Problem 1 Recursion and Iteration Write a function that converts a decimal input into Roman Numerals. Your function will take in a number and output...

Problem 1 — Recursion and IterationWrite a function that converts a decimal input into Roman Numerals. Your function will take in a number and output a string. You will want to make use of the function string-append, which concatenates two (or more) strings together into a single string with no spaces.“abcde”In Roman Numerals, M = 1000, D = 500, C = 100, L = 50, X = 10, V = 5, and I = 1. Combinations of letters next to each other change the total value depending on order. For example, XL = 40, VIII = 8, and MCCXLI = 1241. (1a) Write a recursive version of this function. (1b) Write an iterative version of this function. Problem 2 — Procedures as Parameters and Return Values (2a) Suppose you have a Scheme function that counts the number of patient visits in a certain town to a mobile medical clinic. The clinic visits the town occasionally, so for most days the number of patient visits will be 0. You have data for 128 days.For this problem you will write a Scheme procedure that takes in (i) a function f, that gives the number of patient visits on each day from day 1 to day 128 (at least 20 days worth of data), (ii) an integer a, the start day of your range, and (iii) an integer b, the end day of your range, and returns the average number of patients visits for the days when the clinic was in town.Example: suppose the patient visit function is as follows:(define (visits n)(cond ((= n 10) 20)((= n 18) 18)((= n 39) 52)((= n 52) 12)((= n 78) 23)((= n 88) 34)((= n 103) 18)((= n 111) 11)((= n 126) 33)(else 0)))Then your procedure applied to visits, a = 19 and b = 78 should return 29 because there are 3 days with patient visits during the range, and (52 + 12 + 23) / 3 = 29.