What are reasons A, B, and C in the proof? Prove: (4 · 3)l + (2 · 4)l = 20l Statements Reasons (4 · 3)l + (2 · 4)l = (4 · 3)l + (4 · 2)l A. = 4(3l + 2l) B. = 4(5l) Addition = (4 · 5)l C. = 20l Multiplication A. Commutative Property of Addition B. Distributive Property C. Associative Property of Multiplication A. Commutative Property of Multiplication B. Distributive Property C. Associative Property of Multiplication A. Commutative Property of Multiplication B. Associative Property of Multiplication C. Distributive Property A. Distributive Property B. Commutative Property of Multiplication C. Associative Property of Multiplication

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above