Two people are working in a small office selling shares in a mutual fund. Each is either on the phone or not. Suppose that calls come in to the two brokers at rate λ1=λ2 = 1 per hour,while the calls are serviced at rate μ1 =μ2 = 3.
(a) Formulate a Markov chain model for this system with state space { 0 ,1 , 2 ,12 } where the state indicates who is on the phone. (b) Find the stationary disturbtion. (c) Suppose they upgrade their telephone system so that a call one line that is busy is forwarded to the other phone and lost if that phone is busy. (d) Compare the rate at which calls are lost in the two systems.

The approximate value of y(1) using Euler's method with a step size of h = 0.1 is 1.

Using Euler's method and a step size of h = 0.1, we can use the given initial value problem (IVP) and iterate through the interval [0, 1] in steps of size h to approximate the value of y(1). Let's begin by determining the number of steps required: n = (1-0) / 0.1 = 10.

Utilizing the accompanying recipe, we can repeat through the span beginning with the underlying condition y(0) = 1.

y(i+1) is equivalent to y(i) + h * (t(i) * y(i) + t(i)2), where I is among 0 and n-1, t(i) is equivalent to I * h, and y(i) is the surmised worth of y at t(i).

At each step, we can inexact the upsides of y utilizing the recipe gave:

The approximate value of y(1) is 1, assuming Euler's method and a step size of h = 0.1. y(0) = 1 y(1)  y(0) + 0.1 * (0 * y(0) + 02) = 1 + 0.1 * (0 + 0) = 1.

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Given:

The expressions are:

[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}[/tex]

[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}[/tex]

To find:

The simplified form of the given expressions.

Solution:

We have,

[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}[/tex]

It can be written as:

[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{12a^{2+1}bc^3}{40b^4c^2}[/tex]

[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{3a^{3}c^{3-2}}{10b^{4-1}}[/tex]

[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{3a^{3}c^{1}}{10b^3}[/tex]

Therefore, the value of the given expression is [tex]\dfrac{3a^{3}c}{10b^3}[/tex].

We have,

[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}[/tex]

It can be written as:

[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}=\dfrac{(x+y)(x-y)}{4(x+y)}\cdot \dfrac{x+y}{x-y}[/tex]

[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}=\dfrac{x+y}{4}[/tex]

Therefore, the value of the given expression is [tex]\dfrac{x+y}{4}[/tex].

Answer:

-2, -1, 0, 1

Step-by-step explanation:

you hover over the stars

Answer:

12

Step-by-step explanation:

1st circle - [tex]1+3+6=10[/tex]

3rd circle - [tex]6+2+5=13[/tex]

2nd circle is proboably the same way.

Answer:

Yes it will be appropriate to model the distribution of a sample mean with a normal model

Step-by-step explanation:

Given that the population is not normal, and the sample is sufficiently large, according to the Central Limit theorem, the distribution of the mean pf the sampling distribution will be approximately normal not withstanding the population from which the sample is obtained. Therefore, the mean, [tex]\overline x[/tex], and the standard deviation, [tex]\dfrac{\sigma}{\sqrt{n} }[/tex], of the sample will be equal to the mean, μ, and standard deviation, σ, of the of the population

Therefore, it will be appropriate to model the distribution of a sample mean with a normal model

Answer:

yes

Step-by-step explanation:

i got it right on plato

Since our test statistic is smaller than this critical value, we can conclude that the sample mean of 6.42 is not statistically significant and therefore cannot be used to reject the null hypothesis that the population mean is 6.0.

The first step here is to calculate the test statistic, which is also called a t-statistic or a z-score. This is done by subtracting the population mean from the sample mean, and dividing this difference by the standard deviation of the sample (dividing by the standard error if the population standard deviation is known). In this case, we have:

Test Statistic = (Sample Mean - Population Mean) / (Sample Standard Deviation / √n)

Test Statistic = (6.42 - 6.0) / (7.44 / √29)

Test Statistic = 0.42 / (7.44 / 5.385)

Test Statistic = 0.42 / 1.377

Test Statistic = 0.305

Now that we have the test statistic, we can compare it to the t-table or z-table (depending on if the population standard deviation is known) to determine whether or not the calculated value is statistically significant. For example, if we assume a 95% confidence level, the critical value of z (the p-value) is 1.96.

Since our test statistic is smaller than this critical value, we can conclude that the sample mean of 6.42 is not statistically significant and therefore cannot be used to reject the null hypothesis that the population mean is 6.0.

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Jane's balance right after her last contribution is $23,679.09.

Given that Jane is making quarterly contributions of $280 to her savings account, which pays interest at the APR of 6.6%, compounded quarterly.

The formula to find the interest rate is given as;A = P(1 + r/n)^(nt)

Where;P = $280r = 6.6% or 0.066n = 4 t = 38A = 280(1 + 0.066/4)^(4 * 38)= 280 (1.0165)^152A = $12,734.71

Jane's balance right after her last contribution at 7.5% after 49 contributions would be calculated as;P = $280r = 7.5% or 0.075n = 4 t = 49A = P(1 + r/n)^(nt)A = 280 (1 + 0.075/4)^(4 * 49)= 280 (1.01875)^196A = $23,679.09

Therefore, Jane's balance right after her last contribution is $23,679.09.

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Answer:

A

Step-by-step explanation:

Because That's The Main Idea

Answer:

b(-1,-8)

Step-by-step explanation:

assuming x2 and y2 are the coordinates of b.

and x1 and y1 are the coordinates of A

midpoint are (xm, ym)

formula xm= (x1+x2)/2

ym=(y1+y2)/2

Using the integrating method to solve the given differential equation, we get :

y = -1/4 - (9/4)e^(-2x)

Given equation is:

4y′ + 8y = 7,

y(0) = −2

We are going to use the integrating factor method to solve the differential equation.

Differential equation:

4y′ + 8y = 7

Rearranging the terms, we get:

y′ + 2y = 7/4

Integrating factor:

I.F. = e^(∫2dx)I.F. = e^(2x)

Multiplying I.F. throughout the differential equation, we get:

e^(2x)y′ + 2e^(2x)y = 7/4e^(2x)

Now we are going to apply the product rule of differentiation to the left-hand side. Let v = y and u = e^(2x)

So, v′ = y′ and u′ = 2e^(2x)

Now applying the product rule, we get:

e^(2x)y′ + 2e^(2x)y = 7/4e^(2x)2e^(2x)y + e^(2x)y′ = 7/4e^(2x)2e^(2x)y = -1/2 e^(2x) + C1y = -1/4 + C2e^(-2x)

Now substituting the initial value y(0) = -2C2 = -9/4

Putting the value of C2 in the above equation, we get:

y = -1/4 - (9/4)e^(-2x)

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Answer:

1. and 2. I belive are true sorry if wrong

Step-by-step explanation:

Answer:

#1=8

#2=3

Step-by-step explanation:

Answer:

A) Subtract 5 from each side

Step-by-step explanation:

This would be your first step, then you would want to isolate your variable so you would divide both sides by 2.

The 90% confidence interval for the proportion of smokers is approximately (0.043, 0.137).

The proportion of smokers in the population, we can use the sample proportion and construct a confidence interval.

Given that the sample size is 100 and there were 9 smokers in the sample, the sample proportion of smokers is 9/100 = 0.09.

To calculate the confidence interval, we can use the formula:

CI = p (bar) ± Z  × √(p (bar)(1-p (bar))/n)

p (bar) is the sample proportion, Z is the Z-score corresponding to the desired confidence level, and n is the sample size.

In this case, the confidence interval is not provided directly, so we need to calculate it.

Using a confidence level of 90%, the Z-score corresponding to a 90% confidence level is approximately 1.645.

The confidence interval:

CI = 0.09 ± 1.645 × √(0.09(1-0.09)/100)

CI = 0.09 ± 1.645 ×√(0.0819/100)

CI = 0.09 ± 1.645 × 0.0286

CI = 0.09 ± 0.047

Therefore, the 90% confidence interval for the proportion of smokers is approximately (0.043, 0.137).

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The particle never moves to the right of the origin. Hence, the farthest left of the origin that the particle moves is at x=-∞.

Given that, the position of the particle is [tex]x*d(t)=(1-2)^2*(1-6).[/tex]

Initially, the position of the particle is[tex]x*d(t)=(-1)^2*(-5)=5.[/tex]

The displacement of the particle can be given as the difference between the final position and the initial position. Therefore, the displacement of the particle is [tex]Δx=0-5=-5.[/tex]

(a) Since the value of the displacement is negative, the particle is moving to the left.

(b) The particle will be at rest when the velocity of the particle is zero. Here,[tex]v=d/dt (x*d(t))=x*d'(t)[/tex]

When the velocity of the particle is zero, then x*d'(t)=0.So, either x=0 or d'(t)=0.

When x=0, the particle will be at rest at the origin.

To find out the value of t, substitute x=0 in the given equation,

we get[tex]0=(-1)^2*(-5).[/tex] This is not possible. Therefore, the particle will never be at rest.

(c) When the direction of the velocity changes, the particle changes direction. The velocity of the particle is given as v=d/dt (x*d(t))=x*d'(t).

From the above equation, we see that the velocity of the particle changes direction when x changes direction. The direction of x changes at x=0.

(d) The farthest left of the origin that the particle moves is at x=-∞ when t=0.

Thus, the particle never moves to the right of the origin. Hence, the farthest left of the origin that the particle moves is at x=-∞.

Note: Here, we have considered the absolute values of -1 and -5.

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Answer:

3,410,000

Step-by-step explanation:

3.41 * 10^6 = 3.41 * 1,000,000 = 3,410,000

Answer:

3,410,000

plz mark me as brainliest

The total depreciation amount for 2020 is $547.

We need to know the depreciation method and the asset's useful life in order to calculate the total amount of depreciation for 2020. Let's suppose the assets are being depreciated using the Modified Accelerated Cost Recovery System (MACRS) and have a useful life of five years because the question leaves this information out. The desk for the workplace was bought on April 15, 2018. We must ascertain the number of full years the desk has been in operation as of December 31, 2020, to compute the year's depreciation. By the end of 2020, it would have been in use for three years after it was acquired in 2018.

Using MACRS, the depreciation percentages for the 5-year property are as follows:

Year 1: 20%

Year 2: 32%

Year 3: 19.20%

Year 4: 11.52%

Year 5: 11.52%

Year 6: 5.76% (if applicable)

Since we're calculating depreciation for the 3rd year, we'll use the Year 3 depreciation percentage of 19.20%.

Depreciation for the office desk in 2020:

Depreciation = Cost of the desk × Depreciation percentage

Depreciation = $950 × 19.20% = $182

The executive-style chairs were purchased on August 5, 2018. They would also have been in service for 3 full years by the end of 2020. Using the same depreciation percentages, the depreciation for the chairs in 2020 would be:

Depreciation = Cost of the chairs × Depreciation percentage

Depreciation = $1,900 × 19.20% = $364

Now, let's calculate the total depreciation amount for 2020 by adding the depreciation of the desk and chairs:

Total Depreciation = Depreciation of the desk + Depreciation of the chairs

Total Depreciation = $182 + $364 = $546

Given the answer choices provided, none of them match the calculated total depreciation amount of $546. However, the closest answer is an option I: $547.

The total depreciation amount for 2020 is $547.

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First use the distributive property by multiplying the 3 with each term inside the parentheses:

-8 + 3c + 3 + c

Now combine like terms:

-8 + 3 = -5

3c + c = 4c

Combine for final answer:

-5 + 4c which can also be written as 4c-5

Answer:

first let's multiply 3 by the bracket

-8+3*c+3*1+c=-8+3c+3+c

then add the numbers that have the same variables -8+3+3c+c

=-8+3+4c then add the numbers

=-5+4c is the answer

you can also write it like this

4c-5

Answer:

C) 1/2

Step-by-step explanation:

3 of the 6 numbers on a cube are even. 3/6 = 1/2

Answer: 10/3 units

Step-by-step explanation: sqrt 100/9= 10/3

Answer:

If two secant segments intersect outside a circle, then the product of the secant segment with its external portion equals the product of the other secant segment with its external portion.

45(45) = (2x + 75)(27)

2,025 = (2x + 75)(27)

2x + 75 = 75, so x = 0 and GH = 48

Answer:

To add or subtract two rational expressions with the same denominator, we simply add or subtract the numerators and write the result over the common denominator. When the denominators are not the same, we must manipulate them so that they become the same. In other words, we must find a common denominator.

Step-by-step explanation:

Answer:

To add or subtract two rational expressions with the same denominator, we simply add or subtract the numerators and write the result over the common denominator. When the denominators are not the same, we must manipulate them so that they become the same.

Step-by-step explanation:

Answer:

A. 80

Step-by-step explanation:

There are more points on 80 than on the other ones. By this, you can tell that it's the PEAK of the data set.

Hope this helps! Please brainliest!

Answer:

Step-by-step explanation:

In which point has more balls ( it is on 80)

I hope that is useful for you :)

Answer:

32 percent of 112 is 35.84. 112 -35.84=76.16

Step-by-step explanation:

Brainliest?

Answer:

35.84

Step-by-step explanation:

I used a online calculator

In this hypothesis testing scenario, the null hypothesis (H) states that the mean (μ) weight of a product is equal to 30 grams.

The one-sample t-test is computed using the formula t = (x - μ) / (s / √n), where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size. In this case, the calculated t-value is -0.3.

Based on the decision rule, since the calculated t-value of -0.3 falls within the non-critical region (-1.96 to 1.96), we do not reject the null hypothesis.

Therefore, the conclusion is that there is not enough evidence to support the claim that the mean weight of the product is 30 grams. The data does not provide sufficient statistical evidence to conclude that the mean weight significantly differs from 30 grams.

It's important to note that in hypothesis testing, the result does not prove that the null hypothesis is true; rather, it suggests that there is not enough evidence to reject it based on the given data and significance level.

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Answer:

I would need to see the graph to answer this question.

Kohl's rectangular gold garden has an area of 54 square feet. To determine the dimensions of the garden, we need to find two numbers whose product is 54.

To find the dimensions of the garden, we can factorize the area of 54 square feet. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. Since the garden is rectangular, we are looking for two numbers whose product is 54.

By examining the factors, we can see that the dimensions of the garden could be 6 feet by 9 feet, as their product is indeed 54. Alternatively, the garden could have dimensions of 3 feet by 18 feet, as their product is also 54. Both sets of dimensions result in an area of 54 square feet.

Therefore, the possible dimensions of Kohl's rectangular gold garden could be either 6 feet by 9 feet or 3 feet by 18 feet.

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