Suppose that $S$ is a finite set of positive integers. If the greatest integer in $S$ is removed from $S,$ then the average value (arithmetic mean) of the integers remaining is $32.$ If the least integer in $S$ is also removed, then the average value of the integers remaining is $35.$ If the greatest integer is then returned to the set, the average value of the integers rises to $40.$ The greatest integer in the original set $S$ is $72$ greater than the least integer in $S.$ What is the average value of all the integers in the set $S\,

Robots with telescoping arms are sometimes used to perform tasks (e.g., welding or placing screws) where access may be difficult for other robotic types. during a test run, a robot arm is programmed to extend according to the relationship r = 3 + 0.5cos(4θ) and the arm rotates according to the relationship θ=−π4t2+πt , where r is in feet, θ is in radians, and t is in seconds. use a computer program to plot the path of tip a in x and y coordinates for 0 ≤ t ≤ 4s.

Write a program that uses a random number generator to generate a two digit positive integer and allows the user to perform one or more of the following operations: a. double the number. b. reverse the digits of the number. c. raise the number to the power of 2, 3, or 4. d. sum the digits of the number. e. if the number is a two-digit number, then raise the first digit to the power of the second digit. f. if the number is a three-digit number and the last digit is less than or equal to 4, then raise the first two digits to the power of the last digit. after performing an operation if the number is less than 10, add 10 to the number. also, after each operation determine if the number is prime. each successive operation should be performed on the number generated by the last operation. your program should not contain any global variables and each of these operations must be implemented by a separate function. also, your program should be menu driven. 7. (fraction calculator) write a program that

Me ! evelyn is a manager in a retail unit. she wants to prepare a report on the projected profit for the next year. which function can she use? a. pmt b. round c. division d. what-if analysis