The number of requests for assistance received by a towing service follows a Poisson process with rate a 6 per hour. (a)(5 points) Compute the probability that exactly ten requests are received during a particular 2-hour period. (b) ((5 points)What is the probability that it will be no requests during next 30 min?

The amount of each of the 10 payments will be £1204.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The cost of the boat is £14,200 plus VAT at 20%.

Trevor pays = £5000

He pays the rest of the cost in 10 equal payments.

Now,

We can formulate;

The amount of each of the 10 payments is;

= (14200 + 14200 x 20% - 5000)/10

= (14200 + 2840 - 5000) / 10

= (17040 - 5000) / 10

= 12040 / 10

= 1204

Thus, The amount of each of the 10 payments will be £1204.

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The summation notation to express each of the following calculations:

a) (∑ \(x_i\) )^2

b) ∑ \(x_i^2\)

c) ∑ \(x_i\) - 2

d) ∑(\(x_i\) - 1)^2

Here we have to find the summation notation to express each calculations  

Let the scores be denoted by the sequence \(x_i\) for i = 1, 2, ..., n

Part a

Add the score and then square the sum

(∑ \(x_i\) )^2

Part b

Square each score and then add the squared values

∑ \(x_i^2\)

Part c

Subtract 2 points from each score and then add the resulting values.

∑ \(x_i\) - 2

Part d

Subtract 1 point from each score and square the resulting values. then add the squared values.

∑(\(x_i\) - 1)^2

Therefore, the summation notation of each calculation has been found

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Answer:

72x+243

Step-by-step explanation:

That expression will get you the total amount of money spent

Answer:

incomplete question friend

Answer:

20%

Step-by-step explanation:

as we add 10 +25 = 35

so if we subract 40 from 35 it is 5 so mangoes are 5

5

_ × 100 =20%

25

Answer:

57.3°

Step-by-step explanation:

A 25 feet ladder leans against a building.

The ladder's base is 13.5 feet from the building.

The ladder, the wall of the building and the ground form a right-angled triangle of:

Hypotenuse = 25 feet

Base = 13.5 feet

We are to find the angle of elevation which the ladder makes with the ground (or rather the angle created by hypotenuse and base)

Let's say the angle = X°

According to a trigonometric equation;

cos X° = adjacent side ÷ hypotenuse = \(\frac{13.5}{25}\) = 0.54

\(cos ^{-1} X\) = 57.5=3° (Answer rounded up to nearest one decimal place).

∴ The angle of elevation = 57.3°

The matrix structure is an organizational design that combines functional and divisional reporting lines within the same company. The three conditions which usually exist when the matrix structure is found are multiple projects, interdependency, and a skilled workforce.

This structure facilitates better coordination and communication, allowing organizations to more effectively manage complex and diverse projects.
There are three conditions that usually exist when the matrix structure is found:
1. Multiple Projects: Matrix structures are often used in organizations that manage multiple projects or products simultaneously. These organizations need to allocate resources and personnel efficiently, and the matrix structure enables them to do so by allowing employees to work on various projects while still maintaining their functional roles.
2. Interdependency: In a matrix structure, there is a high level of interdependency among different departments and project teams. This interdependency promotes collaboration and communication, enabling the organization to respond more quickly to changing market conditions and customer needs.
3. Skilled Workforce: Organizations employing a matrix structure usually require a skilled and diverse workforce. These employees must be able to adapt to new challenges, work in cross-functional teams, and possess strong problem-solving skills. The matrix structure allows organizations to leverage the expertise of their workforce by assigning employees to projects based on their unique skill sets.
In conclusion, the matrix structure is an organizational design that combines functional and divisional reporting lines, enabling organizations to manage complex projects more effectively. This structure is typically found in organizations with multiple projects, a high level of interdependency, and a skilled workforce.

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Answer:

Both have important predecessors—our Constitution was influenced by the Magna Carta and the English Bill of Rights of 1689, and the Declaration by John Locke's writings on the consent of the governed and by a document close to home for Thomas Jefferson, the draft version by George Mason of Virginia's Declaration of ...

Step-by-step explanation:

thats what I could find

Answer:

19/25

Step-by-step explanation:

7/10 + 6/100

= 70/100 + 6/100

= 76/100

= 19/25

So, the answer is 19/25

Answer:

Let's define:

G = cost of a goat

S = cost of a sheep.

We know that the total cost for a goat and a sheep is £120, then:

S + G = £120

And the cost of the goat is twice the price of the sheep, then:

G = 2*S

To solve this system, we can just replace the second equation into the first one, then we get:

S + (2*S) =  £120

3*S =  £120

S =  £120/3 =  £40

This means that each sheep costs  £40

And the cost of a goat is:

G = 2* £40 =  £80.

Now we know that he sold both of them, where:

s = price of the sheep

g = price of the goat.

We know that he sold both of them for £180, then:

s + g = £180

And the profit of the sheep is twice the profit of the goat, then:

(s - S) = 2*(g - G)

(s -  £40) = 2*(g -  £80)

s  -  £40 = 2*g -  £160

Then we have a system of equations:

s + g = £180

s  -  £40 = 2*g -  £160

To solve this, we first could isolate g in the first equation:

g = £180 - s

Replacing this in the other equation we get:

s - £40 = 2*( £180 - s) -  £160

s - £40 = £360 - 2*s - £160

s - £40 = £200 - 2*s

s + 2*s = £200 - £40 = £160

3*s = £160

s = £160/3 = £53.33

Then the percentage profit for the sheep is:

percentage profit = (s/S)*100% = (£53.33/£40)*100% = 133.3%

Then the percentae profit is 33.3%, which means that the sheep was sold at 133.3% of its original cost, leaving a profit of 33.3% of its original cost.

The best estimate for the total amount of time Tim would spend answering e-mails over the course of 100 days is 100 hours with a standard deviation of 0.53 hours.

To find the total amount of time Tim would spend answering emails over the course of 100 days, we need to use the concept of the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approaches a normal distribution regardless of the underlying distribution.

To calculate the standard deviation of the total amount of time Tim spends answering emails over 100 days, we can use the formula:

standard deviation = square root of (n * variance)

where n is the number of days and variance is the variance of the amount of time Tim spends in a day answering emails.

Substituting the values, we get:

standard deviation = square root of (100 * 0.0028) = 0.53 hours

Therefore, Tim would spend an average of 100 hours over the span of 100 days responding to emails, with a standard deviation of 0.53 hours, according to the best estimate.

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Answer:

To calculate how long it will take for the plane to reach 18,000 ft, first find the difference between the plane's current altitude and its target altitude:

35,600 ft - 18,000 ft = 17,600 ft

Then, divide this difference by the rate of descent to find the time it will take for the plane to reach its target altitude:

17,600 ft / 3,200 ft/mile = 5.5 miles

Since the rate of descent is given in feet per mile, this result is equivalent to the time it will take for the plane to reach its target altitude. Therefore, it will take the plane 5.5 miles (or a similar amount of time) to reach 18,000 ft.

The average pay-per-hour of the year for Elise will be 13.73 pounds.

From the information, in 2016 she earned £2100 and in 2017 she was awarded a 3% increase on her monthly salary.

Therefore, the new salary will be:

= 2100 + 3%(2100)

= 2100 + 63

= 2163

Now she worked for 42 hours per week for 45 weeks. This will be:

= 42 × 45

= 1890 hours

Therefore, the total earnings for the year will be:

= 2163 × 12 months

= 25956

The average pay-per-hour of the year will be:

= Total amount / Number of hours

= £25956 / 1890

= £13.73

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Answer:

C

Step-by-step explanation:

Calculator

Answer:

Step-by-step explanation:

Part A

The units on 9500 must be miles. So if x is time, then 55 must be the rate at which she travels ie 55 miles per hour. So the answer must be A.

Part B

The trip began when the time was zero. Therefore x is zero. What remains is the mileage on the odometer when x = 0.  The answer must be 1950.

Answer:

8y+2zand^3x+3z+4

Step-by-step explanation:

Answer:

Bart is currently 32, and Art is currently 40.

Step-by-step explanation:

Step 1: Derive an Equation

Since Bart and Art's current ages are in a ratio of \(4:5\), we can let their current ages be \(4x\) and \(5x\), respectively.

In 4 years, their ages will increase by 4. This means that in terms of \(x\), Bart and Art will be \(4x+4\) and \(5x+4\) years old in 4 years, respectively.

We are given that their ages in 4 years will be in the ratio \(9:11\). Therefore, the ratios \(4x+4:5x+4\) and \(9:11\) are equivalent, so \(4x+4:5x+4 = 9:11\).

Ratios can also be written as fractions, so we can derive the following equation:

\(\frac{4x+4}{5x+4}=\frac{9}{11}\)

Step 2: Solve the Equation

Solving for \(x\), we get:

\(\frac{4x+4}{5x+4}=\frac{9}{11}\)

\((4x+4)*11=(5x+4)*9\) (Cross-Multiply)

\(44x+44=45x+36\) (Distribute)

\(44x+44-44x-36=45x+36-44x-36\) (Subtract \(44x\) and \(36\) from both sides of the equation to isolate \(x\))

\(8=x \rightarrow x=8\) (Simplify / Symmetric Property of Equality)

Step 3: Answer the Question

We know that \(x=8\), therefore, Bart is currently \(4*8=\bf 32\) years old and Art is currently \(5*8=\bf 40\) years old. Hope this helps!

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The  hypothetical demand curve for tickets to a particular rock concert is given in the image attached.

According to Samuelson: theory, the law of demand states that people buy more at lower prices and less at higher prices when other things remain constant.

Note that by using the image,

Prices of ticket (cent)    Demand by consumer

5                                   35

4                                  30

3                                    70

2                                    80

1                                    95

Therefore, "Demands curves show how much people will buy the ticket at different prices over time." The Curve shows consumer purchases at different prices.

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To prove that d(Xt Yt) = XtdYt + YtdXt + dXt . dYt, we can use the product rule of stochastic calculus. Applying the product rule, we get:

d(Xt Yt) = Xt dYt + Yt dXt + dXt . dYt + dXt . dYt

Since dXt . dYt is a second-order differential, we can ignore it using the Itô isometry property. Thus, we have:

d(Xt Yt) = Xt dYt + Yt dXt + dXt . dYt

Next, we can integrate both sides of this equation from 0 to t:

∫ d(Xs Ys) = ∫ Xs dYs + ∫ Ys dXs + ∫ dXs . dYs

Using the fundamental theorem of calculus and the fact that dX0 = dY0 = 0, we can simplify this equation as:

XtYt - X0Y0 = ∫ Xs dYs + ∫ Ys dXs + ∫ dXs . dYs

Finally, rearranging the terms, we get the desired result:

∫ Xs dYs = XtYt - X0Y0 - ∫ Ys dXs - ∫ dXs . dYs

This is the general integration by parts formula.
Hi! To prove the given equation and deduce the integration by parts formula, we will make use of Ito's lemma and properties of stochastic integrals.

Given Xt and Yt are Ito processes in R, we have:

d(XtYt) = Xt dYt + Yt dXt + dXt dYt

To prove this, we'll apply Ito's lemma to the function F(x, y) = xy, where x = Xt and y = Yt:

dF(x, y) = (∂F/∂x) dXt + (∂F/∂y) dYt + (1/2) [(∂²F/∂x²) (dXt)² + 2(∂²F/∂x∂y) dXt dYt + (∂²F/∂y²) (dYt)²]

Since F(x, y) = xy, we have:
∂F/∂x = Yt
∂F/∂y = Xt
∂²F/∂x² = 0
∂²F/∂y² = 0
∂²F/∂x∂y = 1

Substituting these partial derivatives back into Ito's lemma, we get:

d(XtYt) = Yt dXt + Xt dYt + dXt dYt

Now, let's deduce the integration by parts formula:

∫₀ᵗ Xs dYs = ∫₀ᵗ (XtYt - Yt dXt - dXt dYt) ds

Using the properties of stochastic integrals, we have:

∫₀ᵗ Xs dYs = XtYt - X₀Y₀ - ∫₀ᵗ Ys dXs - ∫₀ᵗ dXs dYs

Thus, the integration by parts formula is:

∫₀ᵗ Xs dYs = XtYt - X₀Y₀ - ∫₀ᵗ Ys dXs - ∫₀ᵗ dXs dYs

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To develop the Branch and Bound (B&B) tree for the given problem, follow these steps:

1. Start with the initial B&B tree, where the root node represents the original problem.

2. Choose \($x_1$\) as the branching variable at node 0. Add two child nodes: one for

\($x_1 \leq \lfloor x_1 \rfloor$ \\(floor of $x_1$) and one for $x_1 \geq \lceil x_1 \rceil$ (ceiling of $x_1$).\)

3. At each node, perform the following steps:

  - Solve the relaxed linear programming (LP) problem for the node, ignoring the integer constraints.

  - If the LP solution is infeasible or the objective value is lower than the current best solution, prune the node and its subtree.

  - If the LP solution is integer, update the current best solution if the objective value is higher.

  - If the LP solution is non-integer, choose the fractional variable with the largest absolute difference from its rounded value as the branching variable.

4. Repeat steps 2 and 3 for each unpruned node until all nodes have been processed.

5. The node with the highest objective value among the integer feasible solutions is the optimal solution.

6. Optionally, backtrace through the tree to retrieve the optimal solution variables.

Note: The specific LP problem and its constraints are missing from the given question, so adapt the steps accordingly.

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The magnitude of the cross product u x v is  \(27\sqrt{3}\).

To compute the vector product (cross product) of u and v, we can use the formula:

u x v = |u| |v| sin(θ) n

Where:

|u| and |v| are the magnitudes of vectors u and v,

theta is the angle between u and v, and

n is the unit vector perpendicular to the plane formed by u and v.

Given:

u = 6

v = 9

θ = 2\(\pi\)/3

To find the magnitude of the cross product, we can use the formula:

|u x v| = |u| |v| sin(θ)

Plugging in the values, we get:

|u x v| = 6 * 9 * sin(2\(\pi\)/3)

       = 54 * \(\sqrt{3}\)/ 2

       = 27 \(\sqrt{3}\)

So the magnitude of the cross product is 27 \(\sqrt{3}\).

To determine the direction of the cross product, we can use the right-hand rule. Since the angle between u and v is 2\(\pi\)/3 (or 120°), the cross product will be perpendicular to the plane formed by u and v, pointing in a direction determined by the right-hand rule.

In conclusion, the vector product of u and v is 27 \(\sqrt{3}\), and its direction is perpendicular to the plane formed by u and v.

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Step-by-step explanation:

3/8 = 15/40= 75/200

2/5 = 16/40 = 80/200

-> 4 rational numbers between 75/200 and 80/200 are 76/200, 77/200, 78/200, 79/200

a)There are \(2^m^n\) possible relation

b)Similarly \(n^m\)

c)\(\frac{n^m}{2^m^n}\)

a)Set A has m elements and set B has n elements

Firstly determine the number of elements A*B by using the multiplication rule

Number of elements\(=A*B=m*n=mn\)

For each element, \(A*B\) we have two option

First element 2 ways

Second element 2 ways

mn element 2 ways

By using the multiplication rule

\(2*2*2......=2^m^n }\)

Then there are \(2^m^n\) possible relation

b)Similarly \(n^m\)

c)\(\frac{n^m}{2^m^n}\)

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Answer:I would say if there are 15 leaches then there will be 20 toads

Step-by-step explanation: I multiplied the 4 times 5

Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

Answer:

Alex has 3x dollars and an extra 15 dollars in his coat pocket. He buys a new Nike shoe for 84 dollars. How much money did Alex spend that was not in his pocket.

Step-by-step explanation:

Answer:

Part A: Word problem

Maria went to the store and purchased some books for her book club. Each book cost $3, and she also bought some bookmarks at $15 each. Maria's total purchase, including tax, amounted to $84. If Maria bought x books, write an equation to represent the situation.

Part B: Solution

To solve the equation 3x + 15 = 84, we need to isolate the variable x on one side of the equation.

Step 1: Subtract 15 from both sides of the equation to eliminate the constant term on the left side:

3x + 15 - 15 = 84 - 15

3x = 69

Step 2: Divide both sides of the equation by 3 to isolate x:

3x/3 = 69/3

x = 23

So, the solution to the equation is x = 23.

Part C: Explanation

In the given equation 3x + 15 = 84, the variable x represents the number of books Maria purchased. The equation states that the cost of x books at $3 each, represented by 3x, plus the cost of $15 for bookmarks, totals to $84. Thus, the value of x represents the number of books Maria bought in this scenario. In the solution, x = 23, it means Maria purchased 23 books for her book club.

Step-by-step explanation: