9 F C a1 22 ak Pk ..... . n = P₁ P₂ < P2 < .…..... < Pk are primes and a; >1 for i = 1, 2,... k.

Q: A person stands at the corner marked A of the square pictured below and tosses a coin. В C 9 ft If…

A: If a random variable takes only specific values then the random variable can be termed as discrete…

Q: 13. Recall Z = {..,-2,–1,0,1,2,..} (the integers). Let Z* = {1,2,3,.} be the positive integers. Let…

A: Given: ℤ=…, -2, -1, 0, 1, 2, … and ℤ+=1, 2, 3, …

Q: !. 2. Find 100 irrational nember s between o andd 3. Find 50 rational numbers betwee and 2. 4. Fmd…

A: We know  2&lt;e&lt;3 So,   0&lt;e1000&lt;1100      as  e&lt;3&lt;10 So, 0&lt;e103&lt;1100 Define ,…

Q: 5. Let a = 2, az = 4, and an+2 a, = 2" for all natural number n. = 5a+1 - 6a, for all n 2 1. Use the…

A: Given information: The given values are a1=2,a2=4 and  an+2=5an+1-6an for all n≥1. To prove : an=2n…

Q: 12.16. Give an example of a prime p of each of the forms: a. 4k + 1 b. 4k + 3

A:

Q: The inductive step of an inductive proof shows that for k ≥ 4, if 2k > 3k, then 2k+1 ≥ 3(k+1). In…

A: We will check the validity of all given steps, then we can decide in which step we used the given…

Q: Births of boys with n = 20 births and p = 0.512 for a boy. In P(fewer than 8 boys)

A: Given, n=20 p=0.512 Normal as approximation to binomial will be given by as follows: X~Nnp,…

Q: 4. Conclude that n2 n=1 ||

A:

Q: Which of the following statements is (are) true for all positive integers? 1) (-) 5³ 5* 2) 9* - 1 is…

A:

Q: Show that there exists i and j with i + j such that p, divides p;. а. b. Show that there exists i…

A: Given: It is given that let p1,p2,...., p51 be their final exam scores . Hence each pi is an integer…

Q: 5.1 Consider the statement: "Let a e N. If a² is an even number, then a is an even number". Choose a…

A:

Q: Given n > 1, let p be a prime number such that n < p < 2n (by the way, 2n there is always a prime…

A: here we need to expand  by using  nr=n!r!×n-r! and then show that expression obtained have a factor…

Q: () is even. 3. Prove that for all positive integers n, the number

A:

Q: IV. Prove the following using mathematical induction. 1. 5" – 1 is divisible by 4, Vn € W. 2. 8" –…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Icm(a,b) = ab if and only if a and b are relatively prime.

A: We know the relation between product of the two numbers their L.C.M and G.C.D Let a and b two…

Q: 10. Let n be an even perfect number. Prove that n=2*(2k+1 – 1), for some integer k.

A:

Q: Suppose A₁, A2, ..., A30 are thirty sets each having 5 elements and B₁, B₂, ..., B₁ are n sets each…

A: Given that A1, A2, . . ., A30 are thirty sets each having 5 elements and B1, B2, . . ., Bn  are 'n'…

Q: 12.16. Give an example of a prime p of each of the forms: a. 4k + 1 b. 4k + 3

A: Let the prime number be

Q: a. Use the formula S, = (a, + a„) to show that the sum 1, 3, 5, .. (2n – 1) = n2. b. Find the sum of…

A: a. Given formula is: Here n is the number of terms and a1 and an are the first and last terms of…

Q: For all n E N,n > 1, there exists a prime p such that p|n. ulgn hi

A: False

Q: truo or false

A: Given statement is true

Q: II (1-) п+1 (for n > 2). 2n i=2

A:

Q: 20 2. С1 1 7 6. s+3 5s-3 6s – 5 3. С1 4s² +7 3s - 2 4. 6! s* +8s+25

A:

Q: Consider Z=~N(0,1), Find P(-1.961.96) O a. 0.75 O b.0.75 Or0 95

A: Given, Z ~ Normal (0,1) where, μ = 0 σ = 1 P(-1.96&lt;z&lt;1.96) = P(z&lt;1.96) - P(z&lt;-1.96) =…

Q: Hence show that for positive integers n and m: P = I P P² for n = 3m for n = = 3m + 1 for n = 3m +2

A:

Q: If p and q are twin primes, then which of the following is true. i. p + q is divisible by 3 ii. pq =…

A:

Q: (":')-(:)·(,".) n +1 n n - Prove that for all integers n > i > 1. i 1

A:

Q: C. 9626 [2 If A = 2 1] 3 find A? -5 A+61 -1 0 1 [1 Select one: [2 3 51 a. 1 2 4 [7 6. 2] b. none 1…

A:

Q: +1 X What are all of the values of x ,such that (-1) n+ converges? 6 06.2 O 0<x<6.3O x26.4O

A:

Q: Q13/ A/ Find A-B? * 1 11 B= | 2 15 If A = 2 4 -4 find .3 4] 3

A: Here, A=112434,B=0-12-453

Q: Time left 1:0 If p and q are twin primes, then which of the following is true. i. p + q is divisible…

A: