Question

Please help me with this two questions

b. Now consider the figure shown here (i) Count the boxes. How many? (ii) Count the dots. How many? (iii) What is the average density (dots per box) of this entire set of boxes? (iv) What is the average density (dots per box) of just the set of boxes 3, 4 and 5? (v) What is the density (dots per box) of just box 2? Box 6? (vi) What is the density (dots per box) of a single box n (where 1sns6)? (vii) Which single box, if any, has a density equal to the average density of the entire set of boxes? c. Now consider the figure shown here, which is longer but has the same density pattern as case b, above Answer all of the questions below without doing any counting, but show your reasoning for each answer (i) What is the density (dots per box) of a single box n (where 1sns9)? (ii) How many total dots are in boxes 2, 5 and 7? (iii) How many dots are there in the whole object? (iv) What is the average density of this entire set of boxes?

Answer 1

1) 6

2)6+5+4+3+2+1=21

3)Avg Density = 3.5 (21/6)

4)=(3+4+5)/3=4

5) Box 2= 2, box 6=6

6)Avg density of box n= n/1, i.e. n; because every nth box contains n dots

7)avg density= 3.5 dots and no box has 3.5 dots, so none