The proportion of all US adults who eat popcorn when they go to the movie theater is p = 0.87. A random sample of 20 US adults was selected and asked if they eat popcorn when they go to the movie theater. Which of the following is the shape of the sampling distribution of p hat ?

a. The sampling distribution of p hat is approximately Normal because n p = 17.4 greater-than 10.

b. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10, the sampling distribution of p hat is not approximately Normal. The sampling distribution of p hat is skewed right and centered at 0.87.

c. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10 , the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the left.

d. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10, the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the right.

Answer:

Hope this helps :)

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{2}{3}[/tex]

When dividing by a fraction, we just have to multiply by the reciprocal, making the equation:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{2}[/tex]

Then we multiply and end up with:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{2}[/tex] [tex]=\frac{3}{4}[/tex]

Answer:

x = 71

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

then

[tex]log_{4}[/tex] (x - 7) = 3 , then

x - 7 = 4³ = 64 ( add 7 to both sides )

x = 71

Ethical guidelines are established to help professional psychologists maintain Professional behavior.

Professional behavior refers to the conduct and standards expected of psychologists in their professional practice. Ethical guidelines provide a framework that outlines the principles, values, and standards that psychologists should follow in their interactions with clients, colleagues, and the broader community.

These guidelines promote ethical behavior by setting expectations for confidentiality, informed consent, competence, integrity, and avoiding conflicts of interest, among other aspects. They ensure that psychologists prioritize the well-being and rights of their clients, maintain professional boundaries, and uphold ethical standards in research and practice.

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Step-by-step explanation:

Let's start by using the formula for the volume of a cylinder:

V = πr^2h

where V is the volume of the cylinder, r is the radius of the cylinder, h is the height of the cylinder, and π is a mathematical constant (approximately equal to 3.14).

Since we are dealing with a drain pipe, we can assume that the height of the cylinder is fixed and does not change. Therefore, we can rewrite the formula as:

V = πr^2h = Ah

where A is the cross-sectional area of the cylinder.

Now, let's use the given information that the drain pipe can carry 36 litres per second. We know that the volume of water that passes through the pipe in one second is equal to 36 litres. We can therefore write:

36 = Ahv

where v is the velocity of the water flowing through the pipe. Since we are assuming that the height of the cylinder is fixed, we can simplify this equation to:

36 = Av

Now we need to determine the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second. Let's call the new diameter d2 and the old diameter d1. We can set up a proportion to solve for d2:

A1/A2 = d1^2/d2^2

We know that A1 and A2 are proportional to the volumes of water the pipe can carry, so we can write:

A1/A2 = 36/60

Simplifying this equation, we get:

A1/A2 = 3/5

Substituting in the formula for the cross-sectional area of a cylinder, we get:

πd1^2/4 / πd2^2/4 = 3/5

Simplifying further, we get:

d1^2/d2^2 = 3/5

Taking the square root of both sides, we get:

d1/d2 = sqrt(3/5)

Now we can solve for d2:

d2 = d1 / sqrt(3/5)

We want to know the percentage increase in the diameter, which we can find using the formula:

% Increase = (New Value - Old Value) / Old Value x 100%

Substituting in our values, we get:

% Increase = (d1 / sqrt(3/5) - d1) / d1 x 100%

Simplifying, we get:

% Increase = (1 / sqrt(3/5) - 1) x 100%

Using a calculator, we get:

% Increase ≈ 34.64%

Therefore, the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is approximately 34.64%.

y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job

x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).

y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.

y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.

y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.

y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.

Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

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The function [tex]f(x) = \sqrt[3]{2x-1}[/tex] is a cubic root function with a linear transformation applied.

The expression inside the root, 2x-1, is a linear function that scales and shifts the input x. The cubic root function then takes the cube root of the result.

This function is defined for all real numbers x, as the cubic root can be calculated for any real number.

Its graph is a transformed version of the standard cubic root function, skewed and shifted depending on the coefficients in the linear function. The function increases monotonically as x increases, and it is continuous and differentiable everywhere.

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The Complete Question

[tex] f(x)=\sqrt[3]{2x-1}[/tex]

Identify this function and solve

Hello!

Answer:

No

Explanation:

A statistical question is answered by collecting data that exhibits variability

[tex]\Huge \fbox{Answer = No}[/tex]

Statistical questions are open ended questions that are created to gather information or data about a population or a sample. Depending on the population or sample being investigated, they often involve variability and can have a variety of possible responses.

Because it is a straightforward factual question that can be answered with a single value, the question being asked is not a statistical one.

There are 1,760 yards in a mile, hence the answer to this question is an exact number. There is no variability or data gathering involved with this response. As a result, the question is not a statistical question.

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A. A graph of the function is shown in the image below.

B. The illumination in foot-candles that the object receives at a distance of 20-feet from the light source is

C. In the context of the problem, a meaningful domain is {x | x ≤ 0} and a meaningful range is {y | y ≥ 0}.

In this exercise, we would plot the illumination on the y-axis (y-coordinates) of a graph while the square of the distance would be plotted on the x-axis (x-coordinate) of a graph on a coordinate plane.

Part B.

The illumination in foot-candles that this object would receive at a distance of 20-feet from the light source can be calculated by substituting the value of d, which is 20 feet into the function as follows;

I(d) = 4500/d²

I(20) = 4500/20²

I(20) = 4500/400

I(20) = 11.25 foot-candles.

Part C.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, 0] ∪ [0, ∞] or {x | x ≤ 0}.

Range = [0, ∞] or {y | y ≥ 0}

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If the events A and B are mutually exclusive, meaning they cannot occur simultaneously, then the probability of both events occurring together is zero. In this case, the formula simplifies to P(A or B) = P(A) + P(B).

The probability that either event A or event B will occur can be calculated using the addition rule of probability. According to this rule, the probability of either event A or event B occurring is equal to the sum of the individual probabilities of each event minus the probability of both events occurring together.

In other words, P(A or B) = P(A) + P(B) - P(A and B)



However, if the events A and B are not mutually exclusive, then the probability of both events occurring together needs to be subtracted from the sum of their individual probabilities to avoid double-counting.

So, the final answer to the question "What is the probability that either event will occur?" depends on the specific probabilities of events A and B and whether they are mutually exclusive or not.

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Answer:

D

Step-by-step explanation:

To reach this, you would divide both by half.

8.5 ÷ 2= 4.25

11 ÷ 2= 5.5

therefore, D

Answer:

B: 2/9

Step-by-step explanation:

There are a total of 9 bills in Scott's pocket, and he has 2 five dollar bills.

This means that the probability of pulling out a 5 dollar bill is 2/9.

The correct comparison symbol from the drop-down box is,

⇒ 0.67 = 0.670

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

To compare between 0.67 and 0.670

Now, We know that;

The value of zero after any number in decimal expression has neglect.

So, By definition of decimal numbers, we get;

The correct comparison symbol from the drop-down box is,

⇒ 0.67 = 0.670

Hence, The correct comparison symbol from the drop-down box is,

⇒ 0.67 = 0.670

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Then you can state that angle DEF is congruent to angle GHJ.

The postulate or theorem that allows you to state that angle DEF is congruent to angle GHJ is the Angle-Angle (AA) Postulate.

This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles must also be congruent.

In this case, if you have two triangles, one with angles DEF and the other with angles GHJ, and

you know that angle D is congruent to angle G and angle E is congruent to angle H, then by the AA Postulate, you can conclude that angle F is congruent to angle J.

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Based on the provided information, we can say that Kibo has a volume of approximately 54.01 cubic meters.

To compare the volume of Kibo, Destiny, and Columbus, we need to calculate the volumes of each module.

The volume of a chamber can be determined utilizing the equation V = πr^2h, where r is the span and h is the level (or length for this situation) of the chamber.

For Kibo:

Radius (r) = 2.2 meters

Length (h) = 11.2 meters

V_kibo = π * (2.2^2) * 11.2

      = 4.84 * 11.2

      ≈ 54.01 cubic meters

For Destiny and Columbus, we would need their respective dimensions to calculate their volumes using the same formula.

Destiny is a U.S. laboratory module on the International Space Station. It is a multi-sided module, so we would need the measurements of each side to calculate its volume.

Columbus is a European laboratory module, which is also multi-sided.

Without the specific dimensions of Destiny and Columbus, we cannot accurately compare their volumes to Kibo. However, based on the provided information, we can say that Kibo has a volume of approximately 54.01 cubic meters.

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Answer:

[tex]q=4, x=-1[/tex]

Step-by-step explanation:

The given equation is:

[tex]2(3+x)=3q-3+5x---(1)[/tex]

Since [tex]x=q-5[/tex] is a solution of the equation above, so substitute x=q-5 into (1) as follows:

[tex]2(3+q-5)=3q-3+5(q-5)\\2(q-2)=3q-3+5q-25\\2(q-2)=8q-28\\q-2=4q-14\\4q-q=-2+14\\3q=12\\q=4[/tex]

Then, it follows:

[tex]x=q-5\\\therefore x=4-5=-1[/tex]

The value of all the expression which have x = 5 asymptotes are,

⇒ g (x) = 3 log (x - 5)

⇒ g (x) = log₁₀ (- x + 5) -  4

⇒ f (x) = (3x + 20) / (x - 5)

We have to given that,

All the expressions are,

⇒ g (x) = 3 log (x - 5)

⇒ f (x) = √(x - 5) + 2

⇒ h (x)= eˣ⁻⁵

⇒ g (x) = log₁₀ (- x + 5) -  4

⇒ h (x) = - ∛(x - 5) + 1

⇒ f (x) = (3x + 20) / (x - 5)

Now, We can check all the expressions for which have x = 5 asymptotes.

Hence, We can substitute x = 5 in each expression and check all expression as which are not defined at x = 5,

⇒ g (x) = 3 log (x - 5)

Substitute x = 5;

⇒ g (x) = 3 log (5 - 5)

⇒ g (x) = 3 log (0)

Which is undefined.

⇒ f (x) = √(x - 5) + 2

Substitute x = 5;

⇒ f (x) = √(5 - 5) + 2

⇒ f (x) = 2

Which is defined.

⇒ h (x)= eˣ⁻⁵

Substitute x = 5;

⇒ h (x)= e⁻⁵

Which is defined.

⇒ g (x) = log₁₀ (- x + 5) -  4

Substitute x = 5;

⇒ g (x) = log₁₀ (- 5 + 5) -  4

⇒ g (x) = log₁₀ (0) -  4

Which is undefined.

⇒ h (x) = - ∛(x - 5) + 1

Substitute x = 5;

⇒ h (x) = - ∛(5 - 5) + 1

⇒ h (x) =  1

Which is defined.

⇒ f (x) = (3x + 20) / (x - 5)

Substitute x = 5;

⇒ f (x) = (3x + 20) / (5 - 5)

⇒ f (x) = (15 + 20) / (0)

Which is undefined.

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The shortest tour from A to B to C and back to A is 50 km.

We have,

A to Zoo and Port and back to A: 10 km

B to Park and Zoo and back to B: 12 km

C to Port and Park and back to C: 13 km

Zoo to Park and Port and back to Zoo: 15 km

To calculate the shortest tour from A to B to C and back to A, we can add up the distances between each pair of stations:

A to Zoo and Port and back to A (10 km)

Zoo to Park and Port and back to Zoo (15 km)

B to Park and Zoo and back to B (12 km)

C to Port and Park and back to C (13 km)

So, Total distance: 10 + 15 + 12 + 13 = 50 km

Therefore, the shortest tour from A to B to C and back to A is 50 km.

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Answer:60

Step-by-step explanation: because I Maltiply 6 by 6 times

The measure of BC is 48x - 168.

In the given diagram of triangle BCD, we are told that E is the midpoint of BD and F is the midpoint of CD. Let's denote the measure of BC as y.

Since E is the midpoint of BD, we can say that BE = ED. Similarly, F is the midpoint of CD, so CF = FD.

Using the information given, we can write the equation EF = -9x + 82. Since F is the midpoint of CD, we can substitute FD for EF, so FD = -9x + 82.

Also, we know that BC = 80 - 6x.

In triangle BCD, we can write the equation BC = BE + EF + FD.

Substituting the given values, we have:

80 - 6x = (BE) + (-9x + 82) + (-9x + 82).

Simplifying the equation:

80 - 6x = BE - 9x + 82 - 9x + 82.

Combining like terms:

80 - 6x = BE - 18x + 164.

Moving the variables to one side and constants to the other side:

6x - BE + 18x = 164 - 80.

Combining like terms:

24x - BE = 84.

Rearranging the equation:

BE = 24x - 84.

Since E is the midpoint of BD, we can write:

BE = BD/2.

Substituting the value of BE:

BD/2 = 24x - 84.

Simplifying the equation:

BD = 48x - 168.

We are required to find the measure of BC, which is y. From the equation BC = BD, we have:

y = 48x - 168.

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Answer:

There are 47.2242 miles in 76 kilometers.

1.6 km = 1 mile

76 km = 76/1.6 = 47.5 mile

There are 47.5 miles in 76 kilometers.

The value of x, applying the trigonometric ratios, is given by the following option:

B) 8.0.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

For this problem, we have that side x is opposite to the angle of 28º, while the hypotenuse has a length of 17.

Hence the length x is obtained as follows:

sin(28º) = x/17

x = 17 x sine of 28 degrees

x = 8.

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Answer:

undefined

Step-by-step explanation:

To find the slope of the line passing through the points (4, 7) and (4, -6), we can use the slope formula:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the coordinates of the points (4, 7) and (4, -6) into the formula:

m = (-6 - 7) / (4 - 4)

m = (-13) / (0)

The denominator is zero, which means the line is vertical and parallel to the y-axis. When the denominator is zero, the slope is undefined.

Therefore, the line passing through the points (4, 7) and (4, -6) has an undefined slope.

A. A table of values and graph of the function is shown below.

B. The object would hit the ground at approximately 8.963 seconds.

Based on the information provided, we can logically deduce that the height (s) in meters, of this object above the​ ground is related to time by the following quadratic function:

s(t) = -4.9t² +39.2t + 42.3

When t = 0, s(t) is given by;

s(0) = -4.9(0)² +39.2(0) + 42.3

s(0) = 42.3

When t = 1, s(t) is given by;

s(1) = -4.9(1)² +39.2(1) + 42.3

s(1) = 76.6

When t = 2, s(t) is given by;

s(2) = -4.9(2)² +39.2(2) + 42.3

s(2) = 101.1

Therefore, the table can be created as follows;

Time (t)     Height s(t)

0                  43.3

1                   76.6

2                  101.1

3                  115.8

4                  120.7

5                  115.8

Part B.

Generally speaking, the height of this object would be equal to zero (0) when it hits the ground. By critically observing the graph (see attachment), we can logically deduce that the object would hit the ground at approximately 8.963 seconds.

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The non-linear graph of the function y = -(x - 1)² + 1. is given by the image presented at the end of the answer.

We have to look at the graph of the function relative to the x-axis, as follows:

The function has a maximum point at (1,1), meaning that:

Considering the end behavior of the function, that it goes to negative infinity at both tails of the graph, a function that satisfies these features is given as follows:

y = -(x - 1)² + 1.

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The value of angle C is calculated by applying cosine rule as  50.67 ⁰.

The value of angle C is calculated by applying cosine rule as shown below;

c² = a² + b² - 2ab cosC

The given parameters in the diagram;

length a = 22

length b = 18

c = 20

The value of angle C is calculated as;

20² = 22² + 18² - (2 x 22 x 18) cos C

792 cos C = 502

cos C = 502/792

cos C = 0.6334

C = arc cos (0.6334)

C = 50.67 ⁰

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From the graph, we can calculate that 6 seconds after the ball is thrown, it will be 20 meters from the ground again.

The equation is as follows:

d = d0 + v0 * t - (1/2) * g * t²

d =  distance from the ground

d0 = the initial height

v0 =  initial velocity

g  =  acceleration due to gravity = 9.8 m/s²

t=  time

20 = 20 + 15 * t - (1/2) * 9.8 * t^2

We simplify as follows:

0 = -4.9 * t² + 15 * t

We then go ahead to solve  this quadratic equation to find the values of t when the ball is 20 meters from the ground again.

t * (-4.9t + 15) = 0

t = 0 or

-4.9t + 15 = 0.

-4.9t + 15 = 0

-4.9t = -15

t = 3.06 seconds

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The choice of measure depends on the characteristics of the data and the purpose of the analysis.

The measure commonly used to describe the center of the data is the arithmetic mean or average. The arithmetic mean is calculated by summing all the data points and dividing the sum by the total number of data points. It provides a representative value that balances the contributions of all the data points.

Another measure of center is the median, which represents the middle value when the data is arranged in ascending or descending order. Unlike the mean, the median is not affected by extreme values or outliers, making it a robust measure of central tendency.

Additionally, there is the mode, which represents the most frequently occurring value in the dataset. It can be useful in cases where identifying the most common observation is important.

Each measure has its strengths and limitations, and researchers need to consider the nature of the data and the research question at hand to determine the most appropriate measure of center

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The angle the vector v, that has components of 9,6 makes with the x- axis is 33.7°

The angle of a vector with x and y components (x,y) is given by

Ф = tan⁻¹(y/x)

Given that vector v has components of 9,6. To determine the angle, Ф, in degrees , that vector v makes with the x-axis, we proceed as follows.

We know that the components of the vector are (9,6) which means that

So, we have that

So, substituting the values of the variables into the equation, we have that

Ф = tan⁻¹(y/x)

Ф = tan⁻¹(6/9)

Ф = tan⁻¹(2/3)

Ф = tan⁻¹(0.6667)

Ф = 33.69°

Ф ≅ 33.7°

So, the angle is 33.7°

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The value of x in the proportion is -9.

To solve the proportion [(3/4) is to -6] is to [(3/4) is to 3] is to x = [(3/4) is to -9], we can cross-multiply and solve for x.

Starting with the left side of the proportion:

[(3/4) is to -6] is to [(3/4) is to 3]

Cross-multiplying:

(3/4) * 3 = (3/4) * (-6)

Simplifying:

9/4 = -18/4

Now, moving to the right side of the proportion:

[(3/4) is to -9]

Cross-multiplying:

x * (3/4) = (3/4) * (-9)

Simplifying:

(3/4) * x = -27/4

To solve for x, we can multiply both sides of the equation by the reciprocal of (3/4), which is 4/3:

(4/3) * [(3/4) * x] = (4/3) * (-27/4)

Simplifying:

x = -9

Therefore, the value of x in the proportion is -9.

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The equation of the graph is,

⇒ y = 6x + 2

Since, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

For each by sitting job. Adam charges a fee for his bus fare plus an hourly rate.

And, The graph shows how he calculates the cost of a babysitting job.

Now, By graph;

Two points on the line are (1, 8) and (2, 14).

Now,

Since, The equation of line passes through the points (1, 8) and (2, 14).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (14 - 8)) / (2 - 1)

m = 6 / 1

m = 6

Thus, The equation of line with slope 6 is,

⇒ y - 8 = 6 (x - 1)

⇒ y - 8 = 6x - 6

⇒ y = 6x + 2

Therefore, The equation of line will be;

⇒ y = 6x + 2

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