(a) Explanation: In order to prove that X and Y are dependent random variables, we need to show that: pX,Y(x,y)≠pX(x)pY(y) when (x,y) ∈ T which means the joint probability of X and Y is not equal to the product of the marginal probability of X and Y.
For (x,y) ∈ T, pX,Y(x,y) = P (X=1, Y=y) = 1+y
But pX(x) = P(X=1) = Σ pX,Y(1, y) = Σ (1+y)
where the summation is taken over all y for which (1, y) ∈ T. For (1,1) ∈ T,
we get pX,Y(1,1) = 2 and pX(1) = Σ pX,Y(1,y) = 2 + 3 = 5. So, pX,Y(1,1) ≠ pX(1)pY(1) which implies that X and Y are dependent random variables.
(b) E[XY] = Σ Σ xy pX,Y(x,y) where the summation is taken over all x and y for which pX,Y(x,y) > 0.
Substituting the values, we get, E[XY] = Σ Σ xy (1+y) where the summation is taken over all (x,y) ∈ T.
So, E[XY] = (1+1) (1+1) + (1+2) (1+2) + (1+3) (1+3) = 2*2 + 3*4 + 4*6 = 2 + 12 + 24 = 38.
(c) Covariance of X and Y can be determined as follows: Cov(X,Y) = E(XY) - E(X)E(Y)Now, E(X) = Σ x pX(x) and E(Y) = Σ y pY(y)
Substituting the values, we get E(X) = 5/9 and E(Y) = 20/9
Therefore, Cov(X, Y) = E(XY) - E(X)E(Y) = 38 - (5/9) (20/9) = 38 - 100/81 = 998/81.
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what is one of the distinctions between a population parameter and a sample statistic?
One distinction between a population parameter and a sample statistic is that the former describes a characteristic of an entire population, while the latter is characteristic of a subset of the population, called a sample.
In statistics, a population parameter is a numerical value that describes a characteristic of an entire population. It is a fixed value and is usually unknown or difficult to determine precisely. Population parameters are typically denoted by Greek letters (e.g., [tex]\mu[/tex] for the population means, σ for the population standard deviation).
On the other hand, a sample statistic is a numerical value that represents a characteristic of a sample, which is a subset of the population. Sample statistics are used to estimate population parameters. Since a sample is a smaller portion of the entire population, sample statistics can vary from one sample to another. Sample statistics are typically denoted by Latin letters (e.g., [tex]\bar{x}[/tex] for the sample mean, s for the sample standard deviation).
The distinction lies in the scope of the information they provide. Population parameters aim to describe the overall characteristics of a population, while sample statistics provide information about a specific subset of the population, which can be used to infer or estimate the population parameters.
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8 x 10 inch rectangle.Total area is 168 in^2. Calculate the width of the rectangle. Which of the following quadratic equations would be used when solving this?
A - 2x^2 + 18x = 88
B - 4x^2 + 36x = 88
C - 4x^2 + 18x = 88
D - 2x^2 + 36 = 88
Find the area of the figure below
Answer:
you can write 28.5
Step-by-step explanation:
calculate the squared you can find it
Help will mark brainliest show steps pls
Answer:
at first , you need the sum of both equations . It will be like :
2y= 0 + 2
Y=1
_____
now that you know the value of Y , place it in the one of the equation that you like , forexample i place it in the second equation and find out that the value of x is ( -3/2)
1= 2X+5
-4=2X
X= -2
Hope it helps , good luck ^.^
A construction company produces two products (doors and windows) that require two plants (A and B). Management wants to determine how many units of each product should be produced to maximize profit. For each unit of Product 1 (i.E. Door), 2 workers are required in Plant A and 4 workers are required in Plant B. For each unit of Product 2 (i.E. Window), 3 workers are required in Plant A and 4 workers are required in plant B. The company has 40 workers in Plant A and 60 workers in Plant B. Each unit of Product 1 gives a profit of $100. Each unit of Product 2, up to 10 units, gives a profit of $80. Any excess over 10 units of Product 2 brings no profit; so, such excess has to be ruled out.
Answer:
Z max = 1500
x₁ = 15
x₂ = 0
Step-by-step explanation:
From problem statement:
Plant A Plant B Profit $/each
Product 1 (Doors ) x₁ 2 4 100
Product 2 (windows ) x₂ 3 4 80
Product 2 (windows ) x₂ above 10 is scrap
Objective function to maximize
z = 100*x₁ + 80*x₂
Subject to:
Plant A capacity
2*x₁ + 3*x₂ ≤ 40
Plant B capacity
4*x₁ + 4*x₂ ≤ 60
Windows condition:
0*x₁ + x₂ ≤ 10
Model:
Max z = 100*x₁ + 80*x₂
Subject to:
2*x₁ + 3*x₂ ≤ 40
4*x₁ + 4*x₂ ≤ 60
x₂ ≤ 10
x₁ , x₂ ≥ 0 and integers
Afther 6 iterations using Simplex Solver AtomZmath
Z max = 1500
x₁ = 15
x₂ = 0
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0.07 and the probability that the flight will be delayed is 0.19. The probability that it
will not rain and the flight will leave on time is 0.75. What is the probability that it is
raining and the flight is delayed? Round your answer to the nearest thousandth.
Step-by-step explanation:
P(rain and flight delayed) = P(rain) x P(flight delayed) = 0.07 x 0.19
= 0.013 (nearest thousandth)
Answer: 0.01
Step-by-step explanation:
the person above did it wrong, this answer is for sure correct.
13. What is the positive solution to this equation? 4x2 + 18 x= 162
Answer:8.5 is x but there is an extra 1
Step-by-step explanation:18x8.5=153+8=162 with an extra one is 162
Watch help video 6900 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 26 years, to the nearest cent?
The amount in the account after 26 years is approximately $37,120.06.
To calculate the amount of money in an account after a given number of years, you can use the formula for compound interest.
The formula for compound interest is given as follows:
A = P(1 + r/n)^(nt) Where
A is the amount of money in the account after t years.
P is the principal amount.
r is the annual interest rate.
n is the number of times the interest is compounded per year.
t is the number of years 6900 dollars is placed in an account with an annual interest rate of 8.25%.
To find out how much will be in the account after 26 years, we will use the formula for compound interest by applying the given values:
P = 6900 dollars
r = 8.25%n = 1 (as the interest is compounded annually)
t = 26 years
Substituting the values in the formula, we get:
A = 6900(1 + 0.0825/1)^(1*26)
Using a calculator, we get:
A ≈ $37,120.06
Therefore, the amount in the account after 26 years is approximately $37,120.06.
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Write an expression to represent the following:
Two less than the product of five and a number x.?
Step-by-step explanation:
[tex]5x - 2[/tex]
...........
Answer:
2-5x
Step-by-step explanation:
let the number be x, 5 *x = 5x.
2 less means ,2 minus,
>> 2-5x.
Jessica's cat weighs 7lb. The neighbors cat weighs 1/5 more than Jessica's cat. How much does the neighbor's cat weigh?
Answer:
8.4 lbs
Step-by-step explanation:
the cat is 7lbs and the neighbors is 1/5 more. to find 1/5 of 7 you would do 7/5 which equals 1.4
you then add 7+1.4=8.4 lbs
i'm pretty sure that's it!!
Let G=⟨a⟩ be a cyclic group of order n. Show that, for every divisor d of n there exists a subgroup of G whose order is d
This time I have no approach. I haven't found any relation between the divisors of n
and the order of the subgroups of G. How would approach this?
For every divisor d of the order n of a cyclic group G=⟨a⟩, there exists a subgroup of G whose order is d.
To approach this, we can consider the properties of cyclic groups. A cyclic group G generated by a single element "a" has elements that are powers of "a" in the form of [tex]a^k[/tex], where k takes values from 0 to n-1. The order of an element "a" in G is the smallest positive integer k such that [tex]a^k[/tex] equals the identity element.
Now, let's focus on the divisors of n. Each divisor d divides n evenly, meaning n/d is an integer. We can consider the element "[tex]a^(^n^/^d^)[/tex]" in G. The order of "[tex]a^(^n^/^d^)[/tex]" is d because [tex](a^(^n^/^d^))^d = a^n = e[/tex], where e is the identity element of G.
Hence, the subgroup generated by "[tex]a^(^n^/^d^)[/tex]" has an order of d, since it consists of elements of the form [tex](a^(^n^/^d^))^k[/tex], where k takes values from 0 to d-1. Therefore, for every divisor d of n, there exists a subgroup of G whose order is d.
This demonstrates the relationship between the divisors of n and the order of the subgroups in the cyclic group G.
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Help help please please
Answer:
18
Step-by-step explanation:
This is actually pretty easy. Keep this in mind.
There are 34 total students. 16 of them like bananas and the rest like apples. All you really need to do is count up from 16 to 34 to find the answer.
The simple equation for this is: 34-16
Thus, the answer is 18.
Please answer correctly! I will mark you as Brainleist!
Answer:
1047.2 cubic inches
Step-by-step explanation:
V = 4(pi)(r³/3)
V = 4(pi)(125/3)
V = 523.6 cubic inches (1 ball)
V = 2(523.6) = 1047.2 cubic inches (total)
Match the word to its description. The difference between the lowest and highest value 1. mode The middle value 2. mean 3. median The most frequent value PP 4. range The average
Answer:
range
Step-by-step explanation:
The difference between the lowest and the highest number is called the range. The middle value is the median (it's in the "mid"dle, median) The mean is the average. And the mode is the most frequent value.
A plan can travel 420 miles in 80 minutes. Find a unit that describes this situation
Answer:
5.25 miles per minute
Step-by-step explanation:
420/80 = 5.25 so it is 5.25 miles per minute as it is 80 minutes
Explain how to solve 4640 divided by 10. use complete sentences!!
Answer:
464
Step-by-step explanation:
the number has one, zero at the end. same for the ten.
4640 10just take zero for zero and you end up with 464
In circle a the length of the radius is 24 units what is the length of the arc BC?
Answer:
20pi
Step-by-step explanation:
150/360 = 5/12
5/12 * 2*24*pi = 20pi
==============
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What is the theoretical probability of rolling anything other than a two on a fair six sided die?
Answer:
5/6 probability
Step-by-step explanation:
Find the perimeter of a rectangle if the length of one side is 9x + 6y and the width is 13x + 2y.
Answer:
perimeter of rectangle = 2 (length + breadth)
= 2(9x + 6y + 13x + 2y)
= 2(22x +8y)
= 44x + 16y
Step-by-step explanation:
9x+6y
9-9x+6-9y both side subtract 9
x+(-3)y
x-3y the answer
13x+2y
13-13x+2-13y
x+(-11)y
x-11y .
follow me
Can someone solve this equation?
2.6x + ? = 2x
Answer:
−1.666667
Step-by-step explanation:
A waiter determines his salary for a week using the formula S = 3.75h + t, where S is his salary, h is the number of hours he works, and t is his total tips. How much does the waiter make if he works 30 hours in a week and makes a total of $538.75 in tips?
Answer:
$651.25
Step-by-step explanation:
plug your variables into your equation so,
S= 3.75(30)+ 538.75
and solve
S=112.5+538.75
S=651.25
Answer:
$651.25
Step-by-step explanation:
S = 3.75h + t
Given:
h = 30
t = 538.75
Work:
S = 3.75h + t
S = 3.75(30) + 538.75
S = 112.5 + 538.75
S = 651.25
An increase in the real interest rate will
A. most likely lower consumer's purchases of durable goods.
B. most likely lower the cost of borrowing.
C. cause consumers to spend more and save less.
D. most likely lower the reward to savings.
An increase in the real interest rate will most likely lower the reward to savings. The correct answer is D.
When the real interest rate increases, it means that the return on savings and investments is higher in real terms, adjusted for inflation. As a result, individuals are incentivized to save more as they can earn a higher return on their savings.
When the reward to savings is lower, it becomes less attractive for individuals to save. Higher interest rates can discourage borrowing and encourage saving, which reduces consumer spending on durable goods and other discretionary purchases.
Option A is incorrect because an increase in the real interest rate would likely lead to a decrease in consumer's purchases of durable goods, as higher interest rates increase the cost of borrowing, making it more expensive to finance large purchases.
Option B is incorrect because an increase in the real interest rate generally makes borrowing more expensive, as it increases the cost of borrowing for individuals and businesses.
Option C is incorrect because an increase in the real interest rate usually encourages individuals to save more and spend less, as the potential return on savings is higher.
The correct answer is D.
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The following data are the amounts of total fat (in grams) in all sweet treats available at your local donut shop
24 16 23 22 17 15 24 24 24 16
Are these population or sample data? _____Population
What is the range for this data set? ______9
What is the variance for this data set? Round your answer to three decimal places, if necessary. ______15.455
What is the standard deviation for this data set7 Round your answer to three decimal places, if necessary. _____3.931
The data set represent a population.
The range for this data set is 9.
The variance for this data set is 14.05.
The standard deviation for this data set is 3.748.
What is a population?In Statistics, a population simply refers to a set of similar items or events that comprises every member of a group i.e the total number of elements.
Based on the given data set, we would calculate the range by using the following formula:
Range = Highest number - Lowest number
Range = 24 - 15
Range = 9.
Next, we would determine the mean as follows;
Mean = ∑fx/n
Mean = (24 + 16 +23+22+17+15+24+24+24+16)/10
Mean = 205/10 = 20.5
Now, we can calculate the standard deviation and variance by using this formula:
Standard deviation, δ = √(1/n × ∑(xi - μ)²)
Standard deviation, δ = √[1/10 × (24 - 20.5)² + (16 - 20.5)² + (23 - 20.5)² + (22 - 20.5)² + (17 - 20.5)² + (15 - 20.5)² + (24 - 20.5)² + (24 - 20.5)² + (24 - 20.5)² + (16 - 20.5)²]
Standard deviation, δ = √140.5/10
Standard deviation, δ = 3.748.
For the variance, we have:
Variance = δ²
Variance = 3.75²
Variance = 14.05
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2. Determine the value of k such that when the given function f(x) = x4 + kx³ - 3x - 5 a) is divided by (x-3) the remainder is -10 b) Determine the remainder when f(x) is divided by x +3.
To determine the value of k in the function f(x) = [tex]x^4[/tex] + k[tex]x^3[/tex] - 3x - 5, we can consider the remainders when f(x) is divided by (x-3) and (x+3).
a) When f(x) is divided by (x-3), the remainder is -10. To find the remainder, we can use the Remainder Theorem, which states that if a polynomial f(x) is divided by (x - a), the remainder is equal to f(a). Plugging in x = 3 into f(x), we get:
f(3) = [tex]3^4[/tex] + k([tex]3^3[/tex]) - 3(3) - 5
= 81 + 27k - 9 - 5
= 27k + 67
Since the remainder is -10, we can set up the equation:
27k + 67 = -10
Solving this equation, we find:
27k = -77
k = -77/27
b) To determine the remainder when f(x) is divided by (x+3), we can follow a similar process. Plugging in x = -3 into f(x), we get:
f(-3) =[tex](-3)^4[/tex] + k[tex](-3)^3[/tex] - 3(-3) - 5
= 81 - 27k + 9 - 5
= -27k + 85
The remainder is given by f(-3), so we can set up the equation:
-27k + 85 = remainder
Hence, the remainder when f(x) is divided by (x+3) is -27k + 85.
In summary, the value of k such that the remainder when f(x) is divided by (x-3) is -10 is k = -77/27. Additionally, the remainder when f(x) is divided by (x+3) is -27k + 85.
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Three side lengths of a triangle are shown above. Which of the following statements is true?
A random experiment involves drawing a sample of 12 data values from a normally distributed population. The random variable is the minimum of the data set. 44 47 49 52 56 61 63 64 67 69 75 76 Give the random variable. (Appropriate rounding rules still apply.) r.v=__
The random variable is given by :
r.v. = 37.51.
Given that a random experiment involves drawing a sample of 12 data values from a normally distributed population. The random variable is the minimum of the data set.44 47 49 52 56 61 63 64 67 69 75 76, we need to find the random variable i.e., minimum of the given data set.
Converting to normal distribution, we get to know that :
µ = (44+47+49+52+56+61+63+64+67+69+75+76) / 12
µ = 60σ
µ = sqrt((44-60)² + (47-60)² + (49-60)² + (52-60)² + (56-60)² + (61-60)² + (63-60)² + (64-60)² + (67-60)² + (69-60)² + (75-60)² + (76-60)²) / 12
µ= sqrt(2018 / 12)σ
µ = 5.29
Hence, the random variable is given by : r.v = 44-5.29(1.15) ≈ 37.51
Therefore, the random variable is 37.51.
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Summary statistics computed for two population (A & B) are as follows: meanA=100, sigmaA=45, meanB-30, sigma B=14. If two samples of equal sizes 15 are independently drawn from these two population. Find the probability that sample A will have mean of 90.7 more than sample B.
A. 0.152
B. 0.529
C. 0.251
D. 0.0445
The probability that sample A will have mean of 90.7 more than sample B is 0.0475. Therefore the correct answer is (D)
Understanding Probability and Sampling DistributionGiven:
- Population A: meanA = 100, sigmaA = 45
- Population B: meanB = 30, sigmaB = 14
- Sample sizes for both samples: n = 15
We want to find the probability that the sample mean of sample A will be 90.7 or more than the sample mean of sample B.
To find this probability, we need to calculate the standard deviation of the sampling distribution of the difference in sample means. The standard deviation of the difference in sample means (denoted as sigma difference) is calculated as follows:
sigma difference = [tex]\sqrt{(\frac{sigmaA^2}{nA}) + (\frac{sigmaB^2}{nB})}[/tex]
Where:
- sigmaA = standard deviation of population A
- sigmaB = standard deviation of population B
- nA = sample size for sample A
- nB = sample size for sample B
In this case, both samples have the same size, nA = nB = 15.
sigma difference = [tex]\sqrt{(\frac{45^2}{15}) + (\frac{14^2}{15})}[/tex]
sigma difference = [tex]\sqrt{(\frac{2025}{15}) + (\frac{196}{15})}[/tex]
sigma difference = [tex]\sqrt{(135+ 13.07)}[/tex]
sigma difference = [tex]\sqrt{(148.7)}[/tex]
sigma difference = 12.16
Now, we can calculate the z-score, which is the difference between the desired sample mean difference and the population mean difference (mu difference = meanA - meanB), divided by the standard deviation of the sampling distribution (sigma difference).
z = (90.7 - (meanA - meanB)) / sigma difference
z = (90.7 - (100 - 30)) / 12.16
z = (90.7 - 70) / 12.16
z ≈ 1.69
To find the probability that the sample mean difference is 90.7 or more, we need to calculate the area under the standard normal curve to the right of the z-score (1.69).
Using a standard normal distribution table or a calculator, we find that the probability is approximately 0.9525.
However, we want the probability that the sample mean of sample A is 90.7 or more than the sample mean of sample B, which means we need to find the probability to the left of the z-score (-1.69) and then subtract it from 1.
P(z < -1.69) = 1 - P(z > -1.69)
Using a standard normal distribution table or a calculator, we find that P(z > -1.69) is approximately 0.9525.
Therefore, the probability that the sample mean of sample A will be 90.7 or more than the sample mean of sample B is:
P(z < -1.69) = 1 - P(z > -1.69) = 1 - 0.9525 ≈ 0.0475
The closest option is D. 0.0445, but the calculated probability is approximately 0.0475.
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A vendor purchase 8 dozen teacups to sell. She packed them into boxes of 4 and each and sold each box for$60. Calculate the amount of the money she earned from the sale of all the teapcups?
Answer: $1440
Step-by-step explanation:
So if we have 8 dozens that is 8*12=96 teacups
boxes of 4 means 96/4= 24 boxes in total with 4 teacups in each
Since she is being paid 60$ for each of the 24 boxes she makes exactly $1440
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Help me pls, tysm! I will give brainly if you give me the right answer, tysm! I need help on number 6 btw
Answer: 96 feet
Step-by-step explanation:
The inverse of the function f(x) = { x + 10 is shown.
h(x) = 2x-0
What is the missing value?
O 1
O 5
O 10
O20
Answer:
D) 20
Step-by-step explanation:
the missing value is 20
the last option
The equation h(x) = 2x - 0 = x - 10 is satisfied by the value x = -10; the omitted integer is 10.
What is a function?A function is a mathematical formula that illustrates the relationship between the dependent and independent variables. The independent variable's value and the dependent variable's value both change in the function.
Determine x in terms of f(x) in order to determine the inverse of the function f(x) = x + 10:
f(x) = x + 10
f(x) - 10 = x
x = f(x) - 10
Since h(x) is the opposite of f(x), replace x with h(x):
h(x) = f⁻¹(x) = x - 10
Since h(x) is the opposite of f(x), replace x with h(x):
To identify the missing value, compare the expression for h(x) to the supplied function, h(x) = 2x-0. We can see that the appropriate expression for h(x) is:
h(x) = 2x - 0 = x - 10
Find the value of x that allows this equation to be solved:
2x - 0 = x - 10
Simplifying and solving for x,
x = -10
Therefore, the missing value is O 10, since x = -10 satisfies the equation h(x) = 2x - 0 = x - 10
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