To approximate the stationary matrix S for the transition matrix P, we need to compute powers of the transition matrix P until it reaches a stable matrix.
Starting with P = [0.37 0.63; 0.19 0.81], we can compute powers of P as follows:
P^2 = P * P
= [0.37 0.63; 0.19 0.81] * [0.37 0.63; 0.19 0.81]
= [0.2746 0.7254; 0.1538 0.8462]
P^3 = P * P^2
= [0.37 0.63; 0.19 0.81] * [0.2746 0.7254; 0.1538 0.8462]
= [0.2421 0.7579; 0.1873 0.8127]
P^4 = P * P^3
= [0.37 0.63; 0.19 0.81] * [0.2421 0.7579; 0.1873 0.8127]
= [0.2222 0.7778; 0.1941 0.8059]
Continuing this process, we find:
P^5 = [0.2149 0.7851; 0.1957 0.8043]
P^6 = [0.2124 0.7876; 0.1961 0.8039]
P^7 = [0.2117 0.7883; 0.1961 0.8039]
As we can see, the matrix P^7 is very close to the stationary matrix S. Therefore, we can approximate the stationary matrix S as:
S ≈ [0.2117 0.7883; 0.1961 0.8039]
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Assuming the sample was taken from a normal population, test at ů. = 0.05 and state the decision. Họ: H = 13 HA: U < 13 ř= 10 S= 0.7 n = 9
the test statistic (t = -12.857) is smaller than the critical value (-1.860), we have enough evidence to reject the null hypothesis.
To test the hypothesis regarding the population mean, we can perform a one-sample t-test.
Given:
- Null hypothesis (H₀): μ = 13
- Alternative hypothesis (Hₐ): μ < 13
- Sample mean ([tex]\bar{X}[/tex]) = 10
- Sample standard deviation (s) = 0.7
- Sample size (n) = 9
- Significance level (α) = 0.05
To conduct the t-test, we can calculate the test statistic and compare it with the critical value from the t-distribution.
The test statistic (t-score) is calculated as:
t = ([tex]\bar{X}[/tex] - μ) / (s / √n)
Plugging in the values:
t = (10 - 13) / (0.7 / √9)
t = -3 / (0.7 / 3)
t = -3 / 0.233
t ≈ -12.857
To determine the critical value, we need to find the appropriate degrees of freedom (df) for a one-sample t-test. In this case, df = n - 1 = 9 - 1 = 8.
Using a significance level of α = 0.05 and looking up the critical value for df = 8 in the t-distribution table, we find the critical value to be approximately -1.860.
Since the test statistic (t = -12.857) is smaller than the critical value (-1.860), we have enough evidence to reject the null hypothesis.
Decision: Based on the test results, at α = 0.05, we reject the null hypothesis (H₀: μ = 13). There is sufficient evidence to support the alternative hypothesis (Hₐ: μ < 13), suggesting that the population mean is less than 13.
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Given question is incomplete, the complete question is below
Assuming the sample was taken from a normal population, test at α = 0.05 and state the decision. Họ: μ = 13 HA: μ < 13 [tex]\bar{X}[/tex]= 10 s= 0.7 n = 9
Tim is making 30 sundaes with mint, chocolate, and vanilla ice cream.
1/5
of the sundaes are mint ice cream and
1/2
of the remaining sundaes are chocolate. The rest will be vanilla. How many sundaes will be vanilla?
Answer:
12
Step-by-step explanation:
1/5 mint = 6
30 - 6 = 24
Half of 24 is 12
12 is chocolate
so 12 must be vanilla
Rewrite the equation by completing the square. x^{2}+4x-21 = 0
Answer:
x={3,-7}
Step-by-step explanation:
brackets for list
Solve with quadratic formula
separate the solutions
Square
Answer:
2 for the first box and 25 for the second one.
Step-by-step explanation:
Choose the correct classifacation of 4x^4-4x^3+10x^6
Answer:what’s classification
Step-by-step explanation:
HELPPP WILL MARK BRAINLIEST!!!!!!
Answer:
15 by 2
Step-by-step explanation:
15 cubes in each layer with 2 layers
Answer:
Cubes in each layer: 15
Number of layers: 2
Volume : 30 cm^3
Step-by-step explanation:
PLEASE ANSWER THIS ASAP
Answer:
the answer is rotation
hope this helps
8. Which equation is true for all x- and y- values in the table below?
x y
1 7
2 14
3 21
4 28
(1 point)
y = x + 7
y = x – 7
y = x over seven
y = 7x
Answer:
y = 7x
Step-by-step explanation:
you mutiply 7 times 1=7
you just continue to do that
A pump fills a pool at a constant rate. At the end of 1 minute it has filled 6 gallons of water. Which table represents the relationship between the number of minutes and the number of gallons of water in the pool?
Answer:
I would need to see the different tables to answer this question.
Translate into an equation: Twenty-six more than the product of a number and
17 is -42.
What is the solution to the equation x + 11 = 57? (Input a whole number only.)
Answer:
46
Step-by-step explanation:
Answer:
x=46
Step-by-step explanation:
I need a little more help. Sorry for the spam questions.
Ajjwjjwjwjwjsbsbaa shah sash’s
Answer:
okay then
Step-by-step explanation:
Answer: gtyrehretr
Step-by-step explanation:
Find the area of the following figure. Show your work
Question Help
One taco supreme and two pan pizzas provide 3200 calories. Two taco supremes and one pan pizza
provide 3280 calories. Find the caloric content of each item.
Answer:
4324eqW
Step-by-step explanation:
3 + 5 =7
the school choir has 110 members there are 20 more girls than boys there are how many boys the choir
Answer:
65 girls and 45 boys
Step-by-step explanation:
A fair die is tossed twice and let X1 and X2 denote the scores obtained for the two tosses, respectively
Calculate E[X1] and show that var (X1) =
Determine and tabulate the probability distribution of Y = | X1 – X2 | and show that E[Y] =
The random variable Z is defined by Z = X1 – X2. Comment with reasons (quantities concerned need not be evaluated) if each of the following statements is true or false
E(Z2) = E(Y2)
Var(Z) = Var(Y)
1. When a fair die is tossed the expected value E[X1] = 3.5 and the variance var(X1) = 35/12.
When a fair die is tossed, each of the six possible outcomes has an equal probability of 1/6. Let X1 denote the score obtained in the first toss.
To calculate the expected value E[X1], we find the sum of all possible values of X1 multiplied by their respective probabilities:
E[X1] = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) = 3.5
To calculate the variance var(X1), we use the formula:
var(X1) = E[X1^2] - (E[X1])^2
First, we find E[X1^2] by taking the sum of the squares of all possible values of X1 multiplied by their respective probabilities:
E[X1^2] = (1^2 * 1/6) + (2^2 * 1/6) + (3^2 * 1/6) + (4^2 * 1/6) + (5^2 * 1/6) + (6^2 * 1/6) = 91/6
Substituting the values into the formula, we calculate var(X1):
var(X1) = (91/6) - (3.5)^2 = 35/12
Therefore, E[X1] = 3.5 and var(X1) = 35/12.
2. The probability distribution of Y = |X1 - X2| is tabulated as follows:
Y |X1 - X2| P(Y)
0 0 1/6
1 1 2/6
2 2 2/6
3 3 1/6
To calculate E[Y], we find the sum of all possible values of Y multiplied by their respective probabilities:
E[Y] = (0 * 1/6) + (1 * 2/6) + (2 * 2/6) + (3 * 1/6) = 1
Therefore, E[Y] = 1.
3. The statements E(Z^2) = E(Y^2) and Var(Z) = Var(Y) are false.
E(Z^2) and E(Y^2) represent the expected values of the squares of the random variables Z and Y, respectively. Since Z = X1 - X2 and Y = |X1 - X2|, the squares of Z and Y have different probability distributions, leading to different expected values.
Similarly, Var(Z) and Var(Y) represent the variances of Z and Y, respectively. Since Z and Y have different probability distributions, their variances will generally not be equal.
Therefore, E(Z^2) ≠ E(Y^2) and Var(Z) ≠ Var(Y).
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Sails come in many shapes and sizes. The sail on the right is a triangle. Is it a right triangle? Explain your reasoning.
Answer:
not a right triangle
Step-by-step explanation:
you can use the pythagorean theorem to prove whether not this is a right triangle
if this triangle is a right triangle then the following equality should be true
a²+b²=c²
(9.75)²+(3.45)²=(10.24)²
(95.06)+(11.90)=(104.86)
106.96≠104.86
since the following equality is not true, this is not a right triangle.
Work out the size of angle x.
42°
Х
123°
Answer:
42+123+x=180
x=180-165
x=15 degrees
Step-by-step explanation:
Classify a triangle with sides measuring 5, 7 and 8.
Answer:
Scalene
Step-by-step explanation:
Because all 3 sides have different length.
When all 3 sides have the same length: equilateral
When 2 sides have the same length but the 3rd side has a different length: isosceles
When all 3 sides have different length: scalene
Oatmeal is packaged in a right circular cylindrical container that has a radius of 7 centimeters and a height of 16 centimeters.
What is the surface area of this container in terms of pi?
a. 176
b. 254
c. 322
d. 440
Answer:
c. 322
Step-by-step explanation:
Surface area of cylinder = 2πr² + 2πrh.
SA in terms of π = π(2r² + 2rh) →
π(2(7)² + 2(7)(16)) →
π(2(49) + 2(112)) → π(98 + 224) → π(322)
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 600 grams while babies born after a gestation period of 40 weeks have a mean weight of 2800 grams and a standard deviation of 415 grams. If a 34-week gestation period baby weighs 2875 grams and a 41-week gestation period baby weighs 3175 grams, find the corresponding z-scores. Which baby weighs more relative to the gestation period?
Find the corresponding z-scores. Which baby weighs relatively more? Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.)
A. The baby born in week 34 weighs relatively more since its z-score ____, is smaller than the z-score of ____ for the baby born in week 41
B. The baby born in week 41 weighs relatively more since its z-score ____, is smaller than the z-score of ____ for the baby born in week 34
C. The baby born in week 34 weighs relatively more since its z-score ____, is larger than the z-score of for ____ the baby born in week 41 for the baby born in week 34
D. The baby born in week 41 weighs relatively more since its z-score ____, is larger than the z-score of ____ for the baby born in week 34
The corresponding z-scores for the given observations can be calculated using the formula:
[tex]\[z = \frac{{x - \mu}}{{\sigma}}\][/tex]
where [tex]\(x\)[/tex] is the observation, [tex]\(\mu\)[/tex] is the mean, and [tex]\(\sigma\)[/tex] is the standard deviation.
For the baby born in week 34 weighing 2875 grams:
[tex]\[z_{34} = \frac{{2875 - 2500}}{{600}} = 0.625\][/tex]
For the baby born in week 41 weighing 3175 grams:
[tex]\[z_{41} = \frac{{3175 - 2800}}{{415}} = 0.904\][/tex]
To determine which baby weighs more relative to the gestation period, we compare the z-scores.
A. The baby born in week 34 weighs relatively more since its z-score 0.625 is smaller than the z-score 0.904 for the baby born in week 41.
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Jasmine has $50 and saves $4.38 every month. Radha has $0 and saves $5.38 every month. Jasmine's savings after x months can be represented by the function f (x) = 4.38 x + 50. Radha's savings after x months can be represented by the function g (x) = 5.38 x. Round your answer to the nearest hundredth.
After how many months will they both have the same amount in savings? Find the values of x for which f (x) = g (x).
After ____ months, Jasmine and Radha will have the same amount in savings.
What is the solution to the equation below?
4x+8 = 2(x - 4)
A x = -5
B x = 6
Cx = -8
D x = -4
Answer:
C
Step-by-step explanation:
4x +8 = 2x -8
4x = 2x - 16
2x = -16
x = -8
CAN SOMEONE HELP ME PLEASE
Answer: 9 x 6 x 6
Step-by-step explanation: 9 x 6=54 54 x 6 = 324 ft
P(x) = x2 + x +1
How many terms does this polynomial have?
Answer:
3
Step-by-step explanation:
Write an equation of the line that passes through (0, 8) and (6, 8).
Answer:
y = 8
Step-by-step explanation:
Both of the points have the same y, which is 8, meaning that if the line passed through both of those points, then it has to be horizontal, meaning the equation is y = 8 Also, there is no x in the equation because the slope is 0.
Donna bought 5 bags of dog treats for $13.10. What is the cost per bag of dog treats?
A. $18.10
B.$3.28
C.$2.62
D.$0.38
2. A cow gives 24litre milk each day. If the milkman sells 75% of the milk, how many
liters of milk is left with him?
Answer: 6 liters
Step-by-step explanation:
24 liters
He sells 75%
24 x 0.75 = 18 liters
24 - 18 = 6
He still has 6 liters left
A travel agent collected data from a group of past clients regarding what type of reservation they plan to make in the future and which package they plan to choose. The types of reservations offered at the agency are tours, cruises, and resorts, and the packages offered are either basic or deluxe.
The two way table given by option z is a possible representation of the data collected.
How to calculate a relative frequency?A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.
From the first table, we have that:
Half of the packages are basic.Half of the packages are deluxes.Then, for the basic packages, we have that resorts were chosen 2.5 times more than tours, while cruises were chosen 1.5 times more than tours.
Option z shows these same ratios between the amounts, hence it is the correct option.
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What should be done to both sides of the equation in order to solve y - 4.5 = 12.2?
Add 4.5
---
hope it helps
Answer: add 4.5 to both sides
Step-by-step explanation: this will allow the 4.5 to be removed from the y side and since you added it to one side you have to add it to the other side. This will give your y the value of 16.7.
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