Q1. A vending machine dispensing books of stamps accepts onlyone-dollar coins, $1 bills, and $5 bills.a) Find a recurrence relation for an, the number of ways todeposit n dollars in the vending machine, where the order inwhich the coins and bills are deposited matters.( Hint: 3 cases: Case1; the first deposit is a one-dollar coin,Case 2: First deposit is a $ 1 bill. Case 3: First deposit is a $ 5 billNote that your recurrence relation is valid for n 2 6So we will need 5 initial conditions a1,a2,a3,a4,a5.b) In how many ways can you deposit $8 for a book of stamps?Use the recurrence relation that you found in part (a).

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Answered: Q1. A vending machine dispensing books…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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6. Let a be the number of 1 x n tile designs you can make using 1 × 1 squares available in 4 colors and 1 x 2 dominoes available in 5 colors. a. First, find a recurrence relation to describe the problem. Explain why the recurrence relation is correct (in the context of the problem). b. Write out the first 6 terms of the sequence a1, a2,.... c. Solve the recurrence relation. That is, find a closed formula for an.
A string that contains only Os, 1s, and 2s is called a ternary string. do not.. a) Find a recurrence relation for the number of ternary 6 and strings of length n that contain two consecutive Os. b) What are the initial conditions? c) How many ternary strings of length six contain two consecutive Os? 7 "00"! do not contain 00
Consider the task of arranging red, white, and blue flags on an n-foot flagpole with no gaps, where red flags are 4- feet high, white flags are 2-feet high, and blue flags are 1-foot high. Which of the following recurrence relations can be used to determine the number distinct ways x(n) of arranging red, white, and blue flags on the n-foot flagpole for n=1,2,3, ... if the appropriate initial conditions are known? O x(n) = x(n-3) + x(n-2) + x(n-1), n = 5,6,7, .. O x(n) = 4x(n-4) + 2x(n-2) + x(n-1), n 5,6,7, . O x(n) = x(n-4) + x(n-2) + x(n-1), n = 5,6,7, .. O x(n+4) = x(n) + x(n-1) + x(n-2), n = 1,2,3, .. • Previous Next Simpfun
Listed below are the overhead widths (cm) of seals measured from photographs and weights (kg) of the seals. Find the regression equation, letting the overhead width be the predictor (x) variable. Find the best predicted weight of a seal if the overhead width measured from a photograph is 1.8 cm, using the regression equation. Can the prediction be correct? If not, what is wrong? Use a significance level of 0.05. Overhead Width (cm) 7.3 7.4 9.8 9.5 8.8 8.5 Weight (kg) 152 187 286 247 237 231 The regression equation is y =+ (x. (Round the y-intercept to the nearest integer as needed. Round the slope to one decimal place as needed.)
4. True or False? (a) In counting combinations, order matters. (b) In counting permutations, order matters. (c) For a set of n distinct objects, the number of different combinations of these objects is more than the number of different permutations. (d) If we have a set with five distinct objects, then the num- ber of different ways of choosing two members of this set is the same as the number of ways of choosing three members.
Give a recurrence relation that would fit the sequence a1, az, A3, A4, A5, .= 1,2, 5, 26, 677 ...
How many numbers have digits which are all ”1”s and ”2”s, and thedigits add up to 8? A few such numbers are 12212, 112121, and 112121. (HINT: breakthe list into cases and count each one. You can count them by hand, but you will savea lot of time if you apply the right formula.)
provide the explicit explicit formula for the following recurrence relation
2. Let an be the number of ways to write the numbers 1, 2, 3, ..., n in order such that no number i appears immediately before i + 1 (this is a question which appeared on the exam, where an explicit formula was requested!). Explain why an will satisfy the recurrence an = (n-1) an-1+ (n − 2)an-2 for every n ≥ 2.
3. A loan of $5,000 is charged a 1% monthly interest rate. An $80 payment is made each month. O Write a recurrence relation for the loan balance remaining at the beginning of month. Indicate which kind of recurrence relation describes the loan sequence (linear/not-linear, first/second/n-th order, homogeneous or not, constant/no-constant coefficients, divide-and-conquer) Solve the recurrence relation. Consider the geometric progression for the summation with r # 1: a + ar + a² + + ar-1 a ar 1 - 1 How much is left of the loan balance at the beginning of the 19th month?
a. In the following, give the first five terms (b₁,b₂, b, b, b,), and identify the given recurrence relation (linear of degree k, nonlinear, homogeneous, etc.). (3 pts.) b₁ = 3b-1+4, for n≥2, and b₁ = 2 b. Solve the above recurrence relation using back tracking. (4 pts.)

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