Write a C++ program for the given instructions: Summary Suppose that the first number of a sequence is x, where x is an integer. Define: a0 = x; an+1 = an / 2 if an is even; an+1 = 3 X an + 1 if an is odd. Then there exists an integer k such that ak = 1. Instructions Write a program that prompts the user to input the value of x. The program outputs:

(Program) Write a program to simulate the rolling of two dice. If the total of the two dice is 7 or 11, you win; otherwise, you lose. Embellish this program as much as you like with betting, different odds, different combinations for win or lose, stopping play when you have no money left or reach the house limit, displaying the dice, and so forth. (Hint: Calculate the dots showing on each die with theexpressiondots=(int)(6.0randomnumber+1), where random number is between 0 and 1.)

(Program) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters, such as zerocount, onecount, twocount, and so forth, to 0. Then generate a large number of pseudorandom integers between 0 and 9. Each time 0 occurs, increment zerocount; when 1 occurs, increment onecount; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of time they occurred.

(Statistical) In many statistical analysis programs, data values considerably outside the range of the majority of values are simply dropped from consideration. Using this information, write a C++ program that accepts up to 10 floating-point values from a user and determines and displays the average and standard deviation of the input values. All values more than four standard deviations away from the computed average are to be displayed and dropped from any further calculation, and a new average and standard deviation should be computed and displayed.

(Practice) An automobile travels at an average speed of 55 mph for 4 hours. Write a C++ program that displays the distance, in miles, the car has traveled after 1, 2, and so on hours until the end of the trip.

In this chapter, you learned that although a double and a decimal both hold floating-point numbers, a double can hold a larger value. Write a C# program named DoubleDecimalTest that declares and displays two variables-a double and a decimal. Experiment by assigning the same constant value to each variable so that the assignment to the double is legal but the assignment to the decimal is not. In other words, when you leave the decimal assignment statement in the program, an error message should be generated that indicates the value is outside the range of the type decimal, but when you comment out the decimal assignment and its output statement, the program should compile correctly.

A set of instructions thats executed to solve a specific problem is called a(n) __________.

(Program) Write a C++ program that accepts a string from the user and then replaces all occurrences of the letter e with the letter x.

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.)

(Useful utility) Modify the program written for Exercise 3 to search for the first occurrence of a user-entered sequence of characters, and then replace this sequence, when it’s found in the string, with a second user-entered sequence. For example, if the entered string is Figure 4-4 illustrates the output of Program 4-2 and the user enters that 4- is to be replaced by 3-, the resulting string is Figure 3-4 illustrates the output of Program 4-2. (Only the first occurrence of the searched-for sequence has been changed.)