A factory that makes chairs is able to produce between two and four chairs every hour. The factory has already made six chairs today and plans to continue production for six more hours. Which of the following number lines represents the possible number of chairs the factory will have at the end of the day?

The first one.

Step-by-step explanation:

6 hours x 2 chair = 12

6 hours x 4 chair = 24

but don’t forget to add the chairs already made.

12+ 6 = 18

24+6=30

Proof by Contrapositive

The contraposition of the statement is

If 'm is odd and n is even' or 'm is even and n is odd' then 'm+n is odd'.

a)At first we will take one of the statement as 'm is odd and n is even'

As we know the ways to write a even and odd number

m is odd mean

m=2a+1,

n=2b,

where a and b are any integers

Now substitute the values of m and n in (m+n)

m+n = (2a+1)+2b = 2a+2b+1 = 2(a+b)+1           Suppose c =a+b

m+n = 2c+1, which is odd

Since the contrapostive statement is true than the original statement is also true.

Similarly we can take m is even and n is odd, for that

m=2a and n=2b+1, substitute the values of m and n in m+n, we get

m+n = 2a+(2b+1) = 2a+2b+1 = 2(a+b)+1           Suppose c =a+b

m+n = 2c+1, which is odd

Again, Since the contrapostive statement is true than the original statement is also true.