Confidence intervals based on pivotal quantities. Let Y1, Y2, . . . , Yn follow an Exponential distribution with parameter β. Note that βYn ∼ Gamma(n, n) and 2nβYn ∼ χ 2 df=2n are both pivotal quantities. (a) Explain why both statistics are indeed pivotal quantities. (b) Construct a 95% confidence interval for β using each pivot and provide interpretations. (c) Compare both intervals. Which one would you recommend using? Explain why

Answer:

Step-by-step explanation:

[tex]9x6x12[/tex]= 648 the length(12m), width(6m), and height(9m) that all i can give you for now because this got me losing brain sells

Answer:

for the first question the answer is 3

for the second question the answer is 9

Step-by-step explanation:

12/4=3, 6/2=3, 9/3=3

8+8+12+12+6+6 = 52 & 108 + 108 + 72 + 72 + 54 + 54= 468

468 / 52 = 9

The Romberg integration method is used to approximate definite integrals. Given the values R21 = 6 and R22 = 6.28, we can determine the value of R11.

To find R11, we can use the formula:

R11 = (4^1 * R21 - R22) / (4^1 - 1)

Substituting the given values, we have:

R11 = (4 * 6 - 6.28) / (4 - 1)

    = (24 - 6.28) / 3

    = 17.72 / 3

    ≈ 5.9067

Therefore, the approximate value of R11 is approximately 5.9067.

Romberg integration is an extrapolation technique that refines the accuracy of numerical integration by successively increasing the order of the underlying Newton-Cotes method. The notation Rnm represents the Romberg approximation with m intervals and n steps. The general formula for calculating Rnm is:

Rnm = (4^n * Rn-1,m-1 - Rn-1,m) / (4^n - 1)

In this case, R21 represents the Romberg approximation with 2 intervals and 1 step, while R22 represents the approximation with 2 intervals and 2 steps. By substituting these values into the formula, we can calculate R11. The numerator is obtained by multiplying R21 by 4 and subtracting R22. The denominator is calculated by subtracting 1 from 4^n. Evaluating this expression yields the approximate value of R11 as 5.9067.

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Answer:

24

Step-by-step explanation:

added all the sides hope this helps

Let L be the linear operator in R2 defined by L(x) = (3x1 - 2x2, 9x1 - 6x2)T. The bases of the kernel and image of L are to be determined. To find the bases of the kernel and image of L, we first recall the definitions of kernel and image of a linear operator. Definition of Kernel: Let T be a linear operator on a vector space V. Then the kernel of T, denoted as ke T, is the subspace of V that consists of all vectors that are mapped to the zero vector of the range of T. Definition of Image: Let T be a linear operator on a vector space V. Then the image of T, denoted as im T, is the subspace of the range of T consisting of all vectors that are mapped by T to some vectors in the range of T. The kernel and image of L are given as follows. Kernel of L: For L(x) = (3x1 - 2x2, 9x1 - 6x2)T to be zero vector, we must have 3x1 - 2x2 = 0 and 9x1 - 6x2 = 0, which implies that x1 = (2/3)x2.

Therefore, a typical element of the kernel of L can be expressed as (x1, x2)T = (2/3)x2(1, 3)T, where x2 is a scalar. Hence, a basis for the kernel of L is {(1, 3)T}. Image of L: The image of L is the subspace of R2 consisting of all vectors that can be expressed in the form L(x) = (3x1 - 2x2, 9x1 - 6x2)T, where x is any vector in R2. It follows that any vector in the image of L is of the form (3x1 - 2x2, 9x1 - 6x2)T = x1(3, 9)T + x2(-2, -6)T. Therefore, a basis for the image of L is {(3, 9)T, (-2, -6)T}.Hence, the bases of the kernel and image of L are as follows. Kernel: {(1, 3)T}Image: {(3, 9)T, (-2, -6)T}.

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The most cost-efficient container is the Rectangular Prism.

1. Rectangular Prism:

Volume: V = lwh = 10 x 5 x 15 = 750 cubic units

Cost: C = $0.01 x 750 = $7.50

Cost per unit volume: C/V = $7.50 / 750 = $0.01 per cubic unit

2. Rectangular Pyramid:

Volume: V = (1/3) x lwh = (1/3) x 10 x 5 x 15 = 250 cubic units

Cost: C = $0.02 x 250 = $5.00

Cost per unit volume: C/V = $5.00 / 250 = $0.02 per cubic unit

3. Cylinder:

Volume: V = πr²h = π x 5² x 15 ≈ 1178.1 cubic units

Cost: C = $0.015 x 1178.1 = $17.67

Cost per unit volume: C/V = $17.67 / 1178.1 ≈ $0.015 per cubic unit

Now, comparing the cost per unit volume for each container:

a. Rectangular Prism: $0.01 per cubic unit

b. Rectangular Pyramid: $0.02 per cubic unit

c. Cylinder: $0.015 per cubic unit

The container with the lowest cost per unit volume is the Rectangular Prism, with a cost of $0.01 per cubic unit.

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Answer:

yes cs its a orange juice

Step-by-step explanation:

Answer:

taking back the answer spot that is rightfully mine!

Step-by-step explanation:

Answer:

120

equation: 40+8(10)=120

Step-by-step explanation:

The math for this is $40 initial plus $8x the 10 weeks which equals 80 so

40+80=120

Answer to question 1 is D

answer to question 2 is A

Answer:

138.23

Step-by-step explanation:

In this study, there are a total of 40 subjects. The researcher samples 20 healthy people and 20 people with pre-existing conditions. Out of these, 10 healthy people and 10 people with pre-existing conditions are given a flu shot, while the other 10 from each group are not given flu shots.

To calculate the total number of subjects (N), we add the number of healthy people to the number of people with pre-existing conditions:

N = Number of healthy people + Number of people with pre-existing conditions

N = 20 + 20

N = 40

Therefore, the total number of subjects in the study is 40.

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Answer:

[tex]P(A) = \frac{3}{10}[/tex]

Step-by-step explanation:

Given

[tex]S = \{11,12,13,14,15,16,17,18,19,20\}[/tex]

Required

The probability of having a multiple of 3

Let the event of having a multiple of 3 be represented as: A

So:

[tex]A = \{12,15,18\}[/tex]

[tex]n(A) = 3[/tex]

So, the probability is:

[tex]P(A) = \frac{n(A)}{n(S)}[/tex]

Where

[tex]n(S) = 10[/tex] i.e. the sample size

So:

[tex]P(A) = \frac{n(A)}{n(S)}[/tex]

[tex]P(A) = \frac{3}{10}[/tex]

Answer:

The top graph.

Step by step:

Before the tickets go on sale, 120 tickets were already sold.

After that, the tickets sell at a constant rate for a total of 8 hours.

At the end of this time, all the tickets were sold (we have 0 tickets left)

If x (horizontal axis) represents the hours since tickets go on sale, and y (vertical axis) represents the number of raffle tickets sold.

Then, at x = 0, we should already see y = 120

Because we start with 120 tickets sold.

Then, as x increases, the number of tickets sold also should increase, until we get x = 8 hours, where y stops increasing because all tickets are already sold.

Then we should have an increasing line that stops increasing at x = 8 hours.

Then the correct option is the above graph, where we have:

An increasing line.

y = 120 in the vertical axis (y = 120 when x = 0)

Answer:

hope this helps :)

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

12x^3, 6xy, and 18x can all be evenly divided by 6x

Answer:

5 o clock

Step-by-step explanation:

Answer:

x= 11/7 + 3y/7

Step-by-step explanation:

Answer:

y=11 -7/3x

Step-by-step explanation:

subtract the 7

bring the seven to the other side

then divide by 3

Answer:

21?i think

Step-by-step explanation:

The equations Verdita could use to represent the data sets include the following:

A. Data Set A: y = 4x-2

Data Set B: y = x +4

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of data set A;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 + 6)/(1 + 1)

Slope (m) = 8/2

Slope (m) = 4

At data point (1, 2) and a slope of 4, a linear equation for data set A can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 4(x - 1)

y = 4x - 2

At data point (0, 4) and a slope of 1, a linear equation for data set B can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = 1(x - 0)

y = x + 4

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

40.95

Step-by-step explanation:

P = 1500 + 75 = 1575

I = Prt

I = 1575(1.3%)(2)

I = 40.95

The integral ∫ 1/ (z-a)(z-b) dz over the circle Cr, where a and b are complex numbers and |a| < R < |b|, evaluates to 2πi/(a-b).

To show this, we can use the Residue theorem. Since the function 1/(z-a)(z-b) has two simple poles at z=a and z=b within the region enclosed by the circle Cr, we can evaluate the integral by summing the residues at these poles.

The residue at z=a is given by Res(a) = 1/(b-a), and the residue at z=b is given by Res(b) = -1/(b-a). By the Residue theorem, the integral is equal to 2πi times the sum of the residues.

Therefore, ∫ 1/ (z-a)(z-b) dz = 2πi * (1/(b-a) - 1/(b-a)) = 2πi/(a-b).

This result shows that the integral over the circle Cr simplifies to a complex constant determined by the difference between a and b.

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Answer:

wtfrick- that's so confusing

Step-by-step explanation:

sorry I don't have an answer wish this was a comment

Answer:

Minimum: (2,4)

Step-by-step explanation:

h(x)=3([tex]x^{2}[/tex]-4x)+16

=3([tex]x^{2}[/tex]-4x+4-4)+16   (- For the balance of equation, and attention 1)

=3[tex](x-2)^{2}[/tex]-3*4+16

=3[tex](x-2)^{2}[/tex]+4

1. [tex](a-b)^{2}=a^{2} -2ab+b^{2}[/tex]

2. The formula for the vertex form is y = [tex]a(x-h)^{2}+k[/tex], the vertex is (h,k)

Answer:

4 hours and 10 min

Step-by-step explanation:

For this equation we will do ratios:

[tex]\frac{18}{30} =\frac{150}{x} \\\\18x=4500\\x=250[/tex]

250 min =

4 hours and 10 min

4(60) = 240

240 + 10 = 250 minutes

Answer:

54

Step-by-step explanation:

(24^2)+(30^2)

Answer:

54yd^2

Step-by-step explanation:

you need to break up the figure into 2 different boxes. One 3 x 10 and one    6 x 4 which adds up to 30 + 24 = 54.

Answer:

numbers less than 5 are 1,2,3,4 and equal to 5 is 5.

probability of less than 5 is 4/16

while equal to 5 is 1/16

or means additions; so its 4/16 +1/16=5/16

The given differential equation is given by `dy/dx = V*y` and the initial condition is `y(x) = Yo`.

The solution of the differential equation is given by `y(x) = Yo*e^(V*x)`.

Using this formula and the initial condition `y(x) = Yo`,

we get `Yo = Yo*e^(V*x)`.

This implies that `e^(V*x) = 1` or `V*x = 0`.

Thus `x = 0` is the only value of x on which `y(x) = Yo` for any value of `V`.

Now, we are given `y(x) = (1 + x^2)/(x^2 + Yo)` which is valid only if `Yo > 0` (as given). We need to find the largest interval on which the solution is defined. This means that we need to find the largest interval of x-values for which the given expression for `y(x)` makes sense. Since the denominator of the expression `y(x) = (1 + x^2)/(x^2 + Yo)` is `x^2 + Yo`, the expression is defined only if `x^2 + Yo > 0`. As `Yo > 0`, this inequality holds for all values of `x`. Thus, the solution is defined for all `x` in the real line. Therefore, the largest interval on which the solution is defined is `(-∞, ∞)`.

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Answer:

25 grams of protein

Step-by-step explanation:

10 grams of protein is in 1 cup of milk.

To understand how many grams of protein are in 0.5 cups of milk, I would need to divide 10 by 2, to get 5.

There are 5 grams of protein in 0.5 cups of milk.

Now if I want to see how many grams of protein are in 2 cups of milk, I would multiply 10 by 2, to get 20.

There are 20 grams of protein in 2 cups of milk.

But, the question is asking for how much protein is in 2.5 cups of milk.

Since we know how much is in 2 cups, and 0.5, we can just add them together, because 2+0.5 is 2.5.

20+5 is 25 grams.

There are 25 grams of protein in 2.5 cups of milk.