In a survey, the planning value for the population proportion is p* = 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.02? Round your answer up to the next whole number. How large a sample should be selected to provide a 95% confidence interval with a margin of error of 2? Assume that the population standard deviation is 30. Round your answer to next whole number.

Answer:

Mean = 125.136

Median = 110

Mode = 180

Step-by-step explanation:

Given the data:

75 95 180 136 89 75 110 180 100 136 180 95 180 136 75 100 110 180 180 136 75 90

Frequency distribution:

Value(X) ___freq (F) ____cumm frequency

85 _________ 4 _______ 4

89 _________ 1 _______5

90 __________1 _______6

95 __________2 ______ 8

100 _________ 2 ______10

110 __________2______ 12

136 __________4 _____ 16

180 __________6______22

2) Using the frequency distribution :

Mean = Σfx / Σf

[(85*4) + (89*1) + (90*1) + (95*2) + (100*2) + (110*2) + (136*4) + (180*6)]/ 10

= 2753 / 22

= $125.136

Median of grouped data :

Frequency + 1 / 2 = 23/2 = 11.5 th term

The median value = $110

Mode of the data:

Most frequently occurring = 180 (frequency of 6)

The mean of the frequency distribution is $125.136, the median of the frequency distribution is $110, and the mode of the frequency distribution is $180.

Given :

a) The frequency distribution is given below:

Prices              Frequency       Cumulative Frequency

85                           4                                 4

89                            1                                 5

90                            1                                  6

95                            2                                  8

100                           2                                 10

110                            2                                  12

136                            4                                 16

180                            6                                 22

b) The mean is calculated as:

\(\rm Mean = \dfrac{85\times4 + 89\times1 +90\times1 +95\times 2+100\times2 +110\times2 +136\times4 +180\times6 }{10}\)

Simplify the above expression.

Mean = $125.136

c) The median of the frequency distribution is calculated as:

\(\rm Term= Frequency + \dfrac{1}{2}=11.5\)

So, the median is $110.

The mode of the frequency distribution is $180.

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Shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

First, we graph the lines y = -x-2 and y = -5x+2 using their y-intercepts and slopes.

The line y = -x-2 has a y-intercept of -2 and a slope of -1, which means that for every increase of 1 in x, y decreases by 1.

The line y = -5x+2 has a y-intercept of 2 and a slope of -5, which means that for every increase of 1 in x, y decreases by 5.

The shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.

Hence, shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.

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Answer:

To enlarge a triangle by a scale factor of 1/2 with the center (2, 0), each vertex of the triangle should be multiplied by 1/2 and then shifted so that the center of the new triangle is (2, 0).

Step-by-step explanation:

For example, if the original triangle has vertices at (a, b), (c, d), and (e, f), the vertices of the new triangle would be at ((a-2)/2 + 2, (b-0)/2 + 0), ((c-2)/2 + 2, (d-0)/2 + 0), and ((e-2)/2 + 2, (f-0)/2 + 0).

The radius of the truncated cone ,if a sphere with radius 20 is inscribed in it and one of the base has 23 radius is 1.6 units.

Let's denote the radius of the smaller base of the truncated cone as r, and the radius of the larger base as R. Also, let's denote the height of the truncated cone as h.

The sphere with radius 20 is inscribed in the truncated cone, which means it touches the three surfaces of the cone: the smaller base, the larger base, and the lateral surface.

The distance from the center of the sphere to the larger base of the cone =  (radius of the sphere) + (height of the smaller cone that sits on top of the larger cone). This smaller cone is similar to the original cone and has height h/3, radius r, and volume (1/3)πr^2*(h/3).

Similarly, the distance from the center of the sphere to the smaller base of the cone = (radius of the sphere) + (height of the larger cone that sits below the smaller cone). This larger cone is similar to the original cone and has height (2/3)h, radius R, and volume (1/3)πR^2(2h/3).

Since the sphere is inscribed in the truncated cone, the sum of the volumes of the two similar cones equals the volume of the truncated cone. Therefore:

(1/3)πr² * (h/3) + (1/3)πR² * (2h/3) = (1/3)π(R² + r² + Rr) * h

Simplifying, we get:

r² + Rr + R² = (5/4)*20²

r² + Rr + R² = 500

Now, we know that the radius of one of the bases is 23, so let's assume that R = 23. Then, we can solve for r:

r² + 23r + 23² = 500

r² + 23r - 231 = 0

Solving for r using the quadratic formula, we get:

r = (-23 ± √(23² + 41231)) / 2

r ≈ -24.6 or r ≈ 1.6

Since the radius of the base must be positive, we take r ≈ 1.6 as the solution. Therefore, the radius of the other base is approximately 1.6 units.

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Answer:

C. He uses the coffers of the ceiling to place Jesus in the mathematical center, and to create an illusion that extends the room beyond what is visible.

Step-by-step explanation:

See attached. We can see that this option is the best as it reflects what we can see in the painting.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

c

Step-by-step explanation:

false

because they have different variables, they are different terms. if they were both 4y and 4y or 4x and 4x then they would be like terms. but here, they are not.

i hope this helps!

Answer: B.False

Step-by-step explanation:This is because 4 x and 4 y have different terms.4 x has the term x while 4y has the term y.

Hope it helps . :)

[ -8, 2 ] [ -6 , 0 ] [ -4 , - 2 ] are probability of the cards into three pairs with the same total .

What is probability?

( -8 ) + 0 + ( - 6) + 2 + ( -4 ) + ( -2 )   =   -20 + 2 = -18

                                                              { addition of negative numbers }

So, each pair  =  -18 / 3  = -6  { division }

so the pairs are = [ -8, 2 ] [ -6 , 0 ] [ -4 , - 2 ]

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The statement that identifies and explains lim x f(x) is "The limit lim f(x) does not exist because there is oscillating behavior around x = 0."In general, a function f(x) has a limit at x = c if and only if the function approaches the same value L no matter what direction x comes from.

A limit can be determined by evaluating the function at x values very close to c, either from the right or from the left. If both the left-hand and right-hand limits exist and are equal, then the function has a limit at x = c. However, if the left-hand and right-hand limits do not exist or are not equal, then the function does not have a limit at x = c.In this case, the statement "The limit lim f(x) does not exist because there is oscillating behavior around x = 0" identifies and explains lim x f(x).

This is because the graph has oscillating behavior as x approaches 0, and the left-hand and right-hand limits do not exist or are not equal.

Therefore, lim x f(x) does not exist.

The other statements are not correct because they do not accurately describe the behavior of the function near x = 0.

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To show that the general term of the quadratic number pattern is given by \(tn = n^2 + 4n - 12\) , we need to find a quadratic expression that fits the given pattern.

Let's examine the given sequence: -7, 0, 9, 20. We notice that each term is increasing by a certain amount.

First, let's find the differences between consecutive terms:
0 - (-7) = 7
9 - 0 = 9
20 - 9 = 11

We observe that the differences between consecutive terms are not constant, so this indicates that the sequence is not linear.

To determine if the sequence follows a quadratic pattern, let's find the second differences:
9 - 7 = 2
11 - 9 = 2

The second differences are constant, which suggests a quadratic pattern.

Now, let's find the quadratic expression. We know that the general term of a quadratic sequence can be written as \(tn = an^2 + bn + c\), where a, b, and c are constants to be determined.

Using the given terms, we can form three equations:

1.\(For n = 1: -7 = a(1)^2 + b(1) + c\)
2. \(For n = 2: 0 = a(2)^2 + b(2) + c\)
3.\(For n = 3: 9 = a(3)^2 + b(3) + c\)

Simplifying these equations, we get:
1. a + b + c = -7
2. 4a + 2b + c = 0
3. 9a + 3b + c = 9

Solving this system of equations, we find a = 1, b = 4, and c = -12.

Therefore, the general term of the quadratic number pattern is given by\(tn = n^2 + 4n - 12\).

The general term of the quadratic number pattern is \(tn = n^2 + 4n - 12\).

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Answer:

28.4 kg

Step-by-step explanation:

F = ma

F is 25 N and a is 0.88 m/s^2

25 = 0.88m

Divide both sides by 0.88

m = 28.4 kg

The mass of an object is 28.4 kg.

It is required to find the mass of an object.

The capacity to do work or cause physical change; energy, strength, or active power. The push or pull on an object with mass causes it to change its velocity. Force is an external agent capable of changing a body's state of rest or motion. It has a magnitude and a direction.

Given:

Net force = 25 N

Acceleration=0.88 m/s^2

According to given question we have,

F = ma

25 = 0.88m

Divide both sides by 0.88

m = 28.4 kg

Therefore, the mass of an object is 28.4 kg.

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Answer:

x < 3.89

Step-by-step explanation:

12.99x < 50.50

Divided by 12.99 into both sides, and you get

x < 3.89

So, the answer is x < 3.89

The manager can see the eight applicants in 40,320 different ways.

The number of ways the manager can see the eight applicants, one after another, equals the number of permutations of eight objects taken at a time. The given problem depends on a number of arrangements we can make for the applicants to give interviews one by one, which can be calculated as follows:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320

In 40320 ways the applicants are able to give the interview. Therefore, the manager can see the eight applicants in 40,320 different ways.

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Answer: 169

Step-by-step explanation:

It is true that a multiple linear regression model interprets the slope differently than a simple linear regression model.

The link between two variables is determined through simple linear regression. The slope of a straight line used to represent linear regression indicates how changing one variable impacts another variable.

For the complex relationships between data, multiple linear regression is used. More than one variable may contribute to the explanation of this relationship.

One y-intercept and numerous slopes (one for each variable) make up a multiple regression formula. The formula is understood in the same way as a simple linear regression formula, however more than one variable influences the relationship's slope.

Therefore, the statement is true.

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Answer:

200,000 cubic milliliters

Step-by-step explanation:

PLEASE MARK BRAINLIEST

The solution to the given non-homogeneous differential equation, y'' + 3y' - 4y = \(5e^(^-^4^x^)\), using the superposition approach is y(x) = y_h(x) + y_p(x).

To solve the given non-homogeneous differential equation, we use the superposition approach, which involves finding the general solution to the associated homogeneous equation (y_h(x)) and a particular solution to the non-homogeneous equation (y_p(x)).

We start by setting the right-hand side of the equation to zero: y'' + 3y' - 4y = 0. This is the associated homogeneous equation. We assume a solution of the form y(x) = \(e^(^r^x^)\), where r is a constant to be determined. Substituting this into the equation, we obtain the characteristic equation \(r^2\) + 3r - 4 = 0.

Solving this quadratic equation, we find two distinct roots: r1 = 1 and r2 = -4. Therefore, the general solution to the homogeneous equation is y_h(x) = C1\(e^(^x^)\)+ C2\(e^(^-^4^x^)\), where C1 and C2 are arbitrary constants.

We look for a particular solution in the form y_p(x) = A\(e^(^-^4^x^)\), where A is a constant to be determined. Substituting this into the non-homogeneous equation, we obtain -16A\(e^(^-^4^x^)\) + 3(-4A\(e^(^-^4^x^)\)) - 4A\(e^(^-^4^x^)\) = 5\(e^(^-^4^x^)\). Simplifying this equation, we find -27A\(e^(^-^4^x^)\)= 5\(e^(^-^4^x^)\).

Equating the coefficients of \(e^(^-^4^x^)\) on both sides, we get -27A = 5. Solving for A, we find A = -5/27. Therefore, a particular solution is y_p(x) = (-5/27)\(e^(^-^4^x^)\).

Finally, we combine the general solution (y_h(x)) and the particular solution (y_p(x)) to obtain the complete solution to the non-homogeneous differential equation. Therefore, y(x) = y_h(x) + y_p(x) = C1\(e^(^x^)\)+ C2\(e^(^-^4^x^)\) - (5/27)\(e^(^-^4^x^)\), where C1 and C2 are arbitrary constants.

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The utility functions in options a, b, c, and f are not risk-averse on the interval [a,b], while the utility functions in options d and e are risk-averse on the interval [a,b].

In economics and finance, risk aversion refers to a preference for less risky options over riskier ones. Utility functions are mathematical representations of an individual's preferences, and they help determine whether someone is risk-averse, risk-neutral, or risk-seeking. A risk-averse individual would have a concave utility function, indicating a decreasing marginal utility of wealth.

For options a, b, c, and f, the utility functions are and f(x) = -ln(x), g(x) = \(-e^(^-^x^)\), h(x) = \(-4x^2\) - 10x, respectively. These utility functions do not exhibit concavity, which means they are not risk-averse. Instead, they either show risk-seeking behavior (options a and b) or risk-neutrality (options c and f).

On the other hand, options d and e have utility functions f(x) = ln(x), g(x) = 1/(e^(2x)), h(x) = \(-x^2\) + 10,000x and f(x) = ln(-2x), g(x) = -1/(\(e^(^2^x^)\)), h(x) = \(x^2\) - 100,000x, respectively. These utility functions display concavity, indicating a decreasing marginal utility of wealth. Thus, options d and e can be considered risk-averse on the interval [a,b].

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Answer:

11 m= 3      12 slope is 4 and y intercept is 2

Step-by-step explanation:

11 slope = gradient of a line                            formulae        y2-y1  / x2 - x1  

12-6 / 4-2 =3                                

12 slope is the gradient so and is found as m in the equation y=mx + c

so 4 is the slope and the y intercept is where x= 0 so y = 2

Answer:

------------------

Use circumference formula:

Find the radius by rearranging the formula and substituting 32 for C:

Answer:

5.09 in

Step-by-step explanation:

We know that the formula to find the circumference of a circle is:

C = 2πr

Here,

C → Circumference → 32 in

r → radius

Let us find the radius of the circle by substituting the given values.

\(\sf C = 2\pi r\\\\\sf 32 = 2\pi r\\\\Divide\:both\:sides\:by\:2 \pi \:and\:make\:r\:the \:subject\\\\\dfrac{32}{2 \pi} =\dfrac{2 \pi r}{2 \pi} \\\\\red{5.09 \:in=r}\)

Answer:

7.5

Step-by-step explanation

Answer:

Addition Property of Equality to add 18 to both sides.

Step-by-step explanation:

Remember that with the properties of equality the goal is to perform the inverse operation.

Answer:

Step-by-step explanation:

we konw the speed of burn is 1.25 inchs per hour. so, the left candle is

15-1.25t. the answer is L=15-1.25t

Answer:

109

Step-by-step explanation:

9 + |-78| - (-22)

Apply the absolute value which states |-x| = x.

9 + 78 - (-22)

Apply the rule that states x - (-y) = x + y.

9 + 78 + 22

Add 9 and 78.

87 + 22

Add 87 and 22.

109.

Answer:

No solutions

Step-by-step explanation:

Step 1: Write out equation

10 + 5c = 5c

Step 2: Subtract 5c on both sides

10 + 5c - 5c = 5c - 5c

10 ≠ 0

Since 10 doesn't equal 0, we do not have a solution for this equation.

Answer:

no solutions

Step-by-step explanation:

Let's solve your equation step-by-step.

10+5c=5c

Step 1: Simplify both sides of the equation.

5c+10=5c

Step 2: Subtract 5c from both sides.

5c+10−5c=5c−5c

10=0

Step 3: Subtract 10 from both sides.

10−10=0−10

0=−10

Answer:

There are no solutions.

HOPE THIS HELPS!!!!!! :)

<3333333333

Step-by-step explanation:

a number to a negative power is the same as 1/(base).

Answer:

The answer is 16 :) hope it helps even tho its late

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Answer:

Line 3

Step-by-step explanation:

The problem's lines are:

Line 1. 5(x - 5) = 15

Line 2. 5x - 25 = 15

Line 3. 5x - 25 = 15 - 25

Line 4. 5x = -10

Line 5. 5x/5 = -10/5

Line 6. x = -2

The first error is in Line 3, where 25 was subtracted from just the right side, and where 25 should have been added to both sides instead.