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- python nMath: pentagonal numbers) A pentagonal number is defined as n(3n-1)/2 for n=1,2,..., and so on. So, the first few numbers are 1, 5, 12, 22, .... Write a function with the following header that returns a pentagonal number: def getPentagonalNumber(n): Write a test program that uses this function to display the first 100 pentagonal numbers with 10 numbers on each line..Prime NumbersIn this task, you will implement a program that takes as input a number n and produces alist of integers less than or equal to n that are prime. The way to think about a problem isto break it down into individual parts. Start by creating a function isPrime() that checkswhether it’s argument is prime or not. The pseudocode for checking isPrime is givenbelow, there are better ways to do it… this is just one.6Step 1: count = 2Step 2: while count < numberStep 3: if count divides the number evenly return falseStep 4: add 1 to countStep 5: Goto step 2Step 6: return trueLISP Function help please A function that generates a random day of the week, then displays a message saying that "Today is ... and tomorrow will be ...". Then use the built-in function random first to generate a number between 0 and 6 (including). The expression (random) by itself generates a random integer. You can call it with one parameter to return a value within the range from 0 to the value of the parameter-1. For example, (random 10) will return a value between 0 and 9. Next, use the number generated at the previous step to retrieve the symbol for the day of the week from the list. Use the built-in elt. Extract the symbol-name of the day first, then apply the built-in function capitalize to it. Use the result in the princ function call, and do the same thing for the next day. Make the function return true (t) instead of the last thing it evaluates, to avoid seeing the message printed more than once.
- Write a recursive function that computes the sum of the digits in an integer. Use the following function header: def sumDigits(n):For example, sumDigits(234) returns Write a test program that prompts the user to enter an integer and displays its sum.2- The factorial n! of a positive integer n is defined as n! = 1*2*3 . .. * (n-1) * n Where 0! = 1 Write a function to calculate the factorial of a number. Argument: A number n of type unsigned int. Returns: The factorial n! of type long double. Write two versions of the function, where the factorial is • calculated using a loop calculated recursively Test both functions by outputting the factorials of the numbers 0 to 20.7) The ideal gas law allows the calculation of volume of a gas given the pressure(P), amount ofthe gas (n), and the temperature (T). The equation is:V = nRT / PSince we only have used integer arithmetic, all numbers will be integer values with nodecimal points. The constant R is 8.314 and will be specified as (8314/1000). This givesthe same result. Implement the idea gas law program where the user is prompted for andenters values for n, T, and P, and V is calculated and printed out. Be careful toimplement an accurate version of this program. Your program should include a properand useful prompt for input, and print the results in a meaningful manner
- Read Chapter 12 Recursive Lines Write a recursive function that accepts an integer argument, n. The function should display n lines of asterisks on the screen, with the first line showing 1 asterisk, the second line showing 2 asterisks, up to the middle line which shows n asterisks. You will then continue to print less stars until your last line of one asterisk. With an input of 3 your output should look like below. You will need to wind the stack to print up to your largest line. You will print the last set of lines as you unwind the stack or as you come out of your recursion. * ** *** ** *Python code Write a function that, given two integers, return the product of every integer between them, inclusive. #Example function code: #def circle_area(radius): #area = math.pi * radius ** 2 #return areaPython Functions for Statistical Applications 1A. Implementation with the standard def keyword Suppose you have done a statistical comparison using the Z-scores approach. Write a function for calculating the lower bound of the 95% CI. A starter code for this function is already provided to you below. def compute_lower_bound(n, mu, stdev, z=1.96):"""Computes lower bound of a confidence intervalParameters:n: Type int. number of data pointsmu: Type float. sample meanstdev: Type float. sample standard deviationz: Type float. critical value. Default to 95%CI that corresponds to value of 1.96"""# YOUR CODE HERE# Hint: A correct implementation can be as short as just 1 line long! 1B. Using the function of Part 1A Run your function on the following scenario: There are 500 data points. The sample mean is 2525 The sample standard deviation is 7.57.5 The critical value at 95% confidence, ?0.95�0.95, is a constant: 1.96 # YOUR CODE HERE 1C. Application of Part 1A Now, you are asked to do the…
- Exponent y Catherine Arellano mplement a recursive function that returns he exponent given the base and the result. for example, if the base is 2 and the result is 3, then the output should be 3 because the exponent needed for 2 to become 8 is 3 (i.e. 23 = 8) nstructions: 1. In the code editor, you are provided with a main() function that asks the user for two integer inputs: 1. The first integer is the base 2. The second integer is the result 2. Furthermore, you are provided with the getExponent() function. The details of this function are the following: 1. Return type - int 2. Name - getExponent 3. Parameters 1. int - base 2. int - result 4. Description - this recursive function returns the exponent 5. Your task is to add the base case and the general case so it will work Score: 0/5 Overview 1080 main.c exponent.h 1 #include 2 #include "exponent.h" 3 int main(void) { 4 int base, result; 5 6 printf("Enter the base: "); scanf("%d", &base); 7 8 9 printf("Enter the result: ");…Write a recursive function that computes the product of the digits in an integer. Use the following function header: int productDigits(int n) For example, productDigits(912) returns 9 * 1 * 2 = 18. Write a test pro- gram that prompts the user to enter an integer and displays the product of digits.Three numbersa. Write a program that reads three numbers and prints “all the same” if they are allthe same, “all different” if they are all different, and “neither” otherwise.b. Write a program that reads three numbers and prints “increasing” if they are inincreasing order, “decreasing” if they are in decreasing order, and “neither”otherwise. Here, “increasing” means “strictly increasing”, with each value largerthan its predecessor. The sequence 3 4 4 would not be considered increasing.c. Repeat part b. but before reading the numbers, ask the user whetherincreasing/decreasing should be “strict” or “lenient”. In lenient mode, thesequence 3 4 4 is increasing and the sequence 4 4 4 is both increasing anddecreasing