. Let x be a positive real number and d be a positive integer. Prove that the number of positive integers less than or equal to x that are divisible by d is [x/d]. 2. Find the number of positive integers not exceeding 500 that are divisible by 3.  3. Find the number of positive integers between 200 and 500 that are divisible by 3.

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: 1 which of the following is equivalent to 2x-4 O B. -4x²+6x + 5 0 4x²-6x-5 >0 E. 4-2x

A:

Q: 27. 2x + 3 + x2; for x 4 * 17 19 27 of

A: In the given question we have to find the value of  2x+3+x2 for x=4.

Q: Prove the statement if it is true, and give a counterexample if it is not true. a. For every real…

A: Both the subparts are solved with explanation.

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: a. 3.2F> Fn+1 for n23 [Solutions and final ans

A: We need to prove 2Fn>Fn+1 Now, we have formula for fibonacci sequence is Fn=Fn-1+Fn-2

Q: true or false

A:

Q: R² = gen gen

A: see below the reason

Q: 2. The set of all rational numbers in the interval (0, 1).

A:

Q: Show that V12 is irrational

A: A Rational Number is a number that can be written in terms of P/Q.  An irrational number can not be…

Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

A:

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.

A:

Q: 19. Which of the following properties of Real Numbers is NOT true ? * a. Vx ER, x+0 = x b. Vx, y, z…

A:

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: 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: Solve 2|7-x| 8 c. -8 6

A: We have given the inequality; 2|7-x| < 2

Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

A:

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

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: 7. Let y be irrational and x ‡ 0 a rational number. Show that the product xy is irrational.

A: We will prove given statement by method of contradiction.

Q: 3. Find all r so that r-1+r-2| < 5.

A:

Q: The algebraic translation of "x is at most 7" is

A: Given : The algebraic translation of " x is at most 7" is ______________ .

Q: (d) The third quartile for X 提交答案| Tries 0/5 (e) the IQR for X 提交答案| Tries 0/5 (f) P(IX-216|> 41)

A: Given : Let X be a r.v X~N(216 , 18) Here ; μ=216 σ=18

Q: The value of n such that ph pn- ,n> 4 is 15.

A:

Q: Q2 1-The Euler's number (e) is a * rational number a. True b. False

A: Rational numbers are those which can be represented in the from of fraction and those which can not…

Q: Prove by contradiction method : if x>0  then 2 ≤ x + 1/2

A:

Q: 4. Find a number 8 >0 such that if Ix-10] < & then |(2x + 3)-23|< 0.25.

A: I am going to solve the problem by using some simple calculus to get the required result of the…