Simplify the following Boolean functions. F(w, x, y, z) = !w!x!y!z + w!x!y!z + wx!y!z + !w!xy!z + wxy!z + w!xy!z  F(w, x, y, z) = _____answer_______ *Please do not include "F(w, x, y, z) = " in your solution. Add a single space between variables and operators

(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:

(Numerical) a. The following is an extremely useful programming algorithm for rounding a real number to n decimal places: Step 1: Multiply the number by 10n Step 2: Add 0.5 Step 3: Delete the fractional part of the result Step 4: Divide by 10n For example, using this algorithm to round the number 78.374625 to three decimal places yields: Step1:78.374625103=78374.625 Step2:78374.625+0.5=78375.125 Step3:Retainingtheintegerpart=78375Step4:78375dividedby103=78.375 Using this algorithm, write a C++ function that accepts a user-entered value and returns the result rounded to two decimal places. b. Enter, compile, and run the program written for Exercise 11a.

Mark the following statements as true or false: a. To use a predefined function in a program, you need to know only the name of the function and how to use it. (1) b. A value-returning function returns only one value. (2, 3) c. Parameters allow you to use different values each time the function is called. (2, 7, 9) d. When a return statement executes in a user-defined function, the function immediately exits. (3, 4) e. A value-returning function returns only integer values. (4) f. A variable name cannot be passed to a value parameter. (3, 6) g. If a C++ function does not use parameters, parentheses around the empty parameter list are still required. (2, 3, 6) h. In C + + , the names of the corresponding formal and actual parameters must be the same. (3, 4, 6) i. A function that changes the value of a reference parameter also changes the value of the actual parameter. (7) j. Whenever the value of a reference parameter changes, the value of the actual parameter changes. (7) k. In C++, function definitions can be nested; that is, the definition of one function can be enclosed in the body of another function. (9) l. Using global variables in a program is a better programming style than using local variables, because extra variables can be avoided. (10) m. In a program, global constants are as dangerous as global variables. (10) n. The memory for a static variable remains allocated between function calls. (11)

(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.

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.)

When you perform arithmetic operations with operands of different types, such as adding an int and a float, ____________. C# chooses a unifying type for the result you must choose a unifying type for the result you must provide a cast you receive an error message

(Civil eng.) Write a C++ program to calculate and display the maximum bending moment, M, of a beam that’s supported on both ends (see Figure 3.8). The formula is M=XW(LX)/L, where X is the distance from the end of the beam that a weight, W, is placed, and L is the beam’s length. You program should produce this display: The maximum bending moment is xxxx.xxxx The xxxx.xxxx denotes placing the calculated value in a field wide enough for four places to the right and left of the decimal point. For your program, assign the values1.2,1.3,and11.2toX,W,andL.

Write a program that takes as input five numbers and outputs the mean (average) and standard deviation of the numbers. If the numbers are x1,x2,x3,x4,andx5, then the mean is x=(x1+x2+x3+x4+x5)/5 and the standard deviation is: s=(x1x)2+(x2x)2+(x3x)2+(x4x2)+(x5x2)5 Your program must contain at least the following functions: a function that calculates and returns the mean and a function that calculates the standard deviation.

(Numerical) Using the srand() and rand() C++ library functions, fill an array of 1000 floating-point numbers with random numbers that have been scaled to the range 1 to 100. Then determine and display the number of random numbers having values between 1 and 50 and the number having values greater than 50. What do you expect the output counts to be?