Let B = (Bt)tzo be a standard Brownian motion. For any À 0, define the process B = (B)t>0 by B = Bx²t, t≥ 0. Show that B is also a standard Brownian motion.

A graph G(k, n) with a fixed k will have an Euler cycle if n is an even number, ensuring that all vertices have an even degree and the graph is connected.

An Euler cycle, also known as an Eulerian circuit, is a path in a graph that traverses each edge exactly once and returns to its starting point. Let's assume that an undirected graph represented as G(k, n) with k representing the number of vertices and n being the degree of each vertex.

For a graph to have an Euler cycle, it must satisfy two conditions: (1) The graph must be connected, meaning there are no isolated vertices, and (2) all vertices in the graph must have an even degree. The degree of a vertex is the number of edges connected to it.

As your question asks for the values of n for which kn has an Euler cycle, it's important to note that k is fixed, and n will determine whether the graph has an Euler cycle. Since all vertices must have an even degree, it's clear that n must be an even number. Therefore, the values of n for which kn has an Euler cycle are even numbers (e.g., 2, 4, 6, 8, etc.).

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Answer:

y=1/4x-5

Step-by-step explanation:

y=mx+b is slope intercept form

m is slope

b is y intercept

we know m is 1/4 so we fill it in

y=1/4x+b

fill is the coordinates to find b

-3=1/4(8)+b

-3=2+b

-2. -2

-5=b

place b in

y=1/4x-5

hopes this helps

Answer:y=1/4x-5

Step-by-step explanation:

Your point was (8,-3) and your rise is 1 and your run is 4 so if you want to get from 0 to 8 and count by 4 you need to move twice, and if you established that you will move twice then you need a number that you add 2 to that will give you -3. And that number is -5 so your y-intercept is

Answer:

Step-by-step explanation:

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

14 students walk

Step-by-step explanation:

40 total

22 girls

18 boys - 7 boys who cycle = 11 boys - 6 who take the bus. That leaves 5 boys who walk.

9 girls walk

5 + 9 = 14 total.

Order the negative rational numbers from least to greatest.

To order negative rational numbers from least to greatest, we need to convert them into a common denominator. First, we need to find the least common multiple (LCM) of the denominators. Then, we can convert each fraction into an equivalent fraction with the LCM as the denominator.

Finally, we can compare the numerators to determine their order. If the numerators are the same, we can compare the denominators to break the tie. Once we have ordered the fractions, we can simplify them if necessary. If any of the fractions are mixed numbers, we need to convert them into improper fractions before finding the LCM and ordering them.

It is important to keep in mind that when ordering negative rational numbers, the least number is the one that is furthest to the left on the number line, while the greatest number is the one that is furthest to the right.

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Answer:

16%

Step-by-step explanation:

Blue = 6

Green = 7

Purple = 5

Red = 4

Orange = 3

25 Students in total

Probability of Red = 4/25

Or 16/100

16%

Answer:

Probability of Red = 4/25

Step-by-step explanation:

Hope it helps!!!

Transformation of each of the numbers in a normal frequency distribution curve affects the mean, the median, and the shape of the frequency distribution curve. The mean and the median double, and the shape becomes wider.

The number of the curve and the effect of the transformation on the curve depends on the specific transformation. The effects of adding or subtracting a constant from each of the numbers are that the mean and the median shift by the same amount, while the shape remains the same. When multiplying or dividing each of the numbers by a constant, the shape becomes wider or narrower, respectively. In addition, the mean and the median are also multiplied or divided by the constant.

A transformation of the numbers in a normal frequency distribution curve changes the values of the data but does not change the shape of the curve. Therefore, the shape stays the same. When adding or subtracting a constant from each of the numbers, the mean and the median of the data also shifts by the same amount. This is because the value of each of the numbers changes by the same constant. However, when multiplying or dividing each of the numbers by a constant, the shape of the curve becomes wider or narrower, respectively. Additionally, the mean and the median are also multiplied or divided by the constant.

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The value of f left parenthesis 3 right parenthesis is 45.

According to the statement

We have given that the F(x) = 5(x)^2

and we have to find the value when Sophia have a 3 right parenthesis.

So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.

And now we have to find the value for 3 right parenthesis

And for this purpose we have to put the value X= 3 in the f(x) then

F(x) = 5(x)^2

F(3) = 5(3)^2

F(3) = 5*9

F(3) = 45.

here the value of 3 right parenthesis is 45.

So, The value of f left parenthesis 3 right parenthesis is 45.

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Answer:

D

Step-by-step explanation:

We will need to use the compound interest formula:

A = P(1 + r)ⁿ

A = final amount

P = Initial amount

r = rate

n = time applied

Our equation will then look like this

A = 500(1.05)⁸

A = 738.72772

Step-by-step explanation:

Note: I could not find any attached table of values, however, we can make do with the information given

step one:

the cost of sign up = $4

the cost of download for each song= $0.5

Step two:

Required

we want to find the cost of downloading any number of songs.

let the number of songs be x

and let the total cost be y

Hence the cost function is

y=0.5x+4

now supposing the value of x which is the number of downloads from the table is 10, then the total cost for 10 downloads will be

y=0.5(10)+4

y=5+4

y=9

Hence it will cost $9 to download 10 songs, just plug in the value of x into the cost function

In the C-Chart, the value of the C-bar, representing the average count of nonconformities per unit, does not have to be an integer. So, the statement 'In the C-Chart, the value of C-bar must be an integer' is false.

In the C-Chart (also known as the Count Chart), the value of C-bar does not necessarily have to be an integer.

C-bar represents the average count of nonconformities per unit. It can be a decimal value, especially when dealing with continuous data or when the sample size is large.

The C-Chart is a statistical process control chart used to monitor the count of nonconformities in a process. It helps to determine if the process is in control or if there are any unusual patterns or trends in the nonconformity counts. The C-bar value is typically calculated as the total number of nonconformities divided by the number of units or observations.

So, the value of the C-bar in the C-Chart can be a decimal or fractional value, not necessarily an integer.

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The missing statements in the given paragraph proof are:

1)  corresponding angle postulate

2) angles 3 and 1

3) transitive property of parallel lines

In this question, we have been given  a paragraph proof.

we need to complete this proof.

We have been given L || K and M || K

To prove: L || M

Since L || K, ∠2 ≅ ∠1 by the corresponding angle postulate

Since M || K, angles 3 and 1 are congruent for the same reason.

By the transitive property of congruence, ∠2 ≅ ∠3

By the transitive property of parallel lines, L || M

Therefore, the missing statements in the given paragraph proof are:

1)  corresponding angle postulate

2) angles 3 and 1

3) transitive property of parallel lines

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the approximate area of the base of the paint can is 53.5 square centimeters.by using Volume formula is Base Area × Height

To find the approximate area of the base of the paint can, we can use the formula for the volume of a cylinder:

Volume = Base Area × Height

We are given the volume (535 cubic centimeters) and the height (10 cm). We need to solve for the Base Area. Rearranging the formula to solve for Base Area, we get:

Base Area = Volume ÷ Height

Now, substitute the given values:

Base Area = 535 cubic centimeters ÷ 10 cm

Base Area ≈ 53.5 square centimeters

So, the approximate area of the base of the paint can is 53.5 square centimeters.

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The approximate area of the base of the can is 53.5 square centimeters

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

Volume = 535 cubic centimeters of paint

Height of container = 10 cm

The area of the base of the can is calculated as

Base area = Volume/Height

Substitute the known values in the above equation, so, we have the following representation

Base area = 535/10

Evaluate

Base area = 53.5

Hence, the base area is 53.5 square centimeters

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The function \($$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$\)  is continuous on (-∞, ∞).

As per the given data the function f(x) is given by:

\($$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$\)

Here we have to determine that the function f(x) is continuous on (-∞, ∞)

If we show that f(x) is continuous at x = 1 then f(x) is continuous on (-∞, ∞)

What are continuous function?

A continuous function in mathematics is one where changes in the parameter cause constant changes in the function's value (i.e., a change without a leap). This shows that there are no abrupt changes in value or discontinuities.

To show f(x) is continuous at x = 1

\(\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}}\) f(x)

\(\rightarrow \lim _{x \rightarrow 1^{-}} f(x) & =\lim _{x \rightarrow 1^{-}}\left(1-x^2\right) \\\)

= 1 - 1

= 0

\(\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{+}} \ln (x) \\\)

= ln 1

= 0

Therefore  \(\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{-}} f(x)-0\).

Hence f(x) is continuous on (-∞, ∞)

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The number of revolutions the small wheel make for every 30 revolutions of the big wheel is 40.

The fundamental idea behind dimension is that only quantities that have the same dimensions can be added or subtracted.

Similarly, only if two physical quantities have the same dimensions can they be equal.

Let r be the radius of the small wheel = 15 in.

Let R be the radius of large wheel = 20 in.

Let n be the number of revolution made by small wheel.

Let N be the number of revolutions made by large wheel = 30.

According to the equality of dimension,

rn = RN

15×n = 20 × 30

n = 40

Therefore, the total number of revolution made by small wheel for every 30 revolutions of large wheel is 40.

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Answer:

20 Students chose bananas.

Step-by-step explanation:

You can see that the bananas take up 25% or 1/4 of the chart. To find 1/4 of a number find half of the number twice. Half of 80 is 40 and half of 40 is 20. So, 20 students chose bananas.

The correct option is a) $5161.24

To evaluate the expression P(1+rt) with the given values:

P = 1575

r = 0.055

t = 168/365

First, let's calculate rt:

rt = 0.055 * (168/365)

= 0.0252836 (rounded to 7 decimal places)

Now, substitute the values into the expression P(1+rt):

P(1+rt) = 1575 * (1 + 0.0252836)

= 1575 * 1.0252836

= 1615.85846 (rounded to 5 decimal places)

The result is approximately $1615.86.

Therefore, the correct option is a) $5161.24

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Answer:

B

Step-by-step explanation: B is the only reasonable answer

Therefore, Ben can do 390 loads of laundry with one box of laundry detergent.

Ben bought a box of laundry detergent that contains 195 scoops. Each load of laundry uses 1/2 scoop.

To determine how many loads of laundry Ben can do with one box of detergent, we divide the total number of scoops by the scoops used per load:

Number of loads = Total scoops / Scoops per load

Number of loads = 195 scoops / (1/2 scoop per load)

Number of loads = 195 scoops * (2/1) = 390 loads

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Answer:

C) g(x) = f(x) + 4

Step-by-step explanation:

A vertical shift is where you shift, slide or translate the whole graph up or down (on a graph) The way this shows up in the equation is just a number tacked on to the end of the equation. A +anumber (like the +4 in the answer) slides the function UP four units. A

-anumber would slide the function DOWN instead.

As for the other answers:

A) the 3multiplied in front is a vertical STRETCH.

D) the 1/2 multiplied in front is a vertical shrink (smash)

B) The -3 in close tight with the x is a horizontal shift(slide, translate) It is a RIGHT shift. A +anumber would be a LEFT shift. Horizontal shift seem kind of backwards. + goes LEFT and - goes RIGHT.

Answer:

25 boxes.

Step-by-step explanation:

Because we know that 5 boxes of pasta cost $13 and we want to find the total number of boxes that can be bought with $65, we can set up a proportion:

\(\frac{5_{boxes} }{13.00}=\frac{x_{boxes} }{65}\\ 13x=325\\ x=25\)

The description of how you can fold a sheet of paper to create two parallel lines that are perpendicular to the same line is as follows,

Take a paper.

Horizontally fold 1/3rd part of it.

Again fold the 1/3rd part of it (Horizontally).

Open the paper, you will find two parallel lines.

Now, fold the paper in half vertically.

Open the paper.

You will find a line that is perpendicular to both parallel lines.

This is how you can fold a sheet of paper to create two parallel lines that are perpendicular to the same line.

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Answer:

Step-by-step explanation:

Let's start by defining the variables for the problem. Let's say that:

w = the width of the rectangular garden (in meters)

l = the length of the rectangular garden (in meters)

We know that the length is 45 meters more than twice the width, so we can write:

l = 2w + 45

We also know that we have 1350 meters of fencing available to enclose the rectangular garden. The perimeter of the rectangular garden is equal to the sum of the lengths of all four sides. Since there are two sides of length w and two sides of length l, we can write:

Perimeter = 2w + 2l

Substituting the expression for l that we derived earlier, we get:

Perimeter = 2w + 2(2w + 45)

Perimeter = 6w + 90

We know that the perimeter of the rectangular garden is equal to 1350 meters, so we can write:

1350 = 6w + 90

Solving for w, we get:

6w = 1260

w = 210

Now that we know the value of w, we can use the expression for l that we derived earlier to find the length:

l = 2w + 45

l = 2(210) + 45

l = 465

Therefore, the dimensions of the rectangular garden should be 210 meters by 465 meters.

Answer:

ummm yes

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

so times it by two because there's two friends. Divide the numerator by 2 which is one there's Ur answer or u could just divide it by two which is basically timing the denominator

Step-by-step explanation:

First start with the graph of    y = | x|

  then shift it RIGHT one unit

         | x -1 |

  then shift it DOWN one unit

  y=   |x-1| -1