PERM AND COMB!?

I'm surprised that I actually understand this now. At first, I was lost but now I'm not. HAh. But hopefully I get a few minutes to study just before the test. Gaahh.......

Permutations and Combination Test

It was an ok unit. I think im gonna fail the test though. =P. I didn't get to study last night and i forgot to blog, again! It's just hard to see in the problem if it will be permutation or combination. Oh well, good luck on the test!

oh test. . .

It's a pretty easy unit. I still get confuse on the binomial theorem and the whole expansion thingy. Well not much to say. goodluck onthe test. =)

/

This unit is okay, but I feel like I always mix up which to use for what problems. Hopefully I've studied enough to recognize which goes with which. Good luck to everyone on the test :)

...blogging before the test. Hmm, this unit went by pretty quick. its like, we just finished one test and now we're writing another. Anyways, yes... this unit involved alot of thinking. It's kinda confusing... I still need to practice some of the steps to figure out the questions so I'm gonna end this here. Good luck everyone!

sdjfalkh

OMIGOD! its another test. yeeap. so this one will probably a bad one cause i missed a lot. but yeea ill try my best and do my exercises that i havent done yet. so how is this unit so far? it's confusing. there's a lot of steps to this just to figure out one thing but i got the hang of it. i think. i just need more practice. okay well i've got to start studying and do good on the test, so to everyone good luck.

CIRCLE PERMUTATIONS

* formula: (n-1)!

EX 1. There are tem people. How many permutations are there for them to sit around a table?

(n-1)! = (10-1)!
= 9!
= 362 880


EX 2. Lorena and Caroline must sit together. (They are able to switch around in order)

The table alos must seat: Jackie, Jennifer, and Eddie...

n=4
(n-1)! = 3!
= 3! * 2!
= 12 ways

EX 3. Now, we have Lorena + Carloine and Jackie + Jennifer who must sit together, leaving Eddie all lone.


* Eddie and the pair of two girls are considered to be represented by 2!

n=3 -> (n-1)!=2!
=2!
=2!
= 2! * 2! * 2! = 8 ways


EX 4. Lastly, Lorena and Caroline don't want to be near each other.

(5-1)!=4!

* You aren't done yet. This equation will help solve for this specific problem:

total - together = not together
= 24-12 =12


I love Regine is the next scribe!

NEW UNIT!

ugh! well im the scribe for today. since jeng picked me. but its okay, im fine with it...so yeea blahblah im the scribe and here are todays notes (november 15)...

first we chose a type of car...a Toyota Celica.
Colours: yellow, pink, silver, and black
Trans: Automatic or Standard

There are many possibilities for this car which is shown below :


since there are 8 possibilities to this problem...how many more if you add in the colours?

8 - possibilities
4 - colours

so.. we get 4 x 8 = 32
therefore there's 32 possible cars that can be made

we break it down like this:


if we wanted to know how many possibilities for 3 cars we could just mulitply 3 (which is how many cars we have) to the above ^^

Then mrs. ingram gave us examples which she show'd us how to do:

example 1) Shaun has 2 different shirts and 3 different pairs of pants. How many outfits can he make from these?
2 - shirts
3 - pants

2 x 3 = 6 pairs of outfits.

example 2) How many different 3-digit numbers can be made using the seven digits 1, 2, 3, 4, 5, 6, 7 without repitition?

there are 7 possibilities for all seven numbers to fit in the first spot.
since seven #'s can go there, 6 #'s are left to go into the second spot.
and if two numbers have been taken by the first two only 5 possible #'s can fit into the ones place.

like before we multiply the numbers:
7 x 6 x 5 = 210 #'s

(hard to explain but im trying)

Using the same numbers but even #'s only
(2, 4, 6 - are the even numbers)

we now know that only 3 numbers can go in the ones place.
now we know that, 6 #'s can go into the hundreds place.
and 5 #'s can go into the tens place.
we get...

6 x 5 x 3 = 90 possible even #'s

example 3) how many greater numbers than 300?
5 #'s can go into the 1st position
6 #'s in the second and
5 #'s in the third

5 x 6 x 5 = 150 #'s that are over 300

example 4) we chose 4 different bands/ singers.
1.black eyed peas
2.Wu-tang Clan
3.Madonna
4.Hulk Hogan's Daughter

we wanted to know how many different types of orders we can make out of these four cd's.

any 4 cd's can go into the first position.
so we get left with 3 cd's in the 2nd position and 2 cd's in the 3rd position and 1 in the 4th position.

we multiply all #'s to get 24 combinations
(4 x 3 x 2 x 1 = 24)

we can also write it like this : 4!

when a number is multiplied by any consecutive # after is called a factorial

Factorial- the product of consecutive natural numbers in decreasing order to the number one.

n! = n(n-1)(n-2)(n-3)...and so on.

Now we are simplifying factorial expressions

7!/3!= (7)(6)(5)(4)(3)(2)(1)/(3)(2)(1)
----= (7)(6)(5)(4)(3)(2)(1)/(3)(2)(1) : the 3, 2, 1's cancel each other
----=840

9!/5!= (9)(8)(7)(6)(5)(4)(3)(2)(1)/(5)(4)(3)(2)(1)
----= (9)(8)(7)(6)
----=3024

17!/13!=(17)(16)(15)(14)= 57120

and there you go. thats all the notes for today. hopefully you get it for those who didnt go to class. i bet you'll have a hard time understanding this. so yeea anyways. exercise 28 was assigned to us. and for those who didnt go this afternoon we just continued the exercise. yeea. thats all. k byyye! :)

OOOH! I CHOOSE.... JANET TO BE THE NEXT SCRIBE ..HEHHE..HAHAH. OKAY!

HOW I FEEL ABOUT UNIT 4

This is the first time I've enjoyed a unit. I think it was pretty comprehensible, but I'm not looking forward to doing the test...because I hate tests involving math. Sorry Ms. Ingram I was sick on Monday and today but I think I can go to school tomorrow. I doubt you'll read this but I'm going to school around 8 to ask some questions and do the test. Um, hopefully it will be really good.

LOGARITHMS.

Oh, logs! At first I was fine with them. They were pretty easy. But now, when it comes to those CONTINUING COMPOUNDS and POPULATION GROWTH and stuff, it just gets to me. Like, I understand a bit of it but sometimes getting the right equation gets me so confused. So, I'm glad I actually did my homework to help me at least a little bit. But yes, anyways, I hope the test isn't that hard. So good luck to everyone! =).

Logarithmic Equations

I think this unit is the easiest unit so far. I like it. I hope I do good on the test. I still need to work on the word problems and some of the equations but other than that, its all good ^_^.

Good luck everyone!!!

blog some logs . . .

I almost forgot this thing! eep! well, what can i say. Its pretty easy. I mean well not really. It gets confusing at times. But atleast I know what I'm doing at some parts. Which is a good thing. Too tired to think. That's all. Good luck on the test tomorrow everyone! ahhh -_-"

Rawr! TEST TMRW!

Done Another Unit. Can You Say Finally?! K Whatever. Anyways. This Unit Was The Best. Since I Know What Im Doing. I Just Have Trouble With The Whole Word Problem Thinger-ma-bob. It Makes Me Go Craazzzy! (Not Really) But Yeea...This Unit Went By Quick As Someone Has Mentioned Before. Hopefully I Do Better On This Test Than The Others Cause I Really Need My Mark Up There With The Others. Yes, I Think I Should Start Studying It's Really Late And I Know I'll Regret Studying This Late. So Good Luck To Me And To You All Who'll Be There Tomorrow...In Their Seats With The Dun Dun Dun....TEST In Front Of Them. K Bye!! Oh Yes Thanks Mrs. Ingram For Those Extra Word Problems. It's Gonna Help Me A Lot!! (oh yess. i am the scribe. whoo hoo! im so excited [NOT!])

LOGGGGGGGGGSSSS

Thank you, `I_loveRegine` for picking me as a scribe for today , haha chhyyeaah as iff, buut thanks though for telling me because I wouldn't even bother checking who the scribe was. Well here's todays note. . .




EXPONENTIAL DECAY is when the function is decreasing.
EXPONENTIAL GROWTH is when the function is increasing.

**********

THE COMPOUND INTEREST FORMULA
A = P ( 1 + r/n ) ^tn

A is the amount at the end of the investment period.
P is the principle amount originally invested.
r is the percent rate of the return written as a decimal.
n is the number of times the prinpicle is compounded each year.
t is the time in years.

**********

INTEREST COMPOUND CONTINOUSLY

A = P e ^rt

A is the ampunt at the end of the investment period.
P is the principle amount originally invested.
r is the percent rate of the return written as a decimal.
t is the time in years.

**********

Y _t = Y _o e ^kt

Y_t original amount
Y_o final amount
k rate
t time

**********

EXAMPLES
1. If 1000 type A bacteria at present and of increase 0.025 per hour. How many bacteria in 24 hours?

Y_t= Y_oe^kt
Y _t = 1000e ^0.025(24)
*punch it in your calculator*
you should get . . . 1822 bacteria!!

2. A radioactive substance decay at a daily rate of 0.13. How long will i take for the substance to decompose half its size?
Y_t=Y_oe^kt
x = 2xe^-0.13t (divide both sides by "2x")
0.5 = e^-0.13t
ln0.5 = -0.13t lne (remember from regine's post that lne = 1)
ln0.5 = -0.13t (divide both sides by "-0.13t")
the answer is t = 5.33 days

3. If you can invest money at 6% compounded annually. How long will it take for investment to double?

A=P(1+r/n)^tn (n=1)
therefore, A=P(1+r)^t
2x = x(1+0.6)^t (divide both sides by "x")
2 = (1.06)^t
log² = t(log^1.06) (divide both sides by "log^1.06")
the answer is t = 11.9 years

4. forest has 500 rabbits on May 31^st. June 20^th there are 800. How many should be on June 28^th?

Given:
t_t = 800
Y^o = 500
t = 20 days
k = ?

First is you have to find "k"
Y_t=Y_oe^kt (use 20 for "t")
800 = 500e^20k (divide both sides by "500")
1.6 = e^20k
ln1.6 = 20k lne
ln1.6 = 20k (divide both sides by "20")
the answer is k = 0.0235

Now you know "k" you can solve the problems and find how much bunnies there are on June 28^th.

Y_t=Y_oe^kt (use 28 for "t")
Y_t = 500e^0.0235(28)
the answer is 965 bunnies. wow talk about energizer bunnies! -_-"


Hope you understand. That's all for tonight. Man, I'm tired! Do exercise 27. That's all for now, have a great weekend! The next scribe is ...... B00T5