Q: true or false  every set of negative real numbers has a supremum.

A: True

Q: Prove: An odd number squared is an odd number. (2n + 1)2 = [? ]n²? + [ ]n+ [ = [ ](2n2 + 2n) +[ ]…

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Q: Let x be a real number. Which of the following is the same as P(Z x) c) P(Z ≤ -x) d. none of the…

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Q: In class we proved that if n is a multiple of 3, then fn is even. Prove the converse of this…

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Q: 5.44. Show that there exist two distinct irrational numbers a and b such that a" is rational. 5.45.…

A: We will show that there exist no real a, b such that 5.45 holds.

Q: 4.A.2. Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3…

A: Yes there is an integer that has a remainder 2 when divided by 5 and a remainder of 3 when divided…

Q: 1) Let R represent the set of all real numbers. Suppose f:R -> R has the rule f(x)=3x+2. Determine…

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Q: Find two positive real numbers such that they add to 40 and their product is as large as possible.

A: Suppose that the numbers are x and y then given that

Q: 3. Invent two interesting and original positive integers a and b. Let f(x) = ax +3. (a) (b) What is…

A: Given function is fx=ax+3. To find:  a  f10   (b). A number x such that fx=b Solution: Given…

Q: Prove using deductive reasoning the following conjectures. If the conjecture is FALSE, give a…

A: Given an odd and even integer. By Deductive reasoning we prove the conjectures using variable to…

Q: Find an integer such that its square is 81 less than 18 times the integer

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Q: 3 16. Which of the following are true about Write all of the correct answers in the space provided.…

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Q: 4.* Let a > -1 be a real number. Prove that (1+x)" > 1+nx holds for any integer n >0 (this is called…

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Q: How do you describe thr denominators of all terminating decimals? What are those which will yield…

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

Q: (a) Suppose x is an irrational number. Show that there is an integer n such that |x – n| < 1/2. (b)…

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Q: T F 41. There exist irrational numbers with repeating decimals.

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

Q: 1. A rectangular playing field with a perimeter of 190 meters is to have an area of at least 450…

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Q: (d) Norma does not get along with Oona (who is also in the pool of prospective members) and would be…

A: d) Consider the following events, A:Oona does not chair the committeeB:Norma and Norman, both are in…

Q: A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey…

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Q: P Express 3.927927927. .. as a rational number, in the form where p and q have no common factors.…

A: Given:- 3.927927927......  To find:- Express given expression into p/q form

Q: (b) Define G: R - R by the rule G(x) = 2 - 3x for each real number x. Is G onto? Scratch work: Let y…

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Q: 3. Use a number line to find the interval(s) on which the function (x) = 3* - 9xIn(3) is increasing.…

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Q: 7.1 Example: Is the function fwell defined? We know that Q represents the set of all rational…

A: For a system to be well defined-  For any input, output of the function should be uniquely…

Q: The smallest positive number for which

A: Given equation - sint+cos2t = 0sint+1-2sin2t = 0…

Q: Every nonzero real number has a reciprocal. 12. For all nonzero 11. All nonzero real real numbers r,…

A: 11)   All nonzero real numbers have reciprocal.

Q: C. Prove by CASES: . Let x be an integer. If 3 does not dividex, then 3 divides x-1. 2. Prove that…

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Q: Determine if 0.4 is rational or irrational and give a reason for your answer. The number 0.4 is…

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Q: Approximating a number A rational number is a number that can be written as a fraction of integers.…

A: Let's find.

Q: I am a positive integer. All my digits are odd. I am equal to the sum of the cubes of my digits.  I…

A: There are two possible answers for the given situation.If it is a single digit number, then it…

Q: by x * y = 1 + x + y on the set of real numbers. Show that * is commutative but not associative

A: Given: x*y =1+x+y To show: * is commutative and associative.

Q: Question A positive integer is 15 less than another. If 4 times the reciprocal of the smaller…

A: Here we find the integer.

Q: an n+3 Find the smallest number M such that:

A: Given: limn→∞n+3n+5

Q: I am having trouble figuring out question b. Could you please give me an idea how to solve it?

A: Given that

Q: 29. A rational in disguise. Show that the number (v2") is a rational numbe even though it might look…

A: (29) Show that the number 222 is a rational number even though it might look irrational. What…

Q: State whether or not the following are statements. In the case of a statement, indicate if it is…

A: Topic :- Numbers As per our guidelines , only three subparts of a question will be answered at a…

Q: d. The sum of any rational number and any irrational number is irrational. e. Any two consecutive…

A: To prove the three parts d, e, f of the problem.

Q: V4 is 3 None of these an irrational number a rational number that is not an integer an integer O not…

A: Solution-

Q: Apopulation of fruit flies is growing in such a way that each generation is 1.25 times as large as…

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Q: Prove using deductive reasoning the following conjectures. If the conjecture is FALSE, give a…

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

Q: An approximation of an exact number is called a

A: Introduction: An exact number is a number that is unique with no further simplification possible,…

Q: Not sure how to do This?

A: Since there are multiple questions in the screenshot provided, we are answering only the first…

Q: i am a positive integer all my digits are odd i am equal to the sum of the cubes of my digits i…

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Q: R.2. Prove that for every real number x, if x 0 and x +1 then there is a unique real number y such…

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Q: Question A positive integer is 7 less than another. If 6 times the reciprocal of the smaller integer…

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Q: 7) Express 55C13+55C₁4 as a single term from Pascal's triangle.

A: 8

Q: A train leaves a station and travels north at a speed of 50 km/h. Five hours later, a second train…

A: A detailed solution is given below

Q: Trivia: There is a famous conjecture that for every integern, there exists an integer k such that f*…

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Q: (a) Prove that the real number V3 is an irrational number. That is, prove that If r is a positive…

A: Rational number: A number is known as rational number if it can be expressed as the ratio of two…

Q: The greatest integer in a real number a, denoted by x, is the largest integer less than or equal to…

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Q: Ex1: The sum of two even integers equals an even integer prove:? Ex2: if n is an odd integer, then…

A: Integer