1. The local animal shelter currently has 20 dogs and 35 cats. They are holding an adoption event and want
to have the local TV news show pictures of a representative sample of the animals. They number the
pets from 1 to 55 and randomly choose 10. Does this sampling method result in a simple random
sample? Explain.

Yes, this sampling method results in a simple random sample because they are randomly choosing 10 from numbering the animals 1-55, which can end up in many different ways.

3; 9 is 8 to -4

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