Angie makes wedding cakes with three tiers. She needs 800 grams of sultanate

The average of children per household is approximately 2.1387931034482758.

What is average ?

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

To compute the average number of children per household, you would add up the total number of children in all the surveyed households and divide that number by the total number of households surveyed. You can use the following formula:

Average = (Sum of (children x frequency)) / (Total number of households surveyed)

Children Frequency Children x Frequency

0         2                 0

1         8                 8

2         10                 20

3         4                 12

4         3                 12

5         2                 10

Sum of (children x frequency) = 8 + 20 + 12 + 12 + 10 = 62

Total number of households surveyed = 2 + 8 + 10 + 4 + 3 + 2 = 29

Average = 62 / 29 = 2.1387931034482758

So the average number of children per household is approximately 2.1387931034482758

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The account increases in value by 1% every quarter, which is equivalent to 1/4% every month.

Savings interest is calculated on a daily basis and deposited into the account on the first day of the next quarter. The interest rate will depend on the balance in the account. Now it's between 3% and 3.5%.

To find the increase in value for an account with an APR of 4% and quarterly compounding, we'll first need to convert the APR to a quarterly interest rate.
1. Divide the APR by the number of compounding periods in a year: 4% / 4 = 1%.
2. The account increases in value by 1% every quarter.

Your answer: a. 1%

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Answer:

If you are looking for d the answer is -32.

Step-by-step explanation:

-5=d/4+3

-3         -3

(4)-8=d/4(4)

-32 =d

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

This is the Taylor series expansion for the function f(x) = x⁴ - 6x² + 1 centered at a = 2.

What is Taylor Series?

In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the derivative of the function at a single point. For most common functions, the function and the sum of its Taylor series near this point are the same.

To find the Taylor series for the function f(x) = x⁴ - 6x² + 1 centered at a = 2, we can use the formula for the Taylor series expansion:

f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ...

First, let's find the values of f(a) and its derivatives at x = a = 2:

f(2) = (2)⁴ - 6(2)² + 1 = 16 - 24 + 1 = -7

f'(x) = 4x³ - 12x

f'(2) = 4(2)³ - 12(2) = 32 - 24 = 8

f''(x) = 12x² - 12

f''(2) = 12(2)² - 12 = 48 - 12 = 36

f'''(x) = 24x

f'''(2) = 24(2) = 48

Now, we can substitute these values into the Taylor series formula:

f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ...

f(x) = -7 + 8(x - 2)/1! + 36(x - 2)²/2! + 48(x - 2)³/3! + ...

Simplifying the terms:

f(x) = -7 + 8(x - 2) + 18(x - 2)² + 8(x - 2)³ + ...

This is the Taylor series expansion for the function f(x) = x⁴ - 6x² + 1 centered at a = 2.

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The ball will hit the ground after approximately 0.14 seconds or 1.86 seconds

To find how long it will take the ball to reach 18 feet, we need to solve the equation h = 18:

-16t²  + 32t + 2 = 18

Simplifying, we get:

-16t²  + 32t - 16 = 0

Dividing by -16:

t²  - 2t + 1 = 0

Factoring:

(t - 1)²  = 0

Taking the square root:

t - 1 = 0

t = 1

Therefore, the ball will reach 18 feet in 1 second.

To find when the ball will be at 10 feet, we need to solve the equation h = 10:

-16t²  + 32t + 2 = 10

Simplifying, we get:

-16t² + 32t - 8 = 0

Dividing by -8:

2t² - 4t + 1 = 0

Using the quadratic formula:

t = (4 ± √(16 - 8)) / 4

t = (4 ± 2) / 4

t = 1 or t = 1/2

Therefore, the ball will be at 10 feet after half a second or 1 second.

To find when the ball will hit the ground, we need to solve the equation h = 0:

-16t² + 32t + 2 = 0

Using the quadratic formula:

t = (-32 ± √(32² - 4(-16)(2))) / 2(-16)

t ≈ 0.14 or t ≈ 1.86

Therefore, the ball will hit the ground after approximately 0.14 seconds or 1.86 seconds (rounded to the nearest hundredth).

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Answer:

Step-by-step explanation:

a1 = 100

r = 1/5

an = 100 (1/5)^(n - 1)

Try it. We have the answer for a_3

a_3 = 100 * (1/5)^(3 - 1)

a_3 = 100 * (1/5)^2

a_3 = 100 * 1/25

a_3 = 4  which is just what the series says should be the answer.

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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The solid line has length and makes an angle with the negative y-axis, the length of the dashed line is l × cos(α).

Given, the solid line has length l and makes an angle α with the negative y-axis. By using trigonometry, we can determine the length of the dashed line using l and α. From the figure, we can see that: cos(α) = length of the adjacent side / length of the hypotenuse cos(α) = length of the dashed line / length of the solid line

Therefore, length of the dashed line = length of the solid line × cos(α)

Substituting the given values, length of the dashed line = l × cos(α)

Therefore, the length of the dashed line is l × cos(α).

The length of the dashed line is l × cos(α).

By using trigonometry, we can determine the length of the dashed line using l and α. From the figure, we can see that: cos(α) = length of the adjacent side / length of the hypotenuse cos(α) = length of the dashed line / length of the solid line. Therefore, length of the dashed line = length of the solid line × cos(α)Substituting the given values, length of the dashed line = l × cos(α).

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The area of the original garden is 7200 square feet.

Given,

a rectangular garden has a length that is twice its width. the dimensions are increased so that the perimeter is doubled and the new shape is a square with an area of 3600 square feet.

we are asked to determine the area of the original garden = ?

let the width be x

and the length be 2x

area of the square = 3600 sq feet

Perimeter of the rectangle = 2(l+b)

⇒ 2(2x+x)

⇒ 2(3x)=6x

area of square = a²

a² = 3600

a = √3600

a = 60

now we get the width = 60

length = 2(60)

= 120

Now calculate the area of the rectangle:

= l×b

= 60 × 120

= 7200

hence we get the area as 7200 square feet.

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The number of adults in the museum, using the fractional value of girls and boys, is 75.

A fractional value refers to a portion of the total value.

A fractional value can be depicted in fractions, decimals, or percentages.

A fractional value can also be represented as a ratio or proportion.

In this situation, the fractional number of adults is determined using subtraction.

The total number of people in a museum = 250

The fraction of girls in the museum = 2/5

2/5 of 250 = 100 girls

The fraction of boys in the museum = 3/10

3/10 of 250 = 75

Alternatively:

2/5 + 3/10 = 7/10

7/10 of 250 = 175

Therefore, the number of adults = 75 [250 - (100 + 75)]

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There are 250 people in the museum.

2/5 of the 250 people are girls.

3/10 out of the 250 people are boys.

The rest of the 250 people are adults.

Work out the number of adults in the museum.

Answer:

x = 22

Step-by-step explanation:

Add the expressions for the angle measures.

5x + (3x + 4) + (3x + 4) + 5x = 360

Combine like terms.

16x + 8 = 360

Subtract 8.

16x = 352

Divide by 16.

x = 22

Answer:

22⁰

Step-by-step explanation:

5x + 3x + 4 + 3x + 4 + 5x = 360⁰

=> 16x + 8 = 360

=> 16x = 360 - 8

=> 16x = 352

=> x = 352/16

=> x = 22

Hence,

Value of x is 22⁰

The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.

How to find the volume of a rectangular prism and pyramid?

The formula for the volume of a rectangular prism is:

Volume = Length * Width * Height

The formula for the volume of a pyramid is:

Volume = (Base Area * Height) / 3

The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.

This is because the volume of a rectangular prism is calculated by multiplying its three dimensions together, whereas the volume of a pyramid is calculated by multiplying the base area by the height and dividing the result by 3.

Hence, the volume of the rectangular prism is greater than the volume of the pyramid with the same height and base. This is because the rectangular prism has additional volume in the form of its width, which the pyramid does not have.

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The type of sampling being used in this scenario is systematic sampling.

Systematic sampling refers to the process of selecting a sample from a population with a specified pattern or system. In this type of sampling, a pattern is determined beforehand, and then data are collected by choosing every n^th individual.

Systematic sampling is useful for large sample sizes since it simplifies the process of data collection. It also ensures that the sample is representative of the entire population, making the results more accurate. This type of sampling is widely used in various fields like research, surveying, and public opinion polling to ensure that the sample is random and unbiased.

In this case, the ushers place a survey card on every sixth seat, which is an example of systematic sampling. Therefore, systematic sampling is the type of sampling being used in this question.

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The 8-puzzle problem can be categorized as a "Pathfinding problem."

The 8-puzzle is a classic problem in artificial intelligence and computer science. It involves a 3x3 grid with eight numbered tiles and one empty space. The objective is to rearrange the tiles from an initial configuration to a goal configuration by sliding them into the empty space.

The reason why the 8-puzzle problem is classified as a pathfinding problem is that it involves finding a sequence of moves or actions to reach a desired state or goal. In this case, the desired state is the goal configuration of the puzzle. The problem requires determining the optimal sequence of moves that lead to the goal state while considering the constraints and limitations of the puzzle.

Pathfinding problems involve finding the shortest or optimal path from a starting point to a goal or destination. In the 8-puzzle problem, the empty space serves as the movable "agent" that can slide adjacent tiles. The objective is to find the shortest sequence of moves or actions to transform the initial configuration into the goal configuration, effectively finding a path to the solution.

Therefore, due to its nature of finding an optimal sequence of moves to reach a goal state, the 8-puzzle problem can be categorized as a pathfinding problem.

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The equation for x for the given expression -1+√3x-8 = 7 is : 9.24.

In order to solve the equation for x we have to isolate variable x, simplify and solve for x.

Let isolate the variable x on one side of the equation.

-1 + √3x - 8 = 7

Simplify the left side by combining the constants:

-9 + √3x = 7

Isolate √3x by adding 9 to both sides:

√3x = 16

Solve for x by dividing both sides by √3:

x = 16/√3

x= 9.237

x = 9.24 ( Approximately)

Therefore the equation is 9.24.

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Answer:0.48

Step-by-step equation:

Option B :The solution for x in the given circle is x = 5 + 2√6 or x = 5 - 2√6 is near to value 5.

In the given figure, we have two tangents and a secant that intersects the circle at points A and B.

By the tangent-secant theorem, we know that the product of the lengths of the secant segment (AX) and the exterior segment (XB) is equal to the product of the lengths of the entire secant (AB) and the interior segment (CX).

So, we have:

AX * XB = AB * CX

Substituting the given values, we get:

(3 + x) * (7 - x) = 5 * 5

Expanding the left side and simplifying, we get:

\(21 - x^2 = 25 - 10x\)

Bringing all the terms to one side and simplifying, we get:

\(x^2 - 10x + 4 = 0\)

Using the quadratic formula, we get:

x = (10 ± √(\(10^2 - 414\))) / (2*1)

x = (10 ± √96) / 2

x = 5 ± 2√6

Therefore, the solutions for x are:

x = 5 + 2√6 or x = 5 - 2√6

So, the answer is (B) 5.

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When a thesis test is being performed for a population mean, the probability of a type II error isn't dependent on the sample mean. Option B is the right answer.

A type II error occurs when a null thesis isn't rejected despite it being incorrect. It's worth noting that the threat of making a type II error is affected by several factors, including the sample size, the true population mean, the position of significance, and the variability of the data.

As a result, the larger the sample size, the lower the threat of making a type IIerror.The true population mean also has an impact on the liability of a type II error. As the difference between the true mean and the hypothecated mean grows, the threat of a type II error decreases.

The position of significance is also pivotal in determining the threat of a type II error. As the significance position increases, the threat of a type II error decreases.

So, the correct answer is B

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Answer:

504 m³

Step-by-step explanation:

The volume of the rectangular prism is V = 504 m³

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

Let the volume of the prism be represented as V

Now , the value of V is

Let the height of the rectangular prism be H = 9 m

Let the length of the rectangular prism be L = 7 m

Let the width of the rectangular prism B = 8 m

where the base area of prism B = L x W = 7 x 8 = 56 m²

Now , the volume of the prism V = B x H

The volume of prism V = 56 x 9 = 504 m³

Hence , the volume of the rectangular prism V = 504 m³

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Note that given the above triangle and exterior angle, the value of x is 28° while the value of the exterior angle is 60° (Option D). This is solved using the exterior angle theorem.

If a triangle side is constructed, the outside angle formed is equal to the sum of the two inside opposing angles.

In this case, the opposing triangles are:

∠PQR = x° and

∠QPR = 60°

While the exterior angle is: (2x+4)°

Given the above theorem,

2x+4 = x + 60
⇒ 2x = 60 -4 (Having collected like terms)

x = 56/2

thus,

x = 28°

Since x is given as approximately 28°

The external angle is given as:

2(28) + 4

⇒ 56 +4

= 60° (Option D)

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Answer: The answer is 121

The determinant of the inverse of matrix A, det(A⁻¹ ), is equal to the reciprocal of the determinant of matrix A, i.e., 1/det(A).

If A is an invertible matrix, then the determinant of A is non-zero, i.e., det(A) ≠ 0.

We know that the determinant of a matrix is related to its inverse by the following equation:

det(A) det(A⁻¹) = det(A A⁻¹) = det(I) = 1,

where I is the identity matrix.

Multiplying both sides of the equation by det(A⁻¹), we get:

det(A⁻¹) = 1/det(A)

Therefore, the determinant of the inverse of matrix A, det(A⁻¹), is equal to the reciprocal of the determinant of matrix A, i.e., 1/det(A).

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It takes approximately 22.4 seconds for the tank to empty.

(a) To find the cross-sectional area of the tank at height y, we note that the tank is conical and use the formula for the area of a circle with radius r: A = πr^2. Since the radius of the tank varies with y, we express it in terms of y using similar triangles:

y / (225 cm) = r / (75 cm)

r = (y/225) * (75 cm)

Substituting this expression for r into the formula for the area, we get:

A(y) = π[(y/225) * (75 cm)]^2

= π(1/3) * y^2 / 4

Simplifying, we get:

A(y) = (π/12) * y^2 / 2

= (π/24) * y^2

Using this expression for A(y), we can write the differential equation for y(t).

(b) Taking the time derivative of the given equation and substituting in A(y) from part (a), we get:

d/dt [y^(3/2)] = -2g(π/24)y^2 / 2.2 cm^2

Simplifying and solving for dy/dt, we get:

dy/dt = - (4/3) * (g/2.2 cm^2) * y^(1/2)

This is a separable differential equation that can be solved by separating the variables and integrating:

∫ y^(-1/2) dy = - (4/3) * (g/2.2 cm^2) ∫ dt

2√y = (4/3) * (g/2.2 cm^2) * t + C

where C is the constant of integration. To determine C, we use the initial condition y(0) = 225 cm:

2√225 = (4/3) * (g/2.2 cm^2) * 0 + C

C = 30 cm

Substituting C into the equation above, we get:

2√y = (4/3) * (g/2.2 cm^2) * t + 30 cm

Squaring both sides and simplifying, we get:

y = [(3/4) * (2.2 cm^2/g)]^2 * (t - (4/3) * (2.2 cm^2/g) * 30 cm)^2

(c) The tank will empty when y = 0. Solving for t, we get:

t = (4/3) * (2.2 cm^2/g) * 30 cm

t ≈ 22.4 s

Therefore, it takes approximately 22.4 seconds for the tank to empty.

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Answer:

It is -5,7

Step-by-step explanation:

The reason is this is because x go's first, which is -5, and y go's second, which   is 7, therefore it's -5,7.

Answer:

-6,4 would be your cup of tea

Answer:

3

Step-by-step explanation:

the graph intersects at (1,3) and its asking for y so its 3

Answer:

put A because if u see that

To find the length of the model, we need to use the given scale, which states that 1 inch on the model represents 1.5 feet in reality.

The length of the actual object is given as 18 feet. Let's calculate the length of the model:

Length of model = Length of actual object / Scale factor

Length of model = 18 feet / 1.5 feet/inch

Length of model = 12 inches

Therefore, the length of the model is 12 inches. Therefore, the correct option is (a) 12 inches.

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Answer: 100 - 76=24

Step-by-step explanation:

Answer:

1) 4

2)I think 2

3)4

4)3

5)2

6)1

7)3

Step-by-step explanation:

1) since the x is to squared it is a quadratic equation

3) A and D have same slope=0.5

others were solved using Excel

Answer:

c

Step-by-step explanation:

Answer:

72.22 inches