4. given subspaces h and k of a vector space v, the sum of h and k, written as h + k is the set of all vectors in v that can be written as the sum of two vectors, one in h and the other in k. in other words, h+k (vh+k, for some he h for some kek show that h+k is a subspace of v.(5 pts)

Ascientist studied a population of workers to determine whether verbal praise and/or tangible rewards affect employee productivity. in the study, some workers were offered verbal praise, some were offered tangible rewards (gift cards, presents, and some were offered neither. the productivity of each participant was measured throughout the study by recording the number of daily tasks completed by each employee. which inference might the scientists make based on the given information? a.) the number of daily tasks completed by each employee may influence the dependent variable, which is whether the employee receives verbal praise, tangible rewards, or neither. b.) verbal praise and/or tangible rewards may influence the independent variable, which is the number of daily tasks completed by each employee. c.) verbal praise and/or tangible rewards may influence the dependent variable, which is the number of daily tasks completed by each employee. d.) the dependent variables, which are verbal praise and tangible rewards, may influence the number of daily tasks completed by each employee.