Answer : a) a random variable X can only take the six values (1,2,3,4,5, and 6 ). If each value has equal probability, then p(1) = p(2) = p(3) = p(4) = p(5) = p(6) = 1/6
b) The pmf of the random variable X is:p(0) = 1/9p(1) = 2/9p(2) = 2/9p(3) = 4/9
Explanation :
A probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value.[1] Sometimes it is also known as the discrete density function.
The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.
a) If each value has equal probability, the pmf of the random variable X which can only take the six values (1,2,3,4,5, and 6) is : p(1) = p(2) = p(3) = p(4) = p(5) = p(6) = 1/6
b)If the probabilities of X(0,1,2, and 3) are 1/9,2/9,2/9, and 4/9. The pmf of the random variable X is:p(0) = 1/9p(1) = 2/9p(2) = 2/9p(3) = 4/9
The sum of these probabilities is:p(0) + p(1) + p(2) + p(3) = 1/9 + 2/9 + 2/9 + 4/9 = 9/9 = 1
So, the pmf is defined for all X.
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not sure what the answer is
Given:
Base dimensions of a rectangular prism = 15 cm × x cm
The height of the prism = 8 cm
Volume of the prism = 600 cm.
To find:
The value of x.
Solution:
Base area of the prism is:
[tex]B=length\times width[/tex]
[tex]B=15\times x[/tex]
[tex]B=15x[/tex]
Volume of the prism is:
[tex]V=Bh[/tex]
Where, B is the base area and h is the height of the prism.
Putting [tex]V=600,B=15x,h=8[/tex], we get
[tex]600=15x\times 8[/tex]
[tex]600=(8)(15)x[/tex]
[tex]\dfrac{600}{(8)(15)}=x[/tex]
Therefore, the correct option is C.
Now consider the so-called random walk with absorbing barriers on 1 = {0, 1, 2, 3, 4}. This is also a Markov chain on N = {0,1,2,3,4} with the following transition probability matrix P =
[1 0 0 0 0]
[1/2 0 1/2 0 0]
[0 1/2 0 1/2 0]
[0 0 1/2 0 1/2]
[0 0 0 0 1]
(a) Draw a graphical diagram that shows how this chain moves. (b) Is this chain irreducible? Why or why not? (c) Find E(X5 | X3 = 1, X0 = 2).
The random walk with absorbing barriers on the set {0, 1, 2, 3, 4} can be represented as a Markov chain with a transition probability matrix. This chain is irreducible since it is possible to reach any state from any other state. By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.
(a) The graphical diagram representing the random walk with absorbing barriers on {0, 1, 2, 3, 4} can be visualized as a directed graph. Each state is represented by a node, and the arrows indicate the transition probabilities between states according to the given transition probability matrix P.
(b) The chain is irreducible because it is possible to reach any state from any other state. Starting from any state, there is always a positive probability of transitioning to any other state, including the absorbing states (0 and 4). This means that the chain does not have any disjoint subsets of states that are unreachable from one another.
(c) To find E(X5 | X3 = 1, X0 = 2), we condition on the starting state X0 = 2 and the state at time step 3, X3 = 1. Given this condition, we can calculate the expected value of X5, which represents the expected state at time step 5.
To compute this expectation, we can use the Markov property, which states that the future behavior of the chain depends only on its current state. Since X3 = 1 is known, we only need to consider the possible transitions from state 1 to other states according to the transition probability matrix P. By following these transitions, we can calculate the probability of reaching each state at time step 5 and then compute the expected value of X5 accordingly.
By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.
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What is the rate of change of the function described in
the table?
A. 12/5
B. 5
C. 25/2
D. 25
Answer:
B. 5
Step-by-step explanation:
This table does not describe a linear relationship. This is because the table does not have a constant rate of change; between the first two points, the function changes by
(1/2 - 1/10)/(0--1) = (5/10 - 1/10)/(1) = 5/10 - 1/10 = 4/10 = 2/5
Between the second two points, the function changes by
(5/2-1/2)/(1-0) = (4/2)/1 = 4/2 = 2
Comparing the first two y-coordinates, we have 1/10 and 1/2 = 5/10. This is the result of multiplication by 5.
Comparing the second two y-coordinates, we have 1/2 and 5/2. This is the result of multiplication by 5.
Comparing the rest of the y-coordinates, we can see that each time, the y-coordinate is multiplied by 5. This means the rate of change is 5.
At a high school soccer league, each team has m players. There are 20 teams in
the league. Write the expression of the total number of players at the league.
Answer:
20m
Step-by-step explanation:
Given:
Number of players per team = m
Number of teams in the league = 20
The number of players in the league is the product of the number of payers in each team and the number of teams in the league.
This the expression to obtain the total number of players goes thus :
Total number of players in the league = 20 * m
Total Numbr of players in the league = 20m
HELP!!! 100 POINTS!!! Find the total surface area of a cylinder with a height of 7 cm and radius of 3 cm. Leave your answer in terms of π.
140π cm2
91π cm2
60π cm2
51π cm2
Just put the answer below for brainly.
The surface area of the cylinder is 60π cm².
What is the surface area of a cylinder?
The surface area of a cylinder indicates the total area of two plane surfaces (bases) and one curved surface.
If a cylinder has a radius of r cm and height of h cm, then the total surface area of the cylinder = 2πr(r + h)
Given, r = 3 cm and h = 7 cm.
Therefore, the total surface area of the cylinder
= 2πr(r + h)
= 2π × 3(3 + 7) cm²
= 2π × 3 × 10 cm²
= 60π cm²
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Answer:
C. 60π cm2
Step-by-step explanation:
This part has 3 problems of equal weight. Show all the work to get full credit
1. Consider the fixed-point iteration P_k= g(P_k), where g is continuously differentiable on [a, b].
(a) State conditions under which the iteration will converge to the fixed point p € (a, b) for any p_o in that interval.
(b) x= g(x) for g(x)=1/3x²-2/3x+4/3 has two fixed points: 1 and 4. What is the rate of convergence for x_k sufficiently close to each of these two fixed points?
a) The required conditions are i. g(p) = p for p ∈ [a, b].ii. | g'(p) | < 1 for p ∈ (a, b).
b) |x1 - 1| ≤ a|x0 - 1|² for some a > 0, which implies that the iteration converges quadratically to 1 if x0 is sufficiently close to 1.
1. Consider the fixed-point iteration Pk= g(Pk), where g is continuously differentiable on [a, b].
(a) To converge to the fixed point p ∈ (a, b) for any p0 in that interval, the following conditions are required:
i. g(p) = p for p ∈ [a, b].ii. | g'(p) | < 1 for p ∈ (a, b).
(b) For g(x) = 1/3x²-2/3x+4/3, we have two fixed points: 1 and 4.
Let x be sufficiently close to 1:Then, x₁ = g(x₀) = 1/3x₀²-2/3x₀+4/3.
Since g is twice continuously differentiable on (1, 4), by Taylor’s theorem with the integral form of the remainder, we obtain x₁ - 1 = 1/2g"(c)(x₀ - 1)² ≤ 1/2k(x₀ - 1)², where k = supc∈[1,x] | g"(c) | < ∞.
Therefore, |x₁ - 1| ≤ a|x₀ - 1|² for some a > 0, which implies that the iteration converges quadratically to 1 if x0 is sufficiently close to 1.
Similarly, if x is sufficiently close to 4, the iteration converges quadratically to 4.
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Center: (-10, -4), Point on Circle: (4, -2)
Use the information given to write an equation of the vircle.
Answer:
Step-by-step explanation:
Left hand side.
The left hand side is the general equation that includes the center of the circle.
The center is at -10,-4
(x + 10)^2 + (y + 4)^2 = r^2
Finding the radius.
the radius is found from the given point on the circle
Givens
x1 = -10
x2 = 4
y1 = - 4
y2 = - 2
Equation
r^2 = (y2 - y1)^2 + (x2 - x1)
r^2 = (-2 - - 4)^2 + (4 - - 10)^2
r^2 = 2^2 + 14^2
r^2 = 200
Note:
The graph below shows two things: the first is that the center is at -10,-4The second is that the radius is a little more than 14. The equation of a circle always expresses the radius as r^2Two boys want to balance a seesaw perfectly. One boy weighs 240 pounds and is sitting four feet from the fulcrum. The other boy weighs 160 pounds. Where should the lighter boy sit to balance the seesaw?
Answer:
Step-by-step explanation:
Two boys want to balance a seesaw perfectly. One boy weighs 240 pounds and is sitting four feet from the fulcrum. The other boy weighs 160 pounds. Where should the lighter boy sit to balance the seesaw?
We solve using the formula
Distance on the fulcrum × Weight of the boy
= 4 × 240 = x × 160
4 × 240 = 160x
x = 4 × 240/169
Need Help On This Question!
Answer:
Just multiply the exponents of the numbers
So this is the order from top to below and I'll mark as 1 to 5
2
1
4
5
3
Ruth read a total of 14 books over 7 months. After belonging to the book
club for 10 months, how many books will Ruth have read in all? Assume
the relationship is directly proportional.
Answer:
20 books
Step-by-step explanation:
Well 14 books in 7 months.
Find the unit rate
14/7=2
So 2 books each month
We have Ruth here that was in the book club for 10 months.
And since 2 books each month,
2*10=20
20 books
When h is 1/2 and j is 1/3,g is 4. If g varies jointly with h and j, what is the value of g when h is 2 and j is 3?
Answer:
The value of g is 144 when h is 2 and j is 3 .
Step-by-step explanation:
If g varies jointly with h and j.
g = khj
Where k is the constant of proportionality.
Put value in the above
k = 4 × 6
k = 24
As when h = 2 , j = 3 and k = 24 .
Put in the above
g = 2 × 3 × 24
g = 144
Therefore the value of g is 144 when h is 2 and j is 3 .
4*10^(-3x)=18 Express the solution as a logarithm in base-101010.
Answer:
Hi how are you doing today Jasmine
Answer:
x= -1/3•log10(9/2)
x= -0.218
Events A and B are mutually exclusive. P(A) = 0.9 and P(B) = 0.1. Find P(AUB) to one decimal place. P(AUB) =
Since events A and B are mutually exclusive, they cannot occur together. Therefore, the probability of the union of events A and B is equal to the sum of their individual probabilities. P(AUB) = P(A) + P(B) - P(A ∩ B) Where, P(A) = 0.9P(B) = 0.1Since the events are mutually exclusive, P(A ∩ B) = 0Thus,P(AUB) = P(A) + P(B) - P(A ∩ B)= 0.9 + 0.1 - 0= 1 Hence, the value of P(AUB) is 1.
The most common method for distinguishing between integers and non-integers is the decimal numeral system. It is the expansion to non-number quantities of the Hindu-Arabic numeral framework. Decimal notation is the method used to represent numbers in the decimal system.
Decimal spots are places of the digits to one side of a decimal point. The process of reducing a decimal number to a specified degree of accuracy is known as rounding. To do this we find the decimal spot we wish to adjust to and check out at the digit to one side of that number.
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A convex polyhedron has 18 edges and 4 more vertices than faces. How many faces does the polyhedron have?
Answer:
its 22 a yusd the cauculader on mi iPhone ll pro max luser b an f
Answer:
The polyhedron has 8 faces
Step-by-step explanation:
I got it right on the quiz
edge 2021
Marie's dad drives an SUV that uses 2.5 litres of fuel for every 20 km driven. He drives to work 20 km each way, 5 days a week. How much fuel does he use to get to work every week?
Answer: 12.5 litres
Step-by-step explanation:
The SUV takes 2.5 litres for every 20 km driven.
The trip to work is 20 km which means that going to work costs Marie's father 2.5 litres every day in fuel.
In a week, there are 5 working days.
The amount of fuel used per week is therefore:
= 2.5 * 5
= 12.5 litres
Container holds 5 red balls, 3 yellow balls and 2 blue balls. A ball is randomly drawn from the container. If the ball is red or blue, it is kept outside the box and a second ball is drawn from the box. If the ball is yellow, it is replaced into the box and a second ball is drawn. Determine the probability that the second ball drawn is yellow.
The probability that the second ball drawn is yellow is 4/9. This is determined by considering the initial probabilities and applying the law of total probability.
Initially, there are a total of 10 balls in the container: 5 red, 3 yellow, and 2 blue. The probability of drawing a yellow ball on the first draw is P(yellow) = 3/10. In this case, the yellow ball is replaced back into the container, so the number of yellow balls remains the same.
If the first ball drawn is not yellow, it means a red or blue ball was drawn. These balls are kept outside the container, so they are not available for the second draw. Now, there are 7 balls remaining in the container: 2 yellow and 5 red (initially there were 5 red and 2 blue, but we only consider the red balls since the blue balls are not relevant for the second draw). The probability of drawing a yellow ball on the second draw, given that the first ball was red or blue, is P(yellow | red or blue) = 2/7.
To find the overall probability that the second ball drawn is yellow, we need to consider the probabilities of the different scenarios and their corresponding probabilities. Since the first ball can either be yellow or not yellow, we can use the law of total probability:
P(second ball is yellow) = P(yellow) * P(yellow on second draw | yellow) + P(not yellow) * P(yellow on second draw | not yellow)
P(second ball is yellow) = (3/10) * (2/10) + (7/10) * (2/7) = 4/9
Therefore, the probability that the second ball drawn is yellow is 4/9.
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10. Show how to multiply 4/5 by 1/3 using the rectangular model.
To multiply 4/5 by 1/3 using the rectangular model, follow the given steps below:
Step 1: Draw a rectangle and divide it into equal parts (columns and rows) based on the denominator of the given fractions. Here, 5 parts in a row (horizontally) and 3 parts in a column (vertically).
Step 2: Shade in the portion of the rectangle that corresponds to 4/5.
Step 3: Shade in the portion of the rectangle that corresponds to 1/3. You can do this by dividing the height into three equal parts and shading the top part of the rectangle.
Step 4: Find the area of the shaded region of the rectangle. The area of the shaded region of the rectangle is the product of the fractions 4/5 and 1/3. In other words, it is the product of the number of shaded squares in both the shaded regions.
Step 5: Simplify the answer. In this case, you should simplify the product 4/5 × 1/3 before finding the answer. The rectangular model of 4/5 by 1/3 is shown below:
Given fractions: 4/5 and 1/3To find: Multiplication of 4/5 and 1/3 using the rectangular model. The rectangular model is one of the methods to find the multiplication of two fractions visually.
By using this method, we can multiply two fractions by drawing a rectangle that is divided into equal parts based on the denominators of the given fractions and shade in the required portions of the rectangle.
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Under her cell phone plan, Lily pays a flat cost of $40 per month and $4 per gigabyte.
She wants to keep her bill under $60 per month. Write and solve an inequality which
can be used to determine x, the number of gigabytes Lily can use while staying within
her budget.
Answer:
16
Step-by-step explanation:
60-44
The inequality is $40 + 4x < $60 and she has to spend 5 gigabytes to stay within her budget
Note that:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The total amount Lily has to spend has to be less than $60
The total amount she can spend can be represented with this equation
Flat cost + variable cost < $60
Flat cost = $40
Variable cost = cost per gigabyte x gigabyte
$4 × x = $4x
$40 + 4x < $60
To solve for x, combine similar terms
$4x < $60 - $40
$4x < $20
x < 5
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What is the value of x in this equation?
2x + 2 = -52
pls someone help
Answer: x= −27 or x = 27
Step-by-step explanation:
Answer:
-27
Step-by-step explanation:
Subtract 2 from both sides
2x= -54
Divide both sides by 2
x = -27
What is a function
Answer:
In mathematics, a function is a binary relation between two sets that associates to each element of the first set exactly one element of the second set. Typical examples are functions from integers to integers, or from the real numbers to real numbers
Step-by-step explanation:
PLSSS HELP!!!! in need of help immediately! (check whole picture) and pls don’t leave a link.
Answer: C!!!!!!!
Step-by-step explanation:
Decomposers ( however you spell it ) are things that eat and uhh remove the waste and let other decompopers eat they waste
Please help me I only need d.
Answer:
true
Step-by-step explanation:
Please help! I need the right answer as soon as possible! PLEASE!
Answer:
Volume of the figure = 68 in.³
Step-by-step explanation:
The figure is composed of a rectangular prism and 2 equal triangular prism
Volume of the figure = volume of rectangular prism + 2(volume of triangular prism)
✔️Volume of triangular prism = L*W*H
L = 14 in.
W = 2 in.
H = 2 in.
Volume = 14*2*2 = 56 in.³
✔️Volume of triangular prism = ½*a*c*h
a = 3 in.
c = 2 in.
h = 2 in.
Volume = ½*3*2*2 = 6 in.³
✅Volume go the figure = 56 + 2(6) = 56 + 12
Volume of the figure = 68 in.³
Help wit this? 10m-8m+2+10
Answer:
2m+12
Step-by-step explanation:
add like terms
2m+12
PLSS HELPP Find the equation of the line below. If necessary, use a slash (1) to indicate a
division bar.
(6,1)
Answer: 3, -2
Step-by-step explanation: Just divide 6,1 i guess
ASAP. If a central angle has a measure of 100 degrees, determine the approximate length of the arc created by the two radii measuring 4 inches. Convert your answer to radians. Round your answer to two decimal places.
Answer:
234.9 million km
Step-by-step explanation:
The central angle is a quarter of a circle: 360° / 4 = 90°. Use the central angle calculator to find arc length. You can try the final calculation yourself by rearranging the formula as: L = θ * r. Then convert the central angle into radians: 90° = 1.57 rad, and solve the equation: L = 1.57 * 149.6 million km. L = 234.9 million km.
Miguel wants to estimate the average price of a book at a bookstore. The bookstore has 13,000 titles, but Miguel only needs a sample of 200 books. How could Miguel collect a sample of books that is:
cluster sample?
multistage sample?
oversamples?
To best collect a sample of books from the 13,000 titles at the bookstore, Miguel should use a cluster sampling method.
What is the best sampling method?The best sampling method Miguel should use is a cluster sample.
A cluster sample involves dividing the population into clusters or groups and randomly selecting entire clusters to include in the sample.
In this situation, Miguel could divide the bookstore's titles into clusters, such as by genre or shelf location, and randomly select clusters to sample books from.
his method would help ensure representation from different areas of the bookstore and provide a diverse sample of books.
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PLEASE HELP I HAVE TO TURN THIS IN IN 1 HOUR!
A round clock on a classroom wall has a diameter of 12 inches. What is the approximate area of the clock?
A. 38 square inches
B. 113 square inches
C. 226 square inches
D. 452 square inches
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Let w = { 9:,ber) with the standard operations in M22. Which of the following statements is true? W is not a subspace of Mzxz because it does not contain the zero matrix the above is true The 2x2 identity matrix is in W W is a subspace of M2x2. the above is true None of the mentioned
The correct statement is : W is a subspace of M2x2.
TO show that W is a subspace of M2x2, we need to verify that it satisfies the three properties of a subspace:
1. W contains the zero matrix:
The zero matrix in M2x2 is the 2x2 matrix with all entries equal to zero, which is not in W . However , we can see that the matrix {0,0;0,0} can be obtained as the difference between two matrices in W: {9,0;0,0} -{0,ber;0,0} = {0,0;0,0}. So , W does contain the zero matrix.
2. W is closed under addition:
Let A and B be two matrices in W. Then, A ={9,0;0,0} + {0,ber;0,0} and B = {9,0;0,0} + {0,ber;0,0}, which is also in W. Therefore, W is closed under addition.
3. W is closed under scalar multiplication:
Let A be a matrix in W and c be a scalar. Then ,A = {9,0;0,0} + {0,ber;0,0}, and c A = c {9,0;0,0} + c{0,ber;0,0}.
Since {9,0;0,0} and {0,ber;0,0} are both scalar multiples of A, c {9,0;0,0} and c{0,ber;0,0} are also in W . Therefore , W is closed under scalar multiplication.
Since W satisfies all three properties of a subspace, we can conclude that W is a subspace of M2x2.
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The heights of adults who identify as men in the U.S. are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.63 inches. The heights of adults who identify as women in the U.S. are also normally distributed, but with a mean of 64.6 inches and a standard deviation of 2.53 inches.
a) If a person who identifies as a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
z =
b) If a person who identifies as a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
z =
(a) If a person who identifies as a man is 6 feet 3 inches tall, his z-score will be 2.96.
(b) If a person who identifies as a woman is 5 feet 11 inches tall, her z-score will be 2.17.
(a) To find the z-score, if a person who identifies as a man is 6 feet 3 inches tall.
Explanation: First, convert 6 feet 3 inches to inches.
6 feet 3 inches = (6 x 12) + 3 inches
= 72 + 3 inches
= 75 inches
The formula for calculating the z-score is: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.
Substitute the given values in the above formula.
z = (75 - 69.2) / 2.63
= 2.21 / 2.63
= 0.8382
≈ 2.96 (to two decimal places)
(b) To find the z-score, if a person who identifies as a woman is 5 feet 11 inches tall..
Explanation: First, convert 5 feet 11 inches to inches.
5 feet 11 inches = (5 x 12) + 11 inches
= 60 + 11 inches
= 71 inches
The formula for calculating the z-score is: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.
Substitute the given values in the above formula.
z = (71 - 64.6) / 2.53
= 6.4 / 2.53
= 2.5336
≈ 2.17 (to two decimal places)
Therefore, the z-score for the given heights of men and women in the US are 2.96 and 2.17 respectively.
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