Jacob and ashley run an animal shelter that houses only cats and dogs. they have 37 adult animals 21 cats and 16 dogs. a group of 8 adult animals is chosen at random from the shelter. what is the most likely number of cats and dogs in this group and what is the probability of that arrangement happening? give your probability to four decimal placements. i'm pretty sure the arrangement is 5 cats to 3 dogs but i don't know how to get the probability

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

, 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