Simplify the following Boolean expression. F(W,X, Y, Z) = !WX!Y!Z + WX!Y!Z + !WXY!Z + WXY!Z + !W!XZ + W!X!YZ+W!XYZ

(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.

(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) Heron’s formula for the area, A, of a triangle with sides of length a, b, and c is A=s(sa)(sb)(sc) where s=(a+b+c)2 Write, test, and execute a function that accepts the values of a, b, and c as parameters from a calling function, and then calculates the values of sand[s(sa)(sb)(sc)]. If this quantity is positive, the function calculates A. If the quantity is negative, a, b, and c do not form a triangle, and the function should set A=1. The value of A should be returned by the function.

(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.

(Statics) An annulus is a cylindrical rod with a hollow center, as shown in Figure 6.7. Its second moment of inertia is given by this formula: I4(r24r14) I is the second moment of inertia (m4). r2 is the outer radius (m). r1 is the inner radius (m). a. Using this formula, write a function called annulusMoment ( ) that accepts two double-precision numbers as parameters (one for the outer radius and one for the inner radius), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 5a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.

(Statics) A beam’s second moment of inertia, also known as its area moment of inertia, is used to determine its resistance to bending and deflection. For a rectangular beam (see Figure 6.6), the second moment of inertia is given by this formula: Ibh3/12 I is the second moment of inertia (m4). b is the base (m). h is the height (m). a. Using this formula, write a function called beamMoment() that accepts two double- precision numbers as parameters (one for the base and one for the height), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 4a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.

(Conversion) a. Write a C++ program to convert meters to feet. The program should request the starting meter value, the number of conversions to be made, and the increment between metric values. The display should have appropriate headings and list the meters and the corresponding feet value. If the number of iterations is greater than 10, have your program substitute a default increment of 10. Use the relationship that 1 meter = 3.281 feet. b. Run the program written in Exercise 6a on a computer. Verify that your program begins at the correct starting meter value and contains the exact number of conversions specified in your input data. c. Modify the program written in Exercise 6a to request the starting meter value, the ending meter value, and the increment. Instead of the condition checking for a fixed count, the condition checks for the ending meter value. If the number of iterations is greater than 20, have your program substitute a default increment of (ending value - starting value) / 19.

(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.

(Practice) Write C++ statements for the following: a.b=sinxcosxb.b=sin2xcos2xc.area=( cbsina)/2d.c= a 2 + b 2 e.p= | mn|f.sum= a( r n 1) r1