in a stable m/m/1 queue with arrival rate and service rate , show that lq d 2 1 and wq d 1 1 :

If she follows the path shown by the dotted line in the graph, the distance from her house to the store would be = 128m. That is option B.

To calculate the distance between her house and the store the Pythagorean formula should be used which is given as follows;

C² = a² + b²

where;

a= 80

b= 100

c= ?

That is;

c²= 80²+100²

= 6400+10000

= 16,400

c = √16400

= 128.1m

Learn more about triangle here:

https://brainly.com/question/28470545

#SPJ1

In algebra, RHS and LHS refer to the right-hand side and left-hand side of an equation, respectively. The RHS represents the expression or value on the right side of the equal sign, while the LHS represents the expression or value on the left side of the equal sign.

In an equation, both the RHS and LHS are separated by an equal sign (=), indicating that the two sides are equal to each other. The equation expresses a relationship or equality between the two sides, and it can be solved to find the value of the variables involved.

To determine which part of an equation is the RHS and which is the LHS, you can look at the position of the equal sign. The expression or value to the left of the equal sign is the LHS, and the expression or value to the right of the equal sign is the RHS.

In conclusion, RHS and LHS are terms used in algebra to refer to the right-hand side and left-hand side of an equation, respectively. The RHS represents the expression or value on the right side of the equal sign, while the LHS represents the expression or value on the left side of the equal sign. The equal sign in an equation separates the RHS and LHS, indicating that the two sides are equal to each other.

Learn more about RHS here:

brainly.com/question/30298176

#SPJ11

4 units is the value of the x for the given secant.

From the two-secant theorem,

⇒a(a+b)=c(c+d)

or in given terminology,

[tex]\frac{VW}{VT} =\frac{VU}{VQ}[/tex]

In the given case,

VW =9

VQ =9+15 = 24

VU = 8

VT = 5x-1+8=5x+7

Thus the ratio,

9*24=8*(5x+7)

5x+7=27

5x=20

x=4

therefore, the value of the x for the given secant is 4 units.

Learn more about secants here:

https://brainly.com/question/23026602

#SPJ1

The length of the missing side v is given as follows:

v = 267.1 cm.

The law of sines is used in the context of this problem as we have two sides and two opposite angles, hence it is the most straightforward way to relate the side lengths.

We consider a triangle with side lengths and angles related as follows:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

For this problem, the parameters are given as follows:

Hence the length v is obtained as follows:

sin(26º)/v = sin(80º)/600

v = 600 x sine of 26 degrees/sine of 80 degrees

v = 267.1 cm.

More can be learned about the law of sines at https://brainly.com/question/4372174

#SPJ1

Therefore, The area between y=2x and y=2√x is approximately 0.3333 (rounded to four decimal places).

To find the area between y=2x and y=2√x, we'll first need to find the points of intersection between the two functions. Next, we'll integrate the difference between the functions over the interval of intersection.
Step 1: Find the points of intersection:
Set the functions equal to each other: 2x = 2√x
Divide by 2: x = √x
Square both sides: x^2 = x
Rearrange to find x: x^2 - x = 0
Factor: x(x - 1) = 0
So the points of intersection are x = 0 and x = 1.
Step 2: Integrate the difference between the functions:
Integral(2√x - 2x)dx from 0 to 1
Step 3: Calculate the area:
Area = ∫[2√x - 2x]dx from 0 to 1
= [4/3 * x^(3/2) - x^2] evaluated from 0 to 1
= (4/3 * 1^(3/2) - 1^2) - (4/3 * 0^(3/2) - 0^2)
= (4/3 - 1) - 0
= 1/3

Therefore, The area between y=2x and y=2√x is approximately 0.3333 (rounded to four decimal places).

To learn more about the decimal number system visit:

brainly.com/question/1827193

#SPJ11

if a tesselation is regular, then the tessellating regular polygon must have either 3, 4, or 6 sides.

a regular tesselation is a pattern of shapes that completely covers a surface without any gaps or overlaps. In a regular tesselation, all of the shapes are the same size and shape, and they fit together perfectly to create a repeating pattern. The tessellating regular polygon is the shape that is repeated in the tesselation.

There are only three regular polygons that can form a regular tesselation: triangles, squares, and hexagons. These polygons have angles that evenly divide 360 degrees, allowing them to fit together perfectly without any gaps or overlaps. Therefore, the tessellating regular polygon in a regular tesselation must have either 3, 4, or 6 sides.

a regular tesselation can only be formed using regular polygons that have angles that evenly divide 360 degrees. Therefore, if a tesselation is regular, the tessellating regular polygon must have either 3, 4, or 6 sides.

To know more about polygon visit:

https://brainly.com/question/23846997

#SPJ11

The calculated value of f(2) is 182 given that the function f(x) = 5(6)ˣ + 2

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

f(x) = 5(6)ˣ + 2

To calculate the value of f(2), we set x = 2

Using the above as a guide, we have the following:

f(2) = 5(6)² + 2

Evaluate the exponent

This gives

f(2) = 5 * 36 + 2

Evaluate the product

This gives

f(2) = 180 + 2

So, we have

f(2) = 182

Hence, the value of f(2) is 182

Read more about functions at

https://brainly.com/question/27915724

#SPJ1

The surface area is approximately 161.47 square units.

To find the surface area generated by revolving the curve about the x-axis, we can use the formula:

S = 2π∫[a,b] f(x)√(1+[f'(x)]^2) dx

where f(x) is the given curve.

Here, f(x) = 36 - 2√(x^2+1) and we need to revolve it about the x-axis.

To find the limits of integration, we note that the curve is symmetric about the y-axis and therefore we can find the surface area of one half of the curve and multiply it by 2. So, we need to integrate from 0 to 4.

S = 2π∫[0,4] (36 - 2√(x^2+1))√(1+((x(-2x))/((x^2+1)^2))) dx

S = 2π∫[0,4] (36 - 2√(x^2+1))√((x^4+4x^2+1)/(x^4+1)^2) dx

Simplifying the integrand,

S = 2π∫[0,4] (36(x^4+1) - 2(x^2+1))√((x^4+4x^2+1)/(x^4+1)^2) dx

S = 2π∫[0,4] (36x^4-70x^2+34)√((x^4+4x^2+1)/(x^4+1)^2) dx

This integral is difficult to evaluate analytically, but it can be approximated using numerical integration techniques. Using a calculator or software, we find that the surface area is approximately 161.47 square units.

Learn more about surface area here

https://brainly.com/question/26403859

#SPJ11

Answer:

Step-by-step explanation:

After calculating the rate at which water is being filled in Tank A and the rate at which water is being leaked from Tank B, it can be determined that both tanks will hold the same amount of water after 4 hours. Therefore, the correct answer is option a) 4 hours.

The comparison distribution in a t test for dependent means is a distribution of the differences between the pairs of scores on the dependent variable.

This distribution is used to determine whether the observed differences between the means of two related groups are statistically significant or could have occurred by chance. The t statistic is calculated by dividing the mean difference between the pairs of scores by the standard error of the mean difference, which is based on the variance of the differences in the sample. The t statistic is then compared to a t distribution with degrees of freedom equal to the number of pairs of scores minus one to determine the probability of obtaining the observed difference by chance.

Learn more about standard error here:

https://brainly.com/question/14524236

#SPJ11

(a) The divergence of F is zero.

(b) The flux out of the sphere is ∫∫(r³ sin²(θ) cos²(φ) / ||r||³) dθ dφ.

What is flux?

Flux is a concept in vector calculus that measures the flow or movement of a vector field across a surface. It represents the amount of a vector field that passes through or crosses a given surface.

To find the divergence of vector field F = r/||r||^3, where r ≠ 0, we need to compute ∇ · F.

Let's start by finding the divergence of F. The divergence of a vector field F = (F₁, F₂, F₃) is given by the following formula:

∇ · F = (∂F₁/∂x) + (∂F₂/∂y) + (∂F₃/∂z)

Now, let's find the partial derivatives of F:

F₁ = [tex]x/||r||^3[/tex]

F₂ = [tex]y/||r||^3[/tex]

F₃ = [tex]z/||r||^3[/tex]

∂F₁/∂x = [tex]1/||r||^3 - 3x^2/||r||^5[/tex]

∂F₂/∂y = [tex]1/||r||^3 - 3y^2/||r||^5[/tex]

∂F₃/∂z = [tex]1/||r||^3 - 3z^2/||r||^5[/tex]

Therefore, the divergence of F is:

∇ · F = (∂F₁/∂x) + (∂F₂/∂y) + (∂F₃/∂z)

[tex]= 1/||r||^3 - 3x^2/||r||^5 + 1/||r||^3 - 3y^2/||r||^5 + 1/||r||^3 - 3z^2/||r||^5\\\\= 3/||r||^3 - (3x^2 + 3y^2 + 3z^2)/||r||^5\\\\= 3/||r||^3 - 3/||r||^3\\\\= 0[/tex]

The divergence of F is zero.

Now, let's calculate the flux out of the sphere using the divergence theorem. The flux of a vector field F across a closed surface S is given by:

Flux = ∫∫(F · n) dS

Where n is the outward unit normal vector to the surface S, and dS is the differential surface area element.

In this case, the surface S is the sphere S₂: x² + y² + z² = 1. The outward unit normal vector to a sphere is simply the position vector normalized: n = (x, y, z) / ||r||.

Therefore, we can rewrite the flux formula as:

Flux = ∫∫(F · (r/||r||)) dS

Since the surface is a sphere, we can use spherical coordinates to simplify the integral. The equation of the sphere in spherical coordinates is:

x = r sin(θ) cos(φ)

y = r sin(θ) sin(φ)

z = r cos(θ)

The differential surface area element in spherical coordinates is given by: dS = r² sin(θ) dθ dφ.

Substituting the expressions for F and n, we get:

Flux = ∫∫((r sin(θ) cos(φ) / ||r||) (r sin(θ) cos(φ), r sin(θ) sin(φ), r cos(θ)) / ||r||) r² sin(θ) dθ dφ

Simplifying further:

Flux = ∫∫(r³ sin²(θ) cos²(φ) / ||r||³) dθ dφ

To evaluate this integral, we need to set up the limits of integration.

Therefore, (a) The divergence of F is zero.

(b) The flux out of the sphere is ∫∫(r³ sin²(θ) cos²(φ) / ||r||³) dθ dφ.

To learn more about flux visit:

https://brainly.com/question/28168699

#SPJ4

The slope and intercept values of the data obtained from the graph given are 11.11 and 80 respectively.

Slope = change in y-axis / change in x - axis

Slope = (400 - 200) / (30 - 12)

Slope = 200 / 18

Slope = 11.11

The intercept of the line is the point where the line of best fit intersects the x-axis of the graph. From the plot, the intercept is 80.

Therefore, the slope and intercept values of the data are 11.11 and 80 respectively.

Learn more on slope and intercept ; https://brainly.com/question/25722412

#SPJ1

The fee for a private vehicle at Arches National Park during peak visiting time is $2.

Let's assume that v represents the fee for a private vehicle in dollars. According to the given information, the total earnings during peak visiting time at Arches National Park is $115,200. This amount is 3,600 times the sum of $30 and v.

To express this situation as an equation, we can set up the following equation:

115,200 = 3,600 * (30 + v)

We multiply the sum of $30 and v by 3,600 because the total earnings are 3,600 times that value. Solving this equation will give us the value of v, the fee for a private vehicle.

To solve the equation, we start by dividing both sides by 3,600:

115,200 / 3,600 = 30 + v

This simplifies to:

32 = 30 + v

Next, we subtract 30 from both sides to isolate v:

32 - 30 = v

2 = v

Therefore, the fee for a private vehicle at Arches National Park during peak visiting time is $2.

For more such questions on National Park,click on

https://brainly.com/question/29015109

#SPJ11

Answer:

For point P to be the centroid of triangle JKL, the following must be true:

- P must be the intersection point of the three medians of the triangle, which are the line segments connecting each vertex to the midpoint of the opposite side.

- Each median must pass through P, dividing the median into two equal parts.

- The centroid is the center of mass of the triangle, so the three medians must intersect at a point that divides each median into two parts in the ratio of 2:1.

Option 3 satisfies all these conditions. If LN is a perpendicular bisector of JK, then it passes through the midpoint of JK, dividing it into two equal parts. Similarly, JO is a perpendicular bisector of LK and MK is a perpendicular bisector of JL, so they each pass through the midpoint of the opposite side, dividing it into two equal parts. Therefore, all three medians pass through P and divide each median into two parts in the ratio of 2:1, making P the centroid of triangle JKL.

Answer: C

JM = ML, LO = OK, and KN = NJ.

Step-by-step explanation:

I just finished the review, Good luck y'all.

Answer: 66

Step-by-step explanation:

The solution set of the inequality is the one in option B;

x> 1 or x < -1

Remember that the absolute value inequality can be descomposed into two inequalities.

Here we have the simple inequality:

|x| > 1

Then we can decompose this into a compound inequality:

x > 1

x < -1

Then the solution is:

x > 1 or x < -1

The correct option is B.

Learn more about inequalities:

https://brainly.com/question/24372553

#SPJ9

Answer:

g = [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

4 - [tex]\frac{1}{12}[/tex] g - 2 = [tex]\frac{3}{2}[/tex] g + 1 - [tex]\frac{5}{6}[/tex] g

multiply through by 12 ( the LCM of 12, 2 and 6 ) to clear the fractions

48 - g - 24 = 18g + 12 - 10g

- g + 24 = 8g + 12 ( subtract 8g from both sides )

- 9g + 24 = 12 ( subtract 24 from both sides )

- 9g = - 12 ( divide both sides by - 9 )

g = [tex]\frac{-12}{-9}[/tex] = [tex]\frac{12}{9}[/tex] = [tex]\frac{4}{3}[/tex]

Answer:

252

Step-by-step explanation:

have a great day and thx for your inquiry :)

The defined sets are as follows:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10....25}

A = {3, 6, 9, 12, 15, 18}

A' = {1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 21, 22, 23, 24, 25}

The universal set contains natural numbers that are at most 25. Natural numbers are counting numbers.

Therefore,

universal set = U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10....25}

A is the set of multiples of 3 that are less than 20. Therefore,

A = {3, 6, 9, 12, 15, 18}

A'(A prime) is the number that is not in the A set but is present in the universal set.

Therefore,

A' = {1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 21, 22, 23, 24, 25}

learn more on sets here: https://brainly.com/question/27529130

#SPJ1

Step-by-step explanation:

To find f(t), we need to take the inverse Laplace transform of 1/(s^2 - 4s + 5).

We can start by factoring the denominator of the Laplace transform:

1/(s^2 - 4s + 5) = 1/[(s - 2)^2 + 1^2]

We can recognize this as the Laplace transform of the function f(t) = e^2t * sin(t). Therefore,

ℒ^{-1} {1/(s^2 - 4s + 5)} = e^{2t} sin(t)

Thus, f(t) = e^{2t} sin(t).

The magnitude of the vector a⃗ is 5.41 m. This means that the length of the vector is 5.41 meters,

The question asks for the magnitude of the vector a⃗ = (4.8 m) x^ + (-2.5 m) y^, which represents a vector in two-dimensional space. The magnitude of a vector represents the length of the vector and is always a non-negative scalar quantity.

To calculate the magnitude of a two-dimensional vector, we can use the Pythagorean theorem. This theorem states that the magnitude of a vector is equal to the square root of the sum of the squares of its components. In this case, the components of the vector a⃗ are (4.8 m) in the x direction and (-2.5 m) in the y direction.

By applying the Pythagorean theorem, we can compute the magnitude of a⃗ as follows:

|a⃗| = sqrt((4.8 m)^2 + (-2.5 m)^2)

|a⃗| = sqrt(23.04 m^2 + 6.25 m^2)

|a⃗| = sqrt(29.29 m^2)

|a⃗| = 5.41 m

Therefore, the magnitude of the vector a⃗ is 5.41 m. This means that the length of the vector is 5.41 meters, and its direction is determined by the angle between the vector and the positive x-axis.

To learn more about Pythagorean theorem click here

brainly.com/question/14930619

#SPJ11

The Trigonometric Equation solutions  to the equation 36 sin²θ - 1 = 0 are:

[tex]θ ≈ 22.08°[/tex] + 360°k, 157.92° + 360°k, 202.08° + 360°k, 337.92° + 360°k

where k is an integer.

We can start by using the trigonometric identity:

sin²θ + cos²θ = 1

Rearranging the terms, we get:

sin²θ = 1 - cos²θ

Substituting this into the original equation:

36 sin²θ - 1 = 0

36(1 - cos²θ) - 1 = 0

Expanding and simplifying:

36 - 36cos²θ - 1 = 0

35 = 36cos²θ

cos²θ = 35/36

Taking the square root of both sides:

cosθ = ±√(35/36)

Now we can use a calculator to find the approximate values of θ:

[tex]θ ≈ 22.08°[/tex], 157.92°, 202.08°, 337.92°

To find all solutions, we need to add multiples of 360° to each of these angles:

[tex]θ ≈ 22.08°[/tex] + 360°k, 157.92° + 360°k, 202.08° + 360°k, 337.92° + 360°k

where k is an integer.

Therefore, the Trigonometric Equation solutions to the equation 36 sin²θ - 1 = 0 are:

[tex]θ ≈ 22.08°[/tex] + 360°k, 157.92° + 360°k, 202.08° + 360°k, 337.92° + 360°k

where k is an integer.

For such more questions on Trigonometric Equation Solutions.

https://brainly.com/question/28025415

#SPJ11

It can be deduced as the final answer that about 45.23% of the time headways are less than 6 seconds and about 4.06% of the time headways are 10 seconds or greater.


Using the Poisson distribution with the mean rate λ, we can solve for the probability of no cars arriving in 20 seconds, which is:

P(X = 0) = e^(-λ) = 18/120

Solving for λ, we get:

λ = -ln(18/120) = 0.6052

Then we can use the Poisson distribution again to solve for the probability of exactly three cars arriving in 20 seconds, which is:

P(X = 3) = (λ^3 / 3!) * e^(-λ) ≈ 0.1097

Finally, we can multiply this probability by the total number of 20-second intervals to estimate the number of intervals in which exactly three cars arrive:

0.1097 * 120 ≈ 13.16

Therefore, we can approximate that 13 of the 120 intervals will have exactly three cars arrive.

The headway between vehicles is the time gap between the arrivals of two consecutive vehicles. We can estimate the percentage of time headways that are 10 seconds or greater and those that are less than 6 seconds by using the exponential distribution with the same mean rate λ as in problem 5.9.

For a headway X, the probability density function of the exponential distribution is given by:

f(x) = λ * e^(-λx)

Therefore, the probability of a headway being less than 6 seconds is:

P(X < 6) = ∫[0,6] λ * e^(-λx) dx = 1 - e^(-6λ)

Similarly, the probability of a headway being 10 seconds or greater is:

P(X ≥ 10) = ∫[10,∞) λ * e^(-λx) dx = e^(-10λ)

Using the value of λ obtained in problem 5.9, we can estimate these probabilities as:

P(X < 6) ≈ 0.4523 or 45.23%

P(X ≥ 10) ≈ 0.0406 or 4.06%

Therefore, we estimate that about 45.23% of the time headways are less than 6 seconds and about 4.06% of the time headways are 10 seconds or greater.

Learn more about poisson's distribution here:-brainly.com/question/30388228

#SPJ11

Answer: 64.3738

Step-by-step explanation:

for an approximate result, multiply the speed value by 1.609

Answer:

64.374 kph

Step-by-step explanation:

1 mph = 1.6093427125258 kph

40 x 1.6093427125258 = 64.373708501033 kph

We can use the alternating series error bound to estimate the error between the infinite series S and its partial sum P. The alternating series error bound states that the error between S and P is less than or equal to the absolute value of the first neglected term. That is:

|S - P| <= |a_{n+1}|

where a_{n+1} is the (n+1)-th term in the series.

In this case, we have:

S = -1 + 1/2 - 1/3 + 1/4 - ...

P = -1 + 1/2

and

a_{n+1} = (-1)^{n+1} / (n+1)

We want to find the least value of k for n=1 such that |a_{n+1}| is less than the error bound that guarantees that |S - P| < k. That is:

|a_{n+1}| < k

Substituting n=1 and P= -1 + 1/2, we get:

|a_2| = 1/3 < k

Therefore, the least value of k for n=1 that satisfies the error bound is k = 1/3.

To check which option is correct, we need to calculate the value of S - P and see if it is less than 64, 66, 68, or 70. We have:

S - P = -1/3 + 1/4 - 1/5 + 1/6 - ...

The sum of the first two terms is approximately -0.25, which is less than 0.33 (the error bound). Therefore, we have:

|S - P| < 0.33

So the correct answer is (A) 64, since 0.33 is less than 64.

Learn more about Error here:- brainly.com/question/10218601

#SPJ11

The monomial expression that best estimates the behavior of x − 4 as x → ± [infinity] is simply x.

An algebraic expression known as a monomial typically has one term, but it can also have several variables and a higher degree.

When 9 is the coefficient, x, y, and z are the variables, and 3 is the degree of the monomial, for instance, 9x3yz is a single term.

This is because as x approaches infinity or negative infinity, the constant term (-4) becomes negligible in comparison to the magnitude of x.

Therefore, the behavior of x − 4 can be approximated by the monomial expression x in the long run.

Know more about monomial expression here:

https://brainly.com/question/2279092

#SPJ11

In order to construct a confidence interval for the population mean when the population standard deviation is known, two assumptions must be met. Firstly, the sample data must be a simple random sample from the population being studied.

Secondly, the variable being measured must have a normal distribution or the sample size must be sufficiently large. The first assumption of a simple random sample ensures that the sample is representative of the population being studied, which is necessary for valid statistical inference. The second assumption is necessary because the confidence interval calculation relies on the assumption that the sample mean follows a normal distribution. When the variable being measured has a normal distribution, the sample mean will also have a normal distribution regardless of the sample size. When the variable being measured does not have a normal distribution, the sample size must be large enough (typically at least 30) in order for the sample mean to follow a normal distribution due to the central limit theorem. By meeting these two assumptions, we can be confident in the accuracy of the resulting confidence interval for the population mean.

Learn more about normal distribution here: brainly.com/question/31493997

#SPJ11

Two pairs of points that would be appropriate to determine the equation is given as follows:

(12, 14) and (15, 16).

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

Hence the graph of the line of best fit should have the smallest possible residual values, meaning that the points on the scatter plot are the closest possible to the line.

Hence the pairs of points in this problem should be exactly on the line, and they are given as follows:

(12, 14) and (15, 16).

More can be learned about residuals at brainly.com/question/1447173

#SPJ1

Answer:

C

Step-by-step explanation:

(k - 1)(6k + 5)

each term in the second factor is multiplied by each term in the first factor , that is

k(6k + 5) - 1(6k + 5) ← distribute parenthesis

= 6k² + 5k - 6k - 5 ← collect like terms

= 6k² - k - 5

The value of the integral ∫[4,-2] f(x) 8dx is -576.

If the average value of a continuous function f on the interval [−2, 4] is 12

∫ 4−2 f(x) 8 dx = 12 (4 - (-2) )

∫ 4−2 f(x) 8 dx =  72

The integral of ∫ [4,-2] f (x) 8dx is constant value

∫ [4,-2] f (x) 8 dx = 8 ∫ [4,-2] f (x) dx

we already know that ∫ [-2,4] f (x) dx = 72

The integral over the interval [4,-2] by using the property of definite integrals

∫ [a, b] f (x) dx = -∫ [b, a] f (x) dx

∫ [4,-2] f (x) dx = -∫ [-2,4] f (x) dx = -72

Putting value back into the original expression, we get:

∫ [4,-2] f (x) 8dx = 8 ∫ [4,-2] f (x) dx = 8(-72) = -576

The value of the integral ∫ [4,-2] f (x) 8dx is -576.

To know more about integral click here :

https://brainly.com/question/31401227

#SPJ4