Given a positive integer n, how many decimal strings of length n begin or end with an even digit? (assume inclusive or).O (10)" - 5² (10)^-2O 5(10) "¹+5(10)"-1O 5(10)-1 +5(10)"-¹-5(10)-2O 5(10)-1 +5(10)-¹-5(2)(10)-²O None of these.

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Answered: Given a positive integer n, how many…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose L = {+, X, S, <, 0} is the first-order language of number theory (Peano's arithmetic). Write a term-calculation for S(n x (m + S(0)) + S(S(0 × n))). What is the value of this term when n = 2 and m = 3?
Writing and Proof:
4) Consider the following recursive formula an = an-1- V3, where n2 2and the first term is a = 12. Which of the following could be the explicit equation? A an = 12 – V3-n, where n>0 B a, = 12 – V3 -n, where n20 c an = 12 - V3 -n, where n 21 D an = 12 - V3- (n – 1), where n20 E) n = 12 - V3 - (n – 1), where n 21
(a) Let the integers 1 to 23 be written on a straight line. Can you insert “+” and “−“ signs between them so their sum is zero. Explain! (b) How many numbers less than 700 are divisible by 4 or 11? Explain!
1. Find the LCM of 22 -81 and r? - 12x +27. (6 – 2) O O (2 - 9)(x - 3) O ( + 9)(2 - 9)(a+ 3) O ( + 9)(2 - 9)(2 – 3)
389-390
10) The composite figure below is a combination of a square with side length x units and a rectangle with length 2x + 3 units and width x + 1 units. x X 2x + 3 x + 1 Create the expression that gives the value of the area of the composite figure in terms of x.
(a) How many strings of 1our decimal digits have all four digits that are different? (b) How many strings of four decimal digits end with an even digit? (c) How many strings of four decimal digits have exactly three digits that are 9? (d) Write down the coefficient of the x°yt term in the expansion of (x + 2y)1º. (e) Your grandma has prepared eight pieces of bakery of different flavor. You want to choose three for breakfast, two for lunch, two for dinner, and one for tea time in the afternoon. How many ways are there to choose?
Eli currently has 45 tulips in his yard. Each year he plants 9 more. (a) Which of the following is a recursive formula for the number of tulips Eli has? P₁ = 45 Pt= Pt + 45 Pt +9 Pt-1+9 Pt-1 + 45 (b) Write an explicit formula for the number of tulips Eli has. P₁ =

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Given a positive integer n, how many decimal strings of length n begin or end with an even digit? (assume inclusive or). O (10)" - 5² (10)-2 O 5(10)-1+5(10)"-1 O 5(10)-1 +5(10)"-1 -5(10)-2 O 5(10)-1 +5(10)-¹ — 5(2)(10)¹-2 O None of these.