25. The Poisson process {N(t), t≥ 0} with mean λt is given by the probability function e-xt (at)k P(N(t) = k) = k! Show that Poisson process is a Markov process.

Answer:

Step-by-step explanation:

1. Let the number be x

x^2 + 4x = 21

x^2 + 4x - 21 = 0

Solve the quadratic equation using factorization method

x^2 - 3x + 7x - 21 = 0

x(x - 3) + 7(x - 3) = 0

(x - 3)(x+7) = 0

x - 3 = 0 x + 7 = 0

x = 3 x = -7

The number is either 3 or -7

2. Same solution as number 1

3. Let

Width = x

Length = 2x - 3

Area of the rectangle = 9 square ft

Area of a rectangle = length × width

9 = (2x - 3) (x)

9 = 2x^2 - 3x

2x^2 - 3x - 9 = 0

Solve using quadratic formula

a = 2

b = -3

c = -9

x = -b +or- √b^2 - 4ac / 2a

= -(-3) +or- √(-3)^2 - 4(2)(-9) / 2(2)

= 3 +or- √ 9 - (-72) / 4

= 3 +or- √9 + 72 / 4

= 3 +or- √81 / 4

= 3 +or- 9 / 4

x = (3 + 9)/4 or (3 - 9) / 4

= 12 / 4 or -6 / 4

x = 3 or -3/2

Width can not be a negative value

So,

Width = x = 3 ft

Length = 2x - 3

= 2(3) - 3

= 6 - 3

= 3ft

2.if the sum of the square of the number and 4 time that number is 21 the what is the number?

3. the length of the rectangle is 3 less than twice the width. if the area is 9 square ft, the length and width of the rectangle.

4.given the figure below. find the area of the shaded part of the rectangle if the area of the big but angle is 6 times the area of the unshaded rectangle ​

Unshaded area

Length = 2x

Width = x

Shaded area

Length = (2x+3)

Width = (x+3)

Area of the shaded area = 6 × the unshaded area

(2x) (x) = 6(2x + 3)(x+3)

2x^2 = 6(2x^2 + 6x + 3x + 9)

2x^2 = 12x^2 + 36x + 9x + 54

2x^2 = 12x^2 + 45x + 54

12x^2 + 45x + 54 - 2x^2 = 0

10x^2 + 45x + 54 = 0

We can find the variance of a uniform distribution, using the following formula: Variance = (b - a)² / 12. Here: a is the lower limit of the uniform distribution, b is the upper limit of the uniform distribution.

The formula for the variance of a uniform distribution is based on the fact that the variance of a continuous uniform distribution is equal to the square of the range (i.e., the difference between the upper and lower limits) divided by 12.

For example, let's say we have a uniform distribution between 0 and 10. To find the variance, we would use the formula:

Variance = (10 - 0)² / 12

Variance = 100 / 12

Variance = 8.33

Therefore, the variance of a uniform distribution between 0 and 10 is 8.33.

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The probability of obtaining a sample mean between 4.1 and 4.11 in a random sample of size 511 is 0.

To calculate the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in a discrete uniform population with x = 2.4, we can use the properties of the sample mean and the given population.

In a discrete uniform population, all values are equally likely. Since the mean of the population is x = 2.4, it implies that each value in the population is 2.4.

The sample mean is calculated by summing all selected values and dividing by the sample size. In this case, the sample size is 511.

To find the probability, we need to calculate the cumulative distribution function (CDF) for the sample mean falling between 4.1 and 4.11.

Let's denote X as the value of each individual in the population. Since X is uniformly distributed, P(X = 2.4) = 1.

The sample mean, denoted as M, is given by M = (X1 + X2 + ... + X511) / 511.

To find the probability P(4.1 < M < 4.11), we need to calculate P(M < 4.11) - P(M < 4.1).

P(M < 4.11) = P((X1 + X2 + ... + X511) / 511 < 4.11)
           = P(X1 + X2 + ... + X511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(X1 + X2 + ... + X511 < 4.1 * 511)

Since each value of X is 2.4, we can rewrite the probabilities as:

P(M < 4.11) = P((2.4 + 2.4 + ... + 2.4) < 4.11 * 511)
           = P(2.4 * 511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(2.4 * 511 < 4.1 * 511)

Now, we can calculate the probabilities:

P(M < 4.11) = P(1224.4 < 2099.71) = 1 (since 1224.4 < 2099.71)
P(M < 4.1) = P(1224.4 < 2104.1) = 1 (since 1224.4 < 2104.1)

Finally, we can calculate the probability of the sample mean falling between 4.1 and 4.11:

P(4.1 < M < 4.11) = P(M < 4.11) - P(M < 4.1)
                 = 1 - 1
                 = 0

Therefore, the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in the given discrete uniform population is 0.

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Answer:

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

time * speed

in seconds 60x *4 = 2.5(60x + 900)

x= 25

25 min * 4cm/2

distance = 60 meters

CHEck!!!

Using a system of linear equations, the distance between points A and B is 6000 cm

Time taken = Distance / speed

Let ; distance = d

To time :

Fro time :

(t + 15 × 60) = d / 2.5

2.5(t + 900) = d

2.5t + 2250 = d ______(2)

Equate (1) and (2)

4t = 2.5t + 2250

4t - 2.5t = 2250

1.5t = 2250

t = 1500 seconds

From (1) :

d = 4t

d = 4(1500)

d = 6000 cm

Therefore, the distance from point A to B is 6000 cm

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Answer: 30

Step-by-step explanation: To solve this problem, we're going to have to use the Pythagorean theorem...

a² + b² = c²

24² + 18² = c²

576 + 324 = c²

c² = 900

\(\sqrt{900}\)

30

30 = c

I hope this helps!

Answer:

429

Step-by-step explanation:

Answer:

\(5.7 \times {10}^{ - 3} \)

Step-by-step explanation:

0.0057

first number

5

then the rest

7

equal

5.7

There's three zeros behind the number 5 which mean it will be -3

\( \times {10}^{ - 3} \)

final answer

\(5.7 \times {10}^{ - 3} \)

another example and it will be clear

0.0000403

first number

4

then the rest

03

equal

4.03

There's five zeros behind the number 4 which mean it will be -5

\( \times {10}^{ - 5} \)

final answer

\(4.03 \times {10}^{ - 5} \)

The volume of the right prism include the following: 8,640 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Next, we would determine the area of the triangle at the base of the right prism as follows:

Base area = 1/2 × ( 36 × 12)

Base area = 1/2 × 432

Base area = 216 in².

Now, we can calculate the the volume of this right prism:

Volume = base area × height

Volume = 216 × 40

Volume = 8,640 in³.

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A statistical technique called linear regression is used to determine the relationship between two variables, one of which is the dependent variable and the other the independent variable.

The average number of runs a pitcher gives up per inning in this situation is the dependent variable, and the average number of strikeouts per inning and the average number of home runs per inning are the independent variables. Based on the values of the independent variables, the developed regression equations can be used to forecast the value of the dependent variable.

a. We need to perform a simple linear regression to create an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of strikeouts per inning pitched. The equation will be of the form Y = a + bX, where Y represents the number of runs given up per inning and X represents the number of strikeouts per inning. The estimated regression equation is Y = 0.52 + 0.35X.

b. We need to perform a simple linear regression to create an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of home runs per inning pitched. The equation will be of the form Y = a + bX, where Y represents the number of runs given up per inning and X represents the number of home runs per inning. The estimated regression equation is Y = 0.63 + 1.70X.

c. We need to perform a multiple linear regression in order to create an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of strikeouts per inning pitched and the average number of home runs per inning pitched. The equation will be of the form Y = a + b1X1 + b2X2, where Y represents the number of runs given up per inning, X1 represents the number of strikeouts per inning, and X2 represents the number of home runs per inning. The estimated regression equation is Y = -0.12 + 0.44X1 + 1.78X2.

d. Using the estimated regression equation developed in part (c), we can predict the average number of runs given up per inning for A. J. Burnett as follows:

Y = -0.12 + 0.44(0.91) + 1.78(0.16)

Y = 0.43

Therefore, the predicted average number of runs given up per inning for A. J. Burnett is 0.43.

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The factor of the expression will be (x + 1) and (x + 1). Then the product of two binomials will be (x + 1) and (x + 1).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The expression is given below.

⇒ x² + 2x + 1

Factorize the expression, then the factor of the expression will be

⇒ x² + x +  x + 1

⇒ x(x + 1)x + 1(x + 1)

⇒ (x + 1)(x + 1)

⇒ (x + 1)²

The product of two binomials will be (x + 1) and (x + 1).

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Answer:

50.24

explanation

The diameter of the circle is the length of the square which is =16

using the furmla π r = 3.14×16= 50.24

This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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Answer:  D) Potrick con cot Out 1, 2, 3, or times per week.

(hope this helps!)

In general, in the case of two independent events X and Y,

Therefore, in our case,

Answer:

C

Step-by-step explanation:

Verify, give me brainliest, and rate, and say thank you

Answer:

log ( \(\frac{x^2-2x(x-1)}{(x-1)^2}\) )

Step-by-step explanation:

to find (f ◦ g)(x) , substitute x = g(x) into f(x)

= log ( ( \(\frac{x}{(x-1)^}\) )² - 2(\(\frac{x}{x-1}\) ) )

= log ( \(\frac{x^2}{(x-1)^2}\) - \(\frac{2x}{x-1}\) ) ← express as a single fraction

= log ( \(\frac{x^2-2x(x-1)}{(x-1)^2}\) )

Answer:

0.6 ÷ 0.3 - Option 2.

0.2 × 0.9 - Option 3.

For the given data set, the 1st quartile (Q1) is 12, the median (Q2) is 17.5, and the 3rd quartile (Q3) is 28.

For the given data set:
7 8 11 13
15 16 19 20
24 25 27 27
29 30 31 32
First, arrange the data in ascending order:
7 8 11 13 15 16 19 20 24 25 27 27 29 30 31 32
There are 16 data points in total.
To find the median (2nd quartile), since there's an even number of data points, we take the average of the two middle values:
Median (Q2) = (16 + 19) / 2 = 17.5
To find the 1st quartile (Q1), we find the median of the lower half of the data:
7 8 11 13 15 16 (excluding 19 and above)
Since there are 6 data points, we take the average of the two middle values:
Q1 = (11 + 13) / 2 = 12
To find the 3rd quartile (Q3), we find the median of the upper half of the data:
24 25 27 27 29 30 31 32 (excluding 20 and below)
Again, since there are 6 data points, we take the average of the two middle values:
Q3 = (27 + 29) / 2 = 28
So, the 1st quartile (Q1) is 12, the median (Q2) is 17.5, and the 3rd quartile (Q3) is 28.

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We are expected to find the volume of the item which contains a cylinder and a cone = The volume of the item is 108 in³

The volume of a cylinder = πr²h

π = 3

r =/2 = 4 in/2 = 2 in

h = 8 in

The volume of a cylinder = πr²h

= 3 × (2 in)² × 8 in

= 3 × 4 in² × 8 in

= 96 in³

The volume of a cone = πr²h/3

= (3 × (2 in)² × 3 in)/3

= (3 × 4 in² × 3 in)/3

= 36 in³/3

= 12 in³

The volume of the item can be found by adding the volume of the cylinder and the volume of the cone

Total volume = Volume of a cylinder + Volume of a cone

= 96 in³ + 12 in³

= 108 in³

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Answer:

wfek

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

120 times 0.75 =90

The researcher will need 25 participants to obtain 20 measurements within each of the 25 conditions in this within-subject design.

To determine the number of participants needed for a within-subject design with 25 conditions and 20 measurements within each condition, we need to consider the concept of counterbalancing. Counterbalancing involves systematically varying the order of conditions across participants to account for potential order effects.

In this case, each participant will need to complete all 25 conditions, with 20 measurements within each condition. Therefore, we can calculate the total number of measurements per participant:

Total measurements per participant = Number of conditions × Number of measurements per condition

Total measurements per participant = 25 × 20

Total measurements per participant = 500

To determine the number of participants needed, we divide the total number of measurements by the number of measurements per participant:

Number of participants = Total measurements / Measurements per participant

Number of participants = 500 / 20

Number of participants = 25

Therefore, the researcher will need 25 participants to obtain 20 measurements within each of the 25 conditions in this within-subject design.

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She should order 8 large pizzas to serve 36 guests.

We know that two large pizzas serve 9 people. To determine the number of pizzas she should order to serve 36 guests, we can set up a proportion:

2 pizzas / 9 people = x pizzas / 36 people

Cross-multiplying, we get:

2 * 36 = 9 * x

72 = 9x

Dividing both sides of the equation by 9, we find:

x = 8

Therefore, she should order 8 large pizzas to serve 36 guests.

To serve 36 guests, she should order 8 large pizzas based on the information that two large pizzas serve 9 people.

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The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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Answer:

84$

Step-by-step explanation:

It says it costs $3 per visit and Ella went 18 times

So we can describe that as x represents the times she has visited, x=18, so 3(18)

now we just add $30 dollars since she only went in one month and $30 is the fee per month so that would be (3*18=) 54+30

which would then give you $84 dollars!

hope it helps!!

Answer:

C.) $84

Step-by-step explanation:

The solution to the equation in this problem is given as follows:

y = -4.

The equation for this problem is defined as follows:

\(\frac{y - 6}{y^2 + 3y - 4} = \frac{2}{y + 4} + \frac{7}{y - 1}\)

The right side of the equality can be simplified applying the least common factor as follows:

[2(y - 1) + 7(y + 4)]/[(y + 4)(y - 1)] = (9y + 26)/(y² + 3y - 4)

The denominators of the two sides of the equality are equal, hence the solution to the equation can be obtained equaling the numerators as follows:

9y + 26 = y - 6

8y = -32

y = -32/8

y = -4.

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