27. Show that if x and y are positive real numbers that have the same first n digits in their decimal representations, then y approximates x with relative error less than 101-". Is the converse true?

Q: Find the least integer n such that (2x^3+x^2logx) is O(x^n).

A: The given expression is 2x3+x2logx. Concept used: Let f and g from the set of integers or the set of…

Q: 7. Remwrite the..either.five.exated.nt.agrmls. 1-X FCX ng , Z)dydzdx ZA z= 1-x2 ...... y=1-メ

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Q: Suppose that ƒ′(x)<= 1 for 1<= x<= 4. Show that ƒ(4) - ƒ(1)<=3.

A: Show that:

Q: Derive u and show that 7 X is biased estimator of 2. Can you modify 7T -X in order to get an…

A: The expected value of X is defined as  μ=∫λ∞x.f(x)dx And an estimator to be unbiased its expected…

Q: 14. Demonstrate that 21 has no primitive root.

A: An integer n≥2 has a primitive root if and only if the the number n is one of the following; 2,4,…

Q: Show with the help of Fermat’s little theorem that if n is a positive integer, then 42 divides n7 −…

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Q: 4. Find the critical numbercs) for gx) =IRCX+1) t, en cuaracterize ealh, one as 1ocal min, or…

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Q: Find the product and addition of the approximate numbers x, = 32.452 and x, = 24.3595 all of whose…

A: x1=32.452 and x2=24.3595 To Find: a) Product and addition of the approximate numbers. b) Relative…

Q: Students are sometimes uncertain about which zeros in decimals can be dropped and which can't (with-…

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

Q: (c) Use a calculator to verify that Σx = 135, Σx2 = 7055, Σy = 151, Σy2 = 4815, and Σxy = 3193.…

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Q: 2. Show that In (- - ) = ( + 2nn)i where n = | .... .... ..

A: Consider the following expression: x=ln-12-32iex=-12-32icosx+isinx=-12-32i

Q: 4. Prove that the difference between the square of any odd integer and the integer itself is always…

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Q: then x* 1 is odd." Give a proof by contradicton to show "1fx s even integer,

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Q: show that 2 tan 1/3 + tan 1/7 =n/4

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Q: Suppose 5 of every 9 dentists recommend Mintyfresh Toothpaste. Suppose ten dentists are chosen (a)…

A: A binomial distribution can be thought of as simply the probability of a success or failure outcome…

Q: Calculate the coefficient of x7y5zx7y5z in (x+y+z)13(x+y+z)13. (b) In her discrete math class,…

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Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

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Q: Suppose that a certain country conducted tests of a certain type of bomb in 2009 and 2013, and…

A: Define X1: random variable for the power of the explosive in the year 2009 X2: random variable for…

Q: Suppose the product of 22 integers is equal to 1. Prove that their sum is not equal to 0.

A:

Q: 9. Prove that there are as many positive real numbers as there are real numbers.

A: Consider the set X and Y. Then we said that |X| = |Y| if there exists bijective function from X to…

Q: 6. Find f'(1) if Ax) = nx

A:

Q: Show that 100 1 arctan(100) – arctan(2) + 1 1 < arctan(100) – arctan(2) + 1+ 1002 1+ k2 k=2 1+ 22

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Q: P-value = 0.072, a = 0.05 O reject Ho O do not reject Ho P-value = 0.005, a = 0.001 O reject Ho O do…

A: We need to determine the decision based on the given p-values and significance level.

Q: (c) Use a calculator to verify that x = 62, x = 10 = 1042, y = 650, y = 95,502, and xy = 9,765. %3D…

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Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

Q: (4) Prove that there is no smallest positive real number.

A: I have to prove that there is no smallest positive real number . Suppose that there is a smallest…

Q: bute 80 identical pencils in a class consisting of 10 boys and 20 girls in such a way that each of…

A: Given:- Number of boys=10 Number of girls = 20 Number of Pencils=80

Q: Show that the set of real numbers in the interval [0,1] that do not have a 7 in their infinite…

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Q: All Fermat's number is clearly odd numbers

A: Fermat number.

Q: Compute [rN (1- ) ]- d. K

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Q: 3 1 Without using a calculator, prove that 2 4

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Q: (8) Prove that if A and B are similar, then their transposes are also similar.

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Q: : a number is even  if

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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: 1. Find two non-negative numbers such that the product of the first squared and the second is 108…

A: 1) Given data:   The given expression for the product of the squared of the first number and the…

Q: Students are sometimes uncertain about which zeros in decimals can be dropped and which can't (with-…

A: We have to tell when can zeros in decimals are dropped and which can't without changing the meaning…

Q: 2. Find the largest negative x € Z that simultancously satisfies 4x = 9 (mod 5) 2x = 0 (mod 6) x =0…

A: Given : 4x = 9 (mod 5) 2x = 0 (mod 6) x = 0 (mod 4)

Q: d the sum of the critical numbers of f(x) = 3x4-4x3 +2. %3D ISwer.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2 In x | Show that 4 x* +1 16

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Q: Prove that no number of form 4k+3 (where K is a positive integer) can ever be the sum of two perfect…

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Q: sum of two even integers is even

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Q: The sum of any two integers of the from 4k + 1 is always: Even O prime Zero Odd

A: If a number n is not divisible by 2 then it is an odd number.  If a number n divisible by 2 then it…

Q: Show that the set of numbers of the form k/5", where k is an integer and n a positive integer, is…

A: The set of numbers of the form k5n where k is an integer are dense if every real number has rational…

Q: 4. Show that if ki = (X; - X)/[Σ(X; – X)2], then (a) Σki = 0; = (b) Σk? = 1/[Σ(X; − x)2]; (c) Σκ;(X;…

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Q: Suppose that x is a negative real number and that x < 1/x. Prove that x <-1.

A: Since we know for any real number a,b  If a &lt; b then -b &gt; -a

Q: Prove that the expression 2y2 - 128 is equal to 2(x² + 2) (x² – 2) (x8 + 4x+ + 16) Swer:

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Q: Let x and y be positive integers. When is x + y3 a prime number? When is x+y a composite number?…

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Q: Express in both (6+j5) ® (-16-j9)

A: 16+j53 x+jy3 and x=6, y=5∴r= 62+52r=36+25r=61and α=tan-156=39.81°θ=180+39.81=219.81Polar form…