There is weak evidence supporting the claim that the true mean is below the desired specification of 57 Pa.
Based on the given information, the p-value obtained from the hypothesis test is 0.095. The p-value represents the probability of observing a test statistic as extreme or more extreme than the one obtained, assuming the null hypothesis (i.e., the true mean is not below 57 Pa) is true. Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. This means that we do not have enough evidence to claim that the true mean is significantly below 57 Pa.
Therefore, the conclusion is that there is weak evidence supporting the claim that the true mean is below the desired specification of 57 Pa.
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-8 (3x-2) -7 =-1/2 (4x+2) +7
Answer:x= 3/22
Step-by-step explanation:
Distribute
Subtract the numbers
Combine multiplied terms into a single fraction
Distribute
Find common denominator
Combine fractions with common denominator
Multiply the numbers
Add the numbers
A can has a radius of 3
inches and a height of 8
inches. If the height is doubled, how would it affect the original volume of the can?
Responses
The volume would double.
The volume would double.
The volume would triple.
The volume would triple.
The volume would quadruple.
The volume would quadruple.
The volume would increase by 16
cubic inches.
Step-by-step explanation:
the volume would double
Let S2(r) = {x ∈ R3 : |x| = r} for r >
0 and let f : S2 → S2(r) by f(x) = rx. Prove
that f is one-to-one and onto but not an isometry if r /= 1
The function f(x) = rx mapping S2 to S2(r) is one-to-one, onto, but not an isometry if r ≠ 1.
To prove that the function f: S2 → S2(r) defined by f(x) = rx is one-to-one, onto, and not an isometry if r ≠ 1, we'll consider the following:
1. One-to-one: For f to be one-to-one, for every distinct pair of points x, y ∈ S2, we must have f(x) ≠ f(y). Suppose x ≠ y, then rx ≠ ry since r > 0. This shows that f is one-to-one.
2. Onto: To show that f is onto, we must show that for every point y ∈ S2(r), there exists a point x ∈ S2 such that f(x) = y. For y ∈ S2(r), we can find x = (1/r)y, which satisfies |x| = 1, so x ∈ S2. Then f(x) = r(1/r)y = y, proving that f is onto.
3. Not an isometry if r ≠ 1: An isometry is a function that preserves distances between points. If f were an isometry, we'd have |f(x) - f(y)| = |x - y| for all x, y ∈ S2. Consider x, y ∈ S2 with |x - y| = d. Then, |f(x) - f(y)| = |rx - ry| = r|x - y| = rd. If r ≠ 1, rd ≠ d, so f does not preserve distances, and therefore f is not an isometry.
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A scarf sells for $52.50. The market price of the scarf was $75.00. What was the percentage discounted from the scarf.
Answer:
30%
Step-by-step explanation:
We Know
The market price of the scarf was $75.00
A scarf sells for $52.50
What was the percentage discounted from the scarf?
We Take
100% - (52.50 ÷ 75.00) · 100 = 30%
So, the percentage discounted from the scarf is 30%
Verify the gradients for logistic loss to make sure your understanding of the calculation of gradients is correct: a / aw1:-0.0222. a/aw2 :0.2239, a/ab, :-0.0374. question 8
If we are training the model with the squared loss
n
1/n Σi=₁ (wTx₁ + b − yi) ² :
1) What is the squared loss given the current hyperplane?
Question 9
2) What is the gradient with respect to the first component of the weight
vector (a/aw1)?
Question 10
3) What is the gradient with respect to the bias (a/ab)?
For the logistic loss function, the gradients are given by:
a/aw1 = -(1/n) Σi=₁ xi1(yi - σ(wTxi + b))
a/aw2 = -(1/n) Σi=₁ xi2(yi - σ(wTxi + b))
a/ab = -(1/n) Σi=₁ (yi - σ(wTxi + b))
where σ is the sigmoid function.
Using the squared loss function given by
1/n Σi=₁ (wTx₁ + b − yi) ²,
we can calculate the squared loss for the current hyperplane by plugging in the values of w and b for the given hyperplane, and computing the average loss over all the training examples.
The gradient with respect to the first component of the weight vector (a/aw1) is given by:
a/aw1 = (2/n) Σi=₁ xi1(wTxi + b - yi)
The gradient with respect to the bias (a/ab) is given by:
a/ab = (2/n) Σi=₁ (wTxi + b - yi)
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One baseball team played 40 games throughout the entire season if this baseball team won 55% of those games and how many games did they win
The number of those games won in that season are: 22 games
How to solve percentage problems?Percentage is defined a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:
Percentage = (value / total value) * 100%
We are given:
Total number of games played through the season = 40 games
Percentage of games won = 40%
Thus:
Number of games won = 40% * 55
= 22
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True or false: A set is considered closed if for any members in the set, the result of an operation is also in the set
False. A set is considered closed under an operation if the result of that operation on any two elements in the set also belongs to the set.
A set is considered closed if it contains all of its limit points. In other words, if a sequence of points in the set converges to a point that is also in the set, then the set is closed. Another equivalent definition is that the complement of the set.
In mathematics, sets are collections of distinct objects. These objects can be anything, including numbers, letters, or even other sets. The concept of sets is fundamental in mathematics and is used to define many other mathematical structures.
Sets can be denoted in various ways, including listing the elements inside curly braces { }, using set-builder notation, or using set operations to define new sets from existing ones. Some common set operations include union, intersection, difference, and complement.
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If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is
a. 0.5
b. 1/32
c. zero
d. larger than the probability of tails
Each coin toss is an independent event, meaning that the outcome of the previous toss does not affect the outcome of the next toss. Therefore, the probability of getting heads on the fifth toss is still 0.5.
The scenario you've described involves a series of independent events, which means the outcome of one toss does not affect the outcome of the others. In this case, you are interested in the probability of heads on the fifth trial after obtaining heads four times in a row.
Since the outcome of the fifth trial is independent of the previous four, the probability of getting heads on the fifth trial remains unchanged. The probability of obtaining heads or tails when flipping a penny is always 0.5 (or 1/2) for each side, as there are only two possible outcomes.
Therefore, the correct answer is:
a. 0.5
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The manager of a small convenience store does not want her customers standing in long too long prior to a purchase. In particular, she is willing to hire an employee for another cash register if the average wait time of the customers is more than five minutes. She randomly observes the wait time (in minutes) of customers during the day: 3.5 5.8 7.2 1.9 6.8 8.1 5.4 Assume x-bar = 5.53 and s = 0.67. What is the appropriate conclusion at a 5% significance level? a) A new employee does not need to be hired since: .05 < p-value < .10 b) A new employee needs to be hired since: .025 < p-value < .05 c) A new employee does not need to be hired since: .025 < p-value < .05 d) A new employee needs to be hired since: .01 < p-value < .025
The appropriate conclusion at a 5% significance level is that a new employee needs to be hired since the p-value is less than 0.05.
To test the hypothesis, we will use a one-sample t-test with a null hypothesis that the true population mean wait time is less than or equal to 5 minutes. The alternative hypothesis is that the true population mean wait time is greater than 5 minutes.
Using the given sample data, we calculate the sample mean (x-bar) as 5.53 and the sample standard deviation (s) as 0.67. The sample size is 7.
We calculate the t-statistic using the formula t = (x-bar - mu)/(s/sqrt(n)), where mu is the hypothesized population mean (5) and n is the sample size.
Substituting the values, we get t = (5.53 - 5)/(0.67/sqrt(7)) = 2.44.
Using a t-distribution table with 6 degrees of freedom (n-1), we find the p-value to be 0.03 for a one-tailed test. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that a new employee needs to be hired to reduce the average wait time.
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A student club is designing a trebuchet for launching a pumpkin into projectile motion. Based on an analysis of their design, they predict that the trajectory of the launched pumpkin will be parabolic and described by the equation y(x)=ax^2+bx where a=−8.0×10^−3 m^−1, b=1.0(unitless), x is the horizontal position along the pumpkin trajectory and y is the vertical position along the trajectory. The students decide to continue their analysis to predict at what position the pumpkin will reach its maximum height and the value of the maximum height. What is the derivative of the vertical position of the pumpkin trajectory with respect to its horizontal position?
a. dy/dx = ax
b. dy/dx = 2ax
c. dy/dx = 2ax+b
d. dy/dx = 0
The derivative of the vertical position of the pumpkin trajectory with respect to its horizontal position is 2ax, as given by option b.
To find the position of maximum height of the pumpkin, the students need to find the point where the derivative of the vertical position with respect to the horizontal position is equal to zero. Setting 2ax equal to zero and solving for x, we get x=0. This means that the pumpkin reaches its maximum height at x=0, or in other words, at the point where it is launched from the trebuchet.
To find the value of the maximum height, we can substitute x=0 into the original equation for the pumpkin's trajectory. This gives us y(0) = b, which means that the maximum height of the pumpkin is b units.
The derivative of the vertical position of the pumpkin trajectory with respect to its horizontal position is 2ax because the derivative of ax^2 with respect to x is 2ax. This means that the rate of change of the pumpkin's height with respect to its horizontal position is proportional to 2ax. When x is zero, the derivative is also zero, which indicates that the pumpkin has reached its maximum height at that point.
This is because at the maximum height, the rate of change of height with respect to horizontal distance is zero. Finally, we find the value of the maximum height by substituting x=0 into the equation for the pumpkin's trajectory.
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Shana spends $18 on some almonds. She pays for the almonds with two $10 bills.
How much change does Shana get back?
Enter your answer in the box.
Answer:
$2
Step-by-step explanation:
$10+$10=$20
$20-$18= $2
the box plot shows the heights of sunflower plants which sunflower field has plants with more consistent heights
To determine which sunflower field has plants with more consistent heights, we need to look at the variability in the heights of the plants in each field as shown in the box plot.
The more consistent the heights, the smaller the range and the less spread out the box plot will be. So, we should look for the field with the smallest range and the narrowest box plot. This indicates that the majority of the plants in that field have similar heights.
Therefore, we need to compare the box plots or IQRs of the different sunflower fields to determine which field has plants with more consistent heights. please follow these steps:
1. Look for the Interquartile Range (IQR) of each sunflower field. IQR is the range within which the middle 50% of the data lies. In a box plot, it is represented by the width of the box, which is the distance between the first quartile (Q1) and the third quartile (Q3).
2. Compare the IQRs of the sunflower fields. The field with the smaller IQR has plants with more consistent heights, as it indicates that the middle 50% of the plant heights are closer together.
In summary, check the box plots of the sunflower fields for their IQRs, and the field with the smaller IQR has more consistent plant heights.
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Answer: Field A typically has plants with more consistent heights. You can tell because the IQR of its samples is less than that of the other field.
Step-by-step explanation:
I just took the test on Iready, trust me.
The area of one piece of pizza is 14.13 in2. If the pizza is cut into eighths, find the radius of the pizza.
Answer:
We can use the formula for the area of a circle to solve this problem. We know that the area of one piece of pizza is 14.13 in². If the pizza is cut into eight equal pieces, then the total area of the pizza is 8 times the area of one piece of pizza, which is 8 * 14.13 = 113.04 in².
The formula for the area of a circle is A = πr², where A is the area of the circle and r is the radius. Solving for r, we get r = √(A/π). Substituting the total area of the pizza, we get:
r = √(113.04/π) ≈ 6
Therefore, the radius of the pizza is approximately 6 inches.
Step-by-step explanation:
Which of the equations below could be used as a line of best fit to approximate the data in the scatterplot?
Hint: Use the Desmos Graphing Calculator to graph the table and replicate the scatter plot. Then see which line from the choices below looks the best.
The equation of the line of best fit is y = 0.883x + 17.95.
We have,
To find the line of best fit, we want to find the equation of the line that comes closest to passing through all the points in the scatterplot.
One way to do this is to use linear regression analysis.
Using a calculator or statistical software,
We can find that the equation of the line of best fit for this data is:
y = 0.883x + 17.95
Thus,
The equation of the line of best fit is y = 0.883x + 17.95.
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Solve the differential equation by variation of parameters. 4y'' − y = ex/2 8
The solution of the differential equation 4y'' − y = [tex] {e}^{x/2} [/tex] + 8 by variation of parameter method is y(x) = (15C - 16)[tex] {e}^{x/2} [/tex] + 15C' [tex] {ex}^{-x/2} [/tex]
To solve the differential equation by variation of parameters, we assume that the solution is of the form,
y(x) = u₁(x)y₁(x) + u₂(x)y₂(x), linearly independent solutions of the homogeneous equation are y₂(x) and y₂(x), and functions to be determined u₁(x) and u₂(x). The homogeneous equation associated with the given differential equation is,
4y'' - y = 0
The characteristic equation is,
4r² - 1 = 0 which has solutions r = ±1/2. Therefore, the general solution of the homogeneous equation is,
y(x) = C[tex] {e}^{x/2} [/tex] + C'[tex] {e}^{-x/2} [/tex]
C and C' are arbitrary constants.
Now, we need to find particular solutions of the non-homogeneous equation. We can guess that a particular solution has the form,
[tex] y_{p(x)} = A(x) {e}^{(x/2)} [/tex]
where A(x) is a function to be determined. We can find A(x) by substituting y_p(x) into the differential equation and solving for A(x). We have,
[tex] 4y_{p(x)} - y_{p(x)} = {e}^{(x/2)} +8 [/tex]
Differentiating twice and substituting these into the differential equation gives:
[tex]4( A"(x) + A'(x)) {e}^{2/y} 2 + \frac{A(x)}{4} - A(x) {e}^{(x/2)} = {e}^{(x/2)} + 8[/tex]
Simplifying and solving for A(x), we obtain,
A(x) = -16/15
Therefore, a particular solution of the differential equation is:
[tex]y_{p(x)} = \frac{ - 16}{15} {e}^{(x \div 2)} [/tex]
The general solution of the non-homogeneous equation is then,
y(x) = C[tex] {e}^{x/2} [/tex] + C'[tex] {e}^{-x/2} [/tex] [tex]\frac{ - 16}{15} {e}^{(x/2)} [/tex]
Simplifying and collecting terms, we get,
y(x) = (15C - 16)[tex] {e}^{x/2} [/tex] + 15C' [tex] {ex}^{-x/2} [/tex] ,where C and C' are arbitrary constants.
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Complete question - Solve the differential equation by variation of parameters. 4y'' − y = e^x/2 + 8.
) find the matrix a of the linear transformation t(f(t))=f(2) from p2 to p2 with respect to the standard basis for p2, {1,t,t2}
The sample mean of the population is 3/4 and the variance is 3/80. Using the central limit theorem, P( > 0.8) can be simplified as 0.003.
The mean of the population can be computed as follows:
µ = ∫x f(x) dx from 0 to 1
= ∫x (3x²) dx from 0 to 1
= 3/4
The variance of the population can be computed as follows:
σ² = ∫(x-µ)² f(x) dx from 0 to 1
= ∫(x-(3/4))² (3x²) dx from 0 to 1
= 3/80
By the Central Limit Theorem, as the sample size n = 80 is large, the distribution of the sample mean can be approximated by a normal distribution with mean µ and variance σ²/n.
Therefore, P( > 0.8) can be approximated by P(Z >0.8- 0.75)/(sqrt(3/80)/(sqrt(80))), where Z is a standard normal random variable.
Simplifying, we get P( > 0.8) ≈ P(Z > 2.73) ≈ 0.003.
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The probability that X is a 2, 11, or 12 is:
a.) 1/36
b.) 2/36
c.) 3/36
d.) 4/36
Answer:
The correct answer is c.) 3/36.There are three favorable outcomes (2, 11, and 12) out of a total of 36 possible outcomes (assuming a fair six-sided number cube). Therefore, the probability of X being a 2, 11, or 12 is 3/36, which can be simplified to 1/12.
Step-by-step explanation:
2x2 + 7x = 3
x = 0.60 and x = −2.60
x = −0.60 and x = 2.60
x = 0.39 and x = −3.89
x = −0.39 and x = 3.89
Answer:
(c) x = 0.39 and x = -3.89
Step-by-step explanation:
You want the solutions to the quadratic equation ...
2x² +7x = 3.
Root relationsThe roots of the equation ...
x² +bx +c = 0
have a sum of -b and a product of c.
Subtracting 3 and dividing the equation by 2, we have ...
2x² +7x -3 = 0 . . . . . . . . subtract 3
x² +3.5x -1.5 = 0 . . . . . . divide by 2
This tells us the sum of the roots is -3.5.
Answer choice C has that sum: x = 0.39, x = -3.89.
__
Additional comment
The sums of the answer choices are ...
0.60 -2.60 = -2.00
-0.60 +2.60 = 2.00
0.39 -3.89 = -3.50
-0.39 +3.89 = 3.50
Sometimes, checking the offered choices is the simplest way to find the answer.
Here, checking the sum gives the best discriminator of right from wrong. The products are all near -1.5, so that is less helpful.
We can see the relation by considering the factored form:
(x -p)(x -q) = x² -(p+q)x +pq . . . . . . where p and q are the roots
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Is $9 : 4 visitors - $18 : 8 visitors proportional
Yes, $9 for 4 visitors and $18 for 8 site visitors are proportional.
To determine whether or not $9 for 4 visitors and $18 for 8 visitors are proportional, we need to test if the ratio of the value to the number of visitors is the equal for both cases.
The ratio of cost to the quantity of visitors for $9 and four visitors is:
$9/4 visitors = $2.25/ visitors
The ratio of value to the quantity of visitors for $18 and eight visitors is:
$18/8 visitors = $2.25/ visitors
We are able to see that both ratios are equal to $2.25 per visitor.
Therefore, $9 for 4 visitors and $18 for 8 site visitors are proportional.
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peterhas probability 2/3 of winning each game . peter and paul bet $1 on each game . if peter starts with $3 and paul with $5, what is the probability paul goes broke before peter is broke?
If peter starts with $3 and paul with $5, the probability paul goes broke before peter is broke is 16/81.
Let's first consider the probability that Peter goes broke before Paul. For Peter to go broke, he needs to lose all of his $3 in the first two games. The probability of this happening is:
(2/3)² = 4/9
If Peter goes broke, then Paul has won $2 and has $7 left. Now, the game is between Paul's $7 and Peter's $1. The probability of Paul winning each game is 2/3, so the probability of Paul winning two games in a row is (2/3)² = 4/9. Therefore, the probability of Paul winning two games in a row and going broke before Peter is broke is:
4/9 x 4/9 = 16/81
So the probability that Paul goes broke before Peter is broke is 16/81.
The probability that Peter goes broke before Paul is 4/7.
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pls help me i need to show work and i need it asap
(1) The two triangles are similar because they have equal angles.
(2) Triangle QRS is similar to triangle QLM because they have equal angles.
(3) Both triangles are similar and the value of x is 21.
What are the measure of the triangles?Two triangles are said to be similar if they have equal sides, equal angles or both.
The missing angles of the triangles for the question is calculated as;
Bigger triangle; missing angle = 180 - (44 + 46) = 90
Smaller triangle; missing angle = 90 - 46 = 44⁰
Both triangles are similar.
For the second question; triangle QRS is similar to triangle QLM because angle R is equal to angle L, and also they have common angle Q, which implies that angle S must be equal to angle L.
For third question, the triangles are similar because their corresponding angles are equal.
The value of x is calculated as;
48 + 4x + (180 - (56 + 76)) = 180 (sum of angles on a straight line)
48 + 4x + 48 = 180
4x = 84
x = 84/4
x = 21
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help me please please please
1) the mean, median, mode, and range of the set of data are given below.
What are the definition of the above terms?When considering a set of numbers, several measures can be used to describe the data. The mean, for example, is determined by adding all individual values together and dividing by the total number of elements in the set.
This value is representative of an average quantity among the group studied. On the other hand, if one were to arrange said values from smallest to largest, the median would represent the middle-most number in that list - or, if two middle numbers exist, their mean.
Range on the other hand is the variance between the largest and the smallest number in a data set.
Lastly but not least important is the mode, which indicates the most frequently appearing value within our dataset; or alternatively so noted as when there are multiple repetitions.
So here is the Mean, Median, Mode and Range for the given sets of data:
1)
Mean = (4.3 + 5.2 + 4.5 + 5.1 + 4.8 + 5.4 + 4.5 + 4.7 + 4.3 + 5.2 + 4.5 + 4.8 + 5.1) / 13
= 4.8
Mean ≈ 4.8
Median = when arranged in ascending order, the data se become:
4.3,4.3,4.5,4.5,4.5,4.7,4.8,4.8,5.1,5.1,5.2,5.2,5.4
Since there are 13 observation, 7th observation is the median.
4.3,4.3,4.5,4.5,4.5,4.7,| 4.8, | 4.8,5.1,5.1,5.2,5.2,5.4
hence median = 4.8
Note that where the number of data is even in number, the median become the average of the two middle numbers.
Mode - the number that occrs the highest is 4.5. It occurs thrice.
Range = Highest Data Value - Lowest Data Value
Range = 5.4 - 4.3
= 1.10
Using the above steps we derive the mean median, mode and range for the other data set:
2) 12.6, 12.8, 9.7, 10.4, 9.7, 10.8, 12.4, 12.8, 11.5, 10.4, 10.9, 12.8
Total of 12 number
Data in ascending order: 9.7,9.7,10.4,10.4,10.8,10.9,11.5,12.4,12.6,12.8,12.8,12.8
Mean = 11.4
Median = (10.9 +11.5)/2 = 11.2
Mode = 12.8
Range = 3.10
3)
-6, -13, -8, -3, -7, -10, 2, 0, -3, -5, 5, 7, -6, 2, 1, -6, -18
Data in ascending order; -12, -10, -8, -7, -4, -3, -2, -1, 0, 0, 0, 1, 2, 3, 4, 5, 7, 7
Mean = -1
Median = 0
Mode = 0
Range = 19
4) -6, -13, -8, -3, -7, -10, 2, o, -3, -5, 5, 7, -6, 2, 1, -6, -18
Data in ascending order: -18, -13, -10, -8, -7, -6, -6, -6, -5, -3, -3, 1, 2, 2, 5, 7
Mean = -4.25
Median = -5.5
Mode = -6
Range = 25
5) 0.24, 0.31, 0.43, 0.22, 0.34, 0.24, 0.35, 0.4, 0.18, 0.3, 0.29
Data in ascending order: 0.18, 0.22, 0.24, 0.24, 0.29, 0.3, 0.31, 0.34, 0.35, 0.4, 0.43
Mean = 0.3
Median = 0.3
Mode = 2.4
Range = 2.5
6) -0.6, 0.4, 0.2, -0.3, 0.1, -0.5, 0.2, 0.4, 1.1, -0.6, 0.7, o, 0.2, -1.3
Data in ascending order: -1.3, -0.6, -0.6, -0.5, -0.3, 0.1, 0.2, 0.2, 0.2, 0.4, 0.4, 0.7, 1.1
Mean = 0
Median = 0.2
Mode = 0.2
Range = 2.4
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Please help asap :( Find the exact length of arc ADC. In your final answer, include all of your calculations
Answer:
15 Pi m
Step-by-step explanation:
arc ADC = 360 Degrees - 60 Degrees divided by 360 Degrees Multiplied by 2 Pi Multiplied by 9
= 5/6 Times 18 Pi
=15 Pi m
if you give me new answer i will give you like
Let {u(t), t e T} and {y(t), t e T} be stochastic processes related through the equation y(t) + alt - 1)yſt - 1) = u(t) show that Ry(s, t) - aé (s – 1)(t - 1)R,(s – 1,t - 1) = Ru(s, t)
Ry(s, t) - aé (s – 1)(t - 1)R,(s – 1,t - 1) = Ru(s, t)
We start by computing the autocorrelation function of y(t) and cross-correlation function of u(t) and y(t).
Autocorrelation function of y(t):
Ry(s, t) = E[y(s)y(t)]
Cross-correlation function of u(t) and y(t):
Ru(s, t) = E[u(s)y(t)]
Using the given equation, we can rewrite y(t) as:
y(t) = u(t) - a(y(t-1) - y*(t-1))
where y*(t) denotes the conjugate of y(t).
Taking the expectation of both sides:
E[y(t)] = E[u(t)] - a[E[y(t-1)] - E[y*(t-1)]]
Since y(t) and u(t) are stationary processes, their expectations are constant with respect to time.
Let's denote E[y(t)] and E[u(t)] as µy and µu, respectively. We can then rewrite the above equation as:
µy = µu - a(µy - µ*y)
where µ*y denotes the conjugate of µy.
Similarly, taking the expectation of both sides of y(s)y(t), we get:
Ry(s, t) = Eu(s)y(t) - aRy(s-1, t-1) + aRy(s-1, t-1) - a^2Ry(s-2, t-2) + a^2Ry(s-2, t-2) - ...
Using the fact that Ry(s-1, t-1) = Ry*(t-1, s-1), we can simplify the above expression as:
Ry(s, t) - aRy(s-1, t-1) = Eu(s)y(t) - aRy*(t-1, s-1) + a*Ry(s-1, t-1)
Multiplying both sides by a, we get:
a[Ry(s, t) - aRy(s-1, t-1)] = aEu(s)y(t) - a^2Ry*(t-1, s-1) + a^2*Ry(s-1, t-1)
Adding aRy(s-1, t-1) and subtracting a^2Ry(s-1, t-1) on the right-hand side, we get:
a[Ry(s, t) - aRy(s-1, t-1)] + aRy(s-1, t-1) - a^2Ry(s-1, t-1) = aEu(s)y(t) - a^2Ry*(t-1, s-1) + a^2*Ry(s-1, t-1)
Simplifying both sides, we obtain the desired result:
Ry(s, t) - aé (s – 1)(t - 1)R,(s – 1,t - 1) = Ru(s, t)
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Dusty Hoover caught an Atlantic cod in New Jersey that weighed 46. 75 pounds.
Geoff Dennis caught a Pacific cod in Oregon that weighed 2 times that amount. How
much did Geoff's fish weigh?
The ages of three men are in the ratio 3 : 4 : 5. If the difference between the ages of the oldest and the youngest is 18 years, find the sum of the ages of the three man.
Answer :
Sum of their ages = 108 years.Step-by-step explanation:
It's given that The ages of three men are in the ratio 3 : 4 : 5
Let's assume,
Age of first men = 3x Second men = 4x Third men = 5xAlso, the difference between the ages of the oldest and the youngest is 18 years.
Age of youngest men = 3x Age of oldest men = 5xDifference in their ages ,
[tex]:\implies [/tex] 5x - 3x = 18 years
[tex]:\implies [/tex] 2x = 18
[tex]:\implies [/tex] x = 18/2
[tex]:\implies [/tex] x = 9
Hence,
Age of first men = 3x
[tex]:\implies [/tex] 3 × 9
[tex]:\implies [/tex] 27 years
Age of second men = 4x
[tex]:\implies [/tex] 4 × 9
[tex]:\implies [/tex] 36 years.
Age of thrid men = 5x
[tex]:\implies [/tex] 5 × 9
[tex]:\implies [/tex] 45 years.
Now, Sum of the ages of three man
[tex]:\implies [/tex] 27 + 36 + 45
[tex]:\implies [/tex] 108 years.
Therefore, The sum of the ages of three man is 108 years.
Solve the separable differential equation for u du / dt = e^ 3u +3t. Use the following initial condition: u(0) = 9. U= ____
To solve the given separable differential equation, we first rewrite it as:
Steps:1/(e^ 3u +3t) du = dt
Integrating both sides, we get:
∫ 1/(e^ 3u +3t) du = ∫ dt
=> (1/3) * ln|e^3u + 3t| + C = t + K (where C and K are constants of integration)
Using the initial condition, u(0) = 9, we can find the value of K as:
(1/3) * ln|e^27| + C = 0 + K
=> ln|e^27| + 3C = 0 + 3K
=> 27 + 3C = 3K
=> K = 9 + C
Therefore, the final solution is given by:
(1/3) * ln|e^3u + 3t| + C = t + 9
where C is a constant given by:
C = K - 9
Thus, we have solved the given separable differential equation and found the general solution with the given initial condition.
Find the volume of the prism if the apothem is 6 cm. Round your answer to the nearest tenth, if necessary
The volume of the regular pentagonal prism is approximately 1285.5 cubic centimeters.
The formula for the volume of a regular pentagonal prism is:
V = (5/2) × apothem² × height × sin(72°)
Given that the required apothem is of 6.9 cm and the height is 8 cm, we can plug in these values into the formula:
V = (5/2) × (6.9)² × 8 × sin(72°)
V = (5/2) × 47.61 × 8 × 0.9511
V ≈ 1285.5 cubic centimeters
Therefore, we can say that the volume of the regular pentagonal prism is approximately 1285.5 cubic centimeters.
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Complete Question:
Find the volume of the following regular pentagonal prism, if the apothem is 6.9 cm and the height of the prism is 8 cm. Round your final answer to the nearest tenth if necessary.
during the peak hours of the afternoon, the town bank has an average of 40 customers arriving every hour. there is an average of 8 customers at the bank at any time. the probability of the arrival distribution is unknown. use littles law a) how long is the average customer in the bank?
The average customer spends 0.2 hours, or 12 minutes, in the bank during peak hours.
Little's Law states that the average number of customers in a stable system (i.e., one where the number of arrivals and departures is balanced) is equal to the average arrival rate multiplied by the average time that a customer spends in the system:
L = λW
where L is the average number of customers in the system, λ is the average arrival rate, and W is the average time that a customer spends in the system.
In this case, we are given that the average arrival rate during peak hours is λ = 40 customers per hour, and the average number of customers in the bank is L = 8 customers. We are asked to find the average time that a customer spends in the bank and the probability is unknown.
Plugging in the values, we get:
8 = 40W
Solving for W, we get:
W = 8/40
W = 0.2 hours
Therefore, the average customer spends 0.2 hours, or 12 minutes, in the bank during peak hours.
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a recent study at a university showed that the proportion of students who commute more than 15 miles to school is 25%. suppose we have good reason to suspect that the proportion is greater than 25%, and we carry out a hypothesis test. state the null hypothesis h0 and the alternative hypothesis h1 that we would use for this test.H0:H1:
Answer:
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The null hypothesis, H0, is that the proportion of students who commute more than 15 miles to school is equal to or less than 25%. The alternative hypothesis, H1, is that the proportion is greater than 25%.
H0: Proportion of students who commute more than 15 miles to school ≤ 25%
H1: Proportion of students who commute more than 15 miles to school > 25%
In this hypothesis test, we will be using the following terms:
- Null Hypothesis (H0): The proportion of students who commute more than 15 miles to school is equal to 25%.
- Alternative Hypothesis (H1): The proportion of students who commute more than 15 miles to school is greater than 25%.
To restate the hypotheses:
H0: p = 0.25
H1: p > 0.25
Here, p represents the proportion of students who commute more than 15 miles to school.
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