Write a function that returns true if all the characters in a string are lower case letters and false otherwise. The function prototype is provided below. bool allLowerCase(string); Write a function that given a list of numbers as an array of doubles A of size n, will return the number of elements that are larger than the average of the array. The function prototype is provided below. E.9. if Au 10, 34, 1, 4, 7,-3, 9, 22), then larger Thanaverage (1,8) will return 2 (since the average is 10.5 and there are only two elements larger than 10.5) int largerThanAverage(double, int); You are given two sorted vectors of doubles (v1 and v2). Write a function that given the two vectors, will returned the merged v1 and v2 (i.e., a sorted vector that contains the elements of v1 and v2). The function prototype is provided below. E.g. V1={10, 20, 30, 40,50), V2={12, 15, 25, 65, 70), then vmwmerge(V1, V2) will return [10, 12, 15, 20, 25, 30, 40, 50, 65, 70} vector double> merge vector double>, vector double)