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The Fibonacci numbers F are defined as follows. F is 1, F is 1, and
Fi+2 = Fi + Fi+1 |
i = 0, 1, 2, … . In other words, each number is the sum of the previous two numbers. The first few Fibonacci numbers are 1, 1, 2, 3, 5, and 8. One place that these numbers occur is as certain population growth rates. If a population has no deaths, then the series shows the size of the population after each time period. It takes an organism two time periods to mature to reproducing age, and then the organism reproduces once every time period. The formula applies most straightforwardly to asexual reproduction at a rate of one offspring per time period.
Assume that the green crud population grows at this rate and has a time period of 5 days. Hence, if a green crud population starts out as 10 pounds of crud, then in 5 days there is still 10 pounds of crud; in 10 days there is 20 pounds of crud, in 15 days 30 pounds, in 20 days 50 pounds, and so forth. Write a
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- The Fibonacci sequence is listed below: The first and second numbers both start at 1. After that, each number in the series is the sum of the two preceding numbers. Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, ... If F(n) is the nth value in the sequence, then this definition can be expressed as F(1) = 1 F(2) = 1 F(3) = 2 F(4) = 3 F(5) = 5 F(6) = 8 F(7) = 13 F(8) = 21 F(n) = F(n - 1) + F(n - 2) for n > 2 Example: Given n with a value of 4F(4) = F(4-1) + F(4-2)F(4) = F(3) + F(2)F(4) = 2 + 1F(4) = 3 The value of F at position n is defined using the value of F at two smaller positions. Using the definition of the Fibonacci sequence, determine the value of F(10) by using the formula and the sequence. Show the terms in the Fibonacci sequence and show your work for the formula.arrow_forwardIn the example below, the sum of the fourth powers of each digit that forms the 4-digit numbers gives the number itself: 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474 = 94 + 44 + 74 + 44 And sum of these numbers is 1634 + 8208 + 9474 = 19316. Find the sum of all numbers that can be written as the sum of the fifth forces of their numbers. (P.s.: You have to done it by C++)arrow_forwardLet's begin with a lesson in roulette. Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1–36 are colored red and half are black and the numbers 0 and 00 are green. Each number occurs only once on the wheel. We can make many different types of bets, but two of the most common are to bet on a single number (1–36) or to bet on a color (either red or black). These will be the two bets we will consider in this project. After all players place their bets on the table, the wheel is spun and the ball tossed onto the wheel. The pocket in which the ball lands on the wheel determines the winning number and color. The ball can land on only one color and number at a time. We begin by placing a bet on a number between 1 and 36. This bet pays 36 to 1 in most casinos, which means we will be paid $36 for each $1 we bet on the winning number. If we lose, we simply lose whatever amount of money we…arrow_forward
- Let's begin with a lesson in roulette. Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1–36 are colored red and half are black and the numbers 0 and 00 are green. Each number occurs only once on the wheel. We can make many different types of bets, but two of the most common are to bet on a single number (1–36) or to bet on a color (either red or black). These will be the two bets we will consider in this project. After all players place their bets on the table, the wheel is spun and the ball tossed onto the wheel. The pocket in which the ball lands on the wheel determines the winning number and color. The ball can land on only one color and number at a time. We begin by placing a bet on a number between 1 and 36. This bet pays 36 to 1 in most casinos, which means we will be paid $36 for each $1 we bet on the winning number. If we lose, we simply lose whatever amount of money we…arrow_forwardMany companies use telephone numbers like 555-GET-FOOD so the number is easier for their customers to remember. On a standard telephone, the alphabetic letters are mapped to numbers in the following fashion:A, B, and C = 2D, E, and F = 3G, H, and I = 4J, K, and L = 5M, N, and O = 6P, Q, R, and S = 7T, U, and V = 8W, X, Y, and Z = 9Create an application that lets the user enter a 10-character telephone number in the format XXX-XXX-XXXX. The application should display the telephone number with any alphabetic characters that appeared in the original translated to their numeric equivalent. For example, if the user enters 555-GET-FOOD, the application should display 555-438-3663.arrow_forwardPlease answer it in Python Suppose we play a game where each round takes place in the following way: first, we roll a dice, and its result gives the number of points at stake. Then, the player can, if he wishes, trigger his bonus "double account" or his bonus "triple account". Then, the player answers a number of questions, and calculates his percentage of correct answers. The points awarded to the player for that round are then calculated based on the percentage of correct answers and the number of points in play rounded to the nearest integer (for example, with 50% correct answers and 6 points in play, the player gets 3 points; with 45% correct answers and 8 points in play, the player gets 4 points). Finally, this number of points is possibly multiplied by two or three if the corresponding bonus has been used. Write a function points_match that takes as an argument the percentage, the number of points at stake, and as an optional argument the multiplier (which is worth 2 in a double…arrow_forward
- When you borrow money to buy a house, a car, or for some other purpose, you repay the loan by making periodic payments over a certain period of time. Of course, the lending company will charge interest on the loan. Every periodic payment consists of the interest on the loan and the payment toward the principal amount. To be specific, suppose that you borrow $1,000 at an interest rate of 7.2% per year and the payments are monthly. Suppose that your monthly payment is $25. Now, the interest is 7.2% per year and the payments are monthly, so the interest rate per month is 7.2/12 = 0.6%. The first months interest on $1,000 is 1000 0.006 = 6. Because the payment is $25 and the interest for the first month is $6, the payment toward the principal amount is 25 6 = 19. This means after making the first payment, the loan amount is 1,000 19 = 981. For the second payment, the interest is calculated on $981. So the interest for the second month is 981 0.006 = 5.886, that is, approximately $5.89. This implies that the payment toward the principal is 25 5.89 = 19.11 and the remaining balance after the second payment is 981 19.11 = 961.89. This process is repeated until the loan is paid. Write a program that accepts as input the loan amount, the interest rate per year, and the monthly payment. (Enter the interest rate as a percentage. For example, if the interest rate is 7.2% per year, then enter 7.2.) The program then outputs the number of months it would take to repay the loan. (Note that if the monthly payment is less than the first months interest, then after each payment, the loan amount will increase. In this case, the program must warn the borrower that the monthly payment is too low, and with this monthly payment, the loan amount could not be repaid.)arrow_forwardWe have n glasses which can hold a varying amount of liquid. We will say that glass1 is size q1 quarts and glass2 is size q2 quarts, etc. We now give you a size, say x quarts. You must give me a glass of exactly x quarts. You are allowed to fill any glass to exactly its size and to pour any liquid from one glass into another. When you pour, you either have to empty the glass you are pouring from or fill the glass you are pouring into. Can you do it?More concrete example: G1 has size 10 quarts. G2 has size 4 quarts. G3 has size 1 quart. You can get a 5 quart drink by filling G1, pouring 4 quarts from it into G2 and 1 quart of it into G1. After that, G1 has exactly 5 quarts. In the same problem, we could get 8 quarts by filling G2 twice and emptying it into G1 twice. Given This: Write an algorithm to do this and determine its complexity.arrow_forwardSuppose you save $100 each month in a savings account with annual interest rate 3.75%. Thus, the monthly interest rate is 0.0375/12 = 0.003125. After the first month, the value in the account becomes 100 * (1 + 0.003125) = 100.3125, after the second month, the value in the account becomes (100 + 100.3125) * (1 + 0.003125) = 200.938, after the third month, the value in the account becomes (100 + 200.938) * (1 + 0.003125) = 301.878 and so on. Write a Java program that prompts the user to enter a monthly saving amount and displays the account value after the sixth month. (You will use a loop to simplify the code and display the account value for any month.) Sample Output:Enter the monthly saving amount: 100After the first month, the account value is 100.3125After the second month, the account value is 200.9384765625After the third month, the account value is 301.8789093017578Note: The computation should be until 12 months.arrow_forward
- This is a JAVA programming assignment. Program a GeneticAlgorithm to find an integer number between 0 and 31 that maximizes the function f (x) = x2.The initial procedure is given as below.• Population size: 6• Crossover probability: 100%• Mutation probability: 5%• Terminating criteria:o When your program produces an average of candidates is equal to or greater than29, then you can accept it as a terminating condition.• Fitness function:o You can use the function itself (f (x) = x2)as your fitness function.1. For the 1st generation, you need to print the process and result of selection, crossover, andmutation operation.you need to print the corresponding integer values and bits (binary values)of selection, crossover, and mutation operation. You also need to decide andprint the crossover point and the mutation point.2. From the 2nd generation, you do not have to print all results of selection, crossover,mutation operations. You can just print the result of each generation. Please provide…arrow_forwardWhen you borrow money to buy a house, a car, or for some other purposes, then you typically repay it by making periodic payments. Suppose that the loan amount is L, r is the interest rate per year, m is the number of payments in a year, and the loan is for t years. Suppose that i = (r / m) and r is in decimal. Then the periodic payment is: You can also calculate the unpaid loan balance after making certain payments. For example, the unpaid balance after making k payments is: where R is the periodic payment. (Note that if the payments are monthly, then m = 12.) Instructions Write a program that prompts the user to input the values of L, r, m, t, and k. The program then outputs the appropriate values. Your program must contain at least two functions, with appropriate parameters, to calculate the periodic payments and the unpaid balance after certain payments. Make the program menu driven and use a loop so that the user can repeat the program for different values. Example of…arrow_forwardLet P be “this book is a non-fiction book” and Q be “the ideas in the book is consistent with physical reality.” Consider a case where both P and Q are false (e.g. a fantasy novel and an unrealistic phenomenon in the novel) and see whether it makes sense that P→Q is true. [Give an example, i.e., the name of a book and a particular idea in that book] Explain why it is possible that P→Q is true yet Q is false. [Type your explanation]arrow_forward
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage Learning