Write a program in python Zeller’s congruence is an algorithm developed by Christian Zeller to calculate the day of the week. The formula is h is the day of the week (0: Saturday, 1: Sunday, 2: Monday, 3: Tuesday, 4: Wednesday, 5: Thursday, 6: Friday). q is the day of the month. m is the month (3: March, 4: April, ..., 12: December). January and February are counted as months 13 and 14 of the previous year. j is the century (i.e., ⌊year/100⌋). k is the year of the century (i.e., year % 100). Write a program that prompts the user to enter a year, month, and day of the month, and then it displays the name of the day of the week. Sample runs of program are given below: Enter year: (e.g., 2008): 2013 Enter month: 1-12: 1 Enter the day of the month: 1-31: 25 Day of the week is Friday Enter year: (e.g., 2008): 2012 Enter month: 1-12: 5 Enter the day of the month: 1-31: 12 Day of the week is Saturday

(Computation) A magic square is a square of numbers with N rows and N columns, in which each integer value from 1 to (N * N) appears exactly once, and the sum of each column, each row, and each diagonal is the same value. For example, Figure 7.21 shows a magic square in which N=3, and the sum of the rows, columns, and diagonals is 15. Write a program that constructs and displays a magic square for a given odd number N. This is the algorithm:

The program in the Programming Example: Fibonacci Number does not check whether the first number entered by the user is less than or equal to the second number and whether both the numbers are non-negative. Also, the program does not check whether the user entered a valid value for the position of the desired number in the Fibonacci sequence. Rewrite that program so that it checks for these things.

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.)

(Numerical) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters to 0, and then generate a large number of pseudorandom integers between 0 and 9. Each time a 0 occurs, increment the variable you have designated as the zero counter; when a 1 occurs, increment the counter variable that’s keeping count of the 1s that occur; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of the time they occurred.

(Computation) Among other applications, Pascal’s triangle (see Figure 7.22) provides a means of determining the number of possible combinations of n things taken r at a time. For example, the number of possible combinations of five people (n = 5) taken two at a time (r=2)is10. Each row of the triangle begins and ends with 1. Every other element in a row is the sum of the element directly above it with the element to the left of the one above it. That is, element[n][r]=element[n1][r]+element[n1][r1] Using this information, write and test a C++ program to create the first 11 rows of a twodimensional array representing Pascal’s triangle. For any given value of n less than 11 and r less than or equal to n, the program should display the correct element. Use your program to determine in how many ways a committee of 8 can be selected from a group of 10 people

(Data processing) Your professor has asked you to write a C++ program that determines grades at the end of the semester. For each student, identified by an integer number between 1 and 60, four exam grades must be kept, and two final grade averages must be computed. The first grade average is simply the average of all four grades. The second grade average is computed by weighting the four grades as follows: The first grade gets a weight of 0.2, the second grade gets a weight of 0.3, the third grade gets a weight of 0.3, and the fourth grade gets a weight of 0.2. That is, the final grade is computed as follows: 0.2grade1+0.3grade2+0.3grade3+0.2grade4 Using this information, construct a 60-by-7 two-dimensional array, in which the first column is used for the student number, the next four columns for the grades, and the last two columns for the computed final grades. The program’s output should be a display of the data in the completed array. For testing purposes, the professor has provided the following data:

(Data processing) Years that are evenly divisible by 400 or are evenly divisible by 4 but not by 100 are leap years. For example, because 1600 is evenly divisible by 400, 1600 was a leap year. Similarly, because 1988 is evenly divisible by 4 but not by 100, it was also a leap year. Using this information, write a C++ program that accepts the year as user input, determines whether the year is a leap year, and displays a message telling the user whether the entered year is or is not a leap year.

15. Write a program to implement and test the algorithm that you designed for Exercise 15 of Chapter 1. (You may assume that the value of . In your program, declare a named constant PI to store this value.)

If the following code segment compiles correctly, what do you know about the variable x? if(x) WriteLine(OK); a. x is an integer variable. b. x is a Boolean variable. c. x is greater than 0. d. none of these