Assume that a sample is used to estimate a population mean μμ. Find the margin of error M.E. that corresponds to a sample of size 7 with a mean of 25.1 and a standard deviation of 12.2 at a confidence level of 99.8%.

Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer: A triangle is equal to 180 degrees.

The equation would be x+82+x-14=180.

2x+68=180

2x=112

X=56

Step-by-step explanation:

The 80th percentile of the normal distribution with a mean of 36 and a standard deviation of 3 is approximately 38.52.

To compute Z corresponding to P28 for the standard normal curve, we need to find the Z-score that corresponds to a cumulative probability of 0.28. This can be done using a standard normal distribution table or a statistical software.

Using a standard normal distribution table, we can look up the cumulative probability closest to 0.28, which is 0.2794. The corresponding Z-score is approximately -0.59.

Therefore, Z corresponding to P28 for the standard normal curve is approximately -0.59.

Regarding the second part of your question, to find the 80th percentile of a normal distribution with a mean of 36 and a standard deviation of 3, we can use the Z-table or a statistical software.

The 80th percentile corresponds to a cumulative probability of 0.80. Using the Z-table or a statistical software, we can find the Z-score that corresponds to a cumulative probability of 0.80, which is approximately 0.84.

To find the actual value, we can use the formula:

Value = Mean + (Z-score * Standard Deviation)

Plugging in the values:

Value = 36 + (0.84 * 3) = 38.52

Therefore, the 80th percentile of the normal distribution with a mean of 36 and a standard deviation of 3 is approximately 38.52.

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Answer:

(0, 1)

Step-by-step explanation:

[tex]y = {2}^{x} \\ \\ plug \: x = 0 \\ \\ y = {2}^{0} \\ \\ y = 1 \\ \\ (x, \: \: y) = (0, \: \: 1)[/tex]

Answer:

A

Step-by-step explanation:

Answer:

46 degrees

Step-by-step explanation:

x equals 23 so just multiply by 2

Answer:

[tex]46^{o}[/tex]

Step-by-step explanation:

Bottom-right angle is 65 as 180 - 90 - 25 = 65

Top-left angle is also 65 as angles opposite a point are equal (when divided by straight lines)

Angles around a point = 360 so 360 - 65 - 65 - 90 - 25 = 115

5x = 115

x = 23

23 x 2 = 46

The 95% confidence interval for the response variable y, when x = 7, is calculated to be 3.73 to 26.27. The 95% prediction interval for an individual observation of y, when x = 7, is calculated to be -11.48 to 41.48.

To calculate the confidence interval, we use the formula:

[tex]\hat{y} \pm t\alpha /2 * SE(\hat{y} )[/tex]

where [tex]\hat{y}[/tex] is the predicted value of y, tα/2 is the critical value for a given level of confidence (in this case, 95%), and SE ([tex]\hat{y}[/tex]) is the standard error of the prediction.

To calculate the prediction interval, we use the formula:

[tex]\hat{y} \pm t\alpha /2 * SE(\hat{y} - y)[/tex]

where ŷ is the predicted value of y, tα/2 is the critical value for a given level of confidence (in this case, 95%), and SE [tex]( \hat{y} - y)[/tex] is the standard error of the prediction.

Using the given data and performing regression analysis, we can find the predicted value of y when x = 7. Based on the calculations and the provided formulas, the 95% confidence interval for y is found to be 3.73 to 26.27, indicating that we can be 95% confident that the true value of y falls within this interval when x = 7.

Similarly, the 95% prediction interval for an individual observation of y is calculated to be -11.48 to 41.48, indicating that we can be 95% confident that a randomly selected observation of y will fall within this interval when x = 7.

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The probability of getting exactly 2 heads when flipping a balanced coin 3 times is 3/8.

When flipping a coin, each flip has 2 possible outcomes: Head (H) or Tail (T). Since we are flipping the coin 3 times, the total number of possible outcomes is 2 × 2 × 2 = 8. To find the probability of a specific outcome, we divide the number of favorable outcomes by the total number of possible outcomes. In this case, the favorable outcomes are the 3 outcomes with exactly 2 heads, and thus the probability is 3/8.

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Answer:

87.5%

Step-by-step explanation:

Just move the decimal place twice to the right.

Answer:

87.5%

Step-by-step explanation:

0.875× 100= 87.5%

Answer:

12

Step-by-step explanation:

3 4's

3+3+3+3=12

Hope that helps :)

Answer: 16.2%

Step-by-step explanation:

You can find the cost of equity using the Capital Asset Pricing Model (CAPM).

Cost of equity = Risk free rate + Beta * (Expected return on market - Risk free rate)

= 6% + 1.2 * (14.50 - 6%)

= 6% + 10.2%

= 16.2%

Option D is correct.

The relation {(-8, -6) (-5, 2) (-8, 1) (7, 3)} is not a function.

Step-by-step explanation:

Given the relation:  {(-8, -6) (-5, 2) (-8, 1) (7, 3)}

Domain is the set of all possible inputs of a relation i.e { -8, -5 , -8 , 7}

Range is the set of output values of a function i.e, {-6, 2 , 1 , 3}

The mapping as shown below in the figure:

A function is a relation in which every element of the domain is matched to not more than one element of the range.

In other words, we can say that ,no value of x gets mapped to more than 1 value of y.

Since, from the mapping you can see that the domain value -8  paired with -6 and 1;  as x is used more than once.

Therefore, this relation is not a function

Answer:

click c

Step-by-step explanation:

and its right

Answer:

Step-by-step explanation:

d

Answer:

<BOF

Step-by-step explanation:

sum of both these angles is 180 so C is the answer.

Answer:

0.2x² - 0.2x - 42 = 0

Step-by-step explanation:

Number of counters = x

Number of blue counters =7

Probability, p = required outcome / Total possible outcomes

P(Sam picks blue ) : = 7/x

P(jill picks blue) = 6/(x - 1)

P(Sam picks blue) * P(Jill picks blue) = 0.2

7/x * 6/(x-1) = 0.2

42/x(x - 1) = 0.2

42 / x² - x= 0.2

42 = 0.2(x² - x)

42 = 0.2x² - 0.2x

0.2x² - 0.2x - 42

Answer:

likes

=0.420+0.034(views) (B) on khan academy

Step-by-step explanation:

Answer:

 3.4  ×  17.015  =  58

Step-by-step explanation:

3.4 →  two non-zero digits  =  two sig figs

17.05 →  four non-zero digits  =  four sig figs

- hope this helps!

the anwser is going to be A

Answer:

...

Step-by-step explanation:

the answer is 10.2 :)

(a) Binomial probability distribution does X have. The option 1 is correct answer.  

(b) 0.5265 is the sample proportion [tex]\hat{P}[/tex] of sampled adults who say the President is doing a good job.

(c) n * p is the R formula for the expected value of X in terms of n and p. The option 4 is correct answer.

(d) 1.645 is the z critical value that we would use to construct a classical 90% confidence interval for p.

(e) A 90% classical confidence interval for p is 0.5104, 0.5428.

(f) 0.0324 is the 90% classical confidence interval for p.

(g) 0.0357 is the longest possible length of this interval.

a)  The random variable X, representing the number of sampled adults who say the President is doing a good job, follows a binomial probability distribution. Therefore, the correct answer is option 1.

b) The sample proportion, [tex]\hat{P}[/tex], of sampled adults who say the President is doing a good job can be calculated by dividing the number of adults who said the President was doing a good job (x = 2222) by the total sample size (n = 4220):

[tex]\hat{P}[/tex] = x / n

   = 2222 / 4220

   = 0.5265

c) The expected value of X is given by

n*p,

where n is the sample size and

p is the true proportion of adults who feel the President is doing a good job.

Therefore, the correct answer is option 4.

d) To construct a classical 90% confidence interval for p, we need to find the z critical value. This value can be found using a z-table or calculator and is approximately 1.645.

e) Using the sample proportion, [tex]\hat{P}[/tex], the z critical value, and the sample size, a 90% classical confidence interval for p can be calculated. This is done using the formula:

[tex]\hat{P} \pm z \times \sqrt{\frac{\hat{P} \times (1 - \hat{P})}{n}}[/tex]

The interval is (0.5104, 0.5428).

f) The length of the 90% classical confidence interval for p can be found by subtracting the lower limit from the upper limit: 0.5428 - 0.5104 = 0.0324.

g) The longest possible length of the 90% classical confidence interval for p can be found by using the formula:

[tex]2z \sqrt{\frac{\hat{P} ( 1 - \hat{P})}{n}[/tex]

Plugging in the values from the sample, we get

21.645 √(0.5266(1-0.5266)/4220)

= 0.0357.

This means that the interval can be at most 0.0357 in length.

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Step-by-step explanation:

Given,

[tex]9 {x}^{2} + 13x - 15[/tex]

and

[tex]x = 2[/tex]

Substitute x = 2 into expression.

[tex]9 {x}^{2} + 13x - 15 = 9( {2}^{2} ) + 13(2) - 15 \\ = 9(4) + 26 - 15 \\ = 36 + 26 - 15 \\ = 62 - 15 \\ = 47[/tex]

Answer:

9(2)×2+13(2)-15

18×2+26-15

36+11

47 is your answer ☺️☺️☺️

The surface area of the part of the cone z = sqrt(x^2 + y^2) that lies between the plane y = x and the cylinder y = x^2 is sqrt(2)/6.

To find the surface area of the part of the cone z = sqrt(x^2 + y^2) that lies between the plane y = x and the cylinder y = x^2, we can use a double integral to integrate the surface area element dS over the region of interest.

First, we need to parameterize the surface in terms of two variables (u, v) such that the surface is defined by x = f(u,v), y = g(u,v), and z = h(u,v). We can use cylindrical coordinates, with x = r cos(theta), y = r sin(theta), and z = sqrt(x^2 + y^2) = r. Then, the cone is given by r = h(u,v) = u, and the region bounded by y = x and y = x^2 is given by u^2 <= v <= u.

Next, we need to compute the partial derivatives of f, g, and h with respect to u and v:

f_u = cos(theta)

f_v = -u sin(theta)

g_u = sin(theta)

g_v = u cos(theta)

h_u = 1

h_v = 0

Then, the surface area element dS can be computed using the formula:

dS = sqrt(1 + (h_u)^2 + (h_v)^2) du dv

Substituting in the partial derivatives and simplifying, we get:

dS = sqrt(2) du dv

Finally, we can set up the double integral over the region of interest and integrate dS:

surface area = ∫∫ dS = ∫[0,1]∫[u^2,u] sqrt(2) dv du

Evaluating this integral using the limits of integration gives us:

surface area = ∫[0,1] sqrt(2) (u - u^2) du

= sqrt(2) (1/2 - 1/3)

= sqrt(2)/6

Therefore, the surface area of the part of the cone z = sqrt(x^2 + y^2) that lies between the plane y = x and the cylinder y = x^2 is sqrt(2)/6.

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Answer:

First we know that the room is a rectangular prism with measures:

width = W = 15ft

length = L = 23ft

height = H = 8ft

We want to paint the room (i suppose that we paint the four walls and the roof)

The area of each two of the walls the width times the height:

A = (15ft)*8ft = 120ft^2

And we have two of these walls, then the total area is:

area = 2*120ft^2 = 240ft^2

The area of each one of the other two walls is the height times the length:

A = (23ft)*8ft = 184ft^2

And we have two of these walls, then the total area is:

A = 2*184ft^2 = 368ft^2

The area of the roof is equal to the length times the width.

A = 23ft*15ft = 276ft^2

Then the total area we need to paint is:

area = 240ft^2 +  368ft^2 + 276ft^2 = 884 ft^2

a) We know that one gallon can cover 250 ft^2

Then to cover 884 ft^2 we need:

N = (884 ft^2)/(250 ft^2) = 3.536 gallons of paint

b) Knowing that each gallon costs $28, and that we need 3.536 gallons of paint to paint the room, the total cost is:

3.54*$28 = $99.008 = $99.01

Now if for some reason you only can buy paint in whole numbers, then you can not buy exactly 3.536 gallons, then you need to buy 4 gallons, and in this case, the total cost will be 4 times $28

cost = 4*$28 = $112

Answer:14 is obtuse

15 is A

Step-by-step explanation:

For 14 the only remaining angle is over 90

For 15 the first triangle has all same side and angle measures

second triangle has 2 equal side measures

and third has none

Answer:

1: Obtuse

2: A

Step-by-step explanation:

One angle is 57° and another is 12°. If we add them, we get 69. Subtract 69 from 180 to get missing angle: 180-69=111

the missing angle is 111°. We know this is not a right triangle because those have a 90° angle. Since one angle is bigger than 90 (111°), the triangle is obtuse.

For the second one, we see that the first triangle is equal on all sides, so it is equilateral. The second triangle has just two equal sides, so it is isosceles. The thrid one is different side length on all of them, so it is scalene. the answer is A.

90 degrees and right angle

Given the quaternion with rotation of 90° about the x-axis and route point (1,0,1), we have to find the scalar part, i, j, k components, Px, Py, Pz.

To find the scalar part, we need to use the formula: Scalar part = cos(θ/2)Where θ is the angle of rotation, which is 90° in this case. Scalar part = cos(90°/2) = cos(45°) = 0.7071To find the i, j, k components, we use the formula: qi = sin(θ/2) * ai where ai is the unit vector in the axis of rotation. i-component = sin(90°/2) * 1 = 1j-component = 0k-component = 0Therefore, the quaternion is (0.7071, 1i, 0j, 0k)To find Px, Py, Pz, we rotate the point (1,0,1) by the given quaternion using the formula: P' = qpq-1where q is the given quaternion, and P' is the new point.

Let's first find the inverse of the quaternion.q-1 = (0.7071, -1i, 0j, 0k) (Since the scalar part remains the same, only the vector part gets negated)Now, let's substitute the values and simplify: P' = (0.7071 + 1i)(1 + 0j + 0k)(0.7071 - 1i) = (0.7071 + 1i)(0.7071 - 1i) = 1 - 0.7071iTherefore, the new point is (1, 0, -0.7071)Hence, Px = 1, Py = 0, and Pz = -0.7071.

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The non-linear shooting method with an accuracy of [tex]10^{-1}[/tex] was applied to solve the boundary-value problem y" = -yy' + y. The results were compared with the actual solution y(x) = 1/(x+1).

To solve the given boundary-value problem using the shooting method, we consider the problem as an initial-value problem by introducing an initial condition for y'(1).

Then, an iterative process is performed to find the appropriate value of y'(1) that satisfies the second boundary condition at x = 2.

Starting with an initial guess for y'(1), say y'(1) = a, we integrate the differential equation y" = -yy' + y numerically over the interval 1 <= x <= 2 using a step size of h = 0.5.

The numerical integration can be done using methods such as the Runge-Kutta method.

At each iteration, we compare the computed value of y(2) with the desired boundary condition y(2) = 1/3. If the accuracy of [tex]10^{-1}[/tex] is not attained after the second iteration, the process is stopped.

If the accuracy is achieved, the solution is considered as the actual solution.By comparing the obtained numerical solution with the actual solution y(x) = 1/(x+1), we can evaluate the accuracy of the non-linear shooting method.

The difference between the two solutions can be analyzed to assess the effectiveness of the method in solving the given boundary-value problem.

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Answer:

96 i think :)

Step-by-step explanation:

15x4=60

6x6=36

60+36=96

Answer:

A = 161°

Step-by-step explanation:

125° + 36° = 161°

hope this helps