You roll two dice numbered from one through six. what is the probability of rolling a dum greater than 11? show your work either by drawing an area model for probability

1/36 or 0.0277... or approximately a 3% chance of rolling a sum greater than 11 (i.e., a sum of 12)

Step-by-step explanation:

Create a 6 x 6 grid on a piece of graph paper. Number the 6 columns 1-6 at the top (for the value of the first die) and number the rows 1-6 on the side (for the value of the second die). You must imagine that you are rolling one die then the other (rather than how people "normally" roll both simultaneously). In the 36 empty boxes in your grid below the column numbers and to the right of the row numbers, put the sums of rolling the die at the top of the column + its corresponding die from the row (for example, use your fingers to match column number 4, say, with row 4 to get a sum of 8). When you've filled out the grid, you will see that a sum of 2 and sum of 12 have the same probability (there's only one way to get a sum of 2 or sum of 12, either 1 + 1 or 6 + 6). But there are many more ways, for example, to get a sum of 7

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.