Problem: Given 20 positive integers as input, calculate the number of divisors for each integer and sort the data set from smallest to largest based on the number of divisors. When multiple integers have the same number of divisors then sort them smallest to largest. Examples: Integer value 12 has divisors 1, 2, 3, 4, 6, 12 for a total of 6. Prime numbers only have divisors of 1 and the number itself. The integer 1, the smallest value that will be provided as input, has only a single divisor, itself. Example Execution #1: Enter 20 integer values -> 21 15 10 6 3 1 28 13 5 7 9 29 31 37 17 19 12 43 24 2 Data sorted by number of divisors: 1 2 3 5 7 13 17 19 29 31 37 43 9 6 10 15 21 12 28 24 Example Execution #2 (data does not have to be unique): Enter 20 integer values -> 9 7 5 3 8 6 4 2 9 7 5 3 8 6 4 2 9 7 5 3 Data sorted by number of divisors: 2 2 3 3 3 5 5 57 7 7 4 4 9 9 9 6 6 8 8

Python question Application: Big-O Notation (Q8-11)  For each of the time complexities in this segment give the tightest bound in terms of a simple polylogarithmic function using big-O notation. Note: use the ‘^’ symbol to indicate exponents, i.e., write O(n^2) for O(n2).   Question 8 (Big-O Notation 1) T(n) =  n2+ log n + n   Question 9 (Big-O Notation 2) T(n) = n/3 + 4 log n + 2n log(n)   Question 10 (Big-O Notation 3) T(n) = 7n5 + 2n   Question 11 (Big-O Notation 4) T(n) = (n%5) + 12,000

Prompt: In Python language, write a function that applies the logistic sigmoid function to all elements of a NumPy array. Code:   import numpy as np import math import matplotlib.pyplot as plt import pandas as pd   def sigmoid(inputArray):               modifiedArray = np.zeros(len(inputArray))               #YOUR CODE HERE:               return(modifiedArray) def test(): inputs = np.arange(-100, 100, 0.5) outputs = sigmoid(inputs) plt.figure(1) plt.plot(inputs) plt.title('Input') plt.xlabel('Index') plt.ylabel('Value') plt.show() plt.figure(2) plt.plot(outputs,'Black') plt.title('Output') plt.xlabel('Index') plt.ylabel('Value') plt.show() test()

6. Given the following data: 35 12 80 6 70 90 10 Illustrate Selection Sort algorithm. Also, give the runtime. Use the table given below: 1 1 2 3 4 A[0] 5 6 7 #comparison Describe the Algorithm