What’s the answer to -8xy+2xy

Answers

Answer 1

Answer:

-8xy+2xy=-6xy


Related Questions

Put the following equation of a line into slope-intercept form, simplifying all fractions.
8x+6y=
8x+6y=
\,\,18
18

Answers

Answer:

do u have a full screenshot of it???

Step-by-step explanation:

Please help me with edge question .

Please help me with edge question .

Answers

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

What is the x coordinate for the patch (and any other patch on the left face)?

Answers

The x coordinate for the patch (and any other patch) on the left face of an object is the smallest x value within the object's domain, as it corresponds to the position of the left face in relation to the coordinate system. All patches on the left face share this same x coordinate value, regardless of their location on the face.

To answer this question about the x coordinate for the patch on the left face, let's break it down:
1. Identify the left face: First, we need to recognize which face of the object is the left face. This is typically the side that faces left when looking at the object in its standard orientation.


2. Find the x coordinate: Since the left face of an object is perpendicular to the x-axis, the x coordinate for any point (or patch) on that face will be the same. This means that all patches on the left face share the same x coordinate value.
3. Determine the specific x coordinate value: To find the actual value of the x coordinate, examine the object's dimensions and/or coordinate system. The x coordinate for the left face will be the smallest x value within the object's domain.

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What is the derivative of f(x)=−3cos(x)+4sin(x) at the point x=π/3? Enter an exact answer.

Answers

The derivative of f(x) =−3cos(x)+4sin(x) at the point x = π/3 is (3√3 + 4)/2.

The derivative of f(x) = -3cos(x) + 4sin(x) at the point x = π/3 can be found by first taking the derivative of the function and then plugging in the given value for x.

The derivative of f(x) is given as f'(x) = 3sin(x) + 4cos(x).

Next, plug in x = π/3 to find the derivative at that point:

f'(π/3) = 3sin(π/3) + 4cos(π/3)

= 3(√3/2) + 4(1/2)

= (3√3 + 4)/2

Therefore, the derivative of f(x) at the point x = π/3 is (3√3 + 4)/2.

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how to find absolute maximum and minimum of a function

Answers

To find the absolute maximum and minimum of a function, determine the critical points and evaluate the function at those points and the endpoints of the interval.

To find the absolute maximum and minimum of a function, you need to follow these steps:

1. Determine the critical points of the function by finding where its derivative equals zero or is undefined. These points can be potential candidates for the maximum or minimum values.

2. Evaluate the function at the critical points and at the endpoints of the interval you are considering. The highest value among these points will be the absolute maximum, while the lowest value will be the absolute minimum.

Let's illustrate this with an example:

Consider the function f(x) = x^2 - 4x + 5 on the interval [0, 5].

1. To find the critical points, we need to find where the derivative is equal to zero or undefined. Taking the derivative of f(x),

we get f'(x) = 2x - 4.

Setting this equal to zero gives us 2x - 4 = 0, which implies x = 2. So, x = 2 is the only critical point.

2. Now, we evaluate the function at the critical point and the endpoints of the interval:
f(0) = 0^2 - 4(0) + 5 = 5
f(2) = 2^2 - 4(2) + 5 = 1
f(5) = 5^2 - 4(5) + 5 = -5

From these evaluations, we see that f(0) = 5 is the absolute maximum and f(5) = -5 is the absolute minimum.

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Develop an essenential smoothing forecast (α=0.45) for penods 11 through 15 Assume that your forecast for penod 10 was 297 Calculate the forecasts for perieds 11 through 15 (enter your responses rocmdod to tivo decimal places)

Answers

The forecasts for periods 11 through 15 are: F11 = 297.4, F12 = 296.7, F13 = 297.1, F14 = 296.9, F15 = 297.0

Given: Smoothing constant α = 0.45, Forecast for period 10 = 297

We need to calculate the forecasts for periods 11 through 15 using the essential smoothing forecast method.

The essential smoothing forecast is given by:Ft+1 = αAt + (1 - α)

Ft

Where,

At is the actual value for period t, and Ft is the forecasted value for period t.

We have the forecast for period 10, so we can start by calculating the forecast for period 11:F11 = 0.45(297) + (1 - 0.45)F10 = 162.35 + 0.45F10

F11 = 162.35 + 0.45(297) = 297.4

For period 12:F12 = 0.45(At) + (1 - 0.45)F11F12 = 0.45(297.4) + 0.55(297) = 296.7

For period 13:F13 = 0.45(At) + (1 - 0.45)F12F13 = 0.45(296.7) + 0.55(297.4) = 297.1

For period 14:F14 = 0.45(At) + (1 - 0.45)F13F14 = 0.45(297.1) + 0.55(296.7) = 296.9

For period 15:F15 = 0.45(At) + (1 - 0.45)F14F15 = 0.45(296.9) + 0.55(297.1) = 297.0

Therefore, the forecasts for periods 11 through 15 are: F11 = 297.4, F12 = 296.7, F13 = 297.1, F14 = 296.9, F15 = 297.0 (All values rounded to two decimal places)

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Given: g(x) = Vx – 4 and h(x) = 2x - 8.
What is g(h(10))?
2V2
VG
* V6 - 8
* 2V6 - 8

Answers

Answer:

\( 2\sqrt{2} \)

Step-by-step explanation:

\( g(x) = \sqrt{x - 4} \)

\( h(x) = 2x - 8 \)

\( h(10) = 2(10) - 8 = 12 \)

\( g(h(10)) = g(12) = \sqrt{12 - 4} \)

\( g(h(10)) = \sqrt{8} = 2\sqrt{2} \)

Answer: \( 2\sqrt{2} \)

Answer:

2 square root 2

Step-by-step explanation:

A triangle has vertices at A (1, 3), B (4,2), and C (3,8). Which transformation would
produce an image with vertices A' (2,6), B'(8,4), C'(6,16)?
A rotation so' counterclockwise.
A dilation with a scale factor of 4.
A rotation 90° clockwise.
A reflection over the x-axis.
A dilation with a scale factor of z.

Answers

Answer:

  A dilation with a scale factor of 2

Step-by-step explanation:

Each image coordinate is double the corresponding pre-image coordinate. That means the figure was dilated by a factor of 2.

FAM I NEED YOU HELP POR FAVOR:
You purchase two bottles of sunscreen and a hat. The hat costs $6.50. You pay 6% sales tax. You pay a total of $16.43. How much does one bottle of sunscreen cost?

Answers

Answer:

I got you fam dont worry

Step-by-step explanation:

if you want me to show my work I dont mind at all but the answer is 4.50

FILL THE BLANK. The average time a molecule spends in its reservoir is known as ________.

Answers

The average time a molecule spends in its reservoir is known as the residence time.

Residence time is an important concept in environmental science, particularly in the study of water quality and pollution. It refers to the average amount of time that a substance, such as a molecule or a pollutant, spends in a particular environment before it is either removed or transformed. For example, in a river, the residence time of a pollutant would be the amount of time it takes for that pollutant to be either broken down by natural processes or transported downstream to another location. By understanding residence time, scientists can better predict how pollutants will move through the environment and where they are likely to accumulate.

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Which of the following vectors is tangent to the surface 3xy 2
+2z 3
=5 at the point (1,−1,1) ?

Answers

The vector tangent to the surface at (1, -1, 1) is given by: \($[3, -6, 6] \times [1, 0, 0] = [0, -18, -6]$\)

Given surface equation: \($3xy^2 + 2z^3 = 5$At the point $(1, -1, 1)$, we have $x = 1$, $y = -1$, and $z = 1$.\)

The gradient of the given surface is given by: \($\text{grad}(f) = \left[\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right]$\)

\(At ~the~ point $(1, -1, 1)$, the ~gradient~ is~ given~ by: $\text{grad}(f) = \left[\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right]_{(1, -1, 1)} = \left[3y^2, 6xy, 6z^2\right]_{(1, -1, 1)} = \left[3(-1)^2, 6(1)(-1), 6(1)^2\right] = [3, -6, 6]$\)

A vector tangent to the surface at (1, -1, 1) must be orthogonal to the gradient of the surface at this point.

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a container with 3 1/2 gallons of weed killer can spray 2 1/4 lawns. how many gallons would it take to spray 2 lawns

Answers

To spray on 2 lawns is required \(3\frac{1}{9}\)  gallons.

Mixed fraction A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given ;

  A container with \(3\frac{1}{2}\) gallons of weed killer can spray =  \(2\frac{1}{4}\) lawans

∵ in \(\frac{9}{4}\) lawn the week killer can spray =  \(\frac{7}{2}\)gallons

∴ in 1 lawn the weed killer is  used = \(\frac{7}{2}\) × \(\frac{4}{9}\) gallon

∴ in 2 lawns the weed killer can spray =\(\frac{7}{2}\)  ×  \(\frac{4}{9}\)× 2 =\(\frac{28}{9}\)  gallon =\(3\frac{1}{9}\)gallons

  \(3\frac{1}{9}\) gallons require to spray 2 lawns.

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PLEASEEEE SOMEONE HELP I GIVE AS MUCH POINTS :’( Thank you!

PLEASEEEE SOMEONE HELP I GIVE AS MUCH POINTS :( Thank you!

Answers

The approximate area of the trapezoid is determined as  13.95 unit².

What is the approximate area of the trapezoid?

The approximate area of the trapezoid is calculated as follows;

Area = ¹/₂(b₁ + b₂)h

Where;

b₁ and b₂ are the lengths of the parallel sidesh is the height

The y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;

y(3/2) = - (3/2)²/2 + 3/2 + 5

y(3/2) = -9/8 + 3/2 + 5

y(3/2) = 5.375

y(4) = -4²/2 + 4 + 5

y(4) = -8 + 9

y(4) = 1

h = 5.375 - 1 = 4.375

The approximate area of the trapezoid is calculated as;

Area = ¹/₂(5.375 + 1) x 4.375

Area = 13.95 unit²

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Prove that the sum of 3 consecutive numbers is always a multiple of 3

Answers

Proof:

3 consecutive integers are x, x+1 , x+2.

Add these values.

x+x+1+x+2

3x+3

3×(x+1)

3(x+1) is the multiple of 3 for any integer value of x.

Answer: We have proved that the sum of 3 consecutive numbers is always a multiple of 3.

Let us assume: 3 consecutive integers are x, x+1 , x+2.

Then add these values.

\(x+x+1+x+2\\=3x+3\\=3(x+1)\)

It is the multiple of 3 for any integer value of x.

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a food truck operator has traditionally sold 75 bowls of noodle soup each day. he moves to a new location and after a week sees that he has averaged 85 bowls of noodle soup sales each day. he runs a one-sided hypothesis test to determine if his daily sales at the new location have increased. the p-value of the test is 0.031. how should he interpret the p-value?

Answers

There is a 3.1% chance of obtaining a sample with a mean of 85 or higher assuming that the true mean sales at the new location are still equal to or less than 75 bowls a day.

What is the P value in statistics?

P value is a part of hypothesis testing. The P value is a measurement used against some data in testing.

Given in question,

    Food Truck in  Old location:

                             Sold =  75 bowls of noodle soup

   New location  Sold =  85 bowls of noodle soup

   p-value = 0.031

there is a 3.1% chance of obtaining a mean with a sample.

similarly, that is we can tell that the true mean sales at the new location will be still equal to or less than 75

  i.e. [P(X=75) ≤ P(X=85)]   bowls a day.

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Danielle constructs a scale model of a building with a rectangular base. Her model is 3 inches in length and 4 inch in width. The scale on the model is 1 inch = 40 feet. What are the actual, dimensions, of the base of the building? Hint: make a table

Danielle constructs a scale model of a building with a rectangular base. Her model is 3 inches in length

Answers

Given:

A scale model of a building having the dimensions of 3 inches in length and 4 inches in width.

Here, 1 inch = 40 feet.

To find the actual dimensions of the base of the building:

Since 1 inch = 40 feet,

So we have,

\(\begin{gathered} l=3\text{ inches} \\ =3\times40 \\ =120\text{ fe}et \\ b=4\text{ inches} \\ =4\times40 \\ =160\text{ fe}et \end{gathered}\)

Thus, the length of the base of the building is 120 feet and the width of the base of the building is 160 feet.

26 points with brainiest and 5 stars and thanks, please help! :[

26 points with brainiest and 5 stars and thanks, please help! :[

Answers

Answer:

\(\Huge \boxed{{9}}\)

Step-by-step explanation:

Let the age of Darrell be x.

Let the age of Bryce be y.

x = y + 8

xy = 153

Substitute x = y + 8 in the second equation.

(y+8)y = 153

Solve for y.

y² + 8y = 153

Subtract 153 from both sides.

y² + 8y - 153 = 0

Factor left side.

(y-9)(y+17) = 0

Set factors equal to 0.

y - 9 = 0, y = 9

y + 17 = 0, y = -17

The value of y has to be positive, so y = 9.

Substitute y = 9 in the first equation.

x = 9 + 8

x = 17

Darrell is 17 years old.

Bryce is 9 years old.

Answer:

\(\huge\boxed{9\ years}\)

Step-by-step explanation:

Let Darrel's Age be x and Bryce's Age be y

Condition 1:

x = 8 + y

Condition 2:

xy = 153

Put the 1st equation in the second one

(8+y)y = 153

y²+8y-153 = 0

y²+17y-9y-153 = 0

y(y+17)-9(y+17) = 0

(y-9)(y+17) = 0

Either,

y-9 = 0   OR    y+17 = 0

y = 9       OR    y = -17 [Contrary to be given, Age can never be negative]

So, y = 9

And

Bryce's Age = 9 years

Note: In the following exercises, answers will vary if a tie is encountered.
Exercises 5–12 use the FedEx travel times shown in Figure 9.56.
Exercises 5–8 involve deliveries to Kinko’s, City Hall, the insurance office, the lawyer’s office, and the bank.
If you must make deliveries from the FedEx warehouse to Kinko’s, City Hall, the insurance office, the lawyer’s office, and the bank, how many different routes are possible? Of Exercises 5, 6, and 7, which assigned exercise generates the best delivery sequence?

Answers

To determine the number of different routes from the FedEx warehouse to the five destinations (Kinko's, City Hall, the insurance office, the lawyer's office, and the bank), we can use the concept of permutations.

Since all the destinations need to be visited, we need to find the number of permutations of the five destinations. This can be calculated as 5 factorial (5!) since the order of the destinations matters.

5! = 5 x 4 x 3 x 2 x 1 = 120

Therefore, there are 120 different routes possible.

To determine the best delivery sequence among Exercises 5, 6, and 7, we would need to examine the specific sequences given in those exercises. Without the specific sequences, it is not possible to determine which exercise generates the best delivery sequence.

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A square has sides of length 6/12 inches. Area of length times width.

What is the area of the square in square inches?

Answers

The area of the square is 1/4inches² in square inches

What is area of square

The area of a square is calculated by multiplying its two sides, that is area = s × s, where, 's' is one side of the square.

The square has side of length = 6/12

this can be simplified as 1/2

so

area of the square = (1/2 × 1/2) inches ²

area of the square = 1/4inches²

Thus, the area of the square is calculated using area = s × s, as 1/4inches²

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Your teacher has disabled instant marking. Your marks will appear after the due date.

35%

Patryk has 7 cards.

There is a number on each card.

|2||3||4||5|| 6 ||7|| 8

Patryk takes two of the cards at random.

He works out the product of the numbers on the two cards.

Work out the probability that the product is an odd number.

EH

Type here to search

O

Answers

1/7 is the probability that the product is an odd number.

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                   Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Total Cards are 7

2 cards out of 7 cards can be selected in ⁷C₂   = 21  ways

Product would be odd if both cards are odd

3 , 5 , 7  are odd cards

2 cards out of 3 Can be selected   in ³C₂  = 3  ways

( 3 , 5) , ( 3 , 7) , ( 5 , 7)

Hence probability  the product of the numbers on the 2 cards  is odd number

= 3/21

= 1/7

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if 20% of an item is 360 what is 85% of the item?​

Answers

The answer to your question would be 1530 because the whole number is 1800 and then the 85% would be 153.

Arrange the equations in the correct sequence to find the inverse of f(2)=y==
33z-zy=y-4
33z +4=y(1+z)
33z-zy=y+4
33x+4=y+zy
1+z
y=f¹ (2) = 33274
+4
33z-zy = y +4
A =
33-
y=f-¹ (z) = 332+4
z (33-y)=y-4




Į

Answers

c ccccccccccccccccccccccccccccc

the sun is shining and a spherical snowball of volume 260 ft3 is melting at a rate of 11 cubic feet per hour. as it melts, it remains spherical. at what rate is the radius changing after 6.5 hours?

Answers

If the spherical snowball is melting , then the rate at which the radius changing after 6.5 hours is 0.208 ft/h  .

A spherical snowball has volume = 260 ft³ that is melting at a rate of 11 cubic feet per hour, while remaining spherical.

We have to find the rate at which the radius is changing after 6.5 hours.

So , let "V" = volume of snowball, "r" = radius of snowball, and "t" = time.

Volume Of Sphere is  V = (4/3)πr³ and dV/dt = -11 ft³/h ;

So,  dr/dt when t = 6.5 hours. is dV/dt = (dV/dr)×(dr/dt)  ;

derivative of volume formula with respect to "r", we get:

⇒ dV/dr = 4πr²   ;

Substituting the given values in chain rule equation, we get:

⇒ -11 = (4/3)πr² × dr/dt  ;

⇒ dr/dt = -11/((4/3)πr²)

For  rate of change of the radius when t = 6.5 hours, we find the radius at that time.

The initial volume of the snowball = 260 ft³.

After 6.5 hours of melting at a rate of 11 ft³/h, the remaining volume will be:  V = 260 - (11 × 6.5) = 188.5 ft³   ;

So , V = (4/3)πr³

⇒ 188.5 = (4/3)πr³

⇒ r³ = (188.5 × 3 / (4π))   ;

≈ 3.55ft

Now we substitute r = 3.55 feet

⇒ dr/dt = -11/[(4/3)π(3.55)²]  ;

⇒ dr/dt ≈ -0.208 ft/h  ;

Therefore , the rate at which radius is changing after 6.5 hours is approximately 0.208 feet per hour and negative sign represents that radius is decreasing  .

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Drag each expression to show whether the expression is equivalent to 12x - 6,
24x+12, or neither.

Drag each expression to show whether the expression is equivalent to 12x - 6,24x+12, or neither.

Answers

Answer:

Drag and drop 6(2x-1) to 12x-6.

Drag and drop 6(4x-2) to Neither.

Drag and drop 3(8x+4) to 24x+12.

Drag and drop 6(4x+2) to 24x+12.

Drag and drop 2(6x-3) to 12x-6.

Step-by-step explanation:

To check these, use distributive property to solve each one.

6(2x-1) = 12x-6

6(4x-2) = 24x-12

3(8x+4) = 24x+12

6(4x+2) = 24x+12

2(6x-3) = 12x-6

Hope this helps!

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Select the correct answer from the drop-down menu. An energy drink company claims that its product increases students' memory levels. To support its claims, the company issues advertisements claiming that 8 out of 10 people (chosen randomly from across the country) who tried their product reported improved memory. The missing component in this study is a .

Answers

Here the missing component in this study is control group.

What is a control group in an experiment?

A control group is a group of participants used to compare different groups in a test or experiment. Consists of participants who did not receive an experimental treatment. Some experiments use multiple control groups to collect more information and improve the accuracy of the results. For example, many medical studies include positive, negative, and placebo control groups to better understand the effectiveness of a treatment or drug.

Given the circumstances, the energy drink company claims that its products boost memory in students. To back up its claims, the company publishes an ad claiming that eight out of 10 people (randomly selected across the country) who tried the product reported improved memory.

But they didn't compose a control group to compare the results for test.

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The complete question is as follows:

An energy drink company claims that its product increases students' memory levels. To support its claims, the company issues advertisements claiming that 8 out of 10 people (chosen randomly from across the country) who tried their product reported improved memory. The missing component in this study is a

A) control group

B) sample group

C) population

D) test group

Answer:

A. Control Group

Plato

Brice worked for 31.5 hours this week. Two-thirds of this time was spent working from home. How many hours did he spend working from home?

Answers

Answer:

21 hours

Step-by-step explanation:

If he worked 2/3 at home you need to divide 31.5 by 3 = 10.5

Then multiply by 2 = 21

Hope this helps! Have a great day :)

Exercise 18-29 (Algorithmic) (LO. 2) In 2021, Chaya Corporation, an accrual basis, calendar year taxpayer, provided services to clients and earned $56,500. The clients signed notes receivable to Chaya that have a fair market value of $48,025 at year-end. In addition, Chaya sold a 36-month service contract on April 1, 2021, and received payment in full of $27,120. Do not round any division. If required, round your final answer to the nearest dollar. How much gross income does Chaya report from these transactions in 2021? 1. From services to clients: 2. From service contract: $

Answers

Chaya Corporation reports $7,533.33 as gross income from the service contract.To determine the gross incom,  we need to consider the revenue from services provided to clients and the revenue from the service contract.

1. From services to clients:
Chaya Corporation earned $56,500 from providing services to clients. This amount is reported as gross income.

2. From service contract:
The service contract sold on April 1, 2021, for $27,120 is considered unearned revenue initially. For tax purposes, the revenue from the service contract is recognized over the contract period. Since the service contract is for 36 months, the revenue recognized in 2021 would be:
$27,120 / 36 months * 9 months (April to December) = $7,533.33

Therefore, Chaya Corporation reports $7,533.33 as gross income from the service contract.

In total, Chaya Corporation reports $56,500 + $7,533.33 = $64,033.33 as gross income from these transactions in 2021. Rounded to the nearest dollar, the gross income reported is $64,033.

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A manufacturer inspects 100 boxes of ice cream cones
after production to make sure no cones are cracked or
damaged. They find that 97 boxes have no defects. If
5,000 boxes of ice cream cones are being shipped to the
grocery stores, predict how many boxes will have damaged
ice cream cones.

Answers

Answer:

4850 boxes

Step-by-step explanation:

97 out of 100 boxes have no defects, can be translated into 97% of boxes have no defects. Using this number, we can find 97% of 5,000 to make an estimate of how many boxes will not have defects
.97(5,000)=4850

esemate 5,840 x 25 i need help please

Answers

Answer:

146,000

Step-by-step explanation:

Simple math let me know if you need anymore help honey, have a nice day!

The local bank has a single line for customers waiting for the next available bank teller. There are four bank tellers who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. Customers arrive at the bank at a rate of about twelve every hour. On average, it takes about 15 minutes to serve each customer. Answers to 2 d.p's.
(a) Calculate the probability that the bank is empty.
(b) Calculate the average time the customer spends waiting to be called.
(c) Calculate the average number of customers in in the bank.
(d) The average number of customers waiting to be served

Answers

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

For more about probability:

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