The summer reading list for your english class has twelve books, and the list for history has eight books. you need to read three books for english and two books for history. how many different sets of books can you read?

Step-by-step explanation:

This is a combination problem from stats.  We have a total of 12 English books from which you have to 3.  The order in which you pick them doesn't matter, you only need to determine how many different combinations are available to you.  This is the combination formula, then:

₁₂C₃ =

I'm just going to simplify the right side and leave off the left side til the end of the algebra because it's easier.  The right side simplifies to

The 9!'s cancel each other out, leaving you with

Therefore,

₁₂C₃ = 220 possible different combinations of English books from which to pick.

We'll do the same for History, which has a combination formula that looks like this:

₈C₂=

That right side expands to

The 6!'s cancel each other out, leaving you with:

Therefore,

₈C₂ = 28 possible different combinations of History books from which to pick.

You may or may not need to add those together to get the answer your teacher is looking for.

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)