1. a group of friends went to the movies, and the three guys each bought two tickets (t), a popcorn (p) and two drinks (d) for themselves and their dates. After distributing, we can represent this situation with the expression. .

6t + 3p + 6d

Step-by-step explanation:

Given - A group of friends went to the movies, and the three guys each      

            bought two tickets (t), a popcorn (p) and two drinks (d) for

            themselves and their dates.

To find - After distributing, we can represent this situation with the

              expression.

Proof -

As given , three guys each bought two tickets (t), a popcorn (p) and two drinks (d) for themselves and their dates.

Let ticket = t

     popcorn = p

     drink = d ,

Then,

The expression becomes -

3[2t + p + 2d ] = 6t + 3p + 6d

∴ we get

We can represent this situation with the expression - 6t + 3p + 6d

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)