Question

@pitamar

Answer 1

i hate these

Answer 2

ok, so were finding c and r gotcha

Answer 3

Oh we're back to those haha
Well, do you remember geometric series? They are of the form:
$$\sum_{k=0}^{n-1} ~ c \cdot r^k$$
So let's try and find c and r for our numbers, ok?

Answer 4

and yes I remember them

Answer 5

We can use the fact that we know that in a geometric sequence each item has a constant ratio with the last one. So if we know first item is 12 and second is 36, then the constant ratio is 36/12 which is what?

Answer 6

36/12 = 3

Answer 7

right, so every item is 3 times the previous one. and indeed 36*3 = 108
Makes sense?

Answer 8

yes, so 108*3

Answer 9

which is 324

Answer 10

Ok, so we can form an expression for an item in the sequence:
$$
a_n = 12 \cdot 3^n
$$And indeed for our first number we have \(a_0 = 12 \cdot 3^0 = 12\)
For our second item we have \(a_1 = 12 \cdot 3^1 = 12 \cdot 3 = 36\)
\(a_2 = 12 \cdot 3^2 = 12 \cdot 9 = 108\)
and so on and so on. ok?

Answer 11

ok

Answer 12

so it has to be bigger then 78,732 then right?

Answer 13

Alright, so basically what we want to do is:
$$ \sum_{k=0}^{n-1} a_k $$
But there is one problem. we don't know \(n\). we don't know the number of items we have in the sequence.
But we know that 78732 is the last number in the sequence so let's find out what term would be.
We know that we have some number \(a_x\) for our final number in the sequence. So:
$$
a_x = 78732 \implies 12 \cdot 3^x = 78732 \implies 3^x = \frac{78732}{12}
$$
So first we have to calculate what 78732/12 is.

Answer 14

6561

Answer 15

Good. now we have to find what power of 3 will give us 6561. Means finding \(x\) in:
$$ 3^x = 6561$$
Do you know logarithms?

Answer 16

yes one sec

Answer 17

log3(6561)=(z)

Answer 18

what's z? what number is that?

Answer 19

or if were solvinv for z its 8

Answer 20

its 354,288 right?

Answer 21

right exactly. so it means that:
$$ 3^8 = 6561 \implies 12 \cdot 3^8 = 12 \cdot 6561 \implies a_8 = 78732$$
So our last term in the sequence is the 8th term

Answer 22

6561/8

Answer 23

its B or C.. I think C

Answer 24

Wanna keep going?

Answer 25

its C right?

Answer 26

let's just calculate this =)

Answer 27

alright

Answer 28

it 's actually not right what I said. we are summing from \(a_0\) to \(a_8\) which means we have 9 terms in our sequence. so \(n = 9\) and we are trying to sum:
$$
\sum_{k=0}^{n-1} c \cdot r ^k = 12 \cdot \sum_{k=0}^{9-1} 3^k = 12 \cdot \sum_{k=0}^{8} 3^k
$$And do do that we can use the formula:
$$
\sum_{k=0}^{n-1} r ^k = \frac{1-r^n}{1-r}
$$can you calcualte what the formula produces for our \(n=9\) and \(r=3\)?

Answer 29

yeah one sec

Answer 30

9841

Answer 31

right so it means that:
$$
12 \cdot \sum_{k=0}^8 3^k = 12 \cdot 9841 = ?
$$

Answer 32

B

Answer 33

Yep

Answer 34

118,092

Answer 35

Wasn't too hard, was it?

Answer 36

wont me to do them here or make a new tab?

Answer 37

actually no it wasnt

Answer 38

idm

Answer 39

idm= i dont mind? or it doesnt matter

Answer 40

lol, I meant the first but they both fit I guess

Answer 41

u stupid howie

Answer 42

we skipped six cause i did it by-myself if u were wondering

Answer 43

yaaay more statistics! k lemme read

Answer 44

lel i geet us help

Answer 45

they are getting easier

Answer 46

after this one

Answer 47

Do you have a z-table or something?

Answer 48

i have this https://mathway.com/

Answer 49

use the stat tab

Answer 50

They expect you to use it?

Answer 51

im not sure

Answer 52

comes in handy though

Answer 53

well I don't know to use this site, but let's try work the problem and then maybe use some z table we find somewhere

Answer 54

http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

Answer 55

http://www.intmath.com/counting-probability/z-table.php

Answer 56

Well, I wasn't completely wasting my time.. I watched many videos. and from what I know (hope I'm not mistaken) the sampling distribution has a variance that is \( \frac{\sigma^2}{n} \) where \(\sigma^2\) is the variance of the original distribution and \(n\) is the sample size.
So in our case that means \(\frac{12^2}{36} = 12 \cdot \frac{12}{36} = 12 \cdot \frac{1}{3} = 4\)
So the variance of the sampling distribution is 4 and therefore the standard deviation is \(\sqrt{4} = 2\).
Now I remember they said something about this value of the standard deviation of the sample not being completely accurate.. but they said it is a pretty good estimate so let's just go with that..
So now they ask what is the probability that our mean sampled value is less than 109.8 inches.
Well, the sampling distribution has the same mean as the original so we can find the z score, which is basically asking 'how many standard deviation this value is from the mean':
$$z = \frac{x - \mu}{\sigma} = \frac{109.8 - 107}{2} = \frac{2.8}{2} = 1.4 $$
So now we have to find the area under the curve up to z = 1.4... so we need a z table

Answer 57

http://en.wikipedia.org/wiki/Standard_normal_table
If you look here for 1.40 you see it is 0.41924 so D

Answer 58

dude hooley crap.... your awesome.. im gonna get u as a admin

Answer 59

well thanks, but I don't think I fit for that hehe
Do you understand what I said? I can go over it with you if you want, in case something is not clear

Answer 60

no I got it. it was very clear. you always write good answers

Answer 61

Ah, thanks =)

Answer 62

read ur testimonials

Answer 63

Brb bathroom 1 min

Answer 64

gotcha

Answer 65

Well, let's try to find which ones have the point (0, -3). that means that if you plug x=0 the whole thing becomes -3
Can you tell me which? it should be easy since \(0^2 = 0\)

Answer 66

the only thing i dont get is what the 0,-3 goes

Answer 67

its either a or b

Answer 68

if you say a function 'has a point' (a,b) it means that if you plug x=a you get a result b
For example, the function \(f(x) = x^2\) has the point (3,9) because: \(f(3) = 3^2 = 9\)
You plugged in 3, you got 9.
You can also write the function as \(y = x^2\) and then a point (a,b) is 'in the function' if you plug x=a and y=b you get an equation. for example the point (-4, 16) is in the function because:
$$
x = -4 \qquad y = 16 \implies 16 = 4^2
$$Which is correct. (2, 25) is not in the equation because:
$$
x = 2 \qquad y = 25 \implies 25 \neq 2^2
$$Get it?

Answer 69

yeah I do get it

Answer 70

so go over the equations, plug x=0 and see what value do you get. it shouldn't be hard at all =)

Answer 71

its A cause A has -3 as an answer! ;)

Answer 72

what about the others?

Answer 73

its A

Answer 74

cant be C or D and isnt B

Answer 75

B doesnnt equal to the -3

Answer 76

Right =)
We can verify the asymptotes too, but it's up to you

Answer 77

already did that were good

Answer 78

I did this one already and got A

Answer 79

ye makes sense

Answer 80

so this is your final exam? that's it? no more math? heh

Answer 81

nope

Answer 82

nope what?

Answer 83

This is it for math but this in only my part A of this course so I still gotta do B .. this is Advanced Algebra A

Answer 84

look on the documents see what i mean

Answer 85

ok. well we have
$$ f(x) = -x^2(1-2x)(x+2) $$ We can write that as:
$$
-1 \cdot x^2 \cdot -1 \cdot (2x - 1) \cdot (x+2) = x^2(2x-1)(x+2)
$$

Answer 86

\(x^2\) is always positive, no matter what. the other two are depended on x. if x goes \(infty\) each will be \(\infty\) as well and if x goes to \(-\infty\) they will approach that as well.
So if x goes infinity the whole thing goes inifnity. if x goes negative infinity, we get negative*negative which becomes positive and this thing still goes infinity..

Answer 87

so they would both be negative then?

Answer 88

actually nvm there 4 of them

Answer 89

if x goes infinity we get something of the kind:
$$
\infty^2 (2 \cdot \infty - 1)(\infty + 1) = \infty^2 \cdot \infty \cdot \infty = \infty
$$If x goes negative infinity then:
$$
(-\infty)^2 (2 \cdot (-\infty) - 1)((-\infty) + 1) = \infty^2 \cdot (-\infty) \cdot (-\infty) = \\
= \infty^2 \cdot \infty^2 = \infty
$$

Answer 90

so would that mean that the third oo is - because of that ^

Answer 91

I don't understand what you mean

Answer 92

I just dont get how you solve these.

Answer 93

\((2 \cdot \infty - 1) = ?\)

Answer 94

i dont know dude.. how do you combine 2 and a infinity sign

Answer 95

lol, just think about it for a second. think of the biggest number you can imagine.. so infinity is bigger than that =)
So let's think about it a little... say I have infinity, bigger than all the numbers I could possibly imagine... and I add 1 to it... what do I get? infinity!
Say I have infinity and I subtract a million from it \(\infty - 1000000\) what do I get? still infinity.
What happen if I take one infinity and add to another infinity? I still get a number bigger than anything I could possibly imagine so \(\infty + \infty = 2\infty = \infty\) so I get infinity.

Answer 96

\[\infty1\]

Answer 97

so \(2\infty - 1 = \infty\)
How about \(\infty^2\)? what will that be?