one-to-one

Q: 4. How many subsets are there of {1, 2, 3, 4, 5}? How many contain at least three elements? How many…

A: Given set is S=1,2,3,4,5 Since we know that, if a set contains n elements, then total number of…

Q: Exercise 8.10.5: Product of primes. About (a) Give a recursive algorithm that takes as input an…

A: A function that calls itself during the time of execution is called a recursive function. The above…

Q: The thirty-one students in a certain discrete mathematics class all live in one of three dorms on…

A:

Q: Select the mathematical expression that is equivalent to the sum 4+20+100+500++4.547 O 548-1 O…

A: Given 4+20+100+500+..........+4.547Formula1+a+a2+............+a(n-1)=(an-1)/(a-1)

Q: vo v5 V10 V12 V17 v7 •V16 v13 V 19 What is the level of v19? What is the parent of v8? What are the…

A:

Q: Sally goes into a candy store and selects 12 pieces of taffy. The candy store offers 75 varieties of…

A: Given: To explain the given statement as follows, The number of taffy selected by Sally r = 12, The…

Q: The function SuperPower given below receives two inputs, x and n, and should return 4-2. x is a real…

A: According to the given data, x is a real number and n is positive integer.

Q: 1) Prove by contradiction: a) If x is a rational number, then x + V2 is an irrational number. b) If…

A: Given a) If x is a rational number  To prove that   is an irrational number.

Q: There are n parking spots 1, 2,..., n on a one-way street. Cars 1, 2,..., n arrive in this order.…

A: There are n parking spots 1, 2, ..., n on a one-way street Cars 1, 2,..., n arrive in this order.…

Q: 4. How many ways are there to add one edge to the graph below to make it strongly connected. 10

A: We have to find How many ways there are to add one edge to the graph below to make it strongly…

Q: n Prove by induction that Σ (− 1) ¹;² = (-1)”n(n+1) 2 i=1 n Prove that Σ i=1 1 i(i+1) = n n+1

A:

Q: (a) Use rules of inference to construct a valid argument that uses the premises p, p→¬q, r→q to…

A:

Q: a. What is the cardinality of N (set of natural numbers)? b. Test the validity of the following…

A:

Q: discrete math

A: (a)It is known that the collection of disjoints subset of a given set or if the union of the subsets…

Q: a с d

A:

Q: The length of the walk V1e1 V2 e2 V3e5 V7 V6 e8 V4 is 5 This is not a walk

A:

Q: 4 Let A and B be nonempty sets. Function f maps A to B. Click on the domain of f on the graph below.…

A: See solution below

Q: -1 If A= BD and 2A + B + X = 0 then the matrix X is O a. 1 - 2 10 3 Ob. 1 7 13 С. 3 2 1 d. 1 2 - 7 –…

A: ans: Given A=2-4-6-8, B=3-215⇒2A+B+X=0⇒X=-2A-B⇒X=-21234-3-215

Q: Color Type Red Blue Totals A bag of marbles has the following composition: Solid 30 20 50 Stripped…

A: Given data table is,Color\ TypeSolid Stripped TotalsRed303161Blue 206989Totals50100150

Q: Question 1 Let a be a hexadecimal string with n-digits. In other words = (1,...,n) where each coor-…

A:

Q: Show that f(x) = 3x - 4 is bijective.

A:

Q: Consider the tree shown below with root vo. a. What is the level of vg? b. What is the level of vo?…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: When can you use the additive principle without needing to apply the principle of…

A: One has to apply additive principle and inclusion/exclusion law:

Q: We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10…

A:

Q: 25. Challenge: What if the centipede wants 50 (possibly different) matching pairs, one pair for each…

A: Given that a centipede own k different colors of socks. Assume that k>50. Then the centipede owns…

Q: After gym class you are tasked with putting the 25 identical dodgeballs away into 8 bins. a. How…

A: The number of ways to put n balls into r distinguishable boxes can be calculates using…

Q: 2. Suppose that someone takes out a loan for a new car for $25, 000. The annual interest rate is 3%…

A: Given - Suppose that someone takes out a loan for a new car for $ 25,000. The annual interest rate…

Q: ) Let f: A-B be a function which is not surjective and g : B C which is bijective. Prove that g of:…

A: See full proof below

Q: The twenty-six students in a certain discrete mathematics class all live in one of three dorms on…

A: Given that The twenty-six students in a certain discrete mathematics class all live in one of three…

Q: Prove by induction on n or disprove by counter example that the following inequality holds for…

A:

Q: Let a be an integer. If a² = 1 mod 4, then a ‡ 0 mod 2.

A:

Q: In a country, 75% of the graduates are citizens,60% of the citizens graduates are employed while…

A:

Q: Prove that the sum of two consecutive odd integers is divisible by 4.

A: Let the two consecutive integers be n and n+2 Then we need to prove that (n)+(n+2) is divisible by 4…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!