Let X be a continuous random variable with probability density function f. We say that X is symmetric about a if for all x,
P(X ≥ a+x)=P(X ≤ a-x).
(a) f(a - x) = f(a + x) if and only if X is symmetric about a.
(b) X is symmetric about a if and only if f(x) = f(2a - x) for all x.
(c) X and Y are symmetric about 3.
(a) To prove that X is symmetric about a if and only if for all x, we have f(a - x) = f(a + x).
Proof: P(X ≥ a+x) = P(X ≤ a-x) ...(1)
Given X is a continuous random variable with probability density function f.
Let F denote the cumulative distribution function of X.
Then, F(x) = P(X ≤ x).
We can now re-write equation (1) as follows: 1-F(a+x) = F(a-x) ... (2).
Taking the derivative of both sides of equation (2) with respect to x, we get: d/dx(1-F(a+x))= d/dx(F(a-x)) ... (3).
Differentiating the LHS of equation (3) using the chain rule, we obtain:- f(a+x) = -d/dx(F(a+x)) ... (4).
Differentiating the RHS of equation (3) using the chain rule, we obtain: f(a-x) = d/dx(F(a-x)) ... (5).
Combining equations (4) and (5), we get: f(a+x) = f(a-x).
Hence, we can conclude that X is symmetric about a if and only if for all x, we have f(a - x) = f(a + x).
Answer: (a) f(a - x) = f(a + x) if and only if X is symmetric about a.
(b) To show that X is symmetric about a if and only if f(x) = f(2a - x) for all x.
Proof: X is symmetric about a if and only if for all x, we have f(a - x) = f(a + x).
Hence, it follows that: f(a + (2a - x)) = f(a - (2a - x)) ... (6).
Simplifying equation (6), we obtain: f(2a - x) = f(x).
Therefore, X is symmetric about a if and only if f(x) = f(2a - x) for all x.
Answer: (b) X is symmetric about a if and only if f(x) = f(2a - x) for all x.
(c) Let X be a continuous random variable with probability density function f(x) = [1 / √(2phi)] e^-(x-3)²/2, x E R, and Y be a continuous random variable with probability density function g(x) = 1 / phi [1 + (x-1)²], x E R.
Find the points about which X and Y are symmetric.
The probability density function of a symmetric random variable X about a is f(x) = f(2a - x).
Therefore, if X is symmetric about a, then we have: f(x) = f(2a - x) ...(7).
Comparing the probability density function of X to the given probability density function f(x), we can observe that X is symmetric about a = 3.
Therefore, we can find the points about which X and Y are symmetric by solving the following equation: g(x) = f(2a - x) ... (8).
Substituting the value of a in equation (8), we get:
f(2a - x) = [1 / √(2phi)] e^-(2a-x-3)²/2
= [1 / √(2phi)] e^-(x-3)²/2
= f(x)
Therefore, X and Y are symmetric about 3.
Answer: (c) X and Y are symmetric about 3.
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I'm begging you please please help please please ASAP please please help please please ASAP please please help please please ASAP please please help please please ASAP
Answer:
15
Step-by-step explanation:
the height of the person is y = 6 and the distance from the ladder is also 6 = x. To find the angle formed by the ladder we use [tex]arctan(\frac{y}{x})[/tex] which in this case is
[tex]arctan\frac{6}{6} = arctan(1)\\= 45 degrees[/tex]
now we know that the person is 9 feet away from wall and 6 feet away from the ladder so the total x distance is 9+6 = 15 = x
to find y we use tan(45) = [tex]\frac{y}{x}[/tex]
multiply both sides by x = 15 and simplify to get y = 15
1. Lukas deposited $3000 into a
savings account that earns
3.7% interest compounded
annually. What is the total
value of the account after 5
years?
Urgent!!!!
Sean bought three pairs of the same socks and a shoe polish for $1450. If the
polish cost $340, how much is the cost of one pair of soc
Show how you got your answer (4marks)
Answer:
One pair of socks is $370.
Step-by-step explanation:
Sean bought three pairs of the same socks and a shoe polish for $1450. If the
polish cost $340, how much is the cost of one pair of socks.
6x - 340 = 1450
6x = 1450 -340
6x = 1110
2x = 1110 / 3
2x = 370
Solve for z. -2 (52 - 4) +62 = -4
Answer:
if you learned, PEMDAS then it be easier! soo I'll help.
Step-by-step explanation:
-2 ( 52- 4 ) is 48. 48 + 62= 110
if that's wrong, then I'm sorry!
1
62
48
——
110
During a weekend, the manager of a mall gave away gift cards to every 80th person who visited the mall.
On Saturday, 1,210 people visited the mall.
On Sunday, 1,814 people visited the mall.
The quastion is on graph theory, matching.
Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B.
Consider taking |E| =aN, i.e., the total number of edges is proportional to the number of vertices. This is a relatively sparse number of edges, given the total number of edges that can exist between A and B.
6) Show that taking |E| = 3/N, the expected number of matchings goes to 0 as N › [infinity]. (5 points)
7) Show that taking |E| = 4.V, the expected number of matchings goes to infinity as N › [infinity]. (5 points)
The expected number of matchings goes to infinity as N › [infinity].
Matching in Graph Theory:A matching in Graph Theory is a set of edges of a graph where no two edges share a common vertex. In other words, a matching is a set of independent edges of a graph. A perfect matching in a Graph Theory is a matching of size equal to half the number of vertices in a graph.The expected number of matchings goes to 0 as N › [infinity]:The expected number of matchings goes to zero as N › [infinity] when |E| = 3/N. It is because 3/N is a relatively dense number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very small in comparison to the total number of matchings possible as N › [infinity].The expected number of matchings goes to infinity as N › [infinity]:The expected number of matchings goes to infinity as N › [infinity] when |E| = 4.V. It is because 4.V is a relatively large number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very large in comparison to the total number of matchings possible as N › [infinity]. Hence the expected number of matchings goes to infinity as N › [infinity].
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Sample size = 100, sample mean = 39, sample standard deviations 13. Find the 95% confidence interval for the population mean.
Given that the sample mean is 100, the sample mean is 39, and the sample standard deviation is 13.
To find the 95% confidence interval for the population mean, we use the formula as follows:
Confidence Interval formula: CI = X ± Z* σ/√nWhere CI = Confidence IntervalX = Sample Mean
Z* = Z-Scoreσ = Standard Deviationn = Sample SizeHere, the sample size(n) is 100, the sample mean(X) is 39, and the sample standard deviation (σ) is 13.The formula for finding the Z-Score is:Z = 1 - α/2,
where α is the level of significance. α is the probability of the event not occurring, so we subtract it from one to get the probability of the event occurring.
Here, the level of significance is 0.05 since we need to find the 95% confidence interval.
Z = 1 - α/2 = 1 - 0.05/2 = 0.975Then we find the Z-Score from the Z-Score table, which is 1.96.
Therefore, the 95% confidence interval is:CI = X ± Z* σ/√n= 39 ± 1.96 (13/√100)= 39 ± 2.548Thus, the 95% confidence interval for the population mean is (36.452, 41.548).
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The 95% confidence interval for the population mean is
[tex]\[\large \left( 36.452,41.548 \right)\][/tex].
Sample size = 100
Sample mean = 39
Sample standard deviation = 13
Confidence level = 95%
To find the confidence interval, we use the formula given below:
Confidence interval formula is as follows:
[tex]\[\large \left( \overline{X}-z\frac{\sigma }{\sqrt{n}},\overline{X}+z\frac{\sigma }{\sqrt{n}} \right)\][/tex]
We are given, sample mean is 39
[tex]\(\overline{X}=39\)[/tex],
sample standard deviation is 13
[tex]\(\sigma=13\)[/tex],
sample size is 100
i.e. n=100, and confidence level is 95%
z=1.96 (From Z table)
By substituting all the given values in the formula, we get the confidence interval as,
[tex]\[\large \left( 39-1.96\frac{13}{\sqrt{100}},39+1.96\frac{13}{\sqrt{100}} \right)\][/tex]
Simplifying the above expression, we get,
[tex]\[\large \left( 39-2.548,39+2.548 \right)\][/tex]
Therefore, the 95% confidence interval for the population mean is
[tex]\[\large \left( 36.452,41.548 \right)\][/tex].
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write the following in simplest form
A)12:33
B)20mm:5cm
A) 12 and 33 can be divided by 3 so 12:33 = 4:11
B= 20 and 5 can be divided by 5 so 20mm:5mm = 4mm:1mm
Answer:
A. 4: 11
B. 4: 1
Step-by-step explanation:
What are these? These are ratios, which show proportion. For example, for every two dogs, there is one cat. They can be written as words, fractions, or with colons, such as in these problems.
How to simplify: To simplify, think of the highest common factor. If you can't think of the highest, just think of a factor both numbers have in common and keep going until the numbers don't have any factors in common.
In this case, for A, the common factor was 3. 12/3=4 and 33/3=11. This cannot be simplified further because 11 is prime, which means it has no factors besides 1 and 11.
For B, the common factor was 4, so it is 4:1.
Is Game of Thrones based on history or hollywood?
Answer:
It is based on history
Step-by-step explanation:
Answer: the answer is based on history
Step-by-step explanation:
Danny is in a 90 m high watchtower. Lily and Bryan are out searching for clues in regards to a route taken by an escaped prisoner. Lily radios to Danny that she has found some evidence and estimates that she is 350 m from the base of the watchtower. Danny radios this information to Bryan, who estimates that from his location, the angle of elevation to the top of the watchtower is 20°. Danny estimates that the angle from Bryan to the base of the watchtower to Lily is 85°.
a) To the nearest meter, how far is Bryan from the base of the watchtower?
b) To the nearest meter, how apart are Bryan and Lily?
a) Bryan is 1,168 meters away from the base of the watchtower
b) The nearest meter, Bryan and Lily are 315
a) To the nearest meter, Bryan is 1,168 meters away from the base of the watchtower.
Let AB be the watchtower. From B, the angle of elevation to the top of the tower is 20°.
We have to find BC.
BC/AB = tan 20°
BC = AB tan 20°
BC = 90 tan 20°
BC = 32.3
Therefore, BC = 32 meters
Now we have to find AC. AC is the distance between the foot of the watchtower and Bryan's position.
To do that, let BD = h be the height of the tower and AD = x be the distance between A and D.
From the information given, we know that tan 85° = h/x.
Rearranging the formula, x = h/tan 85°
x = 90/tan 85°
x = 418.55 meters
Therefore, AC = x + BC
AC = 418.55 + 32.3
AC = 450.85 meters
So, to the nearest meter, Bryan is 1,168 meters away from the base of the watchtower.
b) To the nearest meter, Bryan and Lily are 315 meters apart.
Let E be the position of Lily and AD be the distance from the foot of the watchtower to the position of Bryan. We have already found that AD = 418.55 meters.
Bryan and Lily are along the same horizontal line.
So, BE is the distance between them. We have to find BE.
From triangle AEB, tan 20° = h/AE.
Rearranging the formula, AE = h/tan 20°
AE = 90/tan 20°
AE = 267.9 meters
From triangle DEC, tan 85° = h/DE.
Rearranging the formula, DE = h/tan 85°
DE = 90/tan 85°
DE = 3,442.97 meters
Therefore, EC = DE - DC = 3,442.97 - 350 = 3,092.97 meters
Now, BE = AC - EC
BE = 450.85 - 3,092.97
BE = -2,642.12 meters (negative value means Bryan is to the left of Lily)So, to the nearest meter,
Bryan and Lily are 315 meters apart. Answer: (a) 1168m and (b) 315m
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An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 9:00 A.M. will have assembled f(x)=−x3+12x2+15x units x hours later. a) Derive a formula for the rate at which the worker will be assembling units after x hours. r(x)=_______. b) At what rate will the worker be assembling units at 10:00 A.M.? The worker will be assembling ______ units per hour. c) How many units will the worker actually assemble between 10:00 A.M. and 11:00 A.M. ? The worker will assemble _________ units.
A)the required formula is r(x) = -3x² + 24x + 15.B)the worker will be assembling 36 units per hour at 10:00 A.M.C)the worker will assemble 70 units between 10:00 A.M. and 11:00 A.M.
a) Derive a formula for the rate at which the worker will be assembling units after x hours. The worker assembles f(x)= −x³ + 12x² + 15x units in x hours.
To determine the formula for the rate at which the worker will be assembling units after x hours, we can differentiate the given function with respect to time t.
We can write this function as:f(x) = -x³ + 12x² + 15xf'(x) = -3x² + 24x + 15
On differentiating the given function, we get the rate at which the worker will be assembling units after x hours is:r(x) = -3x² + 24x + 15
Therefore, the required formula is r(x) = -3x² + 24x + 15.
b)The worker arrives at 9:00 A.M. and we want to determine the rate at which the worker will be assembling units at 10:00 A.M, which means the worker will be assembling units after 1 hour.
We can use the formula:r(x) = -3x² + 24x + 15
To find the answer:r(1) = -3(1)² + 24(1) + 15r(1) = -3 + 24 + 15r(1) = 36 units per hour
Therefore, the worker will be assembling 36 units per hour at 10:00 A.M.
c)To find the number of units assembled by the worker between 10:00 A.M. and 11:00 A.M., we need to integrate the function r(x) = -3x² + 24x + 15 with limits 1 and 2.
We can use the formula:Integral of r(x)dx = f(x)
Using the formula, we get:f(2) - f(1) = Integral of r(x)dx between 1 and 2f(x) = -x³ + 12x² + 15x
Substituting the limits, we get:
f(2) - f(1) = [-2³ + 12(2²) + 15(2)] - [-1³ + 12(1²) + 15(1)]f(2) - f(1) = [−8 + 48 + 30] - [−1 + 12 + 15]f(2) - f(1) = 70
Therefore, the worker will assemble 70 units between 10:00 A.M. and 11:00 A.M.
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PLSSSSSSSS HELP MEHHHHHH 12 pointsssss
Answer:
10
Step-by-step explanation:
Answer:
what do you mean?
Step-by-step explanation:
Write a cosine function that has a midline of y=5, an amplitude of 3 and a period of 4/π
The equation for the cosine function is given as;cos(x) = 3 cos(π/2 x) + 5
A cosine function is defined as follows;cos(x) = a cos(b(x - h)) + kwhere a is the amplitude, period is 2π/b, and k is the midline. The amplitude, period, and midline of a cosine function can be used to find its equation.In this case,
we have a cosine function that has a midline of y=5, an amplitude of 3 and a period of 4/π. Thus, the amplitude of the function is given as 3, the midline is given as 5, and the period is 4/π.
The amplitude is the vertical distance from the midline to the highest point on the curve and also to the lowest point on the curve. The period is the distance over which the cosine function completes one full oscillation, or cycle.
In this case, we have a period of 4/π, so we can find b by the formula b = 2π/period = 2π/(4/π) = π/2.To find the phase shift, h, we use the formula h = x₀ - (π/b), where x₀ is the x-coordinate of the maximum or minimum value of the cosine function.
Since the midline is y=5, the maximum value of the cosine function occurs when y=8 and the minimum value occurs when y=2. The maximum and minimum values occur when cos(b(x - h)) = 1 and cos(b(x - h)) = -1, respectively.
Therefore, we have;8 = 5 + 3, cos(b(x - h)) = 1when x - h = 0, so x₀ = h2 = 5 - 3, cos(b(x - h)) = -1when x - h = π/b
Thus, h = 0 for the maximum value, and h = π/2 for the minimum value. We choose the value of h that corresponds to the maximum value of the cosine function, so h = 0.
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help what is The expression 4x gives the perimeter of a square with a side length of x units. What is the perimeter of a square with a side length of 5/7 units?
Answer:
2 6/7 units
Step-by-step explanation:
You substitute 5/7 in for x
4(5/7) = 20/7 = 2 6/7 units
You can also add 5/7 + 5/7 + 5/7 + 5/7 to check your work
Can someone help me? Ill give brainliest :)
Fill in the blank.
pls help asap will give brainliest
Answer:
148 feet squared
Step-by-step explanation:
Hope it's correct!<D
A = 2 (wl+hl+hw) = 2 x (4x6+5x6+5x4) = 148
11.Tell whether each situation can be represented by a negative number, 0, or a positive number. Negative Number 0 Positive Number Situation 1: A football team's first play resulted in a loss of 15 yards. Situation 2: A store marks up the price of a calculator $5.20. Situation 3: Nina withdrew $50 from her bank account. Situation 4: A porpoise is swimming at sea level. Situation 5: Kylie scored 2 goals in yesterday's soccer game.
Answer:
negative
positive
negative
zero
positive
Step-by-step explanation:
Situation 1: A football team's first play resulted in a loss of 15 yards.
negative
Situation 2: A store marks up the price of a calculator $5.20.
positive
Situation 3: Nina withdrew $50 from her bank account.
negative
Situation 4: A porpoise is swimming at sea level.
zero
Situation 5: Kylie scored 2 goals in yesterday's soccer game.
positive
A glass company is repairing a window in the shape of an equilateral triangle. If the length of one side of the triangle is 17 inches and the company charges $12 per square inch, the cost of the replacement window will be $___.
Answer:
the cost of the replacement window will be $1501.44.
Step-by-step explanation:
area of an equilateral triangle:
[tex]A = \frac{\sqrt{3}}{4} a^{2}[/tex]
A = (√3)/4 * (17)^2
A = 125.12 in^2
125.12 * 12 = $1501.44
Someone help me with this
Answer:
the error is ( 4-17) is equal -13 not 13
so if she used - 13 the right answer is 17/34
Step-by-step explanation:
see attached
hope it helps
what are the zeros of the polynomial function? f(x)=x2 9x−70 enter your answers in the boxes.
The zeros of the polynomial function f(x) = x^2 - 9x - 70 can be found by factoring or using the quadratic formula. The zeros are -5 and 14.
To find the zeros of the polynomial function f(x) = x^2 - 9x - 70, we can factor the expression or use the quadratic formula. Let's factor the expression:
f(x) = x^2 - 9x - 70
= (x - 14)(x + 5)
Setting each factor equal to zero, we get:
x - 14 = 0 --> x = 14
x + 5 = 0 --> x = -5
Therefore, the zeros of the polynomial function are x = -5 and x = 14. These values represent the x-coordinates where the function intersects the x-axis, indicating the points where the function equals zero.
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Of 88 adults randomly selected from one town, 69 have health insurance.
(Q) Find 90% confidence interval for the true proportion.
Write the solution with two decimal places, for example: (X.XX, X.XX)
To find the 90% confidence interval for the true proportion of adults in the town with health insurance, we can use the formula:
[tex]\[\text{{Confidence Interval}} = \left( \hat{p} - Z \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p} + Z \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \right)\][/tex]
where:
- [tex]\(\hat{p}\)[/tex] is the sample proportion (69/88 in this case)
- [tex]\(Z\)[/tex] is the Z-score corresponding to the desired confidence level (90% corresponds to [tex]\(Z = 1.645\)[/tex] for a two-tailed test)
- \(n\) is the sample size (88 in this case)
Substituting the values into the formula, we have:
[tex]\[\text{{Confidence Interval}} = \left( \frac{69}{88} - 1.645 \cdot \sqrt{\frac{\frac{69}{88} \cdot \left(1-\frac{69}{88}\right)}{88}}, \frac{69}{88} + 1.645 \cdot \sqrt{\frac{\frac{69}{88} \cdot \left(1-\frac{69}{88}\right)}{88}} \right)\][/tex]
Evaluating the expression, we find the confidence interval to be approximately (0.742, 0.892).
The confidence interval is approximately (0.742, 0.892).
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3. Find the values of x, y, and z. *
125°
Answer:
Your question is Incomplete....
1st statement: In an experimental study we can examine the association between the independent and dependent variable 2nd statement: In an experimental study we can examine the temporal relationship between the independent and dependent variable O Both statements are true 1st statement is false, while the 2nd statement is true o 1st statement is true, while the 2nd statement is false O Both statements are false
The correct option to the statements "1st statement: In an experimental study we can examine the association between the independent and dependent variable, and 2nd statement: In an experimental study we can examine the temporal relationship between the independent and dependent variable" is: a. Both statements are true.
An experimental study can be used to determine the relationship between two variables. It is also used to determine whether there is a cause-and-effect connection between two variables.
In an experimental study, two groups are compared. One group receives the independent variable, and the other group receives the dependent variable.
In an experimental study, the following two statements are true:
In an experimental study, we can examine the association between the independent and dependent variable. It is the correlation or connection between the two variables we are interested in exploring
In an experimental study, we can examine the temporal relationship between the independent and dependent variable. It refers to the timing or sequence of events that occurs between the two variables in question.
The study must include a time element that describes the order in which the dependent and independent variables were introduced to the subjects.
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2. find the surface area of 12 in 6 in 6 in Your answer
Answer:
276 in^2
Step-by-step explanation:
2((6*6)/2) + 2(6*12) + (8*12) = 276 in^2
a cone and a cylinder have equal radii,r, and equal altitudes, h. If the slant height is l, then what is the ratio of the lateral area of the cone to the cylinder?
The ratio of the lateral area of the cone to the cylinder will be √(h²+r²)/2h.
What are a cone and a cylinder?The solid formed by two congruent closed curves in parallel planes along with the surface created by line segments connecting the corresponding points of the two curves is known as a cylinder.
A cylinder with a circular base is known as a circular cylinder. Based on the form of its base, a cone is given a name.
It is given that a cone and a cylinder have equal radii,r, and equal altitudes, h. The ratio of the lateral surface area of the cone to the cylinder will be calculated as below:-
The lateral area of the cone = πr√(h²+r²)
The lateral area of the cylinder = 2πrh
The ratio will be calculated as:-
R = πr√(h²+r²) / 2πrh
R = √(h²+r²) / 2h
Therefore, the ratio of the lateral area of the cone to the cylinder will be √(h²+r²)/2h.
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In the data set #2 {75,80,85,75,85}, what is the mean?
Answer:
80
Step-by-step explanation:
Katie is making bread.
She’s needs 6/3 cups of flour to make one whole loaf of bread.
She has 2/3 cup of flour.
Katie can make less than one whole loaf of bread or more than or exactly one loaf
T
3/6
35. A soccer ball has a diameter of 9 inches. What is the volume to the nearest tenth? (TEKS
8.7A-R)
A 381.7 in
A
B
С
D
E
B 190.9 in
C 268.1 in
D 321.6 In
Answer:
I NEED HELP ON THE SAME QUESTION
Step-by-step explanation:
NO ONE INDERSTANDS JT FOR SOME REASON AND NEITHER DO I
Please help me in it! It's very difficult, i'm in 6th and I still don't understand this. Please, help me in this!!!
Answer:
40
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
the lines on the very end are your subtrct the the lowest one from the highest one
Which of the following possibilities will form a triangle?
Question 4 options:
1)
Side = 15 cm, side = 6 cm, side = 8 cm
2)
Side = 15 cm, side = 6 cm, side = 9 cm
3)
Side = 16 cm, side = 9 cm, side = 6 cm
4)
Side = 16 cm, side = 9 cm, side = 8 cm
Answer:
Option 4
Step-by-step explanation:
The smaller sides must add up to be greater than the largest side so:
1) 6 + 8 < 15
1) No
2) 6 + 9 = 15
2) No
3) 9 + 6 < 16
3) No
4) 9 + 8 > 16
4) Yes