Steady state vector represent the long term market share of both groceries i.e WB and ZA. The long term market share of ZA is 0.727...
What is Steady-State Probability ?The steady-state behavior of a Markov chain is the long-term probability that the system is in each state. In other words, no matter how many transitions are applied to the system, it does not affect the state vector.
We have, WB and ZA are two competing grocery stores.
Probability that a customer who shops this week at WB will shop again here next week , p₁= 64% = 0.64
Probability(not shop again from WB) = 1-p₁
= 1 - 0.64 = 0.36
Probability that a customer who shops this week at ZA will shop again here next week , p₂ = 76% = 0.76
P(not shop again from ZA) = 1- p₂= 1 -0.76
= 0.24
Let market share of WB and ZA be "x" and "y" respectively, So, steady state vectors , s = [x y]
and x + y = 1 ---(*)
The Transition matrix, P=[1- p₁ p₁ ; 1-p₂ p₂]
P = [ 0.36 0.64 ; 0.24 0. 76 ]
we have to determine the value of x and y . So, we solve the following matrix equation, s[ I - P] = 0
matrix where I is identity matrix of 2×2
=> s([ 1 0 ; 0 1 ] - [0.36 0.64 ; 0.24 0. 76 ] ) = [0 0 ; 0 0 ]
=> s[1- 0.36 0- 64 ; 0 - 0.24 1 -0.76]
=[0 0 ; 0 0]
=> s[ 0.64 - 0.64 ; - 0.24 0.24] = [0 0;0 0]
=> [ x y] [0.64 -0.64 ; -0.24 0.24] = [0 0; 0 0]
Matrix multiplication,
=> [ 0.64x - 0.24y ; - 0.64x + 0.24y ]
= [ 0 0 ; 0 0]
equating the LHS and RHS
0.64x - 0.24y = 0 --(1)
- 0.64x + 0.24y = 0 --(2)
If we multiply equation (1) by -1 then we get equation(2). So, both equations are identical and we can collpase them in one equation for further calculation. Now, we have to equations
0.64x - 0.24y = 0 --(3)
x + y = 1
we can solve these equations either matrix method or substitution. We use here substitute
x = 1- y in equation (3) we get
0.64x - 0.24y = 0=> 0.64(1 - y) - 0.24 y = 0
=> 0.64 - 0.64y - 0.24 y = 0
=> 0.64 = 0.88y
=> y = 0.64/0.88 = 8/11 = 0.727
from equation (*) , x = 1 - 8/11 = 3/11 = 0.272
So, Market share of grocery ZA is y i.e 0.727.
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evaluate the expression for the given value of the variable. 56 + 1/6r r= 1/2
Answer:
337 = 3
Step-by-step explanation:
Multiply by LCM
337 = 3
and the sides are not equal so I guess there is no answer but
337 = 3
P(4,6), over the x-axis
The image of point P(4,6) after a reflection over the x-axis is given as follows:
P'(4,-6).
How to obtain the image of point P?The coordinates of the point P in this problem are given as follows:
P(4,6).
Meaning that:
The x-coordinate is of 4.The y-coordinate is of 6.The rule for a reflection over the x-axis is given as follows:
(x,y) -> (x,-y).
Meaning that the x-coordinate remains constant, while the y-coordinate has the signal exchanged.
Applying the rule, the coordinates of the image are given as follows:
x-coordinate of 4, as it remains constant.y-coordinate of -6, as the signal is exchanged.Then the coordinates of the image after the reflection are given as follows:
P'(4,-6).
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Find the demand function for the marginal revenue function. recall that if no items are sold, the revenue is 0. R′(x)=0.06x2−0.05x+138
The revenue function for the given marginal revenue function
R'(x) = 0.06x² - 0.05x + 138 be
R(x) = 0.02x³ - 0.025x² + 138x
Given, a marginal revenue function,
R'(x) = 0.06x² - 0.05x + 138
we have to find the demand function
as, we know that the demand function can be find by integrating the marginal revenue function with respect to the variable x.
So, as the marginal revenue function is given,
R'(x) = 0.06x² - 0.05x + 138
On integrating with respect to x, we get
R(x) = 0.06x³/3 - 0.05x²/2 + 138x + C
where C is an arbitrary constant.
Also, it is given that
R(0) = 0
So, R(0) = 0.06(0) - 0.05(0) + 138(0) + C
0 = C
R(x) = 0.06x³/3 - 0.05x²/2 + 138x + 0
R(x) = 0.02x³ - 0.025x² + 138x
So, the revenue function be R(x) = 0.02x³ - 0.025x² + 138x
Hence, the revenue function be R(x) = 0.02x³ - 0.025x² + 138x
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An airplane make a 10° angle of elevation from the runway when it take off. The airplane hown i 2,000 feet along the ground from it take-off point
Therefore, by using trigonometry and ratios of trigonometry the height of the airplane is 426 feet.
What is trigonometry?Trigonometry is the study of angles and the angular relationships of planar and three-dimensional figures. Trigonometric functions (also known as circular functions) include the cosecant, cosine, cotangent, secant, sine, and tangent.
With this drawing, we can see that this is a right triangle, which can be solved using some trigonometry. To solve the height, we must use the tangent:
for the diagram see the image.
[tex]tanA = \frac{opposite}{adjecent} \\tan (12) = \frac{opposite}{adjecent} \\\frac{0.213}{1} = \frac{height}{2000}\\height = 2000(0.213)\\\\[/tex]
height = 426 feet
Therefore, the height of the airplane is 426 feet.
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in a test of hypothesis the p-value was 0.24 . if the level of significance is 10 % . what is the potential type of statistical error ?
If the level of significance is 10 %, then the potential type of statistical error is type II error.
What is statical error?
The term "error" (also known as "statistical error") refers to the discrepancy between a value obtained through a data gathering procedure and the population's "actual" value. The data are less representative of the population the higher the inaccuracy.
In the given test,
The p-value = 0.24
Level of significance (a) = 0.10
Here,
0.24 > 0.10
P-value > level of significance
Therefore, We failed to reject the null hypothesis that is actually false
This is type II error,
The type II error occurs when one fails to reject a null hypothesis that is actually false itself.
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Lincoln bought a sweatshirt for $45.00. He had a 25% coupon to use to buy his sweatshirt. How much was the total cost?
Answer: 11.25
Step-by-step explanation: you just find out what is 25% of 45.00
Answer:
11.25
Step-by-step explanation:
turn 25 into a decimal and then multiply 45
How much pizza sauce is needed to cover a 16" pizza? (Note: 16" is the diameter of the pizza.)
Responses
A 200.96 in2200.96 in 2
B 803.84 in2803.84 in 2
C 50.24 in250.24 in 2
D 3215.36 in2
Answer:
It is difficult to give a precise answer without more information, such as the thickness of the sauce and the desired coverage. However, if we assume that the sauce is being applied evenly and that a thin layer is desired, the amount of sauce needed to cover a 16" pizza would be approximately 50.24 in2. This is because the area of a circle with a diameter of 16" is approximately 50.24 in2. To calculate the area of a circle, you can use the formula A = πr^2, where A is the area, π is approximately 3.14, and r is the radius of the circle (which is half the diameter). In this case, the radius would be 8" and the area would be approximately 50.24 in2.
Step-by-step explanation:
the buses at the zoo express bus company depart as scheduled 80% of the time. the buses depart and arrive as scheduled 68% of the time. what is the probability that a zoomy express bus arrives as scheduled if it departs as scheduled?
The probability that a zoomy express bus arrives as schedule if it departs as schedule is 0.85.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 indicates certainty. An event's likelihood of occurring increases with its probability.
now , let D = depart on time and A = arrives on time
given that ,
P(D) = 80% = 0.80
P(A∩D) = 68% = 0.68
P(A/D) = [tex]\frac{0.68}{0.80}[/tex]
= [tex]\frac{68}{80}[/tex]
= [tex]\frac{17}{20}[/tex]
= 0.85
Hence , the probability is 0.85.
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Helppppppppppppppp I need helppp
Answer:
4. (2) 0
5. (1) 1/25
Step-by-step explanation:
Definition: a^0 = 1
4.
8(x + 11)^0 - 2x^0 + 6x =
= 8 × 1 - 2 × 1 + 6 × (-1)
= 8 - 2 - 6
= 0
5.
[(5^3)^2]/[(5^2)^4] =
= 5^6 / 5^8
= 5^(-2)
= 1/5^2
= 1/25
The rectangle below has an area of x^2-7x+10x
2
−7x+10x, squared, minus, 7, x, plus, 10 square meters and a width of x-5x−5x, minus, 5 meters.
What expression represents the length of the rectangle?
By using the quadratic equation that can be written with the given information:
x² -7x + 10 = (x - 5)*(x - a)
We will see that the length is:
L = x - 2
How to get the length of the rectangle?Remember that for a rectangle of length L and width W, the area is given by the product:
A = L*W
Here we know that:
The area is: x² -7x + 10
The width is: x -5
The length will be another factor of the quadratic equation, and we know that it should be of the form:
(x - a)
Using the area formula, we will get:
x² -7x + 10 = (x - 5)*(x - a)
Expanding the right side we get:
x² -7x + 10 = x² -5x -ax + 5a
x² -7x + 10 = x² + (-5 - a)*x + 5a
Comparing like terms, we can see that:
-5 - a = -7
5a = 10
The solution of both of these is:
a = 7 - 5 = 2
a = 10/5 = 2
Then the length of the rectangle is:
L = (x - 2)
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On Monday, Jake could lift 25 lbs. One
year later, the weight he could lift
increased by 30%. What is the number
of pounds he can lift a year later?
How can you tell if a formula represents length, an area, or volume? what do you look for in the formula?.
60 people attend a game night. Everyone chooses to play chess, a two-player game, or cribbage, a four-player game. All 60 people are playing either chess or cribbage.
1.Complete this table showing some possible combinations of the number of each type of game being played:he equation. Enter only 1 term in each blank.
2.Write an equation to represent the situation illustrated in the table
3.There are 3 more games of cribbage being played than games of chess being played. Write an equation to represent this relationship. 4.Solve the system of equations you just wrote. There were
chess games, and
cribbage games.
Answer:
8 chess games are being played while 11 cribbage games are being played.
Let x represent the number of chess games and y represent the number of cribbage games.
Since there are 60 people, chess is a two-player game and cribbage is a four-player game, hence:
2x + 4y = 60 (1)
There are 3 more games of cribbage than games of chess, hence:
y = x + 3
-x + y = 3 (2)
Solving equations 1 and 2 simultaneously gives:
x = 8, y = 11
Therefore 8 chess games are being played while 11 cribbage games are being played.
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Step-by-step explanation:
Which of the following sets of numbers could not represent the three sides of a triangle?
How do you find the equation of a plane passing through two points and perpendicular to another plane?
To find the equation of a plane passing through two points and perpendicular to another plane, use the cross product.
First calculate the vector between the two given points,
then use the cross product to find a vector that is perpendicular to both the vector between the two points and the equation of the other plane.
Finally, use the two points and the perpendicular vector to find the equation of the plane.
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Determine the slope of the line that contains the points (15,7) and (6, 13).
Answer: -0.66667
Step-by-step explanation:
Help me I don’t understand
Answer:
C (8,6) A (2,14)
Step-by-step explanation:
(2+m)/2 = 5
2(2+m)/2 = 5 x 2
2+m = 10
m = 10 - 2
m = 8
(-6+n)/2 = 0
2(-6+n)/2 = 2 x 0
-6 + n = 0
n = 6
(-8+x)/2 = -3
2(-8+x)/2 = -3 * 2
-8 + x = -6
x = -6 + 8
x = 2
(-2+y)/2 = 6
2(-2+y)/2 = 6 * 2
-2 + y = 12
y = 12 + 2
y = 14
I WILL GIVE BRAINLIEST PLEASE ANSWER!!
△ABC has the verticies at A(4,5) B(-3,6) and C(-1,8)
the following transformations have been done to the triangle in that order...
rotated 90 degrees
reflected across the line y=0
then translated according to the rule (x+3,y-3)
Once all transformations are complete what are the final points?
Answer:
o answer this question, we need to apply the transformations in the reverse order. So first, we need to apply the translation according to the rule (x+3,y-3). This means that the coordinates of the triangle will become A'(7,2), B'(0,3), and C'(2,5). Next, we need to reflect the triangle across the line y=0. This means that the y-coordinates of the triangle will become negative. So the coordinates of the triangle will become A''(7,-2), B''(0,-3), and C''(2,-5). Finally, we need to rotate the triangle 90 degrees. In a standard cartesian coordinate system, a rotation of 90 degrees counterclockwise is equivalent to the transformation (x, y) -> (-y, x). So the final coordinates of the triangle will be A'''(-2,7), B'''(-3,0), and C'''(-5,2).
Tara and Edward each painted their bedrooms. They finished in the same amount of time, even though Edward's bedroom is bigger. They have 4 hours to start painting the basement before dinner is ready. Who will likely paint a larger part of the basement?
Solve for X in Circle A
The value of x, if In triangle ABC, AC = 18, BC = 30 is 24.
What is circle?A circle is a two-dimensional shape created by a collection of points that are spaced uniformly or uniformly apart from a fixed point (center) on the plane.
Given:
In triangle ABC, AC = 18, BC = 30
As we know, if a tangent is drawn from the circle then it will form a right-angled triangle thus, ∠ ABC = 90°,
Calculate the value of x by using Pythagoras' theorem as shown below,
[tex]AB^2 = BC^2 - AC^2[/tex]
Substitute the values
x² = 30² - 18²
x = √(900 - 324)
x = √576
x = 24
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Given the linear function equation state the function rate.
y = -7x + 1
m=?
Answer:
In the linear function equation y = -7x + 1, the value of m (the slope of the line) is -7. The slope of a line represents the rate at which the y-value changes as the x-value changes. In this case, for every unit increase in the x-value, the y-value decreases by 7 units. Therefore, the function has a rate of -7.
To find the slope of a line from a linear function equation, you can use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. In this case, we can choose any two points on the line and substitute their coordinates into the formula to find the slope. For example, if we choose the points (1, -6) and (2, -13), we get:
m = (-13 - (-6)) / (2 - 1) = -7
Alternatively, we can use the fact that the slope of a line is equal to the coefficient of the x-term in the linear function equation. In this case, the coefficient of the x-term is -7, so the slope of the line is also -7.
Step-by-step explanation:
Find the solutions to x² = 28.
Answer:
[tex]2 \sqrt[]{7} , and -2\sqrt[]{7}[/tex]
Step-by-step explanation:
or:
x=5.29150262…,−5.29150262
Solve.
(3√3)^−x+1 =1/3⋅27^x−5
The required simplified value of the given expression is x = 0.67.
Given that,
To determine the simplified solution of the expression, [tex]\left(3\sqrt{3}\right)^{-x}+1=\frac{1}{3}\left[27^x-5\right][/tex]
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
In order to simplify the given expression, we have to transpose the number across the equal sign as exponents numbers tobe either side and constant on the other side.
[tex]=\left(3\sqrt{3}\right)^{-x}+1=\frac{1}{3}\left[27^x-5\right]\\=\left(\left(3\sqrt{3}\right)^x\right)^{-1}+1=\frac{1}{3}\left[\left(\left(3\sqrt{3}\right)^x\right)^2-5\right]\\= 2 / 3\\= 0.67[/tex]
Thus, the required simplified value of the given expression is x = 0.67.
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What is the value of n when 3/5
of n equals 45? Enter the answer in the box.
At n = 75 the value of 3/5 * n will be 45
What is Fraction?
A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction denotes the number of components of a specific size.
Solution:
Since we are given that 3/5 of n is 45
We can for an equation as 3/5 * n = 45
and to solve this we neeed to use cross multiplication method for the same
Cross Multiplication
n = 45*5/3
n = 15*5
n = 75
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Super easy question
Answer: The correct answer is A. Addition
Step-by-step explanation:
Let's solve for x in 2x+4y=10
Step 1: Add -4y to both sides.
2x+4y+−4y=10+−4y
2x=−4y+10
Step 2: Divide both sides by 2.
2x/2 = −4y+10/2
x = −2y +5
Now let's solve for x in 5x+4y = -12
Step 1: Add -4y to both sides.
5x+4y+−4y=−12+−4y
5x=−4y−12
Step 2: Divide both sides by 5.
5x/5 = −4y−12/5
x = −4/5y + −12/5
Here is what solving for Y looks like
Let's solve for y in 2x+4y=10
Step 1: Add -2x to both sides.
2x+4y+−2x=10+−2x
4y=−2x+10
Step 2: Divide both sides by 4.
4y/4 = −2x+10/4
y = −1/2x + 5/2
Now let's solve for y in 5x+4y = -12
Step 1: Add -5x to both sides.
5x+4y+−5x=−12+−5x
4y=−5x−12
Step 2: Divide both sides by 4.
4y/4 = −5x−12/4
y = −5/4 x−3
addition. thanks for the points. /j
The students at a certain high school have an elective period, where each student chooses an elective from among four options. The following table shows the number of students who selected each elective for the 1,500 students at the high school.
If each student can only choose one elective, picking both is impossible, making the probability 0.
There is no chance of picking a single kid for music and art electives (0).
Information disclosed:
A high school's students are participating in electives.
Since each student is only allowed to choose one elective course from the options provided, they can either choose music or art as their elective.
Therefore, it is impossible to choose a student who has chosen to study art and music.
As a result, there is no chance of picking a student for whom both music and art are electives (0).
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if the numbers denoting the perimeter and area of the square are equal, what is the length of the diagonal?
If the numbers denoting the perimeter and area of the square are equal, the length of the diagonal will be 4√2 units.
What are Area and Perimeter?
An object's shape defines a region as its area. The area of a figure or any other two-dimensional geometric shape is how much space it takes up in a plane.
The whole length encircling a shape is referred to as its perimeter. Simply put, if a shape is stretched into a linear form, its perimeter is its length. In a two-dimensional plane, a shape's perimeter is the sum of its total dimensions.
Let the side of the square to be 'a'.
If Area and Perimeter of a square are equal then,
So, Area = Perimeter
a^2 = 4a
we get, a = 4 units.
Now, we can find the diagonal by using Pythagoras theorem,
We know that, Hypotenuse^2 = Base^2 + Perpendicular^2
Here, the hypotenuse will be the diagonal of the square.
So, We have,
Diagonal^2 = 4^2 + 4^2
= 16 + 16
= 32
∴ Diagonal = √32 = 4√2 units.
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our data analytics team often surveys clients to get their feedback. if you were on the team, how would you ensure the sample is representative of the population as a whole?
To ensure the sample is representative of the population as a whole, try to use some random samples.
What do you mean by sample?A sample refers to a small quantity that is examined to get the knowledge of how the whole product/population will be.
Now, we need feedback from our clients. To ensure that our sample is representative of the population as a whole, we should include clients with different attributes.
Like, choosing 10 clients all living in the same place, same gender, and same age group will be the worse sample.
The best way to do this is to select samples randomly, ensuring that our sample includes people with different ages, gender, height, disabilities(if any) and statuses, etc.
So, A randomized sample is the best for ensuring that the sample is representative of the population as a whole.
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the function y=2^x+4 is shifted left 10 units what is the new equation of the new function?
The new equation of the function y = 2^x + 4 shifted 10 units to the left is y = 2^(x-10) + 4
What is translation?translation moves a shape left, right, up, or down but does not turn. The translated shapes (or the image) appear to be the same size as the original shape, indicating that they are congruent.
Since the function is shifted 10 units to the left, it means the x coordinate of the function is reduced by 10. making the exponent (x) to become (x - 10)
So the function's new equation is y = 2^(x-10) + 4
In conclusion, the new equation is y = 2^(x-10) + 4
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one assumption underlying linear regression is that the x values are normally distributed. true false
One assumption underlying linear regression is that the x values are normally distributed.
This above statement is true.
Linear regression:Linear regression is a linear approach for modeling the relationship between a scalar response and one or more explanatory variables (also called dependent and independent variables). When there is one explanatory variable, it is called simple linear regression. If there are more than one, the process is called multiple linear regression. This concept differs from multivariate linear regression, which predicts multiple correlated dependent variables instead of a single scalar variable.
In linear regression, relationships are modeled using a linear predictor function in which the unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of the response is assumed to be an affine function of the values of the explanatory variables (or predictors) given those values. In rare cases, a conditional median or another quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response variable given the values of the predictor variables, rather than the joint probability distribution of all variables, which is the domain of multivariate analysis.
Assumption:1. Weekly Exogeneous:
It means that we can treat the predictor variable x as a fixed value rather than as a random variable. This means, for example, that the predictor variables are assumed to be error-free, ie not contaminated with measurement error. This assumption is not realistic in many situations, but omitting it makes the within-variable error model much more difficult.
2. Linearity:
This means that the mean response variable is a linear combination of the parameters (regression coefficients) and the predictor variables. . The predictor variables themselves can be arbitrarily transformed. In fact, we can add multiple copies of the same underlying predictor variable, each transformed differently.
3. Constant variance or Homogeneity:
This means that the error variance does not depend on the values of the predictor variables. Therefore, for any given fixed value of the predictor, the variability of the response is the same no matter how large or small the response is. This is often not the case because variables with large mean values usually have more variance than variables with small mean values.
4. Independence from:
This assumes that the response errors are uncorrelated. (True statistical independence is a stronger condition than just lack of correlation and is often unnecessary, but can be exploited when it is known to hold.) Generalized least squares, etc. Some methods in can handle correlated errors, but this usually requires significantly more data unless some kind of regularization is used to bias the model to accept uncorrelated errors Bayesian linear regression is a popular method for handling this problem.
5. Lack of Multicollinearity:
Predictors are not fully multicollinear. For the standard least-squares estimation method, the design matrix X must have perfect column rank p. Otherwise, the predictors are perfectly multicollinear, meaning there is a linear relationship between two or more predictors. This can be caused by erroneously duplicating variables in the data, using linear transformations of the variables together with the original variables, or using multiple variables in the model. It can be caused by inserting a linear combination. as their average. It is also possible that too little data is available relative to the number of estimated parameters.
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