the number of choices in each case is:
a. With no restriction: 10,000 choices.
b. No digit is repeated: 5,040 choices.
c. No digit is repeated, 2 and 5 must be present: 56 choices.
Let's calculate the number of choices in each case:
a. With no restriction:
For each digit in a 4-digit pin code, we have 10 choices (0-9). Since there are 4 digits in total, the number of choices is 10⁴ = 10,000.
b. No digit is repeated:
For the first digit, we have 10 choices (0-9).
For the second digit, we have 9 choices (any digit except the one chosen for the first digit).
For the third digit, we have 8 choices (any digit except the two chosen for the first and second digits).
For the fourth digit, we have 7 choices (any digit except the three chosen for the first, second, and third digits).
The total number of choices is 10 * 9 * 8 * 7 = 5,040.
c. No digit is repeated, and 2 and 5 must be present:
We have two fixed digits (2 and 5) that must be present in the pin code.
For the first fixed digit (2), we have only 1 choice.
For the second fixed digit (5), we have only 1 choice.
For the remaining two digits, we have 8 choices each (any digit except 2 and 5).
The total number of choices is 1 * 1 * 8 * 7 = 56
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Let X is uniformly distributed over (0,1) and Y is exponentially distributed with parameter lambda = 2. Furthermore assume X and Y are independent. The cumulative distribution of Z = X + Y is P{Z lessthanorequalto a} = P{X + Y lessthanorequalto a} =___________________________for 0 < a < 1 P{Z lessthanorequalto a} = P{X + Y lessthanorequalto a} =___________________________for 0 < a < infinity The cumulative distribution of T = x/y is P({T lessthanorequalto a} = P{X/a lessthanorequalto Y} =___________________________for_________< a
To find the cumulative distribution function (CDF) of Z = X + Y, where X is uniformly distributed over (0,1) and Y is exponentially distributed with parameter lambda = 2, we can use the properties of independent random variables.
For 0 < a < 1, we have:
P(Z ≤ a) = P(X + Y ≤ a)
Since X and Y are independent, we can write this as:
P(Z ≤ a) = ∫∫ P(X ≤ x, Y ≤ a - x) dxdy
Since X is uniformly distributed over (0,1) and Y is exponentially distributed with parameter lambda = 2, we have their respective probability density functions (PDFs):
fX(x) = 1, 0 ≤ x ≤ 1
fY(y) = 2e^(-2y), y ≥ 0
Now, we can calculate the CDF of Z:
P(Z ≤ a) = ∫∫ P(X ≤ x, Y ≤ a - x) dxdy
= ∫∫ fX(x) * fY(y) dxdy, since X and Y are independent
= ∫∫ 1 *[tex]2e^(-2y)[/tex] dxdy, for 0 ≤ x ≤ 1 and y ≥ 0
Integrating with respect to x from 0 to 1 and with respect to y from 0 to a - x, we get:
P(Z ≤ a) = ∫[0,1]∫[0,a-x] 1 * 2[tex]e^(-2y)[/tex]dydx
= ∫[0,1] [[tex]-e^(-2y)[/tex]] [0,a-x] dx
= ∫[0,1] (1 - [tex]e^(-2(a-x)[/tex])) dx
Evaluating the integral, we have:
P(Z ≤ a) = [x - [tex]xe^(-2(a-x))[/tex]] [0,1]
= (1 - e^(-2a))
Therefore, the cumulative distribution function (CDF) of Z is:
P(Z ≤ a) = [tex](1 - e^(-2a)),[/tex] for 0 < a < 1
For 0 < a < ∞, the cumulative distribution function of Z remains the same:
P(Z ≤ a) = (1 - e^(-2a)), for 0 < a < ∞
Now, let's move on to the cumulative distribution function of T = X/Y.
P(T ≤ a) = P(X/Y ≤ a)
Since X and Y are independent, we can write this as:
P(T ≤ a) = ∫∫ P(X/y ≤ a) fX(x) * fY(y) dxdy
Using the given information that X is uniformly distributed over (0,1) and Y is exponentially distributed with parameter lambda = 2, we can substitute their respective PDFs:
P(T ≤ a) = ∫∫ P(X/y ≤ a) * 1 * [tex]2e^(-2y)[/tex]dxdy
= ∫∫ P(X ≤ ay) * 1 * [tex]2e^(-2y)[/tex]dxdy
Now, we need to determine the range of integration for x and y. Since X is between 0 and 1, and Y is greater than or equal to 0, we have:
0 ≤ x ≤ 1
0 ≤ y
Using these limits, we can calculate the CDF of T:
P(T ≤ a) = ∫[0,1]∫[0,∞] P(X ≤ ay) * 1 * [tex]2e^(-2y)[/tex] dydx
To evaluate this integral, we need to consider the range of values for ay. Since a can be any positive real number, ay can range from 0 to ∞.
P(T ≤ a) = ∫[0,1]∫[0,∞] P(X ≤ ay) * 1 * 2[tex]e^(-2y)[/tex] dydx
= ∫[0,1]∫[0,∞] (ay) * 1 * 2[tex]e^(-2y)[/tex] dydx, for ay ≥ 0
Integrating with respect to y from 0 to ∞ and with respect to x from 0 to 1, we have:
P(T ≤ a) = ∫[0,1]∫[0,∞] (ay) * 1 * 2[tex]e^(-2y)[/tex]dydx
= ∫[0,1] (2a / (4 + a^2)) dx
Evaluating the integral, we get:
P(T ≤ a) = (2a / (4 + [tex]a^2)),[/tex] for a > 0
Therefore, the cumulative distribution function (CDF) of T is:
P(T ≤ a) = (2a / (4 + [tex]a^2)),[/tex] for a > 0
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6,336 ft. = in league
Answer:
6336 feet = 0.3476 nautical leagues
Consider the equation below. (If an answer does not exist, enter DNE.)
f(x) = x4 − 8x2 + 9
(a) Find the interval on which f is increasing. (Enter your answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer using interval notation.)
The interval on which the function f(x) = x^4 - 8x^2 + 9 is increasing can be expressed in interval notation as (-∞, -2) ∪ (2, ∞). The interval on which the function is decreasing can be expressed as (-2, 2).
To determine the intervals of increasing and decreasing, we need to examine the derivative of the function. Taking the derivative of f(x) with respect to x gives us f'(x) = 4x^3 - 16x. To find the intervals of increasing and decreasing, we need to analyze the sign of the derivative. The derivative is positive when x < -2 and x > 2, indicating an increasing function. The derivative is negative when -2 < x < 2, indicating a decreasing function.
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A decision problem X is self-solvable if X = L(MX) for some polynomial-time oracle TM M, whose oracle queries are always strictly shorter than its input. In other words, when M is executed on an input of length n, it queries its oracle only on strings of length less than n. This is a strange situation, where M has oracle access to the problem that it is trying to solve. But when M is trying to determine whether x € X, it cannot simply query its oracle on x for the answer. ከ. (a) Show that TQBF is self-solvable. Be explicit about what assumptions are you making about how for- mulas are encoded into bit strings. (b) Prove that if L is self-solvable then L E PSPACE.
(a) The TQBF oracle used by M satisfies the condition for self-solvability.
It can handle formulas of length strictly shorter than the input length, ensuring that M's oracle queries are always strictly shorter than its input.
To show that TQBF (True Quantified Boolean Formula) is self-solvable, we need to demonstrate that there exists a polynomial-time oracle Turing machine (TM) M that can solve TQBF using an oracle for TQBF.
Assuming that formulas in TQBF are encoded into bit strings in a standard way, we can construct the TM M as follows:
On input x (the encoded TQBF formula), M starts by generating all possible truth assignments for the variables in the formula.
For each truth assignment, M constructs the corresponding quantified Boolean formula and queries the TQBF oracle with this formula.
If the oracle returns "true" for any truth assignment, M accepts x. Otherwise, if the oracle returns "false" for all truth assignments, M rejects x.
Hence, TQBF (True Quantified Boolean Formula) is self-solvable.
(b) If a language L is self-solvable, it implies that L is in PSPACE (polynomial space complexity class).
To prove that if L is self-solvable, then L is in PSPACE, we can show that a polynomial-time oracle TM M with oracle access to L can be simulated by a polynomial-space Turing machine.
Let M' be a polynomial-space Turing machine that simulates M with oracle access to L. Since L is self-solvable, M' can query the oracle on inputs shorter than its own input.
We can construct a polynomial-space Turing machine M'' that simulates M' without the need for an oracle. M'' uses its own polynomial space to simulate the computation of M'. Whenever M' queries the oracle on an input, M'' runs its own simulation for that input length using its available space.
Since M'' only requires polynomial space and simulates the behavior of M', it follows that L is in PSPACE.
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Connor has a box of 100 T-shirts in different sizes that he will be throwing to fans in the stands at the Greenville Township Allstars baseball game. Since the T-shirts are all mixed together, he's curious about how many of each shirt size is in the box. So, he randomly checks 10 shirts from different parts of the box. Here are the sizes of those shirts: large, small, extra large, medium, small, extra large, large, small, medium, small Based on the data, estimate how many small T-shirts are in the box.
The Sample, we estimate that there are approximately 40 small T-shirts in the box.
The number of small T-shirts in the box, sampling and assume that the proportion of small T-shirts in the sample is representative of the proportion in the entire box.
In the given sample of 10 shirts, we have the following sizes: large, small, extra large, medium, small, extra large, large, small, medium, small.
Out of the 10 shirts, 4 of them are small. To estimate the number of small T-shirts in the entire box, we can set up a proportion:
Small shirts in sample / Total shirts in sample = Small shirts in box / Total shirts in box
Plugging in the values we have:
4 / 10 = x / 100
Cross-multiplying:
4 * 100 = 10 * x
400 = 10x
Dividing both sides by 10:
x = 400 / 10
x = 40
Based on the sample, we estimate that there are approximately 40 small T-shirts in the box.
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What is the measure of ∠x?
Answer:
117+x=180°(sum of straight line)
Step-by-step explanation:
x=180-117
x=63
Joshua is going to invest $9,000 and leave it in an account for 5 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Joshua to end up with $12,500?
Answer:
Step-by-step explanation:
Answer:
6.6%
Step-by-step explanation:
Find the correlation coefficient between x and y
X 57 58 59 59 60 61 62 64
Y 77 78 75 78 82 82 79 81
Answer:
0.603
Step-by-step explanation:
Given the data:
X 57 58 59 59 60 61 62 64
Y 77 78 75 78 82 82 79 81
The Correlation Coefficient, R value gives a measure of the degree of correlation between two variables, the dependent and independent variable. The correlation Coefficient value ranges from - 1 to 1. With negative values depicting a negative relationship and positive values meaning a positive relationship. The closer the R value is to + or - 1, the higher the strength of the relationship. With a value of 0 meaning 'no correlation'.
The correlation Coefficient value of the data above is 0.603, this gives a fairly strong positive correlation
Which function would be produced by a horizontal stretch of the graph of y = sqrt(x) followed by a reflection in the x - axis ?
Answer:
the answer is the first one
Step-by-step explanation:
Explanation: be im smart
Function transformation involves changing the form of a function
A function that could represent the transformed function is function (c) [tex]f(x) = -\sqrt{\frac 12 x}[/tex]
The equation of the function is given as:
[tex]f(x) = \sqrt x[/tex]
The rule of horizontal stretch is:
[tex](x,y) \to (ax,y)[/tex]
Where:
[tex]0 < a < 1[/tex]
Take for instance:
[tex]a = \frac 12[/tex]
So, we have:
[tex]f(x) = \sqrt{\frac 12 x}[/tex]
Next, the function is reflected in across the x-axis.
The rule of this transformation is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex]f(x) = -\sqrt{\frac 12 x}[/tex]
Hence, a function that could represent the transformed function is function (c)
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What’s the volume of the prism
Answer:
384 cubic inches (in^3)
Step-by-step explanation:
volume = length * width * height
So find the volume of the large rectangle of the prism, then find the volume of the small rectangle of the prism. Add the two volumes together and the sum is your final answer.
I would appreciate Brainliest, but no worries.
What is the solution to the equation 4x + 2(x − 3) = 3x + x − 12? (1 point) −3 −1 1 3
3) Arjun was shopping for avocados, which were listed $0.90 each. He brought six avocados to the checkout lane, where he learned that there was a sale on avocados. With the discount, he was charged $4.86 before tax. What was the percent discount on each avocado?
Answer:
Step-by-step explanation:
Total discount = 6×$0.90 - $4.86 = $0.54
discount each = $0.54/6 ≈ $0.09
$0.09/$0.90 = 0.10 = 10%
2. Describe a rigid motion or composition of rigid motions that maps the rectangular bench at (0, 10)and
the adjacent flagpole onto the other short rectangular bench and flagpole.
Answer:
See Explanation
Step-by-step explanation:
Given
Let the bench be B and the flagpole be T.
So:
[tex]B = (0,10)[/tex] --- given
The flagpole is represented by the triangular shape labelled T.
So, we have:
[tex]T = (6,9)[/tex]
See attachment for the rectangular bench and the flagpole
From the attached image, the location of the other bench is:
[tex]B' = (0,-10)[/tex]
And the location of the other flagpole is:
[tex]T' = (-6,9)[/tex]
So, we have:
[tex]B = (0,10)[/tex] ==> [tex]B' = (0,-10)[/tex]
[tex]T = (6,9)[/tex] ==> [tex]T' = (-6,9)[/tex]
When a point is reflected from [tex](x,y)[/tex] to [tex](x,-y)[/tex], the transformation rule is reflection across x-axis.
So the rigid transformation that takes [tex]B = (0,10)[/tex] to [tex]B' = (0,-10)[/tex] is: reflection across x-axis.
When a point is reflected from [tex](x,y)[/tex] to [tex](-x,y)[/tex], the transformation rule is reflection across y-axis.
So the rigid transformation that takes [tex]T = (6,9)[/tex] to [tex]T' = (-6,9)[/tex] is: reflection across y-axis.
7x-12+3x+28=180 degrees
Please help ASAP
Answer:
180 degrees
Step-by-step explanation:
i think im not sure??????? i hope im right
you put it in the question
please help it would be reallyyyy nice tysmmwmsmssmm
Answer:
I think it is 30
Step-by-step explanation:
Answer:
x = 30
Step-by-step explanation:
The angles shown are vertical angles
If you didn't know vertical angles are congruent
That being said we create an equation to solve for x
(because vertical angles are congruent) 104 = 3x + 14
now that we have created an equation we want to solve for x
Step 1 subtract 14 from each side
104 - 14 = 90
14 - 14 cancels out
now we have 90 = 3x
step 2 divide each side by 3
90/3=30
3x/3=x
we're left with x = 30
A group of students were asked if they like Math class and if they like English class.
Partial results are shown in the table.
Like Math
Don't Like Math
Like English
х
9
Don't Like English
26
у
.
Of the students who like math, 40% don't like English.
Of the students who don't like math, 75% don't like English
What is the value of x + y?
A. 35
B. 57
C. 65
D. 66
Why are the triangles congruent
Answer:
The triangles are congruent because they are both exactly the same.
Solve the following system of equations using Desmos.....x-3y=-2 and x+3y=16
Answer:
(7, 3 )
Step-by-step explanation:
Given the 2 equations
x - 3y = - 2 → (1)
x + 3y = 16 → (2)
Adding (1) and (2) term by term will eliminate the y- term
2x + 0 = 14
2x = 14 ( divide both sides by 2 )
x = 7
Substitute x = 7 into either of the 2 equations and solve for y
Substituting into (2)
7 + 3y = 16 ( subtract 7 from both sides )
3y = 9 ( divide both sides by 3 )
y = 3
solution is (7, 3 )
How many sqftwks are used when producing a K flat of cucumbers
for grafting that spent 6 weeks on a bench in the greenhouse?
The number of square feet-weeks used when producing a K flat of cucumbers for grafting is not provided.
To determine the number of sqftwks (square feet-weeks) used when producing a K flat of cucumbers for grafting that spent 6 weeks on a bench in the greenhouse, we need additional information.
The term "sqftwks" represents the product of the area in square feet and the duration in weeks. However, the specific values for the area and the duration of cucumber growth are not provided in the question.
To calculate the number of sqftwks, we would need to know the area occupied by the K flat of cucumbers and the time spent in the greenhouse. Without these specific values, it is not possible to determine the number of sqftwks used for cucumber production.
Therefore, based on the given information, we cannot calculate the number of sqftwks used when producing a K flat of cucumbers for grafting that spent 6 weeks on a bench in the greenhouse.
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The mean salary at a local industrial plant is $28,600$28,600 with a standard deviation of $4400$4400. The median salary is $25,300$25,300 and the 61st percentile is $29,000$29,000.
Step 2 of 5:
Based on the given information, determine if the following statement is true or false.
Joe's salary of $35,060$35,060 is 1.401.40 standard deviations above the mean.
The statement Joe's salary of $35,060$35,060 is 1.401.40 standard deviations above the mean is false.
To determine if the statement is true or false, we need to calculate the number of standard deviations Joe's salary of $35,060 is above the mean.
Given:
Mean salary = $28,600
Standard deviation = $4,400
Joe's salary = $35,060
To calculate the number of standard deviations above the mean, we can use the formula:
Number of standard deviations = (X - μ) / σ
Where:
X is the value we want to compare (Joe's salary)
μ is the mean
σ is the standard deviation
Plugging in the values, we have:
Number of standard deviations = (35,060 - 28,600) / 4,400
= 6,460 / 4,400
≈ 1.4727
Therefore, Joe's salary of $35,060 is approximately 1.4727 standard deviations above the mean, not 1.40.
The statement is false.
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SOMEONE HELPPPP PLEASEEEEEEEEEEEEEEEE
Answer:
No, Collin didn't reach his goal. He got a 81% on his test.
Step-by-step explanation:
4,3,4,7,4,8 step 1 of 3: calculate the value of the sample variance. round your answer to one decimal place.
The sample variance for the given data set is 3.6.
To calculate the sample variance, we follow a series of steps. First, we need to find the mean (average) of the data set. Adding up all the numbers and dividing by the total count gives us the mean, which in this case is (4+3+4+7+4+8)/6 = 30/6 = 5.
Next, we calculate the deviations of each data point from the mean. We subtract the mean from each data point to get the deviations: (4-5), (3-5), (4-5), (7-5), (4-5), and (8-5), which simplify to -1, -2, -1, 2, -1, and 3, respectively.
Then, we square each deviation to eliminate negative values:[tex](-1)^2[/tex], [tex](-2)^2[/tex], [tex](-1)^2[/tex], [tex]2^2[/tex], [tex](-1)^2[/tex], and [tex]3^2[/tex], which simplify to 1, 4, 1, 4, 1, and 9, respectively.
The next step is to find the sum of the squared deviations. Adding up all the squared deviations gives us 20.
Finally, we divide the sum of squared deviations by the total count minus 1 (n-1) to calculate the sample variance: 20/(6-1) = 20/5 = 4.
Rounding the sample variance to one decimal place, we get 3.6 as the final result.
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Sam drinks water at an incredible rate. She drinks 2 1/5 liters of water every 3/4 of an hour. Sam drinks water at a constant rate. About how much water does Sam drink per hour?
Answer:
2.9 litres
or
2 14/15 litres
Step-by-step explanation:
To determine the amount of water Sam drinks in an hour, divide the total amount drunk by the number of hours
Amount drank in an hour = total litres drunk / time
[tex]2\frac{1}{5}[/tex] ÷ [tex]\frac{3}{4}[/tex]
[tex]\frac{11}{5}[/tex] × [tex]\frac{4}{3}[/tex] = [tex]\frac{44}{15}[/tex] = 2[tex]\frac{14}{15}[/tex] litres
will give brainiest + 40 points
Which graph represents the function p(x) = |x – 1|?
Answer:
I think it's the second I e at the top
A cylindrical gas tank holds approximately 401.92 cubic feet of fuel. The radius of the tank is 4 feet. Find the height of the tank in feet. Use 3.14 for π. PLEASE HURRY I NEED THIS
Answer:
8 ft
Step-by-step explanation:
Given:
Volume = 401.92
radius = 4 feet
Volume of cylinder: [tex]\pi[/tex]r^2h
3.14 * 4^2 * h = 401.92 cubic feet
3.14 * 16 * h = 401.92 cubic feet
50.24 * h = 401.92
h = 8 ft
Write 4^3 using repeated multiplication. Then find the value of 4^3
pls help will mark brainlest
Answer:
(5,7) , (2, -3) , (2,4)
Step-by-step explanation:
your first number, the x, is the horizontal number. The second, y, is the vertical number. So if you look at A, the x is 5, and you then have to go up to 7 to reach the intercept
Select the answer closest to the specified areas for a normal density.
(a) The area to the left of 32 on a N(45, 8) distribution. A. 0.948
C. 0.896 D. 0.104
B. 0.052
B. 0.97
(b) The area to the right of 12 on a N(9.4, 1.2) distribution. A. 0.985 C. 0.03 D. 0.015
(c) The area between 43 and 100 on a N(75, 15) distribution: A 0.984 C. 0.936 D. 0.64
The closest answer for each area is B. 0.052, D. 0.015, and C. 0.936, respectively.
(a) The area to the left of 32 on a N(45, 8) distribution. The area to the left of 32 on a N(45, 8) distribution is given by: P(Z < (32 - 45)/8)P(Z < -1.625)= 0.052, approximately. So, the closest answer is B. 0.052.
(b) The area to the right of 12 on a N(9.4, 1.2) distribution. The area to the right of 12 on a N(9.4, 1.2) distribution is given by: P(Z > (12 - 9.4)/1.2)P(Z > 2.166)= 1 - P(Z < 2.166)= 1 - 0.985= 0.015. So, the closest answer is D. 0.015.
(c) The area between 43 and 100 on a N(75, 15) distribution. The area between 43 and 100 on a N(75, 15) distribution is given by: P((43 - 75)/15 < Z < (100 - 75)/15)P(-1.5333 < Z < 1.6666)= P(Z < 1.6666) - P(Z < -1.5333)= 0.9525 - 0.0624= 0.8901. So, the closest answer is C. 0.936.
In conclusion, the closest answer for each area is B. 0.052, D. 0.015, and C. 0.936, respectively.
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10x+9y=-17
10x-2y=16
Answer:
they both = eachother
10x+9y=-17 = 10x-2y=16
Step-by-step explanation:
Set up an integral that represents the length of the part of the parametric curve shown in the graph.
x = 9t^2 − 3t^3, y = 3t^2 − 6t
The x y-coordinate plane is given. The curve starts at the point (12, 9), goes down and left becoming more steep, changes direction at approximately the origin, goes down and right becoming less steep, changes direction at the point (6, −3), goes up and right becoming more steep, changes direction at the approximate point (12, 0), goes up and left becoming less steep, and stops at the point (0, 9).
To find the length of the parametric curve described by the equations x = 9t^2 − 3t^3 and y = 3t^2 − 6t, we can set up an integral using the arc length formula. The curve starts at point (12, 9) and ends at point (0, 9), with several changes in direction along the way.
The length of a curve can be calculated using the arc length formula. For a parametric curve defined by x = f(t) and y = g(t), the arc length can be expressed as:
L = ∫[a,b] √[(dx/dt)^2 + (dy/dt)^2] dt.
In this case, we have x = 9t^2 − 3t^3 and y = 3t^2 − 6t. To find the length of the curve, we need to determine the interval [a, b] over which t varies.
From the given information, we can see that the curve starts at (12, 9) and ends at (0, 9). By solving the equation x = 9t^2 − 3t^3 for t, we find that t = 0 at x = 0, and t = 2 at x = 12. Therefore, the interval of integration is [0, 2].
To set up the integral, we calculate the derivatives dx/dt and dy/dt, and then substitute them into the arc length formula. Simplifying the expression inside the square root and integrating over the interval [0, 2], we can evaluate the integral to find the length of the curve.
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