Peter rolls 2 fair dice and adds the results from each. Work out the probability of getting a total less than 11.

Step-by-step explanation:

Since each dice has a total of 6 numbers, Peter can get a maximum roll of 5 on each dice before the total is 11 or more. Therefore, the probability of rolling a number less than or equal to 5 each roll is 5/6. Now to find the probability of rolling a 5 or less in both rolls together so that the total is less than 11 we need to multiply the probability of each separate roll together.

Therefore the probability of the total being less than 11 is

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,