8. If * is defined as a*b = 3a+b where a and b are real numbers, what is 4*3?

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

A:

Q: Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 1. Show that subtraction is not associative for the set of integers.

A: Definition :Let "." be a binary operation and A is a setThen "." is said to be associative for A if…

Q: A realtor uses a lock box to store the keys to a house that is for sale. The access code for the…

A: Given: Length of access code = 5 Here, first digit cannot be 0 and the last digit will be even.

Q: 3. Prove or disprove (x, y are real numbers a) [x- y] = [x] – by] TRUE FALSE because:

A: Introduction: The integer, that is largest and less than or equal to the number a is known as floor…

Q: h0-60 |--²-1²-₁-²

A:

Q: 6. Use a direct proof to show that if a and b are positive integers, then +2 2. Hint: Rewrite the…

A:

Q: Show by contraposition that for positive real numbers a and b, if ab - a - b ≥0 then a and b are…

A:

Q: Show that on a street with 101 houses where each house has a distinct street number between 1 and…

A: For the solution of the problem follow the next step.

Q: What are the values for x1, x2 and x3? O x1-500 ; x2-57.78, x3-175.56 O x1-500; x2=-175.56, x3-57.78…

A: We have given optimization table and we have to find the values of variables that maximize the…

Q: . Since 10 is the "middle" value of {9,9,10,10,17}, the …………of H is 10.

A:

Q: Suppose that Y and Z are points on the number line If YZ = 16 and Y lies at 4, where could Z be…

A:

Q: Prove that 1+6x-x is always a positive real number if x =3+Ai for some real 33 number 4

A: The given number is  1 + 6x - x2

Q: 6. Show that Vz eC i) z-7 is a real number. ii) (z-2) is a real number.

A:

Q: Find a number that provides a counterexample to show that a given statement is false, For all number…

A:

Q: Show by contraposition that for any real number x if -5 <x<4 then x2+x- 20 <0

A:

Q: 75. If f(7) = 13 and fis one-to-one, what is f(13)?

A: For a function domain is set of values for which the function is defined. The range of a function is…

Q: Suppose thatk and n 2k are fixed positive integer. Justify the identity k+1 jk

A: to prove ∑j=knjk=n+1k+1above equation can be written as S2(j,k)=S2(j-1,k-1)+k.S2(j-1,k)count the…

Q: ) If X is the set of even numbers between 8 and 20 inclusive, and Y is the set of numbers divisible…

A:

Q: If the sum of any two integers is even, then so is their difference.

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Let A be the set of all positive integers whose last two digits form a number that is evenly…

A: We have the given condition as   Let us consider A be the set of all positive integers whose last…

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: 2. Possible whenn A- Zero b. Negutive integer C- Negative Yational d- Positive integer

A: We know that Laplace transform of

Q: Let a, b and c be integers that satisfy 1 1 1 - - - - a b C |(A) 2022 (В) 2025 Find one possible…

A:

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&lt;an, n&gt;N. For n=1 a1=100011! For n=2…

Q: In how many distinct ways can the letters of the word STATICS be arranged? ways

A:

Q: A realtor uses a lock box to store the keys to a house that is for sale . The access code for the…

A:

Q: 27. Show that if x and y are positive real numbers that have the same first n digits in their…

A:

Q: 2. Show that if a]b then a'|b² for all integers a and b (Symbols V, 3, A, V, V,A,→,-)

A:

Q: What is the range of all integers greater than 40 and less than 99 that are multiples of 3

A: To find : The range of all integers greater than 40 and less than 99 that are multiples of 3

Q: Prove that a four-digit number is a multiple of 8 whenever the number formed by the first three…

A: The solution is given by using the expanded form of number as follows

Q: Let C be the set of natural numbers greater than 5 less than 15. Write C using the descriptive…

A:

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: 3. The v77 is between what two integers?

A:

Q: 6. Determine. 2r - 3x 4x SET A.

A: I have stated the used formula in the solution

Q: 20) Show that the sum of two consecutive integers is always odd.

A: Let x be any integer. Then its consecutive integer can be written as x+1.

Q: 2. Find a counterexample to the statement n2 – 4 - V nonzero integers n, is not an integer.

A: 2. Given statement is, ∀ nonzero integers n, n2-4n is not an integer

Q: {xlx is a whole number less than 6} if U is the set of all whole numbers

A:

Q: Prove, that (nezond n73) If x"=5,+hen x is not a rational number.

A:

Q: What is the set of O of odd positive integers less than 10?

A: The odd positive integers less than 10 are 1, 3, 5, 7, 9.

Q: If z < o when -0, then 2 is one of the even numbers that is an odd number. O True

A: NOTE- AS  WE ARE ALLOWED TO ANSWER ONE QUESTION IN ONE SESSION SO, I HAVE ANSWERED FIRST QUESTION…

Q: Suppose that a1, a2, a3, a4, a5 are five numbers. 5 If ak =-7 then (2ak + 3) is equal to... k=1 k=1

A:

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

A:

Q: A realtor uses a lock box to store the keys to a house that is for sale. The access code for the…

A:

Q: If np 25 and

A:

Q: a realtor uses a lock box to store the keys to a house that is for sale. The access code for the…

A: Given The access code for the lock box consists of five digits. The first digit cannot be 9 and the…

Q: If in an AP the sum of m terms is equal to n and the sum of n terms is equal to m .then prove that…

A:

Q: 2. Use prove by contrapositive to show that: (For real numbers a, b, c) If (a – b)² + (b – c)² + (c-…

A:

Q: The number of different codes available is

A:

Q: M is the set of integers that are greater than -1 and less than 4.

A: M is the set of integers