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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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- Interest on a credit card’s unpaid balance is calculated using the average daily balance. Suppose that netBalance is the balance shown in the bill, payment is the payment made, d1 is the number of days in the billing cycle, and d2 is the number of days payment is made before billing cycle. Then, the average daily balance is: averageDailyBalance = (netBalance * d1 - payment * d2) / d1. The interest on the unpaid balance is: interest = averageDailyBalance * interestRate where interestRate is the interest rate per month. Write a program that accepts as input netBalance, payment, d1, d2, and interestRate. The program outputs the interest. Format your output to two decimal places. Analyze and design this program. Write the code, compile and run it. Upload your analysis and design document and your .cpp source code file here.arrow_forwardA flight of stairs has 10 steps numbered 1 to 10 as shown in the figure below. i. How many ways could you climb up the set of stairs, assuming that you can skip any number of stairs with each step, but you must end on step 10 and you can only go up, never down and never remaining on the same step. ii. How many ways could you climb up the set of stairs, assuming you take exactly 4 steps. Again, your staircase climb ends on step 10. JAlthough there are different ways in which you could solve this problem, model the problem as a balls and bins problem for full credit.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
- A number of the form a + ib, in which i2 = -1 and a and b are real numbers, is called a complex number. We call the real part and b the imaginary part of a + ib. Complex numbers can also be represented as ordered pairs (a, b). The addition and multiplication of complex numbers are defined by the following rules: (a + ib) + (c + id) = (a + c) + i(b + d ) (a + ib) * (c + id) = (ac - bd) + i(ad + bc) Using the ordered pair notation, these rules are written as: (a, b) + (c, d) = ((a + c), (b + d )) (a, b) * (c, d) = ((ac - bd ), (ad + bc)) C++ has no built-in data type that allows us to manipulate complex numbers. Construct a data type, complex Type, that can be used to process complex numbers. Overload the stream insertion and stream extraction operators for easy input and output. We will also overload the operators + and * to perform addition and multiplication of complex numbers. If x and y are complex numbers, we can evaluate expressions such as x + y and x * y.arrow_forwardBowling involves 10 frames. Each frame starts with 10 pins. The bowler has two throws to knock all 10 pins down. The total score is the sum of pins knocked down, with some special rules. For the first 9 frames: If all 10 pins are knocked down on a frame's first throw (a "strike"), that frame's score is the previous frame plus 10 plus the next two throws. (No second throw is taken). If all 10 pins are knocked down after a frame's second throw (a "spare"), that frame's score is the previous frame plus 10 plus the next throw. In the 10th frame, if the bowler's first throw is a strike, or the first two throws yields a spare, the bowler gets a third throw. The 10th frame's score is the previous frame's score plus the pins knocked down in the 10th frame's two or three throws. Given integers represents all throws for a game, output on one line each frame's score followed by a space (and end with a newline). Note that the number of throws may be as few as 11 (strikes in first 9 frames,…arrow_forwardBowling involves 10 frames. Each frame starts with 10 pins. The bowler has two throws to knock all 10 pins down. The total score is the sum of pins knocked down, with some special rules. For the first 9 frames: If all 10 pins are knocked down on a frame's first throw (a "strike"), that frame's score is the previous frame plus 10 plus the next two throws. (No second throw is taken). If all 10 pins are knocked down after a frame's second throw (a "spare"), that frame's score is the previous frame plus 10 plus the next throw. In the 10th frame, if the bowler's first throw is a strike, or the first two throws yields a spare, the bowler gets a third throw. The 10th frame's score is the previous frame's score plus the pins knocked down in the 10th frame's two or three throws. Given integers represents all throws for a game, output on one line each frame's score followed by a space (and end with a newline). Note that the number of throws may be as few as 11 (strikes in first 9 frames,…arrow_forward
- The quadratic formula is used to solve a very specific type of equation, called aquadratic equation. These equations are usually written in the following form:ax2 + bx + c = 0The Quadratic Formula x = ( -b ± √( b^2 - 4ac ) ) / ( 2a ) Where a, b, and c are constants with a ≠ 0. (If a = 0, the equation is a linear equation.)The discriminant is the part of the formula in the square root. If the value of the discriminant is zero then the equation has a single real root. If the value of thediscriminant is positive then the equation has two real roots. If the value of thediscriminant is negative, then the equation has two complex roots.Write a program that finds the roots of the quadratic equation using the Quadratic Formula. Write a function named discriminant in the file, Disc.py, to calculate and return the discriminant of the formula. Let the main function call the discriminant function and then calculate the solution(s) of the equation. Do not calculate the solutions in the discriminant…arrow_forward1.In an ancient land, the beautiful princess Eve had many suitors. She decided on the following procedure to determine which suitor she would marry. First, all of the suitors would be lined up one after the other and assigned numbers. The first suitor would be number 1, the secondnumber 2, and so on up to the last suitor, number n. Starting at the first suitor she would then count three suitors down the line (because of the three letters in her name) and the third suitor would be eliminated from winning her hand and removed from the line. Eve would then continue, counting three more suitors, and eliminating every third suitor. When she reached the end of the line she would continue counting from the beginning. For example, if there were 6 suitors then the elimination process would proceed as follows:123456 initial list of suitors, start counting from 112456 suitor 3 eliminated, continue counting from 41245 suitor 6 eliminated, continue counting from 1125 suitor 4 eliminated, continue…arrow_forwardPython tic tac toe. Tic tac toe is a very popular game. Only two players can play at a time. Game Rules Traditionally the first player plays with "X". So you can decide who wants to go with "X" and who wants to go with "O". Only one player can play at a time. If any of the players have filled a square then the other player and the same player cannot override that square. There are only two conditions that may match will be a draw or may win. The player that succeeds in placing three respective marks (X or O) in a horizontal, vertical, or diagonal row wins the game. Winning condition Whoever places three respective marks (X or O) horizontally, vertically, or diagonally will be the winner. Submit your code and screenshots of your code in action. Hints : Have a function that draws the board Have a function that checks position if empty or not Have a function that checks player or won or not expected output:arrow_forward
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage LearningC++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr
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