Determine whether each of these sets is countable oruncountable. for those that are countably infinite, exhibit
a) one-to-one correspondence between the set of positiveintegers and that set.
b) integers divisible by 5 and not 7
c) the real numbers with decimal of all 1’s
d) the real numbers with decimal of all 1’s or 9’s

Answers are given below.

Step-by-step explanation:

a) one-to-one correspondence between the set of positiveintegers and that set.

Whenever we have one to one correspondence with positive integers, the set is countable and here infinite.

b) integers divisible by 5 and not 7 ..This set is all integers divisible by 5 but not by 7.  This is a discrete set and hence countable and infinite.

c) the real numbers with decimal of all 1’s

-- This cannot be counted and hence uncountable but infinite.

d) the real numbers with decimal of all 1’s or 9’s

-- This is also uncountable but infinite.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

120 seems like the most sensible answer.

step-by-step explanation:

if there is only one topping on all caramel apples and there's 120 of them. then all apples should/will be covered in sprinkles. make sense?