To maximize the expression Σ pi' (1 - bi') given the lists bi and Pi, we can use a greedy algorithm. The algorithm works as follows:
1. Sort the lists bi and Pi in descending order based on the values of Pi.
2. Initialize two empty lists, bi' and pi'.
3. Iterate through the sorted lists bi and Pi simultaneously.
4. For each pair (bi, Pi), append bi to bi' and Pi to pi'.
5. Calculate the sum of pi' (1 - bi') to obtain the maximum value.
The greedy expression selects the elements with the highest Pi values first, ensuring that the products pi' (1 - bi') contribute the most to the overall sum. By sorting the lists in descending order based on Pi, we prioritize the higher Pi values, maximizing the sum.
It's important to note that this greedy algorithm may not guarantee an optimal solution in all cases, as it depends on the specific values in the lists. However, it provides a simple and efficient approach to maximize the given expression based on the provided lists bi and Pi.
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Need help with the answer
Answer:
volume of cylinder=pi×r²×h
volume of cylinder =3.14×(11ft)²×10ft
volume of cylinder=3799.4ft³
A projectile was launched from the ground with a certain initial velocity. The militaries used a radar to determine the vertical coordinate you of the projectile for two moments of time measured in seconds from the moment when the projectile was launched. The radar measurements showed that y(3) = 419 meters, 6) = 679 meters. Calculate the maximum of y() if it is known as follows 1. The projectile was moving along a vertical line 2. The acceleration due to gravity gis 9.81 meter second 3. There is an air resistance proportional to the velocity of the projectile. 4. The value of the empirical coefficient p is a constant 5. Time is measured in seconds, and distances are measured in meters A student solved the problem, rounded-off the numerical value of the maximum of y(t) to THREE significant figures and presented it below (15 points) meters your numerical answer must be written here Also, it is required to answer several additional questions as follows: 1. If p is the value of a positive empirical constant (its value is to be found), is the unknown initial velocity of the projectle, then the formula for the altitude y of the projectile at the moment of timetis given by the formula (1 point): = ロロロロロ 2. If p is the value of a positive empirical constant (its value is to be found) is the unknown initial velocity of the projectile, then the value of the velocity of the projectile at the moment of time is given by the formula (1 point): ( *Y-811.pl 3. The maximum of the altitude was achieved by the projectile when time expressed in seconds and rounded-odfo FOUR significant figures) was qual to (3 points) 9.354 DD0000 10:49 10.89 11 35 11.89 12.48.
The maximum altitude attained by the projectile is 720 meters. The maximum altitude was achieved by the projectile when time expressed in seconds and rounded off to four significant figures was equal to 10.89 seconds.
The formula for the altitude y of the projectile at the moment of time t is given by the formula: y(t) = [(v_0 / p)g][1 - exp(-pt / m)] + (m / p)g(t / p) where v_0 is the initial velocity of the projectile, p is the empirical constant, g is the acceleration due to gravity, m is the mass of the projectile, and t is the time.
The formula for the velocity of the projectile at the moment of time t is given by the formula: v(t) = (v_0 / p)exp(-pt / m) + (m / p)g.
Any object launched into space with only gravity acting on it is referred to as a projectile. Gravity is the main force affecting a projectile. This doesn't imply that other forces don't affect it; it merely means that their impact is far smaller than that of gravity. A projectile's trajectory is its route after being fired. A projectile is something that is launched or batted, as a baseball.
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HELP ME QUICKLY I WILL GIVE YOU THE CROWN
Answer:
J
Step-by-step explanation:
Given
5(y + 2) + 4 ← note 4 is outside the parenthesis
Each term in the parenthesis is multiplied by 5, that is
5 • y + 5 • 2 + 4 → J
Assume an exponential function has a starting value of 16 and a decay rate of 4%. Write an equation to model the situation.
During a professional baseball game, every
spectator placed his or her ticket stub into one of
several containers. After the game, the coach
chose twenty people to march in the victory
parade. What is the sample in this situation?
Answer:
20 people chosen to March
Step-by-step explanation:
The sample can be explained as a random subset of the population. It is a given number of draws or selection made usually at Random from the entire or larger population set. The sample is usually smaller Than the population and if done randomly will be representative of the population set. The entire spectator attending the baseball game is the population of interest while the 20 selected from the entire pool to March in the victory parade is the sample data obtained from the population set.
mDE⌢=129°, and mBC⌢=65°. Find m∠A
Answer:
mDE⌢=129°, and mBC⌢=65°. Find m∠A
Step-by-step explanation:
67 is 42% of what number?
Answer:
28.14
Step-by-step explanation:
Please answer correctly! I will mark you Brainliest!
Answer:
158.35
Step-by-step explanation:
Compute r''(t) when r(t) = (118,5t, cos t)
The second derivative of the function r(t) = (118,5t, cos t),
is determine as r''(t) = (0, 0, - cos t).
What is the second derivative of the function?The second derivative of the function is calculated by applying the following method.
The given function;
r(t) = (118, 5t, cos t)
The first derivative of the function is calculated as;
derivative of 118 = 0
derivative of 5t = 5
derivative of cos t = - sin t
Add the individual derivatives together;
r'(t) = (0, 5, - sin t)
The second derivative of the function is calculated as follows;
derivative of 0 = 0
derivative of 5 = 0
derivative of - sin t = - cos t
Adding all the derivatives together;
r''(t) = (0, 0, - cos t)
Thus, the second derivative of the function is determine as r''(t) = (0, 0, - cos t).
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urgente porfa 50 PUNTOS POR LAS 3 FICHAS
You dont deserve answers if ur gonna do that to other people.
Tamara can mow an acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? Write an equation to model and solve the problem. Explain the answer in terms of the problem. Show all work.
Answer:
2 hours
Step-by-step explanation:
please solve question 1 step by step and the others if u have time please
Let the each angle be x , 2x and 3x.
→ x + 2x + 3x = 5600
→ 8x = 5600
→ x = 5600/8
→ x = 700
the value of x is Rs.700.
Now, 2x = 2×700 = 1400
, 3x = 3×700 = 2100
Each one will get Rs.700 , Rs.1400 and Rs. 2100.
Graph y = 2x + 1
Help pleaee
Answer:
Step-by-step explanation:
Answer:
Answer is linked
Step-by-step explanation:
The equation is in slope-intercept form, which is y = mx + b.
To graph the line, first we have to find the slope, m, and the y- intercept, b.
So, the slope is 2 and the y- intercept is 1.
We can graph this, beginning with the y- intercept, 1. The y- intercept is always on the y axis, so the (x) value will always be zero.
Plot a point at (0, 1).
Next, add more points using the slope. The slope is 2, or [tex]\frac{2}{1}[/tex]. Start at the point we have made on the y axis. The slope equals the [tex]\frac{rise}{run}[/tex]. We can rise 2 units, then run one more unit to the right. If the slope is negative, the run goes to the left. However, in this case, the slope is positive, to it slants to the right.
We end on point (1, 3). We can continue this path infinitely, some other points on the graph could be (2, 5), (3, 7), (4, 9) and (5, 11).
Connect these points to make a line.
The finished line is linked below as well.
I hope this helps :] Good luck ^^
Given that P(B AND A) = 0.04 and P(A) = 0.18, what is P(BA)?
P(BA) is the conditional probability of event B given that event A has occurred approximately 0.04
P(BA), we need to know the individual probabilities of events A and B, as well as the probability of the intersection of events A and B.
P(B AND A) = 0.04
P(A) = 0.18
We can use the formula for the intersection of two events:
P(BA) = P(B AND A) = P(A) × P(B | A)
P(B | A) is the conditional probability of event B given that event A has occurred.
To calculate P(B | A), we can rearrange the formula as:
P(B | A) = P(B AND A) / P(A)
Putting in the given values:
P(B | A) = 0.04 / 0.18 ≈ 0.2222
Now we can calculate P(BA) using the formula:
P(BA) = P(A) × P(B | A)
= 0.18 × 0.2222
≈ 0.04
Therefore, P(BA) is approximately 0.04.
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to Find the analyticity region of the function and find it's derivate of the following functions (a) √Z²-2 (b) Sen (log z²) 20 Find the Taylor serie around zero for fuz) = 4+2² and compute the Convergence radius
(a) To find the analyticity region of the function f(z) = √(z² - 2), we need to determine where the function is well-defined. The square root function is defined for non-negative real numbers. In this case, the expression inside the square root, z² - 2, should be greater than or equal to zero.
z² - 2 ≥ 0
Solving the inequality:
z² ≥ 2
Taking the square root of both sides, while considering both the positive and negative roots:
z ≥ √2 or z ≤ -√2
Therefore, the analyticity region of the function f(z) = √(z² - 2) is all values of z greater than or equal to √2 or less than or equal to -√2.
(b) To find the derivative of the function f(z) = Sen(log z²), we can use the chain rule.
Let's break it down:
f(z) = Sen(log z²)
First, find the derivative of the inner function log z²:
d/dz (log z²) = 1 / (z²) * 2z = 2 / z
Now, find the derivative of Sen(u), where u = log z²:
d/dz (Sen(u)) = cos(u) * du/dz
Substituting the value of u:
d/dz (Sen(log z²)) = cos(log z²) * (2 / z)
Therefore, the derivative of the function f(z) = Sen(log z²) is cos(log z²) * (2 / z).
(c) To find the Taylor series around zero for the function f(z) = 4 + 2z², we need to find the derivatives of the function at zero and use them to construct the series.
Let's find the derivatives:
f(z) = 4 + 2z²
f'(z) = 0 + 4z = 4z
f''(z) = 0 + 4 = 4
f'''(z) = 0
All higher-order derivatives will also be zero.
Now, let's construct the Taylor series around zero using these derivatives:
f(z) = f(0) + f'(0)z + (f''(0)/2!)z² + (f'''(0)/3!)z³ + ...
Since the higher-order derivatives are zero, the series simplifies to:
f(z) = 4 + 0z + (4/2!)z² + 0z³ + ...
Simplifying further:
f(z) = 4 + 2z²
The Taylor series around zero for the function f(z) = 4 + 2z² is simply the original function itself.
To compute the convergence radius of the series, we can observe that the function f(z) = 4 + 2z² is a polynomial, and all polynomials have an infinite convergence radius. Therefore, the convergence radius for this series is infinite.
In conclusion, to Find the analyticity region of the function and find it's derivate of the following functions the Taylor series around zero for the function f(z) = 4 + 2z² is 4 + 2z², and its convergence radius is infinite.
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The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function?
Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
Answer:
Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
Step-by-step explanation:
(0, -6) is the y-intercept, as x = 0. Moving up 2, and right 1 represents the slope of the function. Going up is positive in the y direction, and going right is positive in the x direction.
Drawing a line through the 2 points gives a sneak peak on the full function to be graphed
PRO GAMER MOVE: function is y = 2x - 6
Answer:
It's A. (Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.)
Let R be a field and let f(x) € R[x] with deg( f (x)) = n > 1. If f(x) has roots over R, then f(x) is reducible over R. True False
The given statement "If f(x) has roots over R, then f(x) is reducible over R" is a True statement.
The degree of f(x) is greater than one and it has roots over R, then we need to know about the basic theorem which is "If f(x) is a polynomial over a field K and f(a) = 0, then (x-a) divides f(x)".Hence, we can say that "If f(x) has degree greater than one and it has a root over a field R, then f(x) is reducible over R."
Hence, the given statement "If f(x) has roots over R, then f(x) is reducible over R" is a True statement.
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A system is of the form x2=A+f(t) must be 22 and the particular solution to the system in (1) The general solution to the system is (u) If the initial value of the system is (0) - 6 find the solution to the IVP (d) Consider the system of equations = -21; + 1 2 = -1 The system has a repeated eigenvalue of -1, and Fire is one solution to the system. Use the given eigenvector to find the second linearly independent solution to the system.
The solution to a system of the type x2=A+f(t) must be 22 and is given in:
(a) Eigenvalues: λ = -2, 11. Eigenvectors: (1, 1), (-1, 1).
(b) Particular solution: [tex]\begin{equation}x = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t} + f(t)[/tex]
(c) General solution: [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} - \frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}[/tex]
(d) Second linearly independent solution: x = 22t - 23.
Here is the explanation :
(a) The system is of the form x' = Ax + f(t), where A is a 2x2 matrix and f(t) is a 2x1 vector-valued function. The characteristic equation of A is |A - λI| = 0, which in this case gives us λ² + λ - 22 = 0. The eigenvalues are λ = -2 and λ = 11. The eigenvectors corresponding to these eigenvalues are (1, 1) and (-1, 1), respectively.
(b) The particular solution to the system in (a) is given by [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} + f(t)[/tex].
The function f(t) must satisfy the initial conditions x(0) = (1, -6) and x'(0) = (-2, 1). Using these initial conditions, we can find [tex]c_1[/tex] and [tex]c_2[/tex] as follows:
[tex]\begin{equation}c_1 = \frac{1 - 6}{-2 - 11} = -\frac{1}{13}[/tex]
[tex]\begin{equation}c_2 = \frac{-2 + 1}{-2 - 11} = \frac{1}{13}[/tex]
Therefore, the particular solution to the system is
[tex]\begin{equation}x = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t} + f(t)[/tex]
(c) The general solution to the system is given by [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} + u[/tex], where u is a particular solution to the system. In this case, we have already found [tex]\begin{equation}u = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}[/tex].
Therefore, the general solution to the system is [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} - \frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}[/tex].
(d) The system has a repeated eigenvalue of -1, and Fire is one solution to the system. The second linearly independent solution can be found using the method of variation of parameters. In this method, we assume that the second solution is of the form x = vt + w, where v and w are constants to be determined. Substituting this into the system gives us the following equations:
-2v + w = -21
v + 11w = -1
Solving these equations gives us v = 22 and w = -23. Therefore, the second linearly independent solution is x = 22t - 23.
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Hurry!! MATH TEST
Ill make brainlest and pls show work if you can!
Answer:
option 1
Step-by-step explanation:
if it goes up 6 then it means plus 6
Determine all possible digit replacements for x so that the first number is divisible by the second. 95,768,24x; 4 What digit will make the first number divisible by 4? (Use a comma to separate answer
The digit replacements for x in the number 95,768,24x that make it divisible by 4 is either 0, 4, or 8.
To evaluate the digit replacements for x in the number 95,768,24x that make it divisible by 4, we need to determine the possible values for x that satisfy this condition.
For a number to be divisible by 4, the last two digits must be divisible by 4. Therefore, we need to find the values of x that make the number 24x divisible by 4.
The possible values for x that make 24x divisible by 4 are 0, 4, 8. This is because any multiple of 4 ends in 0, 4, 8 when the tens and units place are considered.
Therefore, the possible digit replacements for x are 0, 4, and 8. These values will make the number 95,768,24x divisible by 4.
Hence, the digit that will make the first number divisible by 4 is either 0, 4, or 8.
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I need help!!
A regular heptagon is shown below. What is the value of x? *
Answer:
Value of X=51.43
Step-by-step explanation:
the measure of the central angle of a regular heptagon is about 51.43 degrees which = X
if this helped please leave a rating and mark me brainliest
Enter the result as a single logarithm with a coefficient of 1. log9 (12x^4) - logg (5x^) = ____________
The expression [tex]log9(12x^4) - logg(5x^?)[/tex] can be simplified by combining the logarithms into a single logarithm with a coefficient of 1.
To simplify the expression log9(12x^4) - logg(5x^?), we can apply the logarithmic property of subtraction, which states that loga(b) - loga(c) = loga(b/c). Using this property, we can rewrite the expression as a single logarithm.
First, let's simplify the expression log9(12x^4). Since the base of the logarithm is 9, we can rewrite it as log(12x^4) / log(9).
Next, let's simplify the expression logg(5x^?). Since the base of the logarithm is g, we can rewrite it as log(5x^?) / log(g).
Combining these two expressions, we have:
log(12x^4) / log(9) - log(5x^?) / log(g).
To combine these logarithms into a single logarithm, we need a common base. Let's use the base 10. Applying the logarithmic property of division, we can rewrite the expression as:
log(12x^4) / log(9) - log(5x^?) / log(g) = (log(12x^4) - log(5x^?)) / log(9g).
Finally, we simplify the numerator by applying the logarithmic property of subtraction:
[tex]log(12x^4) - log(5x^?) = log((12x^4) / (5x^?)).[/tex]
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Farm workers are employed on a contract-to-contract basis. The contract lengths follow a normal distribution with a mean of 25 weeks and a variance of 36.
The variance is the average squared deviation of each value from the mean. It calculates how far each value in a group is from the mean, and then it squares the result of each of those calculations. Finally, it averages the sum of the squares to produce a figure that represents how varied the data is from the mean.
The variance formula is as follows:
Var(X) = (Σ (Xi - μ)^2) / (n - 1)
Where, X is a random variable representing the group data, μ is the mean of the group data, Xi is each value in the group data, Σ is the sum of all Xi values, and n is the number of values in the group data.
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According to given information, the probability that a contract will last between 15 and 35 weeks is `0.905`.
To compute the probability that a contract will last between 15 and 35 weeks, we must utilize the standard deviation for the normal distribution.
To solve for the probability of a normal distribution, we use the formula `z = (x - μ) / σ`, where `x` is the value we are looking for, `μ` is the mean, and `σ` is the standard deviation.
We can compute the standard deviation using the variance, which is the square of the standard deviation, which is `σ^2`.
To begin, we first find the standard deviation. `σ = sqrt(36) = 6`.
Next, we will calculate the `z-scores` for 15 and 35.
[tex]`z1 = (15 - 25) / 6 = -10 / 6 = -1.67`[/tex]
and [tex]`z2 = (35 - 25) / 6 = 10 / 6 = 1.67`[/tex].
Now we can use the `Z-table` to find the probabilities that correspond to `z1` and `z2`. We can see that the probability of `z1` is `0.0475` and the probability of `z2` is `0.9525`.
Finally, to obtain the probability that a contract will last between 15 and 35 weeks, we must subtract the probabilities corresponding to `z1` from `z2`.
[tex]`P(15 ≤ X ≤ 35) = P(Z ≤ 1.67) − P(Z ≤ −1.67) = 0.9525 − 0.0475 = 0.905`[/tex].
Therefore, the probability that a contract will last between 15 and 35 weeks is `0.905`.
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Please help me with the three questions on the top ignore the writing
Answer:
1. (1/4 x 5/4 x 5/4) = 25/64
2. (2/4 x 2/4 x 6/4) = 3/8
3. (1/4 x 1/4 x 4/2) 1/8
Step-by-step explanation:
Thank me later.
help me !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
Plug in the points to see which equation is true
Hi can somebody please answer this question for me by matching the definitions to the five math words??? I really need help sense I don’t understand and it would mean a lot if u answered please and thanks!
For the functions f(x) = 2x3- 3 and g(x) = 4x + 4, find (fog)(0) and (gºf)(0)
For the functions f(x) = 2x3- 3 and g(x) = 4x + 4, (gºf)(0) = g(f(0)) = g(-3) = -8.
To find (fog)(0), we need to evaluate the composition of functions f and g at x = 0.
First, we find g(0):
g(0) = 4(0) + 4 = 4.
Next, we substitute g(0) into f:
f(g(0)) = f(4).
Now, we find f(4):
f(4) = 2(4)^3 - 3 = 2(64) - 3 = 128 - 3 = 125.
Therefore, (fog)(0) = f(g(0)) = f(4) = 125.
To find (gºf)(0), we need to evaluate the composition of functions g and f at x = 0.
First, we find f(0):
f(0) = 2(0)^3 - 3 = -3.
Next, we substitute f(0) into g:
g(f(0)) = g(-3).
Now, we find g(-3):
g(-3) = 4(-3) + 4 = -12 + 4 = -8.
Therefore, (gºf)(0) = g(f(0)) = g(-3) = -8.
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What is the volume of the figure?
6 cm
3 cm
8 cm
2 cm
A
3 X 2 X 6
B.
6 X 8 2
C.
8 * 2 * 3
D.
3 * 2 * 8 * 6
Answer:
The given figure is a cuboid
it's volume = length × breadth × height
so the answer should be option (c) 8 × 2 ×3
How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. Estimate with 90% confidence the mean winning's for all the show's players.
With 90% confidence, the lower confidence limit (LCL) for the mean winnings is approximately $34,955.09 and the upper confidence limit (UCL) is approximately $40,485.31.
The mean winnings for all the show's players with a 90% confidence level, we can use the formula for a confidence interval for the population mean.
The sample of winnings:
30,692, 43,231, 48,269, 28,592, 28,453, 36,309, 45,318, 36,362, 42,871, 39,592, 35,456, 40,775, 36,466, 36,287, 38,956
We can calculate the sample mean (x(bar)) and the sample standard deviation (s) from the given data.
Sample mean
(x(bar)) = (30,692 + 43,231 + 48,269 + 28,592 + 28,453 + 36,309 + 45,318 + 36,362 + 42,871 + 39,592 + 35,456 + 40,775 + 36,466 + 36,287 + 38,956) / 15
≈ 37,720.2
Sample standard deviation
s = √[((30,692 - 37,720.2)² + (43,231 - 37,720.2)² + ... + (38,956 - 37,720.2)²) / (15 - 1)]
≈ 6,522.45
The standard error (SE) of the mean is calculated as SE = s /√n, where n is the sample size.
Standard error (SE) = 6,522.45 / √15 ≈ 1,682.12
To calculate the confidence interval, we need to find the critical value corresponding to a 90% confidence level. For a 90% confidence level, the critical value is approximately 1.645.
Margin of error = Critical value × Standard error
= 1.645 × 1,682.12
≈ 2,765.11
Lower confidence limit (LCL) = Sample mean - Margin of error
= 37,720.2 - 2,765.11
≈ 34,955.09
Upper confidence limit (UCL) = Sample mean + Margin of error
= 37,720.2 + 2,765.11
≈ 40,485.31
Therefore, with 90% confidence, the lower confidence limit (LCL) for the mean winnings is approximately $34,955.09 and the upper confidence limit (UCL) is approximately $40,485.31.
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The question is incomplete the complete question is :
How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. Estimate with 90% confidence the mean winning's for all the show's players. 30692 43231 48269 28592 28453 36309 45318 36362 42871 39592 35456 40775 36466 36287 38956 Lower confidence level (LCL) = ? Upper confidence level (UCL) = ?
Determine which of the following functions are differentiable at all the z-plane or some region of it and evaluate the derivatives if they exist. (a) f(3) = x2 + y2 + i2.cy.
The functions are differentiable at all the z-plane is f'(z) = 2x when function is f(z) = x² + y² + i2xy.
Given that,
The function is f(z) = x² + y² + i2xy
We have to determine if the functions are differentiable throughout the z-plane or only a portion of it, and then we must assess any derivatives that may exist.
We know that,
Take the function,
f(z) = x² + y² + i2xy
f(x + iy) = x² + y² + i2xy
f(x + iy) = u + iv
We can say, u =x² + y², v= 2xy
Differentiate u with respect to x
uₓ = 2x
Differentiate v with respect to y
[tex]v_y[/tex] = 2x
So,
uₓ = 2x = [tex]v_y[/tex]
uₓ = [tex]v_y[/tex]
Differentiate u with respect to y
[tex]u_y[/tex] = 2y
Differentiate v with respect to x
[tex]v_x[/tex] = 2y
So,
[tex]u_y[/tex] = -[tex]v_x[/tex] = -2y ⇒ y = 0
Let D = {z : x | x, y∈R}
f is differentiable on D.
The derivative is f'(z) = [tex]u_x + iv_x[/tex] = 2x
Therefore, the functions are differentiable at all the z-plane is f'(z) = 2x.
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