3) Show that 1-2+2-3+3-4+…+(n – 1) - n is O(n³). Also state the values for witnesses C and

Q: 1. If N = 12, k = 8, and n = 5. Find P(2). %3D

A: X follows a hypergeometric distribution with N=12, K=8 and n=5 and k=2 We will use the formula:…

Q: 2 Let A= then det(3A") = 6- -2 - 18 -6

A:

Q: 2. Let S be the set [9] = {1.2..9}. 1 (D) How many derangements of S have 9 in the 2nd position and…

A: We have the set 9=1,2,...,9 We need to find the number of derangements. There are 9 places to fill…

Q: *4. Prove that 1³ +2³+ ... + n² = n²(n+1)² for all ne N.

A: Introduction: A strong and elegant method for proving specific kinds of mathematical claims is…

Q: If n is a positive integer with (n + 1)(n + 3) is odd, then (n + 2)(n+ 4) must be a multiple of 1) 6…

A: Given:  (n+1)(n+3) is odd We will get an odd number from product of two numbers only if the two…

Q: 2n2 – 4n + 1 is even → n is odd

A:

Q: ind witnesses to show that n^3 − 5n^2 − 4n is O(n^3).

A: In this question, order of polynomial can be found with the help of Big-O notation. Big-O Notation…

Q: (3) (2p = 2 (mod p), where (2) n! for 0 <k <n. k!(n - k)!

A:

Q: 'Disprove the statement: For any n E N, if n² +3 is prime, then 2n+7 is prime.

A:

Q: If "C, = K "C,, then K is n-1 %3D

A: Combination problem....

Q: 2. Show that following statements are correct: i. 4n+100=0(n) iii. n³ + O(n²) v. n! = O(n) vii. 3n3…

A: Now , Tn=θfn if Tn=Ofn  and Tn=Ωfn Now, Tn=Ofn if there exist positive integers M, n0 such that Tn≤M…

Q: 4. 5. For n E N, { x ER | |x-x*|<1/n } is open. UA_n is open where A_n=(n-1,n).

A: To determine: If the given statements are always true, sometimes true, or never true: (4.) For n∈ℕ,…

Q: 3. Show that if n = 3 mod 4, then n cannot be the sum of squares of two integers.(i.e there are no…

A:

Q: 1. Will there be at least two people who celebrate their birthday on the same day Yes, definitely O…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Show that n² + 4n + 14 is big-Oh (n²)

A: Take k=4 and C=6

Q: 7. For n > 1, verify that 1? + 3? + 5² + ...+ (2n – 1)? = ( 2" *1 ) %3D -

A: We have to prove that for n&gt;=1 in question number (7) Sum of squares of first n natural numbers…

Q: 5. (1). Prove by contraposition: m, n E Z, if m + n is odd, then m² + n² is odd."

A:

Q: 5. Prove that (n, n + 2) = 1 is n is odd and (n, n + 2) = 2 is n is even.

A: Suppose (n, n+2) = d =&gt; d | n and d | n+2 =&gt; d | (n+2) - n =&gt; d | 2 =&gt; d = 1 or 2.

Q: 28. Compute Ak where A = [4.-3] 2 - 3.

A:

Q: [0,1] is not countabe. صواب İhi O

A: True

Q: 6.20. For which integers n > 2 does there exist a o e A, such that |o|> n?

A:

Q: If k = (0.0003,-0.0012,0.0015,-0.0014)' in R then -5.2| |L = Select one: True False

A: Given  k = 0.0003, -0.0012, 0.0015, -0.0014t in R4.

Q: 2. Compute the convolution of the following signals for n 20 n n x1(n) = and x2 (n) = (;)" u(n) n…

A: Consider the expression of . Determine the z-transform of .

Q: *prove that for . P+2+3+... +n° = 2 n=!,2,3,

A:

Q: If n is not a poime then there exist Some ab€ 7h Such that ab # Itnk fox all

A: Definition: A number which can not be factored as product of two numbers other than the number…

Q: Show that 2n is O(3n) but not that 3n is not O(2n)

A: We need to show that 2n is O3n but 3n is not O2n Definition of Big O notation: Let f be a real…

Q: Prove, using an element-chasing argument, that {15n : n E Z} = {3n : n E Z}N{5n : n E Z}.

A:

Q: Show that, for n > 1 2n 1.3.5... (2n – 1),2n 2.4.6...2n n

A:

Q: تفاضل وتكامل )2( نظري 1 If pconverges, then p could be xP to Select one: а. 3/2 stion 1 b. 1 Oc. non…

A: We have to check

Q: is a1 = 2, a2 =3, and an  = 5an–1 – 4an–2 for n > 2 expressed in explicit formula? true or false?

A:

Q: 16. Ho: μ-85 Ha:μ #85 a=0.1 n=29 a=unknown O a. Left-Tailed, -2.467 O b. Right-Tailed, 2.467 O c.…

A:

Q: Prove that: "C. = 2" {1.3.5...(2n - 1)} n!

A: The left-hand side of the expression is: lhs=Cn2n=(2n)!n!(2n-n)!                               Use…

Q: Prove that 3|(52n – 1) for all ne N.

A: We prove it by mathematical induction. 1st step We show that the statement is true for n = 1.…

Q: 4. Given that aj = 3, ) ak = 1 and ) bk = 5, it follows that k=1 k=1 Eak and > 2ak + bk k=2 k=1 8.…

A: Calculus   -  summation and  series

Q: Theorem 11.3. If p and q = 2p+1: primes, then either q | M, or q| M,+2, but are not both.

A: As per Bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: (– 1)"–1 n=1 2n-1 TT Select one: True False 4.

A:

Q: 45, n-1 on? 12 1 2, ns 1, Al 7(n 11, what is the

A: This is a problem of inhomogeneous recurrence relation and counting.

Q: 1 -2 -1 -2 -3 O 21 = 1, 12 %3D O None Ο λι -1, λ2 O 21 O 21 = -1, 12 = -2 %3D Ο λι-2, λ2

A:

Q: Selected student is male and his age between 21 and 24 years.  e. Selected student is female student…

A:

Q: Prove the soquen enat 2efin ea For n EIN Conv e

A: Introduction: When each term of a sequence is greater than its previous term, the sequence is…

Q: .3 ). Show that x is O(x*) but that x* is not O(x³).

A:

Q: 5 - compute – 5A 3 Given A 3

A: we have to calculate -5A

Q: only Q2(8) 2. Show that following statements are correct: į. 4n+100=0(n) iii. n³ ± O(n²) v. n! =…

A:

Q: 14. If an+1 = 2a, + 2 and ao = 2, then an O 2n + 1 O 2n + n + 1 2n+2 - 2 O 3(2") - 1

A: a0 = 2 an+1 = 2an +2 We need to find an. The solution is given below.

Q: Which of the following are valid witnesses to show that 10n-1 is (n)? O C=1, k=100 O C=10, k=10 O…

A:

Q: 3. Let d = (a, n) where n > 1. Prove that if there is a solution to ax = b (mod n), then d divides…

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.