Katie has a doll house that is a small model of a real Victorian house. The real house has a rectangular window that measures 65 centimeters long by 45 centimeters wide. The length of the window in Katie's house is 13 centimeters long. How wide is the window in Katie's house?

(a) Consider a regular graph, such as a regular 4-regular graph or a 4-cube. (b) It is not possible to have a graph with the given conditions.(c) It is not possible to have a graph with the given conditions. (d) Such a graph is possible.

(a) To have a graph with 16 vertices where every vertex has degree 4, we would need a total degree of 4 * 16 = 64. However, the total degree must be even since each edge contributes 2 to the total degree. But 64 is an even number, which means such a graph is possible. One way to construct such a graph is to consider a regular graph, such as a regular 4-regular graph or a 4-cube.

(b) In a graph with 15 vertices, if 8 vertices have degree 6, then the total degree would be 8 * 6 = 48. Similarly, if 7 vertices have degree 5, the total degree would be 7 * 5 = 35. However, the total degree must be even, and 48 and 35 are both odd numbers. Therefore, it is not possible to have a graph with the given conditions.

(c) If we have a graph on 14 vertices where every vertex has degree 3 and the shortest cycle has length 6, it implies that there are cycles of length 6 but no cycles of length less than 6. This contradicts the fact that if there is a cycle of length 6, there will also be cycles of length less than 6 (such as 3, 4, and 5). Therefore, it is not possible to have a graph with the given conditions.

(d) To have a graph on 11 vertices where every vertex has a degree of at least 6 and there are no cycles of length 3, we can consider a complete bipartite graph K(6, 5). This graph has 6 vertices of degree 6 and 5 vertices of degree 5. It satisfies the given conditions because every vertex has a degree of at least 6, and there are no cycles of length 3 since it is bipartite. Thus, such a graph is possible.

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Answer: The length of the hypotenuse of the right-angled triangle is 31.62 cm.

Step-by-step explanation:  Given , that the legs of the right-angled triangle are 18 cm and 26 cm

Lets assume that the two sides of the right-angled triangle :

AC = 18 cm , BC = 26 cm

According to Pythagoras Theorem - In a right- angled triangle , the square of the hypotenuse side is equal to the sum of squares of two sides .

Therefore, according to the diagram AB² = AC² + BC²

⇒ AB² =  (18)² + (26)²

⇒ AB² = 324 +676

⇒ AB² = 1000

⇒ AB = √1000

⇒ AB = 31.62 cm

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Answer:

12

Step-by-step explanation:

sum of all angles of triangle =180

3x-12+2x+11x=180

16x-12=180

16x=192

x=12

___________

\( \: \)

\(\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}\)

3x - 12 + 2x + 11x = 180°

16x - 12 = 180°

16x = 180 + 12

16x = 192

x = 192 ÷ 16

x = 12✔ (D.)

Depending on the size and thickness of the box, a certain amount of metal is required to cast a cubical metal box.

Depending on the size and thickness of the box, a certain amount of metal is required to cast a cubical metal box. In general, more metal is required for larger, thicker boxes. One must first calculate the box's volume in order to determine how much metal is required. The box's length, width, and height can be multiplied together to get this. The thickness of the metal must next be determined. The total amount of metal required can be estimated by multiplying the volume of the box by the thickness of the metal once the volume and thickness of the metal have been established. For instance, consider a box with dimensions of 6 inches long, 6 inches wide, and 6 inches high and a metal thickness.

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Answer:

88  rooms

Step-by-step explanation:

444 / 5 = 88.8

Answer:

Programmed

Step-by-step explanation:

Programmed Decisons may be classified as those actions which are routinely carried out or performed based on existing rules and protocol. In programmed decision making, the rules are in place, therefore once the criteria or requirement for which the rule or routine is to be enforced arises, programmed Decisons are made. In the scenario, the superintendent required that a programmed Decison be made in cases or situations where enrollment increases by 35 student beyond capacity, Hence, with this, every time this occurs the additional teachers will be hired.

The given series is an arithmetic series and its sum is 36.4

The summation or sigma notation is used to express long summation into a single formula.

The series, given in a summation notation, is:

     \(\sum\limits^{10}_{n=4} {(0.8n-0.4)}\)

The formula inside the sum notation represent the nth term, a(n).

Let evaluate the terms for some n, starts from n = 4 as indicated by the lower limit of the summation notation:

a(4) = 0.8 (4) - 0.4 = 2.8

a(5) = 0.8 (5) - 0.4 = 3.6

a(6) = 0.8 (6) - 0.4 = 4.4

This form a new arithmetic series, with the first term, let say f(1) =2.8 and common difference, d = 0.8.

The number of terms in this new geometric series is given by the upper and lower limit of the summation notation:

number of terms = 10 - 4 + 1 = 7

Use the sum formula for an arithmetic series,

S(n) = n/2 [2.f(1) + (n - 1) . d]

Substitute n = 7, f(1) = 2.8, and d = 0.8 into the formula:

S(7) = 7/2 [2. (2.8) + (7 - 1) . (0.8)]

S(7) = 36.4

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The probability that a randomly selected score will be between 77 and 83 is 0.2841

The probability that a randomly selected score will be between 77 and 83 can be found using the Z-score formula and the standard normal distribution table.

First, we need to calculate the Z-scores for both 77 and 83 using the formula:

Z = (X - μ)/σ

Where X is the score, μ is the mean, and σ is the standard deviation.

For 77:

Z = (77 - 77.4)/7.8 = -0.05

For 83:

Z = (83 - 77.4)/7.8 = 0.72

Now, we can use the standard normal distribution table to find the probability for each Z-score. The table gives us the area to the left of the Z-score on the standard normal distribution curve.

For Z = -0.05, the probability is 0.4801.

For Z = 0.72, the probability is 0.7642.

To find the probability that a randomly selected score will be between 77 and 83, we need to subtract the smaller probability from the larger probability:

0.7642 - 0.4801 = 0.2841

Therefore, the probability that a randomly selected score will be between 77 and 83 is 0.2841.

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Answer:

C is your best bet i got it good on ed

Answer:

-4.5

Step-by-step explanation:

The dimensions for which the printed area is maximized are 16.432 × 10.954 in².

let the height of the poster = x inches

area of the poster = 180 in²

thus, its width is 180/x inches.

The printed area has a height of x - 3 inches due to the 1-inch bottom margin and 2-inch top margin.

The sides have a margin of 1 inch, so the width of the printed area is:

180/x - 2

the area of printed area A is given by the formula of a rectangle,

A = height × width

A = (x-3)(180/x - 2)

A = 180 - 2x - 540/x + 6

the maximized area is when dA/dx = 0

dA/dx = - 2 - 540(- 1/x²) = 0

540/x² = 2

x = √270

hence height = √270 = 16.432 inches,

and width = 180/√270 = 10.954 inches.

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Answer:

Step-by-step explanation:

(a)

\((A+B)^2=A^2+AB+BA+B^2\\\)

(b)

\((A-kI)^3=A^3-3kA^2+3k^2A-k^3I\)

(c)

\(CA=B\ \Longrightarrow\ C=B*A^{-1}\)

To calculate a three-month moving average for monthly forecasting, you need to follow these steps: Gather the historical data, Determine the time period, Calculate the moving average, Repeat the process.

Gather the historical data: Collect the monthly data for the specific variable you want to forecast. For example, if you want to forecast sales, gather the sales data for the past several months.

Determine the time period: Decide on the time period for your moving average. In this case, it is three months.

Calculate the moving average: Add up the values for the variable you are analyzing over the past three months and divide the sum by three to get the average. This will be your moving average value for the third month.

Repeat the process: Shift the time period by one month and calculate the moving average for the new three-month period. Continue this process for each subsequent month, updating the time period and calculating the moving average accordingly.

For example, let's say you have the following sales data for the past six months:

Month 1: 100 units

Month 2: 120 units

Month 3: 110 units

Month 4: 130 units

Month 5: 140 units

Month 6: 150 units

To calculate the three-month moving average for Month 4, you would add up the sales values for Month 2, Month 3, and Month 4 (120 + 110 + 130 = 360) and divide it by three to get an average of 120 units. Repeat this process for each subsequent month to obtain the moving average values for your forecast.

Note that the number of data points you include in the moving average calculation and the frequency of the data (monthly in this case) can be adjusted based on your specific needs and the nature of the data.

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A after calling the function BUILDMAX-HEAP A=⟨50, 22, 30, 10, 7, 15, 8, 9, 5, 3⟩, A after calling the function HEAPINCREASE-KEY  A=⟨55, 22, 30, 10, 7, 15, 8, 9, 55, 3⟩ and A after calling the function HEAPEXTRACT-MAX(A)  max=55, uses the array A resulted from part 1 A=⟨30, 22, 15, 10, 7, 3, 8, 9⟩.

Given, the array A=⟨30,10,15,9,7,50,8,22,5,3⟩

1. BUILDMAX-HEAP(A) builds the max-heap from array A. It is given by:```
BUILDMAX-HEAP(A)
1 heap-size[A] ← length[A]
2 for i ← ⌊length[A]/2⌋ downto 1
3 do MAX-HEAPIFY(A, i)
```Step 1: Calculate the floor value of length of A/2 = 5.  

Step 2: Build a Max-Heap with the following values, the heap at each step is shown below.

i=5:MAX-HEAPIFY(A, 5).

A=⟨30, 10, 15, 9, 7, 50, 8, 22, 5, 3⟩.

i=4: MAX-HEAPIFY(A, 4).

A=⟨30, 10, 15, 22, 7, 50, 8, 9, 5, 3⟩.

i=3: MAX-HEAPIFY(A, 3).

A=⟨30, 10, 50, 22, 7, 15, 8, 9, 5, 3⟩.

i=2: MAX-HEAPIFY(A, 2).

A=⟨30, 22, 50, 10, 7, 15, 8, 9, 5, 3⟩.

i=1: MAX-HEAPIFY(A, 1).

A=⟨50, 22, 30, 10, 7, 15, 8, 9, 5, 3⟩.

2. HEAPINCREASE-KEY(A,9,55) increases the value of the key at index 9 from 3 to 55, and restores the max-heap property by traversing the tree upwards.

It is given by:```HEAP-INCREASE-KEY(A, i, key)
1 if key < A[i]
2 then error “new key is smaller than current key”
3 A[i] ← key
4 while i > 1 and A[PARENT(i)] < A[i]
5 do exchange A[i] ↔ A[PARENT(i)]
6 i ← PARENT(i)```Step 1: Change the key value of A[9] to 55. A=⟨50, 22, 30, 10, 7, 15, 8, 9, 55, 3⟩.

Step 2: Traverse upwards to restore the Max-Heap property, A=⟨50, 22, 55, 10, 7, 30, 8, 9, 15, 3⟩.

3. HEAPEXTRACT-MAX(A) extracts the maximum element from the max-heap A and restores the max-heap property after extraction.

It is given by:```HEAP-EXTRACT-MAX(A)
1 if heap-size[A] < 1
2 then error “heap underflow”
3 max ← A[1]
4 A[1] ← A[heap-size[A]]
5 heap-size[A] ← heap-size[A] - 1
6 MAX-HEAPIFY(A, 1)
7 return max```Step 1: Extract the maximum element and swap it with the last element. A=⟨15, 22, 55, 10, 7, 30, 8, 9, 3⟩.Step 2: Restore the Max-Heap property, A=⟨55, 22, 30, 10, 7, 15, 8, 9, 3⟩.

Therefore, the answers are:

1. A=⟨50, 22, 30, 10, 7, 15, 8, 9, 5, 3⟩

2. A=⟨55, 22, 30, 10, 7, 15, 8, 9, 55, 3⟩

3. max=55, A=⟨30, 22, 15, 10, 7, 3, 8, 9⟩.

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f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

Answer:

it would take them 143 minutes

The minimum number of coin tosses required to have more than a 50% chance of getting at least one head is two.

The possible outcomes of flipping a coin:

If the coin is flipped more than once, there are only two possible outcomes: H or T, whereby each outcome has a 50% chance of occurring.

So let us say that the coin is flipped twice, we have four possible outcomes:

In this case, the only outcome that do not have at least one head is TT.

In conclusion,  the probability of getting at least one head is 1 - (1/2 x 1/2) = 3/4, or 75% which is greater than 50%

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An equation is formed of two equal expressions. We can get Equation B from Equation A by adding 1 to both the sides of equation A, while the solution of both the equations is 8/3.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

1.) The given equation A can be solved as shown below,

3x – 1 = 7

Add 1 to both the sides of the equation,

3x – 1 + 1 = 7 + 1

3x = 8 {∴ Equation B}

Divide both the sides of the equation by 3,

3x/3 = 8/3

x = 8/3

Thus, the solution of the equation is x=8/3.

2.) We can get Equation B from Equation A by adding 1 to both the sides of equation A, while the solution of both the equations is 8/3.

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Answer:

3

Step-by-step explanation:

distance formula

The present age of Earl is 12 years, Robin is 24 years and Adam is 4 years old.

Let us consider the present age of Earl to be x years.

According to the given question, the present age of Robin is twice that of Earl = 2x

And since it is given that Adam is 8 years younger than Earl, then his age

= x - 8

After 6 years, the age of Earl will be x + 6

Robin's age  will be = 2x + 6

Adam's age will be = x - 8 + 6 = x - 2

According to the given question, Robin's age will be thrice the age of Adam.

Hence, 2x + 6 = 3 (x - 2)

⇒ 2x + 6 = 3x - 6     ⇒ 6 + 6 = 3x - 2x     ⇒ 12 = x

Thus, the present age of Earl is 12 years,

Robin's age = 2x = 2 x 12 = 24 years

Adam's age = x - 8 = 12 - 8 = 4 years

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The number of strips Emma will be able to make 22.5 i.e. 22.

According to question

Total paper = Total strips × size of one

9 = n × 2/5

n = 22.5

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Answer:

61 bales of hay

Step-by-step explanation:

38 + 61 = 99

The measure of the angles of the cyclic quadrilateral are:

Arc PQ = 130

QR = 50°

Arc RS = 70°

∠PSQ = 65°

∠PSB = 65°

∠SBP = 80°

AQS = 30°

PS = 110°

From the figure, the arc PQ is subtended by the angle PAQ.

This means that:

PQ = ∠PAQ

Given that ∠PAQ = 130, it means that:

Arc PQ = 130

The measure of PSQ is then calculated using:

∠PSQ = 0.5 * Arc PQ ----- inscribed angle is half a subtended angle.

This gives: ∠PSQ = 0.5 * 130

∠PSQ = 65°

Hence, the measure of ∠PSQ is 65°

The measure of arc QR

A semicircle measures 180°

Thus:

QR + PQ = 180°

Thus, we get:

QR = 180° - PQ

Substitute 130° for PQ

QR = 180° - 130°

QR = 50°

Hence, the measure of QR is 50°

The measure of arc RS

The measure of arc RS is then calculated using:

∠RPS = 0.5 * Arc RS ----- inscribed angle is half a subtended angle.

Where ∠RPS = 35

So, we have:

35 = 0.5 * Arc RS

Multiply both sides by 2

Arc RS = 70°

The measure of angle AQS

In (a), we have:

∠PSQ = 65°

This means that:

∠PSQ = ∠PSB = 65°

So, we have:

∠PSB = 65°

Next, calculate SBP using:

∠SBP + ∠BPS + ∠PSB = 180° ---- sum of angles in a triangle.

So, we have:

∠SBP + 35 + 65 = 180°

∠SBP + 100 = 180

∠SBP = 80°

The measure of AQS is then calculated using:

AQS = AQB = 180 - (180 - SBP) - (180 - PAQ)

AQS = 180 - (180 - 80) - (180 - 130)

AQS = 30°

The measure of arc PS

A semicircle measures 180°

This means that:

PS + RS = 180°

This gives

PS = 180 - RS

RS = 70

Thus:

PS = 180 - 70

PS = 110°

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The end behavior will be as x approaches infinity, and negative infinity, f(x) approaches infinity.

Function is a type of relation, or rule, that maps one input to specific single output.

The function f(x) is defined as:

→ f(x)= 80x* 2 + 640 - 400x - 52

We need the degree and the leading coefficient to determine the behavior.

Since our leading coefficients has a leading even degree of 5, and a positive number,

The function will Rises to the left and falls to the right.

The end behavior will be as x approaches infinity, and negative infinity, f(x) approaches infinity.

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The batting average of a baseball player is classified as a numeric continuous variable.

A batting average is given by the number of hits divided by the number of at bats, hence it is a numeric value.

The batting average is a real number, hence it is also a continuous variable.

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Answer:

i think it's the answer in the pic I have send you okk see and mark me brainliest answer okk thanks

Given:

Width of the building = 2y

Length of the building = 9y-4

Find-:

Area of building in terms of y.

Explanation-:

The area of a rectangle is:

So the area of the given building is:

Area is:

The expression of area is:

Answer:

Step-by-step explanation:

Image result for Identify the vertex of the following parabola. y = x2 - 4x +1

To find the vertex of a parabola, you first need to find x (or y, if your parabola is sideways) through the formula for the axis of symmetry. Then, you'll use that value to solve for y (or x if your parabola opens to the side) by using the quadratic equation. Those two coordinates are your parabola's vertex.