Find the value of x.
Round to the nearest tenth.
B
63
142°
61
A
C
X
x = [ ?
Law of Cosines: c² = a² + b² - 2ab cos C

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.

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Answer:

c i think

Step-by-step explanation:

Answer:

C.) x7      ;)

Step-by-step explanation:

:))))))))))))))

Given:Initial Value Problem,\(y'' + 6y' - 7y\)

= \(11e^(2x)y(0)\)

= \(1, y'(0)\)

= 1To solve the given initial-value problem, we can use the method of undetermined coefficients. The homogeneous equation associated with the given differential equation is\(y'' + 6y' - 7y\)

= 0. Its characteristic equation ism² + 6m - 7

= 0Solving the characteristic equation, we getm

= -7 or m

= 1The complementary solution to the differential equation isy_c

= \(c_1e^(-7x) + c_2e^(x)\)Since the right-hand side of the differential equation is of the form\(11e^(2x),\) we can guess a particular solution of the formy_p(x) = \(Ae^(2x)\)

Substituting y_p(x) in the differential equation, we get\(4Ae^(2x) - 12Ae^(2x) - 7Ae^(2x) = 11e^(2x)\)

Simplifying the above expression, we getA

= -1/3Therefore, the particular solution to the differential equation isy_p(x)

= -\(1/3e^(2x)\)

Therefore, the general solution to the differential equation isy(x)

= y_c(x) + y_p(x)y(x)

= \(c_1e^(-7x) + c_2e^(x) - 1/3e^(2x)\)

Using the initial conditions,y(0)

= 1c_1 + c_2 - 1/3

= 1y'(0)

= 1-7c_1 + c_2 + 4/3

= 1Solving the above system of linear equations, we getc_1

= 1/3 and c_2

= 4/3Therefore, the solution to the initial-value problem isy(x)

= \((1/3)e^(-7x) + (4/3)e^(x) - (1/3)e^(2x)\)

This is the final solution to the given initial-value problem. It is a function of x that satisfies the given differential equation and also the given initial conditions.

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Answer:

Step-by-step explanation:

error = 16 - 15 = 1 fluid ounce

percent error \(=\frac{1}{16} \times 100=\frac{100}{16}=6.25 \%\)

Answer:

1.042755456*10^21

Step-by-step explanation:

Using the law of cosines, it is found that the measure of angle Y is of 64º.

The problem is incomplete, hence we research it on a search engine, and we have that we have a triangle in which:

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 12, b = 17, c = 16, C = Y.

Hence:

c² = a² + b² - 2abcos(Y)

16² = 12² + 17² - 2(12)(17)cos(Y)

408cos(Y) = 177

cos(Y) = 177/408

Y = arccos(177/408)

Y = 64º.

The measure of angle Y is of 64º.

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Answer:

63

Step-by-step explanation:

A negative times a negative is positive.

7 x 9 = 63.

The quadratic parent function is represented by the equation F(x) = \(x^{2}\), so, the correct answer is D.

A quadratic function is a type of mathematical function that can be written in the form:

f(x) = a\(x^{2}\) + bx + c

where a, b, and c are constants and x are the variable. The highest power of x in a quadratic function is 2, which is why it is called a "quadratic" function.

The graph of a quadratic function is a curve called a parabola. The shape of the parabola depends on the value of the coefficient a. If a is positive, the parabola opens upward and has a minimum point, and if a is negative, the parabola opens downward and has a maximum point.

Quadratic functions are used in many areas of mathematics and science, such as physics, engineering, and finance. They are also used in computer graphics to create curves and surfaces.

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Answer:

Step-by-step explanation:

find the semiperiter (1/2 perimeter or L+W)

80 : 2 = 40

now we know that 4z + 2 + 3z + 3 = 40

we solve for z with an equation

4z + 2 + 3z + 3 = 40

7z = 40 - 2 - 3

7z = 35

z = 35 : 7

z = 5

now we find CD

3z + 3 =      (z=5)

3 * 5 + 3 =

15 + 3 =

18

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

check (remember pemdas)

4z + 2 + 3z + 3 = 40

4*5+2+3*5+3 = 40

20+2+15+3=40

40 = 40

the answer is good

Answer:

  ia) center: (0, 0), the origin

  ib) angle: 90°

  ic) direction: CCW

  ii) LM ≅ L'M', ∠L ≅ ∠L'

  iii) (2, 1)

Step-by-step explanation:

A rigid transformation preserves size and shape of a figure, so the image is congruent to the original. The rigid transformations are rotation, reflection, and translation. Each has characteristics that allow one to determine the nature of the transformation(s) involved.

__

angle and direction

One way to determine the angle and direction of rotation of a figure is to compare a horizontal segment on the original with the corresponding segment on the image. Here, a convenient segment is NM, which is horizontal and points to the right. Its angle relative to the direction of the +x axis is 0°.

The transformed segment N'M' points upward, at an angle relative to the +x axis of 90°. This tells you the figure was rotated 90° in the CCW direction. (This is fully equivalent to a rotation of 270° in the CW direction.)

center

Points in a rotated image always remain at the same distance from the center of rotation as the original points. In most cases, the center of rotation is the origin. We can check to see if that is the case by looking at the distances of a couple of points from the origin.

  N is at coordinates (1, 1), so is √(1² +1²) = √2 from the origin

  N' is at coordinates (-1, 1), so is √((-1)² +1²) = √2 from the origin

  L is at coordinates (1, 3), so is √(1² +3²) = √10 from the origin

  L' is at coordinates (-3, 1) so is √((-3)² +1²) = √10 from the origin

This confirms that the origin is the center of rotation.

__

Since each point and its image are on a circle centered at the center of rotation, the line between them is a chord of that circle. The perpendicular bisector of that chord goes through the center of rotation. Here, we observe that the perpendicular bisector of NN' is the y-axis. The perpendicular bisector of LL' is a line with slope -2 through (-1, 2). It will intersect the y-axis at the origin, confirming the origin as the center of rotation.

__

A rigid transformation preserves lengths and angles, so any length or angle on the rotated figure is congruent to the original:

 LM ≅ L'M', MN ≅ M'N', NL ≅ N'L'

  ∠L ≡ ∠L', ∠M ≡ ∠M', ∠N ≡ ∠N'

__

The components of a translation vector add to the corresponding coordinates of a point.

  L +v = L'

  (1, 3) +(1, -2) = (2, 1) . . . image of point L

Answer:

x^2

Step-by-step explanation:

x^3

-------

x

Rewriting

x*x*x

---------

x

Canceling like terms

x*x

------

1

x^2

The square root of 4761 is found to be 69.

If there is a number a, and there is another number b. Now, if we multiply a with a and we get the number b, then we say that the number a is the square root of the number b.

It can be written as,

a = √b

This sign "√" is called the sign on under root. So, now we ae to find the square root of the number 4761,

First we will find the factor of the number 4761 and then make the pair of two each and then multiply to find the root.

4761 = 3 x 3 x 23 x 23

Now, 3 x 23

So, the square root of 4761 is 69.

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Answer:

140

Step-by-step explanation:

20.82 = 21 when rounded to the nearest whole number

6.94 = 7

21*7 = 147

The best estimate is 140

Answer:

I had 61.09090909 repeating as a answer, you can round it, but if you divide 168 by 11 because that is the total amount of people then that gives a decimal place and that doesn't make sense. But I may be right. So best of luck. If I get you wrong then I am truly sorry

Step-by-step explanation:

Answer:

8 pounds

Step-by-step explanation:

"purchased 3 pounds of mac and cheese for $7.50"

You would make this into an equation to figure out the price of one pound of mac and cheese (x):

7.50=3x

x=2.5

Next, you can create an equation to represent the price per pound.

Total price = 2.5(number of pounds)

Now, plug in the information you have:

20 = 2.5x

8=x

Based on the cost of the homes in the area, the down payment that needs to be paid is $100,000.

The down payment that will be paid is the cost of the house less the amount that is paid for mortgages.

Cost = $250,000

Mortgages = $150,000

The down payment is therefore:

= Cost - mortgages

= 250,000 - 150,000

= $100,000

In conclusion, the down payment is $100,000.

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Answer:

y = 5/2 x

Step-by-step explanation:

y varies directly with x meaning this equation : y=kx

you plug in the information given

10 = k(4) and then solve ... k = 10/4 which simplifies to 5/2

The dimensions of the rectangular poster are 9 inches by 22 inches.

Let's assume the width of the rectangular poster is x inches.

According to the given information, the length of the poster is 4 more inches than two times its width. So, the length can be expressed as 2x + 4 inches.

The formula for the area of a rectangle is length × width. In this case, the area is given as 198 square inches.

Therefore, we have the equation:

(2x + 4) × x = 198

Expanding the equation:

\(2x^2 + 4x = 198\)

Rearranging the equation to standard quadratic form:

\(2x^2 + 4x - 198 = 0\)

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

x = (-b ± √\((b^2 - 4ac\))) / (2a)

Plugging in the values:

x = (-4 ± √\((4^2 - 4(2)(-198)))\) / (2(2))

x = (-4 ± √(16 + 1584)) / 4

x = (-4 ± √1600) / 4

x = (-4 ± 40) / 4

Simplifying:

x = (-4 + 40) / 4 = 9

x = (-4 - 40) / 4 = -11

Since we are dealing with dimensions, the width cannot be negative. Therefore, the width of the poster is 9 inches.

Substituting the value of x back into the length equation:

Length = 2x + 4 = 2(9) + 4 = 18 + 4 = 22 inches

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Answer: 6=22  

7=24

8=26

9=28

10=30

Step-by-step explanation:

Answer:

1= 37

2= 37

3= 37

4= 37

5= 106

Step-by-step explanation:

Answer:

cos(11π/3) = 1/2

Explanation:

To find the value of cos(11π/3), we first need to find a coterminal angle. This is because 11π/3 is greater than 2π, which is the angle of the complete circle. Then, we can find the coterminal angle as

11π/3 - 2π = 5π/3

Now, we need to find cos(5π/3), so we will use the unit circle as follows

Therefore, the value of cosine is the first coordinate of the point in the unit circle. It means that

cos(5π/3) = 1/2

Then, cos(11π/3) = 1/2

So, the answer is

cos(11π/3) = 1/2

Latanya can use up to 5 gigabytes while staying within her budget.

To determine the number of gigabytes Latanya can use while staying within her budget, we need to write an inequality that represents her monthly cell phone bill.

Let x be the number of gigabytes she uses. Then, her monthly bill can be represented as:

35 + 4x < 55

This inequality represents her monthly bill, which is the flat cost plus the cost per gigabyte, being less than $55.

To calculate the value of x, we'll isolate x on one side of the inequality:

35 -35 + 4x < 55 -35

4x/4 < 20/4

x < 5

So, Latanya can use up to 5 gigabytes while staying within her budget.

Note that this solution is in terms of the number of gigabytes and not the total bill amount. The total bill amount would be 35 + 4x, which should be less than or equal to 55.

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To prove a closed rectangular box of maximum value with the surface area s is a cube we need to maximize volume V with respect to the surface area which is S.

To show that a closed rectangular box of maximum volume having a prescribed surface area (S) is a cube, we can use the following steps:
1. Let's denote the dimensions of the rectangular box as length (L), width (W), and height (H).

2. The surface area (S) of a closed rectangular box can be expressed as:
S = 2(LW + LH + WH)

3. The volume (V) of a closed rectangular box can be expressed as:
V = LWH

4. To find the maximum volume, we need to express one dimension in terms of the others using the surface area equation. For example, let's express H in terms of L and W:
H = (S - 2LW) / (2L + 2W)

5. Substitute H in the volume equation:
V = LW[(S - 2LW) / (2L + 2W)]

6. To find the maximum volume, we need to find the critical points of V by taking the partial derivatives with respect to L and W, and setting them to 0:
∂V/∂L = 0
∂V/∂W = 0

7. Solving these equations simultaneously, we obtain:
L = W
W = H

8. Since L = W = H, the dimensions are equal, and the rectangular box is a cube.

In conclusion, a cube is a closed rectangular box of maximum volume with a prescribed surface area (S).

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Answer:

your answer would be D

Step-by-step explanation:

Substitute the x= 3y-1 in place of the x in the second equation

Subtract Like terms

Add 3 to both sides

Divide by 3(the coeffcient of y)

Answer is 5