1) let w ⊂ z+, w = {1,4,9,25,}. is set w countable?

Yes

Step-by-step explanation:

Let's remember the definition of countable:

A countable set is a set with the same number of elements as some subset of the set of natural numbers. Whether finite or infinite, the elements of a countable set can always be counted one at a time and, although the counting may never finish, every element of the set is associated with a unique natural number.  

Let's take a look to our set W = {1,4,9,25, 36, …}.

We can rewrite it as {}

We can associate each element of the set with a unique natural number (the number 4 it's not in the list but that's not a problem, it fulfills the definition anyway). In other words, there is a bijection between W and the natural numbers.

Therefore, W is countable.

step-by-step explanation:

i hate black

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: