Answer:
The answer your looking for is, C.
Write 4^3 using repeated multiplication. Then find the value of 4^3
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
An archer hits a target 50% of the time. Design and use a simulation to find the experimental probability that the archer hits the target exactly four of the next five times.
MARK AS BRAINLEST FOR THE CORRECT ANSWER
Given:
An archer hits a target 50% of the time.
To find:
The experimental probability that the archer hits the target exactly four of the next five times.
Solution:
It is given that an archer hits a target 50% of the time. It means the probability of hitting the target is
[tex]p=\dfrac{50}{100}[/tex]
[tex]p=0.5[/tex]
The probability of not hitting the target is
[tex]q=1-p[/tex]
[tex]q=1-0.5[/tex]
[tex]q=0.5[/tex]
Binomial distribution formula:
[tex]P(x=r)=^nC_rp^rq^{n-r}[/tex]
We need to find the probability that the archer hits the target exactly four of the next five times. So, [tex]n=5,r=4,p=0.5,q=0.5[/tex].
[tex]P(x=4)=^5C_4(0.5)^4(0.5)^{5-4}[/tex]
[tex]P(x=4)=\dfrac{5!}{4!(5-4)!}(0.5)^4(0.5)^{1}[/tex]
[tex]P(x=4)=5(0.5)^{5}[/tex]
[tex]P(x=4)=0.15625[/tex]
Therefore, the experimental probability that the archer hits the target exactly four of the next five times is 0.15625.
SOMEONE HELPPPP PLEASEEEEEEEEEEEEEEEE
Answer:
No, Collin didn't reach his goal. He got a 81% on his test.
Step-by-step explanation:
Evaluate the double integral where R is the region enclosed by y = x² and y = 9. Answer: I =
Given that R is the region enclosed by y = x² and y = 9. The value of the double integral over the region is I =81.
We are given the region R that is enclosed by y = x² and y = 9.
The x values range from -3 to 3.
The y values range from x² to 9.
We thus evaluate the double integral as follows:
I = [tex]\int_{(-3)}^ {(3)} \int_{(x^2)}^{( 9)[/tex] dA
I= [tex]\int_{(-3)}^ {(3)} \int_{(x^2)}^{( 9)[/tex] dydx
We integrate the integral with respect to y from x² to 9, and then integrate that expression with respect to x from -3 to 3.
We get: I = [tex]\int_{(-3)}^ {(3)} \int_{(x^2)}^{( 9)[/tex] dydx
I= [tex]\int_{(-3)}^ {(3)[/tex] (9 - x²) dx
= [tex]\int_{(-3)}^ {(3)} 9 dx - \int_{(-3)}^ {(3)[/tex] x² dx
= 18[tex]\int_{(0)}^ {(3)} x dx - \int_{(-3)}^ {(3)[/tex] x² dx
= 18[(3²/2) - (0²/2)] - [(3³/3) - (-3³/3)]
= 18(9/2) - 54
= 81
Answer: I = 81.
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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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Susan paints a stack of 30 blocks in a pattern. Starting from the bottom, she paints every 3rd block red and every 5th block green. Wherever red and green land on the same block, she paints that block yellow.
The 3rd block from the bottom that is painted green is how many blocks up from the bottom?
Answer:
20 blocks
Step-by-step explanation:
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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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
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
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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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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Gradient methods are used to find local optima of functions. Apply the Method of Steepest Descent to the function f(x1, x2) = 3xí + 2xż starting from the initial point Xo = (2, 1) (you should only perform the first 2 iterations of the algorithm). e) If the initial start point xo is changed to a different position, how might this affect the operation of the algorithm?
The first two iterations of the Method of Steepest Descent algorithm starting from the initial point Xo = (2, 1) for the function f(x1, x2) = 3x1 + 2x2 are as follows:
Iteration 1:
1. Compute the gradient at the current point Xo: ∇f(Xo) = [∂f/∂x1, ∂f/∂x2] = [3, 2].
2. Choose a step size (learning rate) α.
3. Update the current point Xo using the gradient and step size: X1 = Xo - α * ∇f(Xo).
Iteration 2:
1. Compute the gradient at the current point X1: ∇f(X1) = [∂f/∂x1, ∂f/∂x2].
2. Choose a step size (learning rate) α.
3. Update the current point X1 using the gradient and step size: X2 = X1 - α * ∇f(X1).
In the given function f(x1, x2) = 3x1 + 2x2, the partial derivatives with respect to x1 and x2 are 3 and 2, respectively. These represent the gradients in the x1 and x2 directions at any given point (x1, x2).
The Method of Steepest Descent is an iterative optimization algorithm that aims to minimize a function by moving in the direction of the steepest descent (negative gradient) at each iteration.
It starts from an initial point Xo and updates the current point by taking steps in the opposite direction of the gradient, multiplied by a step size or learning rate α.
In the first iteration, we compute the gradient at the initial point Xo = (2, 1), which is ∇f(Xo) = [∂f/∂x1, ∂f/∂x2] = [3, 2]. Let's assume we choose a learning rate α of 0.1.
Using the gradient and learning rate, we update Xo to X1:
X1 = Xo - α * ∇f(Xo) = (2, 1) - 0.1 * [3, 2] = (2, 1) - [0.3, 0.2] = (1.7, 0.8).
In the second iteration, we compute the gradient at the current point X1 = (1.7, 0.8), which is ∇f(X1) = [∂f/∂x1, ∂f/∂x2]. Let's assume we again choose a learning rate α of 0.1.
Using the gradient and learning rate, we update X1 to X2:
X2 = X1 - α * ∇f(X1) = (1.7, 0.8) - 0.1 * [∂f/∂x1, ∂f/∂x2] = (1.7, 0.8) - [0.1 * ∂f/∂x1, 0.1 * ∂f/∂x2].
The above calculations provide the values of X1 and X2 after the first two iterations of the Method of Steepest Descent algorithm for the given function.
Now, let's move on to the second part of your question.
If the initial start point Xo is changed to a different position, it can significantly affect the operation of the algorithm. The Method of Stee
pest Descent aims to find a local optimum of the function, and the starting point plays a crucial role in determining the convergence behavior.
If the new initial point is closer to a local optimum, the algorithm may converge faster as it takes smaller steps towards the optimal point. However, if the new initial point is far from any local optima, the algorithm may take longer to converge or even converge to a different suboptimal point.
The choice of learning rate α also affects the algorithm's performance. A larger learning rate may lead to faster convergence but can also cause overshooting and instability. On the other hand, a smaller learning rate may lead to slower convergence but better stability.
In summary, changing the initial start point xo can affect the convergence behavior and the final solution obtained by the Method of Steepest Descent algorithm. It is crucial to choose an appropriate initial point and learning rate to achieve the desired optimization outcome.
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Sams gym charges a one time fee of $60 plus $32 per Session for a personal trainer. the new gym in town a membership fee of $350 plus $20 for each session with a trainer. which inequality would be used to determine X the number of sessions with a personal trainer where is the new gym is the better deal?
Answer: i think $35
Step-by-step explanation: have a great day
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.
Plzz its urgent answer my question
Answer:
the answer is option (b)
good day mate
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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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
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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5.) What is the mean of the data?
3, 3, 5, 5, 5, 7, 7, 8, 15, 15
Answer:
How to Find the Mean. The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
What is the measure of ∠x?
Answer:
117+x=180°(sum of straight line)
Step-by-step explanation:
x=180-117
x=63
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.
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:
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 )
10x+9y=-17
10x-2y=16
Answer:
they both = eachother
10x+9y=-17 = 10x-2y=16
Step-by-step explanation:
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%
Why are the triangles congruent
Answer:
The triangles are congruent because they are both exactly the same.
16Acos(x)-Bsin(x)-2Asin(x)+19Bcos(x)=65cos(x) can someone helps me to find the exactly value of A and B ?
The exact values of A and B that satisfy the equation are A = -65/22 and B = 65/11.
To find the exact values of A and B in the equation 16Acos(x) - Bsin(x) - 2Asin(x) + 19Bcos(x) = 65cos(x), we need to equate the coefficients of the corresponding trigonometric functions on both sides of the equation.
Comparing the coefficients of cos(x) on both sides:
16A + 19B = 65 (Equation 1)
Comparing the coefficients of sin(x) on both sides:
-2A - B = 0 (Equation 2)
We now have a system of two equations with two unknowns (A and B). We can solve this system to find the values of A and B.
Let's solve the system of equations:
From Equation 2, we can express B in terms of A:
B = -2A
Substituting this expression for B in Equation 1:
16A + 19(-2A) = 65
16A - 38A = 65
-22A = 65
A = -65/22
Substituting the value of A back into the expression for B:
B = -2A
B = -2(-65/22)
B = 65/11
Therefore, the exact values of A and B that satisfy the equation are:
A = -65/22
B = 65/11
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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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What is the solution to the equation 4x + 2(x − 3) = 3x + x − 12? (1 point) −3 −1 1 3