Enlarge the house using a scale factor of 1 : 2.

Answer:

$9

Step-by-step explanation:

It would cost $36. It is $3 for 4 avocados, so you would need to find out how many packs of 4 you would need. To do that, you do 12 divided by 4 which is 3. Then, to figure out the total cost, you would do 3 times 3 which is 9.

The Chebyshev inequality tells us that P(|Z| >= 0.95) is less than or equal to 1.109.

Chebyshev's inequality, also known as the Bienaymé-Chebyshev inequality, establishes in probability theory that, for a large class of probability distributions, no more than a specific percentage of values can deviate significantly from the mean.

According to the Chebyshev inequality, for any random variable with expected value μ and variance σ², the probability that the random variable deviates from its expected value by a certain amount or more is bounded.

In this case, we have a standard normal variable Z with expected value μ = 0 and variance σ² = 1 (since it is a standard normal variable).

The Chebyshev inequality states that for any k > 0,

P(|Z - μ| >= kσ) <= 1/k².

In our case, we want to find P(|Z| >= 0.95), which can be written as P(|Z - μ| >= 0.95σ) since the expected value μ is 0.

Substituting k = 0.95 and σ = 1 into the inequality, we have:

P(|Z - 0| >= 0.95 * 1) <= 1/0.95².

Simplifying further,

P(|Z| >= 0.95) <= 1/0.9025.

Calculating the value,

P(|Z| >= 0.95) <= 1.109.

Therefore, the Chebyshev inequality tells us that P(|Z| >= 0.95) is less than or equal to 1.109.

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In a Compton scattering experiment, the scattered photon moves in a direction different from the incident photon. It scatters at an angle relative to the incident direction.

In Compton scattering, the incident X-ray photon transfers energy and momentum to the electron it interacts with. As a result, both the electron and the scattered photon change their direction and energy.

When the incident X-ray photon strikes the initially at rest electron, it transfers some of its energy and momentum to the electron. This interaction causes the electron to gain energy and be accelerated in the same direction as the incident photon.

Simultaneously, the scattered photon, which retains some of its energy, moves in a direction different from the incident photon. The angle at which the scattered photon deviates from the incident direction is known as the scattering angle.

The scattered photon's direction depends on the interaction between the X-ray photon and the electron, and it can vary based on factors such as the energy of the incident photon and the scattering angle. The phenomenon of Compton scattering provides valuable insights into the behavior of X-rays and their interactions with matter.

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The statement "If dy/dt=f(t)g(y), the equilibrium solutions can be obtained by finding the solutions to f(t)=0" is not entirely correct.

In a differential equation of the form dy/dt = f(t)g(y), the equilibrium solutions are the constant solutions where dy/dt = 0. These occur when g(y) = 0.

To find the equilibrium solutions, we need to solve g(y) = 0. Once we have found these solutions, we can determine their stability by analyzing the sign of f(t) near these equilibrium values. If f(t) is positive near an equilibrium value, the solution is unstable (i.e., solutions near the equilibrium will move away from it). If f(t) is negative near an equilibrium value, the solution is stable (i.e., solutions near the equilibrium will move towards it).

So, while f(t) = 0 may be useful in some cases for finding equilibrium values, it is not the correct approach for finding all equilibrium solutions in a differential equation of the form dy/dt = f(t)g(y). The equilibrium solutions are found by solving g(y) = 0.

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The cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

A Cartesian equation is essential in mathematics. It corresponds to a mathematical formula that expresses the connection between elements as a function of their positions on a plane known as Cartesian.

A two-dimensional coordinate scheme called the Cartesian plane employs a horizontal x-axis and an upward y-axis to identify locations in space.

Given that, \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\).

So, \(csc\hspace{0.1cm}\theta=cosec \hspace{0.1cm}\theta\).

The equation becomes as follows:

\(r=2cosec\hspace{0.1cm} \theta\)

By using the trigonometric equation \(cosec\hspace{0.1cm} \theta=\frac{1}{sin\hspace{0.1cm}\theta}\), we get

\(r= \frac{2}{sin \hspace{0.1cm} \theta}\)

Multiplying both sides by \(sin\hspace{0.1cm}\theta\), we get

\(r \hspace{0.1cm}sin\hspace{0.1cm}\theta =2\hspace{0.1cm}\frac{sin\hspace{0.1cm}\theta}{sin\hspace{0.1cm}\theta}\)

\(rsin\hspace{0.1cm}\theta=2\)

By the parametric equations \(x=rcos\hspace{0.1cm}\theta\) and \(y=rsin\hspace{0.1cm}\theta\), we get

\(y=2\)

It is a horizantal line.

Hence, the cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

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The cartesian equation for the curve is: y = 2 This is a horizontal line passing through the point (0,2).

To find a Cartesian equation for the curve given by the polar equation r = 2 csc(θ), we will convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the following relationships:

x = r * cos(θ)
y = r * sin(θ)

Step 1: Express r in terms of θ
r = 2 csc(θ)

Step 2: Since csc(θ) = 1 / sin(θ), rewrite the equation as
r = 2 / sin(θ)

Step 3: Express x and y in terms of r and θ
x = r * cos(θ)
y = r * sin(θ)

Step 4: Substitute r from Step 2 into the y equation
y = (2 / sin(θ)) * sin(θ)

Step 5: Simplify the equation
y = 2

The Cartesian equation for the given polar equation is y = 2, which represents a horizontal line passing through the point (0, 2).

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Answer:

¼x+2 pencils

Step-by-step explanation:

¼ of (x+8)pencils

¼×(x+8)

¼x+2

Answer:

3

Step-by-step explanation:

By angle bisector property:

\( \frac{6}{x} = \frac{8}{4} \\ \\ \frac{6}{x} = 2 \\ \\ x = \frac{6}{2} \\ \\ x = 3\)

The value of given triangle of x is 3.

Angle bisector theorem states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle. An angle bisector is a ray that divides a given angle into two angles of equal measures.

We have the given triangle is:

The triangle is ABC

and divide into two parts.

Triangle ADC and Triangle CBD.

The value also given in the figure.

AB = 6

BC = 8

AD = x

DC = 4

We have to find the value of x:

By using the Angle bisector theorem :

\(\frac{AB}{AD} =\frac{BC}{DC}\)

Plug all the values in above formula:

\(\frac{6}{x}=\frac{8}{4}\)

=> 6/x = 2

x = 6/2

x= 3

The value of given triangle of x is 3

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Load vs deformation behavior of wet-mix and dry-mix shotcrete with different reinforcement can be summarized as follows:

Load vs Deformation Behavior of Wet-mix Shotcrete:

- Wet-mix shotcrete exhibits a gradual increase in load with deformation.

- The initial stiffness is relatively low, allowing for greater deformation before reaching its peak load.

- Wet-mix shotcrete tends to exhibit more ductile behavior, with a gradual post-peak load decline.

- The reinforcement in wet-mix shotcrete helps in controlling crack propagation and enhancing overall structural integrity.

Load vs Deformation Behavior of Dry-mix Shotcrete:

- Dry-mix shotcrete exhibits a relatively higher initial stiffness, resulting in less deformation before reaching the peak load.

- It typically shows a brittle behavior with a rapid drop in load after reaching the peak.

- The reinforcement in dry-mix shotcrete primarily helps in preventing the formation and propagation of cracks.

When to Use Wet-mix Shotcrete:

- Wet-mix shotcrete is commonly used in underground construction, such as tunnel linings and underground mines.

- It is suitable for applications where greater flexibility and ductility are required, such as seismic zones or areas with ground movement.

When to Use Dry-mix Shotcrete:

- Dry-mix shotcrete is often used in above-ground applications, such as architectural finishes, structural repairs, and protective coatings.

- It is preferred in situations where rapid strength development is required, as it typically achieves higher early strength than wet-mix shotcrete.

- Dry-mix shotcrete can be used in areas where a more rigid and less deformable material is desired, such as in structural elements subjected to high loads.

Therefore, wet-mix and dry-mix shotcrete exhibit different load vs deformation behavior due to their distinct mixing and application methods. Wet-mix shotcrete offers greater ductility and deformation capacity, making it suitable for applications with dynamic loading or ground movement.

On the other hand, dry-mix shotcrete provides higher early strength and is preferred for applications requiring rapid strength development or where rigidity is essential. The choice between wet-mix and dry-mix shotcrete depends on the specific project requirements, structural considerations, and the anticipated loading conditions.

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The equation of the curve in the XY-plane that passes through (0,3) and whose tangent line at a point (x,y) has slope 2x/y^2 is y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant.

The equation of a curve in the xy-plane is given by F(x,y) = 0. To find such a curve that passes through the point (0,3) and whose tangent line at a point (x,y) has a slope of 2x/y^2, we can use the method of implicit differentiation.

First, we can find the equation of the tangent line at a point (x,y) on the curve by computing the derivative of F(x,y) with respect to x and setting it equal to 2x/y^2. This gives us:

F_x(x,y) = 2x/y^2

Next, we can use the fact that the curve passes through the point (0,3) to set up the following equation:

F(0,3) = 0

Solving for F(x,y) in terms of x and y and substituting in the equation for F_x(x,y) gives the implicit equation of the curve is

y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant

This is the equation of a curve in the XY-plane that passes through the point (0,3) and whose tangent line at a point (x,y) has a slope of 2x/y^2.

Therefore, The equation of the curve in the XY-plane that passes through (0,3) and whose tangent line at a point (x,y) has slope 2x/y^2 is y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant.

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The given trigonometric identity is true.

The given trigonometric identity is:csc A - sin A cos A cot ATo prove this identity, we need to manipulate the left-hand side (LHS) of the identity to obtain the right-hand side (RHS) of the identity. LHS = csc A - sin A cos A cot A(1 / sin A) - sin A (cos A / sin A) (cos A / sin A)1 / sin A - cos^2 A / sin^2 A1 / sin A - (1 - sin^2 A) / sin^2 A1 / sin A - 1 / sin^2 A + 1= (1 + sin A cos A) / sin A cos A= (sin A / sin A cos A) + (cos A / sin A cos A)= cot A + csc A. Therefore, LHS = cot A + csc A = RHS. Hence, the given trigonometric identity is true.

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Answer:

8th generation: 34 relatives

9th generation: 55 relatives

Step-by-step explanation:

Fibonacci sequence is a sequence that is in such a manner that each number will be the sum of the two preceding ones.

Thus, to get how many relatives in the 8th generation, we will need to add the number of relatives in both the 6th and 7th generation.

We are given number of relatives in the 6th and 7th generation as 13 and 21 relatives respectively.

Thus;

No. of relatives in 8th generation = 13 + 21 = 34 relatives

Similarly;

No. of relatives in 9th generation is = no. in 7th generation + no. in 8th generation = 21 + 34 = 55 relatives

An equation of the tangent line to the curve \(x e^y+y e^x=4\) at the point (0, 4) is \(y=-(4+e^4) x+4\).

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  \(\left.y^{\prime}\right|_{x=0, y=4}\) as-

Consider the given equation;

\(x e^y+y e^x=4\)

Differentiate both side with respect to x;

\(\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}\)

Now apply product rule;

\(\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}\)

Applying exponential and power rule;

\(\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}\)

Solve the value of y'

\(y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}\)

Now, find the value of slope m.

\(m=\left.y^{\prime}\right|_{x=0, y=4}\)

\(\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4\)

Now, using the point-slope formula, obtain the line equation as follows.

\(\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}\)

Therefore, an equation of the tangent line to the curve is   \(y=-(4+e^4) x+4\).

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You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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Answer:

204

Step-by-step explanation:

3.4[6(4)+6^2]=

3.4[24+36]=

3.4[60]=

204

Hope this helps!

The simplified form of the expression is, negative five sixths times x plus eight.

What is word problem?

A math word problem is a mathematical question that is stated as one sentence or more and asks students to use their arithmetic skills in a "real-life" situation. Therefore, in order for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Given that:   quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity

It can be write in mathematical form as,

\((-\frac{2}{3}x-6) - (-14+\frac{1}{6}x)\)

Simplifying the parenthesis,

\(= -\frac{2}{3}x-6+14-\frac{1}{6}x\\ = 8 - \frac{15}{18}x\\ = 8 - \frac{5}{6}x\\= -\frac{5}{6}x+8\)

Hence, the simplified form of the expression is, negative five sixths times x plus eight

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Answer:

= 6/7x+2

Step-by-step explanation:

just remove the parenthesis and combine like terms.

i hope this helps :)

Answer:

Step-by-step explanation:

Combine like terms.

2/7x and 4/7x are like terms  

5 and -3 are like terms

\((\frac{2}{7}x + 5) + (\frac{4}{7}x - 3) = \frac{2}{7}x+ \frac{4}{7}x + 5 - 3\\\\\\ = \frac{2+4}{7}x+ 2 \\\\= \frac{6}{7}x+2\)

The smallest possible increase in the money supply is 0.2 times the initial deposit.

To calculate the largest and smallest possible increases in the money supply, we need to consider the required reserve ratio.

The required reserve ratio is the portion of deposits that banks are required to hold as reserves and not lend out. If the required reserve ratio is 20 percent, it means that banks must hold 20 percent of the deposits and can lend out the remaining 80 percent.

To calculate the largest possible increase in the money supply, we assume that all deposits are lent out and that there are no excess reserves. In this case, the money supply can increase by a maximum of 1/required reserve ratio.

Largest possible increase in the money supply = 1 / required reserve ratio

= 1 / 0.2

= 5

Therefore, the largest possible increase in the money supply is 5 times the initial deposit.

To calculate the smallest possible increase in the money supply, we assume that banks hold the entire required reserve ratio as reserves and do not lend out any additional money.

Smallest possible increase in the money supply = required reserve ratio * initial deposit

= 0.2 * initial deposit

Therefore, the smallest possible increase in the money supply is 0.2 times the initial deposit.

Please note that the values provided in the answer are placeholders and should be replaced with the actual values or variables from your specific context to obtain accurate results.

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Answer:

y=5x

Step-by-step explanation:

If y is 25 and x is 5

25 = 5 (5)

25=25

The function in vertex form that models the path of the stream is:

\(y = (-5/9)(x - 3)^2 + 5\)

A location where two or more straight lines or curves intersect is referred to as a vertex . A vertex in geometry is sometimes referred to as a corner or an intersection point. The phrase is frequently used to refer to the highest or lowest point on a curve or surface, the place where two lines intersect to make an angle, and the point where two sides of a polygon meet.

The vertex form of the equation of a parabola is given by:

\(y = a(x - h)^2 + k\)

where (h, k) represents the vertex of the parabola.

Using the given vertex and the point (6,0), we can find the value of "a" and plug it into the vertex form to get the equation of the parabolic path of the water stream.

Step 1: Find the value of "a"

Since the vertex is (3,5), we know that:

h = 3

k = 5

Using the point (6,0), we can find the value of "a" as follows:

\(0 = a(6 - 3)^2 + 5\)

\(0 = 9a + 5\)

\(9a = -5\)

\(a = -5/9\)

Step 2: Plug in the values of h, k, and a into the vertex form:

\(y = (-5/9)(x - 3)^2 + 5\)

Therefore, the function in vertex form that models the path of the stream is:

\(y = (-5/9)(x - 3)^2 + 5\)

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1. Multiply the value of the house by the percent:

250,000 x 0.9 = 225,000

Divide the amount the owner insured by the clause amount:

191,250/225,000 = 0.85

Multiply that by the amount of damage:

0.85 x 80,000 = 68,000

They will receive $68,000

2. Follow the same steps as above:

180,000 x 0.75 = 135,000

101,250 / 135,000 = 0.75

0.75 x 50,000 = 37,500

They will receive $37,500

Answer:

1. They will receive $72,000 in insurance.

2. They will receive $37,500 in insurance.

Step-by-step explanation:

1.Given that the coinsurance is 90 percent.

For the fire that caused a $80,000 in damage, 90 percent of $80,000 will be received in insurance.

90 percent of $80,000 will be received in insurance

90 percent of $80,000 = 0.9 * 80000

= 72,000

Therefore, they will receive $72,000 in insurance

2. The coinsurance is 75 percent, given that they have a loss that results in a $50,000 claim.

they will received 75 percent of $50,000

75 percent of $50,000 = 0.75 * 50000

= 37.500

Therefore, they will receive $37,500

Answer:

The total monthly rent for these three stores is $8,786.25.

Step-by-step explanation:

The monthly cost for a square foot of rental space in each city is as follows:

    Place            Monthly Cost for a Square Foot

Los Angeles                      $5.75

San Francisco                    $6.95

    Seattle                           $4.25

It is also provided that the store in Los Angeles will be 580 square feet, the store in San Francisco will be 500 square feet, and the store in Seattle will be 465 square feet.

Compute the total monthly rent for these three stores as follows:

Total Monthly Rent = Monthly Cost for a Square Foot × Area

                                \(=(5.75\times580)+(6.95\times500)+(4.25\times465)\\\\=3335+3475+1976.25\\\\=8786.25\)

Thus, the total monthly rent for these three stores is $8,786.25.

The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

From the question, we have the following parameters that can be used in our computation:

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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Applying the midpoint formula, the coordinates of the other endpoint are: (-9, -13).

The midpoint formula, which can be used in determining the coordinates of the midpoint between two endpoints is usually expressed as: M[(x1 + x2)/2, (y1 + y2)/2].

Given the following coordinates:

Midpoint of GH --> m(-13/2,-6) = (x, y)

One endpoint ---> G(-4, 1) = (x1, y1)

The other endpoint ---> (x2, y2)

Plug in the values into the formula used in calculating the midpoint:

m(-13/2,-6) = [(-4 + x2)/2, (1 + y2)/2]

Solve for x2

-13/2 = (-4 + x2)/2

-13/2 × 2 = -4 + x2

-13 = -4 + x2

-13 + 4 = x2

-9 = x2

x2 = -9

Solve for y2

-6 = (1 + y2)/2

2(-6) = 1 + y2

-12 = 1 + y2

-12 - 1 = y2

-13 = y2

y2 = -13

Thus, using the midpoint formula, the coordinates of the other endpoint are: (-9, -13).

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The comparision between decimal number are 1.9 = 1.90, 0.05 < 0.2, 3.88 < 6.38

Suppose that the number is abcd.efg and belongs to the decimal numerical system.

Therefore, one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.

Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.

Here we can see that

1.9 = 1.90

0.05 < 0.2

3.88 < 6.38

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It is most likely that John and Dawn live in a "married couple with children" household. They have been married for over 20 years and have three children residing with them in their home in Northville, MI.

John and Dawn have been married for over 20 years and have lived in their home in Northville, MI with their three children for most of those years. To determine the type of household they live in, we can consider the various household classifications provided by the Census Bureau.

Married couple with children: This classification applies to households where a married couple resides with one or more children who are under the age of 18. Since John and Dawn have three children, it is possible that they fall under this category.

Married couple without children: This classification includes households where a married couple resides without any children under the age of 18. However, since John and Dawn have three children, this classification is not applicable to their situation.

Single-parent household: This classification applies when a single parent resides with one or more children under the age of 18. Since John and Dawn are married, this classification is not relevant in their case.

Other household types: There are several other household types defined by the Census Bureau, such as multi-generational households, unmarried partner households, and non-family households. However, based on the given information, none of these classifications seem to apply to John and Dawn's situation.

Considering the information provided, it is most likely that John and Dawn live in a "married couple with children" household. They have been married for over 20 years and have three children residing with them in their home in Northville, MI.

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x     4      3     2      1

f      3      5     4      2

Total number of scores in table are ∈ f =  3 + 5 + 4 + 2 = 14

According to the question, given that

x     4      3     2      1

f      3      5     4      2

Total number of scores are ∈ f =  3 + 5 + 4 + 2 = 14

Therefore, after sum of score we get total number of scores is 14

The average or computed center value of a group of values is known as the mean, and it is used to determine the central tendency of the data. The entire collection of data or distribution is identified by a single number using the statistical metric known as central tendency.

We can use the direct technique, the assumed mean method, or the step deviation method to determine the mean of grouped data. The frequency of several observations or variables that are combined together is the subject of the mean of grouped data. Let's examine each of these approaches in turn.

Direct Method

The direct approach is the most straightforward way to determine the mean of the grouped data. The mean of the data is given by, if the values of the observations are x1, x2, x3, and x4 and their associated frequencies are f1, f2, f3, and f4, respectively.

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Answer:

2

Step-by-step explanation:

(8, 11)

(- 3, - 11)

Rate of change m = \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\) = \(\frac{-11-11}{-3-8}\) = 2

Answer:

2 irdk but i hope it help

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The probability mode for the given value is created. The expected value and standard deviation of prospective winnings are -$0.28 and $18.33. The expected value and standard deviation if the game is played five times are -$1.40 and $40.99. The probability that the person running the game makes a profit is 0.561.

Probability is a way to determine how likely something is to happen. It is computed by dividing the frequency of the event by the total number of outcomes. The formula then becomes P(X) = frequency of the event÷total number of outcomes.

The product of the probabilities determines the likelihood that two or more occurrences will coincide. This is given by, P(A and B) = P(A)P(B).

a) To create a probability model follow the steps. Let X is an occurrence of an event.  The table is attached here.

b)  The expected value is calculated using the formula, E(X) = μ = ∑ x P(x).

\(\begin{aligned}E(X)=\mu&=x_1p_1+x_2p_2+x_3p_3\\&=40\left(\frac{1}{6}\right)+0\left(\frac{5}{36}\right)+(-10)\left(\frac{25}{36}\right)\\&=-\$ 0.28\end{aligned}\)

Also,

\(\begin{aligned}E(X^2)&={x_1}^{2}p_{1}+{x_2}^{2}p_{2}+{x_3}^{2}p_{3}\\&=(40)^2\frac{1}{6}+(0)\frac{5}{36}+(-10)^2\frac{25}{36}\\&=(1600)\frac{1}{6}+(0)\frac{5}{36}+(100)\frac{25}{36}\\&=266.67+69.44\\&=336.11\end{aligned}\)

And the standard deviation is calculated using the formula, σ=√Var[X].

\(\begin{aligned}\sigma=\sqrt{\text{Var}(X)}&=\sqrt{E(X^2)-E(X)^2}\\&=\sqrt{336.11-0.08}\\&=\sqrt{336.03}\\&=\$18.33\end{aligned}\)

c) The expected value and standard deviation for playing the game 5 times are calculated as follows.

The expected value is,

\(\begin{aligned}5\times E(X)&=5(-\$0.28)\\&=-\$1.40\\\end{aligned}\)

The standard deviation is,

\(\begin{aligned}\sigma&=\sqrt{5\times\tex{Var}(X)\\&=\sqrt{5\times336.03\\&=\sqrt{1680.15}\\&=\$40.99\end{aligned}\)

d) The dice rolling is random and the winning chance is independent. The probability the person running the game makes a profit (P(x<0)) is given by,

The population mean, μ(Y) = -$0.28

The standard deviation for a population of 100 is,

\(\begin{aligned}\sigma&=\sqrt{\frac{\text{Var}(X)}{n}}\\&=\frac{18.33}{\sqrt{100}}\\&=1.83\end{aligned}\)

The z-score for mean winning is,

\(\begin{aligned}z&=\frac{x-\mu}{\sigma}\\&=\frac{0-(-0.28)}{1.83}\\&=0.153\end{aligned}\)

For a person to make a profit, the mean winning of the player should be less than the z-score. Then,

The P-value from the z-table, P(z<0.153)=0.5608

The answer is 0.561.

The complete question is -

You pay $10 and roll a die. If you get a 6, you win$50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What’s the probability the person running the game makes a profit?

To know more about z-score:

https://brainly.com/question/15016913

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Answer:The lateral surface area of the triangular prism will be 84 square feet.correct option is D.

What is the surface area of the triangular prism?Let the sides of the triangle be a, b, c, and a height of H. Then the surface area of the prism is given as SA = H(a + b + c)A triangular prism has bases with three congruent sides, each measuring 4 feet. The height of each triangle is approximately 3.5 feet.The distance between the triangular bases is 7 feet.Then the lateral surface area will beSA = 7 (4 + 4 + 4)SA = 7 x 12SA = 84 square feet. the correct option is D

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

We know the first term and common difference so we can write the explicit formula. The formula is:

aₙ = a₁ + (n - 1)d

aₙ = 8 + (n - 1) * 3

aₙ = 3n + 5

This means that a₁₆ = 3 * 16 + 5 = 53

by using the formula for arithmetic sequence, the 16th term of the progression can be obtained. Given A1 = 8 and d = 3,

A16=A1 + (n-1) d

A16=8 + (16-1) (3)

A16 = 53

I hope I helped! Be safe!