Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. 14.What is the probability of receiving at least 2 callers (P(X> 2) in the system within 15 minutes? Hint: customer arrival in M/M/k system is also following the Poisson Distribution. You have the formula in single-server cheat sheet! Select one: O a. 99.84% O b. 95.84% O c. 66.16% O d. 91.56%

Q: 6. Evaluate f z z* –8 dz. A) (x² - 8) +C B) a O b O d

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Q: hich function is even 1) s) = x*- +x 2) %3D J(x) = x-4 3) Ax)- x-2|+5 4) fx) = x %3D

A: A function f(x) is said to be an even function if f(-x)=f(x). For the function f(x)=x2-4 ,…

Q: 9. Solve. a) 4+6(4 *)= 5 b) 2(5) + 2(5) = 4

A:

Q: 6. 4.

A: Given: To find:  x

Q: Solve the followny System fequetions. O by Substition

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Q: Solve. 44 39) Σ (-6n +7) n = 1

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Q: 2. Find NP. M 8

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Q: Prove that (x - i) = > xi i=1

A: We will prove the following result.

Q: 2) 3x+3 10 9,

A: As per the bartleby guideline I have to solve only first question of multiple question if not…

Q: [L,,2] - [D,C]

A: Since all are  represent  unit vector .

Q: 1.) Find v(t) 4+ 37 2-

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Q: Hiw- prove that %3D

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Q: 2. Prove: A – B = ANB

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Q: B 11 13 b.) Find ZB 33 A

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Q: Compute AB, where A AT B = = 24 09 4 -3 -1 and B = 76 (1 %). 6 4

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Q: Q: Find the numbers a,b,c between 2 and 18 such that: (i) their sum is 25. (ii) The number 2,a,b are…

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Q: Q.2) Evaluate r8-z² 4 dzdydx 0.

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Q: 18) 2x y

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Q: Vandermonds Theorem: 2 F₁ (-n, b; c; 1) (c-b) (c)₂

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Q: FCX)=10+x FC2)

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Q: lAcOs3x+B sin sx) この

A: Given solution with condition is  yx=exAcos3x+Bsin3xy(0)=0y'(0)=1

Q: (1) and (.), (.) dz = Find the number of terms in where z = gu, v/ and u

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Q: Find w, x, y, and z so that W X 4 3 8 -3 2 4 -4 |

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Q: Choose the correct Sympy expression to cal Select one: a. diff(f, x, x) b. deriv(f,x) c. diff(f, x)…

A: 1).   To compute this definite integral, pass this argument >> Integrate ( f, (x, 0, π/3))…

Q: dz F|=1 2. C: -국X=+ 2)

A:

Q: How did you get 0.98 from NORM.INV(0.98,0,1)?

A: p=0.32E=0.04

Q: b.) /2x – 2 - Vx + 6+1 = 0

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Q: Question 2 Give the form of a particular solution of y" - 8y' +16y=-2xe 5e4-2. -2z - a) z = = (Ar² +…

A: We have to find Particular solution for given Differential equation  y" - 8y' + 16 = -2xe-2x - 5e4x…

Q: Compute the following. (a) P6, 2. (b) C6, 2. (c) P6, 6.

A: P(n,r)=n!n-r!C(n,r)=n!n-r!.r!

Q: P(z -1.3)

A: Note that, for z-distribution (standard normal distribution), the mean is 0 and the standard…

Q: Find these values. a) [1.1) c) L-0.1) e) [2.99] 即+」 b) [1.11 d) -0.11 f) (-2.991 h) +1+1

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Q: fG) Solve LI4 45(x-4) X-1 4J6C-4) X2-1

A: We solve the limit of given function.

Q: 4.) S x²V5 – x²dx

A:

Q: Let U = {a, b, c, d, e, f,g, h}, A = {a, c, f, g}, B = {a,e}, C = {b,h}, calculate: a. ΑΘΒ b. В@А

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.