1234 Let O is a permutation on X={1, 2, 3, 4}. The length of the cycle o is 3412 04 cycle transposition 3- cycle D 1- cycle

Q: 15-Find the 13th term of an AP in which a = 7, and d = 6: The correct answer is (85) Select one:…

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Q: 1. First we focus on the sequence of squared Fibonacci numbers. Theorem 1 (Sequence of Squared…

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Q: limn0 In(2n-3) -) is 8. n+5 Select one: 2 non of them

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Q: From the top of a cliff 150 feet high, the angle of depression of ship A is 20° and that of ship B…

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Q: Use base-ten blocks to illustrate 111+5. 111 has flat(s), long(s), and unit(s). Starting with the…

A: Given that use base-ten blocks to illustrate 111÷5.

Q: Find the permutation that Followors 720865432 in the lexicographic of }0,t,2,3,4,s, 6573 83 ordexing…

A: Answer

Q: Use the Principle of Mathematical Induction (PMI) to prove that the following statement is true for…

A: To prove: The statement "7 divides 15n+6" is true for all natural numbers n by principle of…

Q: 2 34 5 6 7 8 9 X (b) 9 3 716 5 2 X 4 8 (c) (abc)(cad) (d) (213)(3421)(153)

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Q: primitive root modulo

A: Given: Value of n=223 in  mod n. To find: Primitive root modulo 223.

Q: Test2

A: We know that2198=2128×264×24×22Also we have22≡4(mod 397)24≡16(mod 397)28≡256(mod…

Q: How many divisors does (1000000! + 1) have that are less than 1000000?

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Q: Prove the given statement of divisibility of 13 Divisibility of 13 Method 1:              Step 1:…

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Q: Find the least residue of  -5 -46 modulo 14.

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Q: Determine which binomial is a factor of 3+ 22 40a +64 O (2 8) O (x- 2) O (a + 2) O (a + 4)

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Q: p Pq C N-n N-1

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Q: Find 1112 mod 13.

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Q: (12 3 4) o (2 3 5 4 6) o (3 4 5 6) can be expressed as product of following disjoint cycles Select…

A: To express in disjoint cycles start from right and then go through left to right.

Q: g) Determine the product of Factorial of 5 and Fibonacci of 5 using the recursive function as…

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Q: Inverse of 9 modulo 23 is -18 -17 18 17 Windows by

A: Solution: We have to find the inverse of 9 modulo 23. Let x be the required inverse. Then, 9x≡1mod…

Q: Let n be a positive integer. Using congruences, show that 3n+3 +23n+3 is divisible by 7.

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Q: expand each expression using the Binomial Theorem

A: Given: 19.(x-2)6

Q: Use Pascal's Triangle to expand the binomial (x + 1)° O 25 + 5x4 + 10x + 10x2 + 5x + 1 O g5 - 5x1-…

A: Pascal's triangle…

Q: For the angles a and 3, find cos(a − B). Simplify your answer in exact form. 7 8 3 2 5 B

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Q: Prove this: -n is a integer; If 6| n then 18| n^2 +3n

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Q: 2. What are the prime factors for the below numbers and arrange them in a canonical form. a. 17 b.…

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Q: Sort this permutation [5 213 4] into identity permutation [123 4 5]. Check what's the number number…

A: The permutation is nothing but the arrangement of objects in different orders. If we permute a set…

Q: Suppose 59 cars start at a car race. In how many ways can the top 3 cars finish the race? ... The…

A: There is total 59 cars.

Q: 5. Find the highest power of 2 that divides each of the following integers. a) (101111110)2 b)…

A: Given: (101111110)2 (1010000011)2 (111000000)2 (1011011101)2 Which of these is divisible by 3

Q: Find the remainder of 5130 modulo 28

A: Chinese Remainder Theorem : Let n1​,n2​,n3​,...,nk​∈N , with GCD(ni​,nj​)=1 for each i=j. Let…

Q: True or False. Briefly explain why.  {−13, −6, −3, 1, 10} is a complete residue system modulo 5.

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Q: A bucket of KFC contains four legs and three wings. You by five buckets set up a distributing…

A: Given, A bucket of KFC contains four legs and three wings. Fve buckets are bought To be found :…

Q: Prove that if 10|n, then 10|n^2+n

A: Prove that if 10|n, then 10|n^2+n

Q: Using Euclidean Algorithm, find the Inverse of the integer 13 mod 19.

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Q: ED Write the elemants of Sy. in array notation (24) 2 write the elements of Bu in cycle notation…

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Q: Find 5675 (mod 19)

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Q: Each character in a password is either a digit [0-9] or lowercase letter [a - z]. How many valid…

A: We have to find how many valid passwords are there with the given restriction(s).

Q: Find the 15th term of the geometric 1,2,4, .. O 65, 536 O 8, 192 O 16, 384 O 32,768

A: Hence option (c) is correct.

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.