1.(20 points) Consider a (Q,r) inventory system where an order of Q is placed when the system reaches r. The order arrives following an exponentially distributed time with rate 1 while demands occur one by one following a P.P. with rate u. Model the process when the system does not consider backorder.

Answer:

\(\frac{6}{12}\) \(= \frac{1}{2}\)

Step-by-step explanation:

\(\frac{1}{6} +\frac{2}{4}\)

Find LCM of 6 and 4 which is 12.

6*2=12

4*3=12

Do the same to the top parts of each part.

1*2=2

2*3=6

\(\frac{2}{12} + \frac{4}{12}\)

Now you can add them easily

\(\frac{2}{12} + \frac{6}{12} = \frac{6}{12}\)

Because 6 and 12 can still be divided by the same number (6) you need to divided it in order to get a simpler fraction.

6÷6=1

12÷6=2

\(\frac{1}{2}\)

(An improper fraction is one in which the numerator is larger than the denominator. Nothing in this equation was an improper fraction. Though, for example, \(\frac{12}{6}\) is an improper fraction. To get a mixed number/whole number. You would simply divide the numerator, 12, by the denominator 6. In doing so, you would get 2)

15 candy bars must be bought at the cost of $0.72 per piece to bring the average down to $0.80.

To find the number of candy bars needed to bring the average cost down to $0.80, we can use the formula for average:

(sum of costs)/(number of candy bars).

Let's denote the number of candy bars needed as x. We know that the sum of costs for the group of ten candy bars is 10 * $0.89 = $8.90.

To bring the average down to $0.80, the sum of costs for the x candy bars must be (10 * $0.89 + x * $0.72).

Now we can set up the equation:

(10 * $0.89 + x * $0.72)/(10 + x) = $0.80.

Simplifying this equation, we get:

8.9 + 0.72x = 0.8(10 + x).

Solving for x, we find that x = 15.

Therefore, 15 candy bars must be bought at the cost of $0.72 per piece to bring the average down to $0.80.

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complete question:

A group of ten candy bars has an average cost of $0.89 per candy bar. How many bars must be bought at the cost of $0.72 a piece to bring the average down to $0.80?

6k · 1/6 = 6/6k = k

.......

Step-by-step explanation:

hopefully it is clear and understandable

:)

Answer:

You find an area of a square by multiplying the width and the length.

Answer:

you multiply the length by the width.

Step-by-step explanation:

the attached file shows what the length and width are.

Answer:

\(x = y + 7 \\ \\ x = \frac{3 + y}{2} \: or \: y = 2x - 3\)

Step-by-step explanation:

\(1. \: 2x = 3 + y \\ 2. \: x = \frac{3 + y}{2} \: or \: y = 2x - 3 \\ \\ 1. \: y + 7 = x \\ 2. \: x = y + 7\)

Answer:

Hope this helps

Step-by-step explanation:

Answer:

x-intercepts (-8,0)

y-intercepts(0,4)

Step-by-step explanation:

To find the x-intercept, substitute in 0  for  y  and solve for  x . To find the y-intercept, substitute in  0  for  x  and solve for  y .

Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (4, 3)

m = \(\frac{3-0}{4+5}\) = \(\frac{3}{9}\) = \(\frac{1}{3}\) , thus

y = \(\frac{1}{3}\) x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 3) , then

3 = \(\frac{4}{3}\) + c ⇒ c = 3 - \(\frac{4}{3}\) = \(\frac{5}{3}\)

y = \(\frac{1}{3}\) x + \(\frac{5}{3}\) → A

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

The equation of the line that passes through (-5, 0) and (4, 3) is

y = (1/3)x + 5/3.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

The general equation of a straight line is y = mx + c.

m = slope

c = y-intercept

We have,

A line passes through (-5, 0) and (4, 3)

Slope = m is given by:

m = (d - b) / (c - a)

where (a, b) and (c, d) are the points where the line passes.

Now,

Slope =m = (3 - 0)/(4 - (-5)) = 3/(4+5) = 3/9 = 1/3

We have,

y = mx + c

We can assume any point (-5, 0) or (4, 3) to find the value of the y-intercept.

Case 1.

(-5 , 0) = (x, y)

0 = 1/3(-5) + c

0 = -5/3 + c

c = 5/3

Case 2.

(4, 3) = (x, y)

3 = (1/3)4 + c

3 = 4/3 + c

c = 3 - 4/3

c = 9 - 4 / 3

c = 5/3

We will get the same value for c in both cases.

We have,

m = 1/3 and c = 5/3

The equation of the line can be written as:

y = (1/3)x + 5/3.

Thus the equation of the line that passes through (-5, 0) and (4, 3) is

y = (1/3)x + 5/3.

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The correct answer is option b: ahe increases by​ $0.605 for every​ one-year increase in age.

Based on the given options, the coefficient on age indicates that ahe increases by​ $0.605 for every​ one-year increase in age. This means that as age increases by one year, ahe is expected to increase by​ $0.605.

Therefore, the correct answer is option b: ahe increases by​ $0.605 for every​ one-year increase in age.

- The coefficient on age suggests that there is a positive association between age and ahe.
- For every one-year increase in age, ahe is expected to increase by​ $0.605.

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The minimum value of z is -12.

Given that the system of linear programming

z=-3x+5y

x+y≥-22

x-y≥-4

x-y≤2

Firstly, we will convert the given constraints into equality as

x+y=-22

x-y=-4

x-y=2

Now, we will take the equation x+y=-22 and taking x as 0 as find y and taking y as 0 to find x, we get

If x=0 then y is

0+y=-22

y=-22

If y=0 then x=-22

So, the points lie on the line x+y=-22 is (0,-22) and (-22,0).

Further, we will take the equation x-y=-4 and taking x as 0 as find y and taking y as 0 to find x, we get

If x=0 then y=4

If y=0 then x=-4

So, the points lie on the line x-y=-4 is (0,4) and (-4,0).

Furthermore, we will take the equation x-y=2 and taking x as 0 as find y and taking y as 0 to find x, we get

If x=0 then y=-2

If y=0 then x=2

So, the points lie on the line x-y=2 is (0,-2) and (2,0).

now, we will find the feasible region of the given constraints as shown in figure.

We will find that each constraint will contain origin or not by substituting (0,0), we get

0+0≥-22 containing origin

0-0≥-4 containing origin

0-0≤2 containing origin

From the graph we can see that the minimum value of x is -13 and minimum value of y is -12.

z=-3x+5y

z=-3x+3y+2y

z=-3(x-y)+2y

minmum value of x-y from the given constraints is

-4≤x-y≤2

From here minimum value of x-y is -4

So, z=-3(-4)+2y

z=12+2y

For the minimum value of z the value of y should be minimum.

From the graph we can see the minimum value of y=-12

So, z=12+2(-12)

z=12-24

z=-12

Hence, the minimum value of z for the system of Linear Programming:

z=-3x + 5y, x+y≥-22, x-y≥-4, x - y ≤ 2 is -12.

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Step-by-step explanation:

v = u + at

v-u = at

a = (v -u)/t

When t = 4, u=10, v=50

a = (50-10)/4

a= 40/4

a = 10

Answer:

Infinite amount of solutions

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Where the 2 lines intersect is the solution set to the systems of equations.

If the 2 lines are parallel, they have no solution.

If the 2 lines are the same, they have infinite amount of solutions.

Step-by-step explanation:

y=3x+2

when x=0

y=3(0)+2

y=2

(0,2)

when y=0

3x+2=0

3x=-2

x=+2/3

(-2/3,0)

6x-2y=-4

when x=0

6(0)-2y=-4

-2y=-4

y=2

(0,2)

when y=0

6x-2(0)=-4

6x=-4

x=-4/6

x=-2/3

(-2/3,0)

same line

The value of x and y are -5 and 4 using any of the methods as given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

y = 4x + 24  ______(1)

y = x + 9 _______(2)

We can use the substitution method or elimination method.

Substitution method:

4x + 24 = x + 9

4x - x = 9 - 24

3x = -15

x = -5

And,

y = x + 9

y = -5 + 9

y = 4

Elimination method.

y = 4x + 24

y - 4x = 24 _____(A)

y = x + 9

y - x = 9 _____(B)

From (A) and (B)

  y - 4x = 24

  y - x = 9

(-)   (+)    (-)

      -3x = 15

          x = -5

And,

y - x = 9

y - (-5) = 9

y = 9 - 5

y = 4

Thus,

x is -5 and y is 4

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There are infinitely more possibilities, but the midpoint between 1/2 and 1 is 3/4.

what is fraction?

An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

For any two numbers a and b, the average 1/2(a + b) is lies between them.

Here, the given two numbers are 1/2 and 1.

So, to find the fraction between 1/2 and 1 we can form the average:

1/2(1/2 + 1) = 1/2(3/2) = 3/4

Hence, the fraction that fit between 1/2 and 1 is 3/4.

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The probability that James will take the same mode of transportation twice is 1/9.

To find the probability that James will take the same mode of transportation twice, we need to calculate the probability of each individual transportation option and then multiply them together.

In the morning, James has 3 transportation options: bus, cab, or train. Since he randomly chooses his ride, the probability of selecting any particular option is 1 out of 3 (assuming all options are equally likely).

Therefore, the probability of James selecting the same transportation mode in the morning and evening is 1/3.

Hence, the probability that James will take the same mode of transportation twice is 1/3 multiplied by 1/3:

P(same mode of transportation twice) = 1/3 * 1/3 = 1/9.

Therefore, the probability that James will take the same mode of transportation twice is 1/9.

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Answer:

1 : 14

hard to see image (try using screen shots)

but.... 2 inches to 4 feet would be

2 : 48 which is

1 : 14

Step-by-step explanation:

Thus, the coordinates of ΔF'I'G' after a rotation of 90° clockwise about the origin. are - F'(4,-2), I'(4,-5) and G'(2,-3).

A rotation is a turn made about a specific axis. Both clockwise and anticlockwise rotations are possible. Whereas the image is really the rotating image, the pre-image is the original item.

From the pre-image point, calculate the image. The listed pre-image point is (x , y). Change the x and y coordinates, then multiply this same previous y coordinate by -1 to get a 90 degree anticlockwise rotation. Use the guidelines mentioned below to calculate each rotation.

Clockwise :

Given :

F(2, 4), I(5, 4) and G(3, 2)

After 90 degree rotation: (x , y) ----> (y , -x)

F'(4,-2), I'(4,-5) and G'(2,-3).

Thus, the coordinates of ΔF'I'G' after a rotation of 90° clockwise about the origin. are - F'(4,-2), I'(4,-5) and G'(2,-3).

Graphs for the both triangles are obtained.

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Correct question:

ΔFIG has vertices at F(2, 4), I(5, 4) and G(3, 2). Graph ΔFIG and ΔF'I'G' after a rotation of 90° clockwise about the origin.​

a. One component of each type can be selected in 5 * 4 * 3 * 4 = 240 ways.

b. If both the receiver and CD player are Sony, components can be selected in 1 * 1 * 3 * 4 = 12 ways.

c. If none is Sony, components can be selected in 4 * 3 * 3 * 3 = 108 ways.

d. With at least one Sony component, a selection can be made in 240 - 108 = 132 ways.

e. Probability of at least one Sony component is 132/240 ≈ 0.55. Probability of exactly one Sony component is 12/240 = 0.05.

a. To determine the number of ways one component of each type can be selected, we multiply the number of choices for each component.

Receiver: 5 options (Kenwood, Onkyo, Pioneer, Sony, Sherwood)

CD Player: 4 options (Onkyo, Pioneer, Sony, Technics)

Speakers: 3 options (Boston, Infinity, Polk)

Cassette Deck: 4 options (Onkyo, Sony, Teac, Technics)

Using the product rule, the total number of ways to select one component of each type is:

5 * 4 * 3 * 4 = 240 ways.

b. If both the receiver and the CD player are required to be Sony, we fix the choices for those components to Sony and multiply the remaining choices for the speakers and cassette deck.

Receiver: 1 option (Sony)

CD Player: 1 option (Sony)

Speakers: 3 options (Boston, Infinity, Polk)

Cassette Deck: 4 options (Onkyo, Sony, Teac, Technics)

Using the product rule, the total number of ways to select components with Sony as the receiver and CD player is:

1 * 1 * 3 * 4 = 12 ways.

c. If none of the components can be Sony, we subtract the choices for Sony from the total number of choices for each component and multiply the remaining options.

Receiver: 4 options (Kenwood, Onkyo, Pioneer, Sherwood)

CD Player: 3 options (Onkyo, Pioneer, Technics)

Speakers: 3 options (Boston, Infinity, Polk)

Cassette Deck: 3 options (Onkyo, Teac, Technics)

Using the product rule, the total number of ways to select components with none of them being Sony is:

4 * 3 * 3 * 3 = 108 ways.

d. To calculate the number of ways to select components with at least one Sony component, we subtract the number of ways to select components with none of them being Sony from the total number of ways to select components.

Total ways to select components: 5 * 4 * 3 * 4 = 240 ways

Ways to select components with none of them being Sony: 108 ways

Number of ways to select components with at least one Sony component: 240 - 108 = 132 ways.

e. If someone flips the switches randomly, we need to calculate the probability of selecting a system with at least one Sony component and exactly one Sony component.

Total ways to select components: 240 ways

Ways to select components with at least one Sony component: 132 ways

Ways to select components with exactly one Sony component: 12 ways (from part b)

Probability of selecting a system with at least one Sony component: 132/240 ≈ 0.55

Probability of selecting a system with exactly one Sony component: 12/240 = 0.05

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The height of the tree is approximately 28.87 m.

The height of a tree but cannot measure it directly.

You stand 50 m from the tree and determine that the line of sight from the ground to the top of the tree makes an angle of 30° with the ground.

Here is a diagram for the problem:

[asy]unitsize(0.1cm);  

pair A,B,C;  

B = (0,0);  

A = (50,0);  

C = (50,tan(60));  

draw(B--C--A--C);  

draw(rightanglemark(B,C,A,90));  

\(0.7954=\frac{x}{6}\)

x = 0.7954 × 6 = 4.7724

y = \(\frac{4.7724}{0.6225}\) = 7.6665

Computation: In the diagram, we can see that the height of the tree is given by "h".

And the angle between the line of sight and the ground is given by 30°.

The distance between the tree and the person is given by 50m.

From the diagram, we can see that the height of the tree, h can be represented as follows:tan(30°)

= opp/adj= h/50

Solving for h, we get:

h = 50 * tan(30°)h = 28.87 m

Height of the tree =4.7724+7.6665

= 12.4389

= 12.44 m.

Height of the tree at which it is broken =4.77 m.

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The length and width of the rug are (26−2(2)) feet or 22 feet and (19−2(2)) feet or 15 feet respectively.

Let us assume that the width of the uniform strip be x feet.

Because the length and breadth of the room are 26 feet and 19 feet, respectively, and we are going to add an x feet strip around the rug, the length and width of the rug will be (26x) feet and (192x) feet. The rectangle rug will measure (26x) (192x) square feet.

Cynthia can now afford 330 square feet of carpeting, so we have:

(26−2x) (19−2x) = 330

494 − 52x − 38x + 4x2 =330

4x2− 90x + 164 =0

2x2− 45x + 82 =0

2x2 − 41x −4x + 82=0

x(2x-41)-2(2x-41) =0

(x-2) (2x-41)

So:

2x−41=0

x=41/2

x=20.5

And: x−2=0

x=2

Now, we can see that x=20.5 makes negative length and width of the rug. Since length and width cannot be negative values, so we will neglect x=20.5. Hence, the length and width of the rug are (26−2(2)) feet or 22 feet and (19−2(2)) feet or 15 feet respectively.

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The solution is : the velocity of the person on the walk way with respect to the observers on the ground is D 1.7 m/s.

Here, we have,

In order to find the velocity of the person on the walk way with respect to the person on the ground we have to apply relative velocity concept.

Consider the observer on the ground as B and the person walking on the pathway as A.

The relative velocity is the velocity that the body A would appear to an observer on the body B and vice versa.

Mathematically speaking the relative velocity is the vector difference between the velocities of two bodies.

Relative velocity = Velocity of Body A- Velocity of Body B.

Velocity of the person walking on the walkway (A)= 1.5 m/s.(given)

Velocity of the observer on the ground (B)= -0.2 m/s(given).

Relative velocity of object A with respect to B = 1.5 - (-0.2)= 1.7 m/s.

Thus the velocity of the person on the walk way with respect to the observers on the ground is 1.7 m/s.

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complete question:

A person is strolling along a moving walkway at a constant velocity of +1.00 m/s with respect tot he walkway, which moves at a constant velocity of +0.50 m/s with respect to the ground. An observer on the ground is walking at a constant velocity of -0.2 m/s. what is the velocity of the person on the walk way with respect to the observers on the ground?

A - 0.7 m/s

B + 1.3 m/s

C - 0.3 m/s

D + 1.7 ms

Answer:

i think this is the correct answer

Step-by-step explanation:

Simplifying

8x + -7y = 23

Solving

8x + -7y = 23

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '7y' to each side of the equation.

8x + -7y + 7y = 23 + 7y

Combine like terms: -7y + 7y = 0

8x + 0 = 23 + 7y

8x = 23 + 7y

Divide each side by '8'.

x = 2.875 + 0.875y

Simplifying

x = 2.875 + 0.875y

Answer:

m<A = 35

m<B = 55

Step-by-step explanation:

Complementary angles mean the 2 angles add up to 90 so:

y - 16 + y + 4 = 90

2y - 12 = 90

2y = 102

y = 51

m<A:

y - 16

51 - 16

35

m<B:

y + 4

51 + 4

55

we have shown that ⋀n−1 i=1 ⋀n j=i 1 (¬pi ∨ ¬pj) is true if and only if at most one of p1, p2,..., pn is true.

What is the Boolean algebra?

Boolean algebra is a branch of mathematics that deals with operations on logical values and variables, named after the mathematician George Boole.

Hence, we have shown that ⋀n−1 i=1 ⋀n j=i 1 (¬pi ∨ ¬pj) is true if and only if at most one of p1, p2,..., pn is true.

Let's break down the expression ⋀n−1 i=1 ⋀n j=i 1 (¬pi ∨ ¬pj) into its component parts:

Now, let's consider what happens when we evaluate this expression:

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Answer:

Justification of 'Cost of Match , based on attendants' linear equation

Step-by-step explanation:

Yes , this linear equation might hold right in denoting total cost 'y' for 'x' people attending racing event

Given equation  : y = 13x + 80

Cost 'y' is the variable dependent on explanatory variable ie no. of race attendants. So, y is on LHS, being determined by x on LHS.

80 is the autonomous constant intercept of equation, denoting fixed setup cost irrespective of no. of attendants. +13x denotes every additional attendant increases cost by 13 units (above the level of fixed cost), this is the positive slope of equation (as variables are directly related)  

"Champagne" is a word that is likely from French based on the grapheme representing /sh/.

Based on the grapheme representing /sh/, the word that is likely from French is "champagne."

The /sh/ sound is commonly represented by the grapheme "ch" in English, as in words like "shop" and "sheep." However, in French, the same sound is often represented by the grapheme "ch" as well.

The word "champagne" is a well-known French term used to refer to a type of sparkling wine produced in the Champagne region of France. It contains the "ch" grapheme that represents the /sh/ sound in French.

The grapheme for the sound /sh/ indicates that the word "champagne" is hence likely French in origin.

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The grapheme /sh/ is commonly found in French words. An example from French is 'chaussure' where 'ch' represents the /sh/ sound. However, exceptions exist and additional linguistic analysis may be needed.

The grapheme representing the /sh/ sound is a common characteristic in French words. Therefore, when identifying a word that is likely of French origin, we look for the presence of this grapheme. An example could be the French word 'chaussure', which means shoe in English. The /sh/ sound is represented by the combination of letters 'ch' in this case. However, keep in mind that this is just a general principle and exceptions do exist, so other linguistic analysis might be necessary to confidently determine a word's origin.

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\([Hello,BrainlyUser]\)

Answer:

[5] \(2x^2+xy+-3y^2\)

[6] \(2x^3+-7x^2+-3x\)

[7] \(4a+2b\)

[8] \(6x+2y-5\)

[9] \(x^2-3xy-10y+75\)

Step-by-step explanation:

Let's start with [5]

\(3x^2-2xy-2x^2-(x^2-3xy+y^2)\)

Distribute the Negative Sign:

\(=3x^2-2xy-2y^2-1(x^2-3xy+y^2)\)

\(=3x^2+-2xy+-2y^2+-1x^2+-1(-3xy)+-1y^2\)

\(=3x^2+-2xy+-2y^2+-x^2+3xy+-y^2\)

Combine like term

\(=3x^2+-2xy+-2y^2+-x^2+3xy+-y^2\)

\(=(3x^2+-1x^2)+(-2xy+3xy)+(-2y^2+-y^2)\)

\(=2x^2+xy+-3y^2\)

Answer = \(2x^2+xy+-3y^2\)

-------------------------------------------------------------------------------------------------------------

[6] \(\left(2x^3-5x^2-3x\right)-2x^2\)

Combine like terms

\(\left(2x^3-5x^2-3x\right)-2x^2\)

\(=(2x^2)+(-5x^2+-2x^2)+(-3x)\)

\(=2x^3+-7x^2+-3x\)

Answer = \(2x^3+-7x^2+-3x\)

-------------------------------------------------------------------------------------------------------------     [7]  \(4a-(3a-2b)+3a\)

\(=4a+-3a+2b+3a\)

Combine like terms:

\(=(4a+-3a+3a)+(2b)\)

\(=4a+2b\)

Answer = \(4a+2b\)

-------------------------------------------------------------------------------------------------------------

[8]  \(\left[3x-\left[x-4x+2y\right)+4y\right]-5\)

\(3x-(-3x-2y+4y)-5\)

\(=3x-(-3x+2y)-5\)

\(=3x+3x-2y-5\)

\(=6x-2y-5\)

Answer = \(6x-2y-5\)

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[9] \(x^2-3xy+5\left\{2+\left[y-3\left(y-6\right)-5\right]\right\}\)

Combine likes terms

\(x^2-3xy-10y+75\)

Answer = \(x^2-3xy-10y+75\)

[CloudBreeze]