An inversion of a permutation o is a pair i σj. Let I(n, k) denote the number of permutations in Sn with k inversions. Prove the identity below: ΣI(n, k)x¹ = 1(1+x)(1+x+x²)...(1 + x + ... + x²−¹) k=0

Q: 1. Expand the following expressions: TC(q)-2TR(q) - FC(q) b. 5q-(3-2q)³ 1-In ()² C.

A: a. The expression TC(q) - 2TR(q) - FC(q) can be expanded as follows:   TC(q) - 2TR(q) - FC(q) =…

Q: For Exercise, evaluate the expression. (n – 1)! (n + 1)!

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Q: Please do the following questions with full handwritten working out. Answer is in the image

A: in case of any doubt Please ask in comment section

Q: Consider this expression. |m2 – 7| + n2 - When m = -2 and n = 5, the value of the expression is T.

A: Given ,the expression , m2-7+n2when m = -2 and n = 5

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A: Since you have asked multiple questions in a single request we would be answering only the first…

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Q: x2 - 9 simplifies to x? – 1. 9. True or false:

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Q: (-5)2 n (b) En-1 n²,97n 00

A: Part b,

Q: Use the table below to fill in the missing values. f(z) 2 f(8) - it f(2) -9 then z= Enter an intew…

A: f(8) = 2       If f(x) = 9 then x = 5

Q: Express the expression 5.x² * in into Sigma notation.

A: The binomial expansion:a+bn can be expressed in Sigma notation as: a+bn=∑r=0nnr an-rbr.

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Q: faノ= 4-ズ, と Finel!- ロん。 hf fes 2. on inverse 12] Domain fca) ?

A: Answer and explanation is given below...

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A: Solution

Q: where does come (5/6)6  from??

A: Basic concepts of probability are used.

Q: Sh Evaluate (30 – 6x) dA, where R = [0, 5] × [0, 3].

A:

Q: = e. Convert from multiplicative to additive notation: (1) a²b³; (2) a=²(b=¹c)² =

A: Here we have to convert the multiplicative notation to additive notation of1) a2 (2) a-2(b-1c)2…

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A: We compute the value of each expression in next step. -

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A:

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Q: 2. Use diflerentials to approximate the of 2G Valu e

A: By using differential to approximate the value of 263

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A: given data n= 4 p=0.41-p=1-0.4=0.6x=3we have to find out the probability for x=3here we use formula…

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Q: please could you use Ts and Fs cause i wasnt taught the 0s and 1s format

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Q: R(60)

A: Given ,  No. S R 1 20 1600 2 25 800 3 30 250 4 35 300 5 40 800 6 45 1400 Where, S…

Q: (ANB) %3D 20<X S 30 OR

A: Question belongs to set theory.

Q: :The value of -2|U(A)| is

A: If the value of U(A) is (5) or (-5) then |U(A)| =5 then   -2|U(A)|=-2*5=-10. Otherwise answer is…

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A: Introduction: Once we've determined that a function is one-to-one, we must find its inverse. The x's…

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A: