Prove that the quantity S= -kΣP li(P) r=1 is a maximum when P, = 1/n for all r. Do this by showing that S - kIn n < 0. [Hint: The inequality In[1/(nP,)] < 1/(nP,) – 1 will be helpful. To arrive at an expression in which you can use this inequality, you will have to insert E- P, = 1 in an appropriate place. This is a problem which is easier not using calculus because of the probability constraint.]

Q: N Given: Z1 = Z2 and Z3 = Z4 Prove: MNPQ is a kite 3 4

A: Explanation: Given that,  ∠1≅∠2∠3≅∠4 We know that,  ∠1≅∠2∠3≅∠4NQ=NQ△MNQ≅△PNQ

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A:

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A: We will use the pascal's triangle to expand the given expression.

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A:

Q: (0) c Cal@)

A: We have to prove that &lt;a&gt;⊂ CGa

Q: owing assertion: n

A:

Q: The mean weight of female nurses working at a local hospital is at most 138 lbs. Express the null…

A: given data μ=average weight of all female nurse working in hospitalclaim : μ≤138 lbs

Q: Prove the following statement. You may employ any proof techniques If n € Z, then 4|n² or 4| (n²-1).

A:

Q: The mean weight of female nurses working at a local hospital is equal to 159 lbs. Express the null…

A:

Q: Prove the following statement, using either the contrapositive statement or a proof by…

A: Proof by contradiction is done bellow

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Q: Discrete Mathematics: 3. Prove: 7n -1 is divisible by 3 for n ³ 0

A: We need to prove that the number 7n-1 is divisible by 3 for n&gt;0. We do this as follows: Case-1:…

Q: if JERLA.b] and it hex)- J(x). except for finite mumber of Paint in Cab] then that he Rlab] prove.…

A: if g ∈R[a,b] and if h(x) = g(x) except for a finite number of points in [a,b] then prove that h…

Q: Identify the axiom or postulate that applies to the following statement.     If m = n, then m – z =…

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Q: Question 14 Which assumption would you make to start an indirect proof for the statement "If-8y <

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Q: 7. Prove: Vn e Z, n is odd if and only if n is odd.

A:

Q: 5.71. Below is given a proof of a result. What result is proved? Proof Let a, b, Ce Z such that a² +…

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Q: which one of the following is a proof for AUU = U AUU={x I XEAVXEU} = {x I xO EAVT} = {x I T} = U…

A: Given L.H.S. =A∪U Now, it can be expressed as A∪U=xx∈A∨x∈U=xx∈A∨T=xT=U

Q: S. Given: AD BC LA= LB Prove: BD = AC D Proof: Statement Reasen 1. 1. 2. 2. 3. 3. 4. S.

A: Use the congruent postulate of the triangles.

Q: set of all prime numbers Y = {y% e z}, where Z is the set of all integers TRUE or FALSE: P and Y are…

A:

Q: Prove the proposition that P(n): 1+4+42+.+4n. 40+1-1 %3D ... 3 ,n20.

A: To prove the given proposition, we take S=4+42+43+···+4n. Then we multiply S by 4 and subtract the…

Q: E. Which of the following proportions can be used to prove AE II DK in the proof below? Select all…

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Q: For each exercise place the statements in an appropriate order for a proof. (There may be more than…

A: Given that, RS≅RT. Since the two sides of the triangle △SRT are congruent, △SRT is an isosceles…

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Q: If then |A|=1 O JA|=-1 O |Al=0 O

A: Follow next step

Q: Q. Prove that by mathematically Induction 2" < (n + 1)! , for all integers n 2 2. а.

A: We Solve it by First Principle of Mathematical Induction.

Q: Problem 2) Let Cn,d be the number of integers with 1 ≤ m <n such that gcd (n,m) = d. Explain why the…

A: Given that be the number of integers with  such that To explain why the following identity hold:…

Q: 3. Prove: For all positive integers, n, n(n + 1)(n + 2) >i(i + 1) = 3

A: Kindly find the attachment

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A:

Q: with knowing how to show proofing of  a(bc)=c(ab)

A: Introduction: To make it less hard or difficult; to make it simpler or easier To condense an…

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A:

Q: ich of the following must be true in er to prove that DE=5.75 and DE II

A: We will find the required.

Q: A group consists of 5 Democrats and 8 Republicans. 7 people are selected to attend a conference. a.…

A: In the given group there are 5 Democrats and 8 Republicans.