The inductive step of an inductive proof shows that for k≥4, ifk! 22, then (k+1)! ≥ 2+1 However the lines are not labeled with the proper justification. Which line should be labeled "Because &≥421? (k+1)(k+1)k! (Step 2) (+1)(k+1) k (k-1) (k+1)≥ (k+1)-2* (Step 3) 2-1 (Step 1) (k+1)≥2.2 (Step 4) (+1)≥ 2 (Step 5)

Q: Find the equation of the line using (2,0) and (-2,5)

A: Use the Given Points are We Find the Equation of the line.

Q: (Q1] [20 points] You can leave answers unsimplified. 000 HTAM (A) How many lists of length 4 can be…

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Q: N.Find the set of values of x for which: w - x-2 x+1 12. Solve the inequality:(x-3)(x+2)(x+4) > C 13…

A: 11)  xx-2>1x+1⇒xx-2-1x+1>0⇒xx+1-x+2x-2x+1>0⇒x2-2x-2x+1>0           1 If x<-1 then…

Q: Let P(x) be the statement "x^2−x−20⩽0". a. If the domain consists of −4,0,1 and 2, then "∀x,P(x)"…

A: Given: Here is the given statements, 1. Px=x2−x−20≤0 To find: Is it true or false that "∀x,P(x)" is…

Q: (k+1)! −1+ (k+1) ( K+1)! (k+1)! [₁ + (k+1)] = = (k+1)! (k+²) -1 (k+2)! - 1

A: Introduction: Factorial is a very important symbol in mathematics. It is always applicable to any…

Q: 6) If X is N(45,5) for i = 1, 2,..., 25; find: 25 (a) P (30 < (X-45) < 55) 221 b) P(30< (X -45) 2 <…

A: The objective of the question is to find the probability of two different scenarios for a normally…

Q: X~ N(3,49),  (a) P(X > 3) (b) P1 < X<5) (c) P(-5 < x <9)

A: It is given that  If X~ N(3,49) Here, μ = 3,  σ2 = 49,     σ = 7   Note: According to Bartleby…

Q: 14x +4 4s4

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Q: A is the set of odd number greater than 5 and less than 23 n (A)=

A: A is the set of odd numbers greater than 5 and less than  23

Q: 19) (x +2)4 – )2 +4 = 0 5(x+2,

A: (x+2)4-4(x+2)2-(x+2)2+4=0 (x+2)2((x+2)2-4)-((x+2)2-4)=0 (x+2)2=1,(x+2)2=4 x+2=+-1,x+2=+-2…

Q: In a health examination of the 72 faculties at Brac University, the numbers of faculty with blood…

A: The term probability is defined as the chance of occurrence of an event. The probability value…

Q: inequality. x²-3x-18-0 A) (x1-3 ≤x≤6); [-3.6] C) (x lx s-3 or x = 6); (-,-3] or [6,-) B) (xlx s-3);…

A: Topic:- calculus and algebra

Q: How did they got n(n+1)(2n+1) / 6

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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: Prove Vn € N, 1 1 + 1 2 + 1 3 + + 11 2n - 1 + 2n ≥1+ n 2

A: Let's prove the given inequality step by step:Base Case (n=1):11≥1+12This is true, as 11=1 and…

Q: For all integers n, if 6 | n, then 9 | ((n^2) + 21n/2)

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Q: A scientist noticed that the population of a certain country could be represented by the following…

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Q: 1. Prove that if n is an integer and n is a multiple of 2, then 4n+ 24 is a multiple of 8. 2. Show…

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Q: Show that 2n+1≤2^n  for all n≥3.

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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: The following puzzle has columns and rows. Each box can only be filled with the digits 1 to 4, with…

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