1. A = {x | x is a Prime number such that x <50 } 2. C = {x | x is a square of integer less than 100}

Q: . Prove that for any two nonnegative real numbers, their arithmetic mean is always greater than or…

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Q: . What is the coefficient of a" in (2 – x)"?

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Q: Q2) Use rounding to 6 digits and compute each of the following: a) P(0.01), where P(x) =…

A: Given, P(x)=(ex-1-x)x2 therefore, P(0.01)=(e0.01-1-0.01)0.012                                =…

Q: 74. Prove that for any real numbers a and b, |b − a|=|a − b|.

A: Given; a and b are any real numbers Consider, L.H.S=b-aWe can write it as,=b+-a=-1-b+a=-1a-b…

Q: 13. Let U be the set of real numbers, A = {x |x is a solution of x - 1 = 0}, and B ={-1, 4}.…

A: Let's find.

Q: (a) How many nonnegative integer solutions are there to the equation ₁ + x₂ + x3 + x₁ = a? (b) How…

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Q: n² + n+ 8 2 He has just shown you a convincing proof that if the equation is true for any integer k…

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Q: 49. Prove that x +> 2 (x1/2 – x-1/2)2. 2 for all x > 0. Hint: Consider

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Q: 6. Prove that the statement "If x is a real number such that x² > 4 then x > 2" is false.

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Q: Find the maximum value of a, x, +a,x, + .+ax to the condition that x +x, +. + x =1 for given…

A: We need to find the maximum value of a1x1+a2x2+a3x3+...+anxn to the condition that…

Q: If A = {r|- 23 < x < 3how many negative integers does Acontain? Note that: 'I' means 'Such that'

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Q: Example 5-42. (a) Find the Geometric Mean of 2, 4, 8. 12, 16 and 24. (6) If the observations 2, 4, 8…

A: HEre AS PER POLICY I HAVE CALCULATED FIRST MAIN QUESTION  geometric mean =  a1 *a2*......ann

Q: true or false

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Q: 1. Find the number of zeroes at the end of 100!

A: Introduction :Here, we have asked for the number of zeros at the end of 100 !

Q: 4. Let h(r) = 5 x 6 20 x²3x18 Find all values of N for which h(N) = 3.

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Q: 3.54. If the arithmetic mean of two unequal positive real number 'a' and 'b', (a > b), be twice as…

A: In question, Given that the arithmetic mean of two unequal real numbers a and b be twice of their…

Q: **For what c value is (x-5) a factor of x³ + 2x2 + cx + 10

A: According to our company guidelines we are supposed to answer only one question since you have asked…

Q: 3. In the domain of real numbers, explain what the following statement says in English. A rational…

A: Given: The given statement ∀x∀yy&gt;x→∃zz is a rational number∧x&lt;z&lt;y To find: we need to…

Q: 9. Solve In (x+5) 2 2. O A. (x | x 2 12.3891} B. (x | x 2 2.3891} O C. (x |xs 12.3891} O D. {x |x s…

A: Given:         ln(x+5)≥2

Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: 3x²³-2x² + 3kx + 18 by x- 6 to be equal to zero, k must be equal to.

A: Use division

Q: Prove that (a) For all integers m and n, n + m and n - m are either both odd or both even.

A: Since you have posted multiple questions, according to our guidelines we can solve only first…

Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

A: Mathematical induction is a proof technique used in mathematics to establish the truth of a…

Q: What is the largest number x such that x<200 and x has exactly 4 factors?

A: Factors:    Number that are multiplied together to get a product                              Factor…

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: 21 84 = 1, where x and y are positive real numbers, find the smallest possible y of x + y. If + X…

A: Given   21x+84y=1

Q: ind the interval in the real number line which equals 1 U [4+, 20- n n=1 n

A: Answer given below.

Q: what are the integers for 6<x<7 with a line under each less than sign

A: To determine: The integers for 6 &lt; x &lt; 7 with a line under each less than sign. It means, 6 ≤…

Q: Provide either a proof or a counterexample for  For all positive real numbers x, x^2 - x ≥ 0

A: According to the given information, it is required to prove the given equality or give a counter…

Q: 14) Show that f (æ) = -æ³ +2 is decreasing on the entire real number line. (Show Graph)

A: we have to show that the given function is decreasing and also draw the graph of f(x)

Q: a. The remainder of P(x) = 2x' +mx? –7 when it is divided by x+2 is 6 greater than when it is…

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Q: Suppose there is a currency which only uses 3-cent coins and 7-cent coins. Prove that for all…

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Q: (d) Prôvé that the square of every prime number greater than 3 is one more than a multiple 24.

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Q: 1. Determine the value of x in the following (SHOW ALL WORK!!!). a) x = 5000(1.075)4(7) b) x = 100…

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Q: Prove by contradiction that a real number that is less than every positive real number cannot be…

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Q: 6. Prove that x is a rational number if and only if 2x - 1 is a rational number.

A: To Prove: x is a rational number if and only if 2x-1 is a rational number.

Q: Suppose a special type of small data processing firm is so specialized that some have difficulty…

A: Property of probability distribution function (pdf) :  ∫yf(y) dy =  1

Q: 2. Let x be irrational real number. Prove that 2x+3 is irrational

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Q: Please answer True or False for the following Statements... 1. Let x be an integer. Then if 7x+4 is…

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