Use generating functions to determine the number of differentways 15 identical stuffed animals can be given tosix children so that each child receives at least one but nomore than three stuffed animals.

Q: How many positive integers less than 10000 are there which contain at least one 7 or at least one 9…

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Q: Show that the greater than or equal re lation >) iš a partially order on the Set of integer.

A: Partially Ordered Relation: A relation R on set P is said to be partially ordered if and only if R…

Q: Suppose you draw n lines in the plane so that every pair of lines cross (no lines are parallel) and…

A: Let n be the number of non parallel lines. Given that number of regions= Rn Let Un represent maximum…

Q: The prime f actorization of 7007 is

A: 7007=7×1001       =7×11×91       =7×11×13×7       =72·11·13

Q: Suppose that you know that a golfer plays the first hole of a golf course with an infinite number of…

A: To prove that the golfer plays every hole on the course when given that a golfer plays the first…

Q: Using the generating function to determine the number of ways  18 identical balloons can be given…

A: Given that 18 identical balloons can be given to 3 children such that each child receives at least 5…

Q: Find the number of positive integers X smaller than 12849 which have exactly 2022 positive divisors

A: Theory : Total no of divisor of a number, If its prime factorization, given by ∏i=1hpiai Where p is…

Q: How many positive integers less than 850 are multiples of 8, 3, or 5? Use the Principle of…

A: Using the Principle of inclusion/Exclusion, the formula for A∪B∪C can be written as:…

Q: Use the definition of an r-permutation, or the product rule to de number of trifectas possible in a…

A: Given: To explain the given statement as follows:

Q: Select all the expressions that are greater than 3. Be sure to show your work 1.67 + 1.4 2.97 +…

A: We have to select all the expressions that are greater than 3. (1) 1.67 + 1.4  = 3.07 > 3

Q: Prove that the sum of any three consecutive numbers is divisible by 3

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Q: (a) Show that if seven integers are selected from the first 10 positive integers, there must be at…

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Q: Discrete Math

A: According to the given information, Suppose that:

Q: Which term of the expansion of (x° + 7) contains x 28 ,36 Term number contains æ36

A:

Q: Let n be a number with 3 digits. (i.e 100sns 999) Show that if the sum of digits of n is divisible…

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Q: Let a, be the number of strings of symbols {a, b, c, 1, 2, 3} of length n, such that exactly one of…

A: Given: Only one of the character is a numeric digit from the set(1,2,3,a,b,c).

Q: Determine the identity element of the set N={1,2,3,..} of positive integers with addition.

A:

Q: What two nonnegative real numbers with a sum of 23 have thelargest possible product?

A: we have to find the two non negative real number with a sum of 23 which will have largest possible…

Q: Show that nlgn+3n ≠ θ(n2) , give visualization of the functions in a graph as well. This Question is…

A: Let us check  whether nlogn+3n=ϑ(n²) or not Definition for f(n)=(g(n)):ϑ(g(n)) Let f(n) and g(n) be…

Q: How many bijective functions have [10] as both the domain and codomain

A: Given, 10

Q: 21. How many positive integers x are there such that 3x has 3 digits and 4x has four digits?

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Q: Find the proportion of primes p in the interval from 10^12 and 10^12 + 1000 such that p-1 is B= 105…

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Q: Find the sum of all integers that are multiples of 3 from 4 to 100.

A: We have to find the sum of all integers that are multiples of 3 from 4 to 100 Then, If A denotes the…

Q: The sum of all positive integers less than 300 which are not divisible by 3.

A: Sum of n positive integer is given by, Sn=nn+12

Q: 5. Give a recursive definition of the set of positive integers that are multiples of 5.

A: Solution

Q: 3. If а, 1000". Find N E I, the set of positive integers, such that an+1 N). n!

A: Given an=1000nn!. We have to find the N∈I such that an+1<an, n>N. For n=1 a1=100011! For n=2…

Q: provide a recursive definition for the set X of all powers of 9

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Q: Prove: The product of 2 numbers is equal to the product of their least common multiple and their…

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Q: Consider all numbers between 20000 and 70000. Efficiently determine: A) How many of these numbers…

A: Part A - Let’s represent the number as ABCDE. You have to considere the special cases first, since…

Q: Use generating functions to determine the number of differentways 10 identical balloons can be given…

A:

Q: Find the least natural number a with the property that the sum a + 2a + 3a + .. + 9a is the number…

A: Given sum is  a+2a+3a+4a+5a+6a+7a+8a+9a

Q: provide a recursive definition for the set Y of all negative multiples of 7.

A: Consider the provided question, Recursive definition: Recursion is the general definition term for…

Q: Use generating functions to find the number of ways tochoose a dozen bagels from three…

A: Consider the provided question, Each variety is present at least 2 times in the dozen bagels, the…

Q: If x is an odd integer then 5x – 7 is an even integer. (use direct proof)

A: Given that “x” is an odd integer then “5x-7” is an even integer.

Q: Choose two distinct integers, x and y, between 0 and 9. Derive the number of 9- digit integers that…

A:

Q: Give a recursive definition for the set of all the positive integers that are less than 100 and not…

A: Given: Set of all positive integers that are less than 100. To find: Recursive definition for the…

Q: Find the average of the first 50 natural numbers is……………….

A:

Q: be run under the building. If these two blocks must always be next to each other, how many s can the…

A: Given Here we have 7 blocks ,but we  have to keep 2 perticular blocks together. So we have to…

Q: A decimal string is a string over the alphabet of the 10 characters: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.…

A: Given that a decimal string is a string over the alphabet of the 10 characters 0,1,2,3,4,5,6,7,8,9.…

Q: Use generating functions to find the number of ways to distribute r jelly beans among eight children…

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Q: Find the ordinary generating function for the sequence 0,0,0,0,1,1,1...(Hint: it is not a…

A: We need to find an ordinary generating function. The sequence is 0,0,0,0,1,1,1,.... Consider:…

Q: Find two positive integers such that the four times loo0 and the product large as possible. the .…

A:

Q: Use generating functions to determine the number of 9-digit sequences of the digits 1,2,3,4,5,and 6…

A: We need to find ,  number of 9-digit sequences of the digits 1,2,3,4,5,and 6 in which each even…

Q: (a). Show that the weighted arithmetic mean of firstn natural numbers whose weights are equal to the…

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Q: the sum of any positive integers that is less than 30

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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…

Q: Use generating functions to determine the number of differentways 12 identical action figures can be…

A:

Q: Suppose that you start browsing the internet on a specified page c. Let x be all the websites you…

A: The process in which a function calls itself directly or indirectly is called recursion and the…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.