Select all the statements below which are TRUE: +256 +n³ +n² lg5 n = 0 (n² lgn) □n³ √n+n³ lgn + (lgn)² = 0 (n³.5) □n³ lg (n³) +5n+1000 = 0 (n³ lgn)
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- (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.Evaluate the following expressions if x is 10.5, y is 7.2, m is 5, and n is 2. x / (double)m = x / m = (double)(n * m) = (double)(n / m) + y = (double)(n / m) =Final Expression = x4'x3'x2'x1' + x4x3x2'x1' + x4x3'x2x1' + x4x3'x2'x1 + x4'x3x2x1' + x4'x3x2'x1 + x4'x3'x2x1 + x4x3x2x1 This expression needs simplification with boolean algebra
- The following binary sequences are stored in two distinct 16-bit memory locations: A = 10010001 11000111 B = 01111010 11101000 Hint: You can use calculators/tools, but you should show the calculation procedure for each case Find both binary and decimal values of Z=A+B if A, B, and Z are all signed a integers. Find both binary and decimal values of Z=A+B if A, B, and Z are two's b complement numbers. If A and B are two Boolean vectors (vectors in which every element is TRUE or C FALSE), find the outcome of the following bit-wise logical operation: (A&&B)||(!A&&!B). What would be the data type and the corresponding value of Z=A+B (written d in Python) if A and B represent two ASCII Strings (Find ASCII table in appendix). If A represent the first two bytes (network prefix) and B represents the last e two bytes (host suffix) of a class B IPV4 address, find the corresponding IP address.Suppose you want to deposit a certain amount of money into a savings account, and thenleave it alone to draw interest for the next 10 years. At the end of 10 years, you would like tohave $10,000 in the account. How much do you need to deposit today to make that happen?You can use the following formula, which is known as the present value formula, to find out:The terms in the formula are as follows: [5 marks]• P is the present value, or the amount that you need to deposit today.• F is the future value that you want in the account. (In this case, F is $10,000.)• r is the annual interest rate.• n is the number of years that you plan to let the money sit in the account.Write a method named presentValue that performs this calculation. The method should accept the future value, annual interest rate, and number of years asarguments. It should return the present value, which is the amount that you need to deposit today.Demonstrate the method in a program that lets the user experiment with…The following binary sequences are stored in two distinct 16-bit memory locations: Q1 A = 10010001 11000111 B = 01111010 11101000 Hint: You can use calculators/tools, but you should show the calculation procedure for each case Find both binary and decimal values of Z=A+B if A, B, and Z are all signed a integers. Find both binary and decimal values of Z=A+B if A, B, and Z are two's complement numbers. If A and B are two Boolean vectors (vectors in which every element is TRUE or C FALSE), find the outcome of the following bit-wise logical operation: (A&&B)||(!A&&!B). What would be the data type and the corresponding value of Z=A+B (written d in Python) if A and B represent two ASCII Strings (Find ASCII table in appendix). If A represent the first two bytes (network prefix) and B represents the last e two bytes (host suffix) of a class B IPV4 address, find the corresponding IP address.
- Q8. The factorial of a positive integer n is defined as n! = n*(n-1)*(n-2)*...*2*1. So the factorial of n is the product of all numbers between and including 1 and n. The following table lists the factorial of all numbers between 1 and 10. Number Factorial 1 1 2 2 3 6 4 24 5 120 720 7 5040 8 40320 362880 10 3628800 Use the information given in the above table to write a program that asks the user to specify a number within the limits and then show him the factorial of the number. 1. Nested If/else Please remember that you are allowed to use only simple if statements without else part and that the return statement must be used only once at the end of the main function. 2. Use Switch structure to print factorial.Exercise III: Catalan numbers For n e N, denote by c, to be the number of ways to form a "mountain range" with n upstrokes (U) and n downstrokes (D) that all stay above a horizontal line. For instance: for n = 1, only UD is allowed, so c = 1; • for n = 2, only UUDD and UDUD are allowed, so c2 = 2. 1. Check that c3 = 5 by writing down or drawing all possible options. 2. Consider the power series +00 g(x) = 2 n=0 (by definition co = 1) called the generating function of the sequence (en). Justify that cn < 4" for each n, and deduce that the radius of convergence of g is at least 1/4. 3. It can be show that for r E (-1/4, 1/4), g(x) = 1+ xg(r)? and therefore 1- VI 4.x g(x) = 2.x Use this formula and the known power series of V1+ x to write the first terms of the power series expansion of g, in the form g(x) = co + c1x + c2x2 + C3x + c4x* + ·.. Show how you obtain a few terms, but you do not need to show all computations and you can use a calculator for fractions. Check that you recover co,…/*code Kth Largest Factor A positive integer d is said to be a factor of another positive integer N if when N is divided by d, the remainder obtained is zero. For example, for number 12, there are 6 factors 1, 2, 3, 4, 6, 12. Every positive integer k has at least two factors, 1 and the number k itself.Given two positive integers N and k, write a program to print the kth largest factor of N. Input Format: The input is a comma-separated list of positive integer pairs (N, k). Output Format: The kth highest factor of N. If N does not have k factors, the output should be 1. Constraints: 1<N<10000000000 1<k<600. You can assume that N will have no prime factors which are larger than 13..
- For each of the following statements indicate whether it is true or false and correct the false statements: a. 2n3 +5n2 +log2n = N (n²) b. 3nlogan +n51= o(n51) C. nlog2n +1+2n²= 0 (n²) %3Duser_num1 and user_num2 are read from input. • If user_num1 is less than 0, output 'user_num1 is negative'. • If user_num2 is greater than 10, assign user_num2 with 3. Otherwise, output 'user_num2 is less than or equal to 10'. ► Click here for examples ● 1 user_num1 2 user_num2 3456 = int(input()) int(input()) | "Your code goes here 6 print('user_num2 is', user_num2)e11: Find the value of A for the following: A = (5 + 2* 3+ (( 3-2)* 7)+ -9) /2.
