if need to round to nearest whole number)
Step-by-step explanation:
10 x 10 = 100
5 x 5 x π = 25 π
25 x 3.14 = 78.5
100 - 78.5 = 21.5
digits of pi:3.14...
A carver begins work on the following block of granite. What is the volume of the granite? Be sure to include units.
Answer: volume of rectangular prism is calculated by length x width x height. So 10 x 5 x 20 = 1000 centimeter cubes
Step-by-step explanation:
2x + x + 12 + 96 = 180, What is x?
Answer:
X = 24
Step-by-step explanation:
2x + x + 12 + 96 = 180
combine like terms
3x + 108 = 180
subtract 108
3x = 72
divide by 3
x = 24
Hope this helps. Pls give brainliest.
Fred is participating in an attention study. He is asked to keep his eyes fixed on a cross in the middle of the screen and press a button when a word appears in place of the cross. This task involves using _____ attention.
The task described involves the use of selective attention.
The task described, where Fred is asked to keep his eyes fixed on a cross in the middle of the screen and press a button when a word appears in place of the cross, requires the utilization of selective attention. Selective attention refers to the cognitive process of focusing on specific stimuli while ignoring others. In this case, Fred needs to selectively attend to the appearance of a word while disregarding other visual stimuli on the screen.
Selective attention allows individuals to filter and prioritize relevant information from the environment while minimizing distractions. By keeping his eyes fixed on the cross and waiting for the appearance of a word, Fred is engaging in a form of visual selective attention. This task requires him to direct his attention to a specific location on the screen and monitor it for the presence of the target stimulus (the word).
Selective attention plays a crucial role in everyday tasks, as it helps individuals allocate their cognitive resources efficiently. By focusing on relevant stimuli and filtering out distractions, selective attention enables individuals to process information more effectively and respond appropriately to specific cues or events.
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Δ baryons have spin 3/2, which means that they can have four different spin projections along the z axis. They also have isospin 3/2, which means that there are four different Δ particles with regards to the up and down quarks that they are composed of. Write down the isospin ⊗ spin wavefunctions for the four different spin states of a Δ 0
particle, in terms of the wavefunctions of the quarks it is composed of.
The isospin ⊗ spin wavefunctions for the four different spin states of a Δ0 particle, in terms of the wavefunctions of the quarks it is composed of, are:
|3/2, 3/2⟩ = |u↑d↑⟩
|3/2, 1/2⟩ = (√3/2)|u↓d↑⟩ + (√1/2)|u↑d↓⟩
|3/2, -1/2⟩ = (√1/2)|u↓d↑⟩ - (√3/2)|u↑d↓⟩
|3/2, -3/2⟩ = |u↓d↓⟩
The Δ baryons are composed of three quarks: two down (d) quarks and one up (u) quark. The isospin of a particle represents its behavior under rotations in the isospin space, which is related to the behavior of the particle under the strong force. The spin of a particle represents its intrinsic angular momentum.
For the Δ0 particle, which has isospin 3/2, there are four different spin states. Each spin state corresponds to a different combination of up and down quark spin projections along the z axis. The isospin ⊗ spin wavefunctions represent the composite wavefunctions of the quarks that make up the Δ0 particle for each spin state.
In the first spin state, |3/2, 3/2⟩, both the up and down quarks have their spins aligned in the upward direction. In the second spin state, |3/2, 1/2⟩, the up quark has its spin aligned upward while the down quark has its spin aligned downward. The third spin state, |3/2, -1/2⟩, has the up quark with its spin aligned downward and the down quark with its spin aligned upward. Finally, in the fourth spin state, |3/2, -3/2⟩, both the up and down quarks have their spins aligned in the downward direction.
These wavefunctions provide a mathematical description of the different spin states of the Δ0 particle, taking into account the wavefunctions of the constituent quarks. They help us understand the quantum mechanical properties and behavior of the Δ0 baryon in terms of its quark composition.
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Which of the following gives the correct range for the piecewise graph?
51y
-5 -4 -3
0-2≤x≤5
O-2≤y≤5
O-4≤x≤3
O-4 sys3
4
3
2
1
-2 -1 0
-2
-3
A
-5
1
2
3
4
X
5
The range of the given piecewise function is -
-4 ≤ x ≤ 3.
What is Piecewise function?A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function.
Given is the piecewise function as shown in the image.
Range is the set of values that exist for a specific value in the domain of the function. So, we can write the range as the set of {y} values for the function. From the graph, we can write the range as -
-4 ≤ x ≤ 3
Therefore, the range of the given piecewise function is -
-4 ≤ x ≤ 3.
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PLEASE HELP ONLY HAVE FOUR MINUTES
if f is continuous and 8 f(x) dx = 10, 0 find 4 f(2x) dx. 0
The integral of 4f(2x)dx from 0 to 1 is 5.
To find the integral of 4f(2x)dx from 0 to 1 when given that f is continuous and the integral of f(x)dx from 0 to 8 is 10, follow these steps:
1. Make a substitution: Let u = 2x, so du/dx = 2 and dx = du/2.
2. Change the limits of integration: Since x = 0 when u = 2(0) = 0 and x = 1 when u = 2(1) = 2, the new limits of integration are 0 and 2.
3. Substitute and solve: Replace f(2x)dx with f(u)du/2 and integrate from 0 to 2:
∫(4f(u)du/2) from 0 to 2 = (4/2)∫f(u)du from 0 to 2 = 2∫f(u)du from 0 to 2.
4. Use the given information: Since the integral of f(x)dx from 0 to 8 is 10, the integral of f(u)du from 0 to 2 is (1/4) of 10 (because 2 is 1/4 of 8). So, the integral of f(u)du from 0 to 2 is 10/4 = 2.5.
5. Multiply by the constant factor: Finally, multiply 2 by the integral calculated in step 4:
2 * 2.5 = 5.
Therefore, the integral of 4f(2x)dx from 0 to 1 is 5.
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A bag contains 3red, 4white, 5green balls. Three balls are selected without replacement. Find the probability that the three balls chosen are:
A) all red
B) all green
C)one of each color
Answer:
A. 1/220 B. 1/22 C. 3/11
Step-by-step explanation:
This question uses combinations -- counting the number of ways a selection can be made from a set of objects (without arranging them after the selection is done).
Notations for combinations:
The number of ways to select r things from a set of n things is
\(C(n,r)=\frac{n!}{r!(n-r)!}\) where the exclamation points mean factorial.
\(n!=1\cdot2\cdot3\ldots\cdot n\) and 0! is defined to be 1.
There are two other commonly used symbols for this:
\(_nC_r\) and \(n \choose x\).
In all three parts, the number of ways to choose 3 balls from a set of 12 is
\(C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot4\cdot3\cdot2\cdot1}{(3\cdot2\cdot1)(9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)}\)
Notice that 9 factors in the denominator cancel 9 factors in the numerator, leaving
\(C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10}{3\cdot2\cdot1}=220\)
A. The number of ways to choose 3 red balls from the 3 red balls is C(3, 3) = 1, so the probability is 1 / 220.
B) The number of ways to choose 3 green balls from the set of 5 green balls is \(C(5,3)=\frac{5!}{3!(5-3)!}=\frac{5!}{3!2!}=\frac{5\cdot 4}{2}=10\) out of 220, so the probability is 10/220 = 1/22.
C) The number of ways to choose 1 red is C(3, 1) = 3. Choose 1 green in C(5, 1) = 5 ways. Choose 1 white in C(4, 1) = 4 ways.
The probability is \(\frac{3\cdot 5 \cdot 4}{220}=\frac{60}{220}=\frac{3}{11}\)
Answer:
a) 1/220
b) 1/22
c) 3/11
Step-by-step explanation:
Check the attachment.
Town officials want to estimate the number of households that own a dog. Answer the following.
There are 300 households in the town.
Estimate how many households that own a dog
__ households
The estimated number of households that own a dog in the town is 120 households.
To estimate the number of households that own a dog in the town with 300 households, you will need to follow these steps:
1. Collect a random sample of households from the town. The sample size should be large enough to be representative of the entire population.
2. Determine the proportion of sampled households that own a dog.
3. Multiply the proportion of dog-owning households in the sample by the total number of households in the town (300).
For example, let's say you collected data from 50 households and found that 20 of them owned a dog. The proportion of dog-owning households would be 20/50 = 0.4 (40%).
To estimate the total number of households that own a dog in the town, multiply 0.4 by 300:
0.4 * 300 = 120 households
So, the estimated number of households that own a dog in the town is 120 households.
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the mean iq of statistics teachers is greater than 140. state this claim mathematically.write the null and alternative hypotheses. identify which hypothesis is the claim.
In the hypothesis testing, the null and alternative for the claim that mean iq of statistics teachers is greater than 140, are
\(H_0 :\mu \leqslant 140\)
\(H_a : \mu > 140\)
and the alternative hypothesis is the hypothesis of this claim.
Hypothesis testing in statistics is a process where you to test the results of a survey or experiment based sample to look if you have meaningful results. It is based on hypothesis. The null hypothesis of a test always shows no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship. The null hypothesis is the fact that should be tested and the alternative is everything else.
We have mean iq of statistics teachers is greater than 140. We have to identify the hypothesis for which this claim is true. Now, the null and alternative hypothesis are defined as in this case, \(H_0 :\mu ≤ 140\)
\(H_a : \mu > 140\)
where μ --> mean iq of statistics
From above, the hypothesis which identify the claim that mean iq of statistics teachers is greater than 140 is alternative hypothesis. Hence, the required answer is alternative hypothesis.
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Mathematically, the claim can be expressed as follows:
µ > 140
where µ represents the population mean IQ score of statistics teachers.
The null hypothesis (H0) is that the population mean IQ score of statistics teachers is not greater than 140:
H0: µ ≤ 140
The alternative hypothesis (Ha) is that the population mean IQ score of statistics teachers is greater than 140:
Ha: µ > 140
Note that the claim corresponds to the alternative hypothesis, Ha.
Null hypothesis (H0): The mean daily attendance at the park is μ = people.
Alternative hypothesis (Ha): The mean daily attendance at the park is not equal to μ ≠ people.
The claim is represented by the alternative hypothesis (Ha), which states that the mean daily attendance at the park is different from the claimed value of people.
Note that the value of μ is not specified in the claim, but it is assumed to be equal to people. The null hypothesis (H0) reflects this assumption, and the alternative hypothesis (Ha) challenges it by stating that the true mean attendance may be different from this value.
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in chicago, there is a probability of 30% that it will snow on any given day from january to march. what is the probability that it will snow on 3 consecutive days?
The probability that it will snow on 3 consecutive days is 2.7 %
What is Probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Probability of event to happen P(E)
= Number of favorable outcomes/Total Number of outcomes
Given, probability of 30% rain that it will snow on any day,
The probability of snow over a 3-day period is the product of the probabilities of rain for each day:
P3-day = (P1-day)(P1-day)(P1-day)
= (30/100)³
= (3/10)³
= 27/1000
= 2.7%
Hence, 2.7% is the probability that it will snow on 3 consecutive days.
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can anyone help me with this question?
Answer:
45 and 13…......
Step-by-step explanation:
devide
2. Pilihan ganda30 detik1 ptQ. Which of the following algebraic rules represents a dilation?Pilihan jawaban(x, y) --> (3x, 3y)(x, y) --> (3x, 2y)(x, y) --> (x - 3, y + 5)(x, y) --> (0.5x, 0.5y)(x, y) --> (3x, 0.5y)
Answer:
Is 50
Step-by-step explanation:
I don’t know
Determine the domains of the following functions. Write your answer in interval nota-tion. Need help solving question b
Carl has a piece of string that is 14 inches long. What is the length of the string in centimeters? Show your work.
What are exponents and how do you evaluate them?
Answer:
Exponents, often known as powers, are a type of mathematical notation that shows how many times a base value should be multiplied by itself. They are frequently stated as a base value raised to the power of an exponent. For instance, 3^2 represents 3 to the power of 2, which is 3 x 3 = 9.
To evaluate an exponent, do the multiplication specified by the exponent. 533, for example, is 5 increased to the power of 3, which becomes 5 x 5 x 5 = 125. If the exponent is negative, it signifies that the reciprocal of the base value should be multiplied by itself the number of times specified by the exponent's positive version. For example, 2(-3) denotes the reciprocal of 2, 1/2 increased to the power of 3, which is (1/2) x (1/2) x (1/2) = 1/8.
Furthermore, exponents can be coupled utilising exponent laws such as the product law, power law, and quotient law. These principles allow for the simplification and manipulation of exponentiated expressions.
In space, how many planes can be perpendicular to a given line at a given point on that line in space?
A. 1
B.0
C. 3
D. infinitely many
In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.
The correct answer is Option D.
The key concept here is that a plane is defined by having at least three non-collinear points.
When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.
Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.
Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.
The correct answer is Option D.
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the equation xequalspplustv describes a line through v parallel to p. true or false?
True. The equation
x = p + tv
describes a line through vector v parallel to vector p.
The equation x = p + tv represents a parameterized line equation, where x, p, and v are vectors, and t is a scalar parameter. In this equation, p represents a point on the line, and v represents the direction or slope of the line.
By adding the scalar multiple tv to the point p, we can obtain various points along the line. The scalar t determines the position of each point relative to the point p. As t varies, the resulting points lie on a line that is parallel to vector p and passes through vector v.
Therefore, the statement is true. The equation
x = p + tv
describes a line through vector v parallel to vector p.
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which, if any, of the following are antiderivatives of the function e x 2 ? circle all that apply, or ‘none’ as appropriate. z x 2 1 e t 2t dt z x √ 2 e t 2 dt e x 2 2x z x 2 0 e t dt n
The anti derivative of the function eˣ² is eˣ²/2x.
What is defined as the anti derivative?Derivatives are the inverse of antiderivatives. An antiderivative is a function that does the opposite of what a derivative does. There are many antiderivatives of one function, but they all take the shape of a function + an arbitrary constant. Indefinite integrals rely heavily on antiderivatives.An antiderivative, F, of the a function, f, is a function that may be differentiated to get the original function, f. In other words, an antiderivative is defined mathematically as follows: ∫ f(x) dx = F(x) + C, where C is the integration constant.The given function is; eˣ².
To find the anti derivative of the function, integrate the function with respect to x.
Let y = eˣ²
Integration of exponential function remains same but applying the chain rule, the derivative of the power of exponent comes at the denominator.
∫y. dx = ∫eˣ² .dx.
∫eˣ² .dx. = eˣ²/(d/dx)x²
∫eˣ² .dx. = eˣ²/2x
Thus, the anti derivative of the function is found as eˣ²/2x.
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