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Correct....!!!!

10/ 8 = 1.25

Look at  A......

The third one

So it's C?

\(\text{so much text...}\\ A = \{\text{even on 2nd run}\}\\ B = \{\text{odd on 1st run}\}\\ \text{Choices}\\ P[A|B] = P[A]\\ P[A|B] = \dfrac{P[B\cap A]}{P[B]}\\ P[A|B] = \dfrac{P[B]}{P[A]}\\ P[A|B] = \dfrac{P[A]}{P[B]}\)

1) is true if A and B are independent

2) is always true

3) may or may not be true depending on A and B, it being true doesn't say anything about independence of A and B

4) if A and B are independent then P[A|B] = P[A], and thus this choice shows A and B are not independent

LOL!!!!....I know the feeling.....!!!

Using the answer to your other "Golden Ratio" post...remember that it evaluates to ≈ 1.618

So....take each answer and divide the larger number by the smaller

The closest to 1.618 wins  !!!!

Yeah I have been quite busy

by the way..Im 18 now

Because we haven't seen you in a while....

why is that?

Hey, Manuel.....good to see you....I thought you might be in the Witness Protection Program....!!!

We can find the scale factor from the first cylinder to the second just by comparing any two similar parts

Note that the radius of the first = 1

And the radius of the second  =3

So...the scale  factor   =   1/3

For volume comparison....the ratio   =  (scale factor)^3  =  (1/3)^3  =  1 / 27

Thanx for the clarification, Chris !   

We need to first evaluate   [ 1 + sqrt (5) ] / 2

This equals ≈  1.618

Note that the first can't be correct .....  6/6  = 1

Look at the second .....7/5  =  1.4

Look at the third .....7.5 / 4.5   = 1.66

And the last.....7.75 /4.25  = 1.82

So.....which is closest to     1.618  ????

a₁  = 2  =  1st term

We need to find the common ratio from one term to the next

r =  common ratio   =    subsequent term / previous term  = 6/2 = 3

To find any term, a_n.....we have

a_n =  a1 * r^{(n - 1)}  =    2(3)r^n-1      where n is the nth term

So....for example....if we wanted the 4th term...we have

2 (3) ^4-1  =  2(3)³  =    2*27    =   54      .....as expected  !!!

Thanks, EP

Yeah....I remember using this method when I  tutored....it seems pretty easy....!!!!

OK.....good move....these can be confusing because of the strange notation used!!!!

I hope that we're helping you learn some stuff.....

I like that determination !     Thnx    ~EP

Yea it kind of makes sense but I am a little confused. I am gonna talk to my teacher to help me with these types of questions.

Note that   a_n  is the next term following a_n-1

And

a_n+1 is the next term after a_n

The common difference is  0.4 - 1.2  = -0.8 

And the first term is 1.2  = a₁

So....we have

Next term  =  Previous term - 0.8,  a_n = 1.2

So....the answer that makes sense is

a_n = a_n-1 - 0.8, a1 = 1.2

[ Second answer ]

Does this make sense???

d**n you're right....

time for new glasses.

a1=2       an = a(n+1)/3    (I think)      or maybe    a(n-1) = a(n) / 3    

An = 8(1/2)^n

x = small pkgs

10x = weight of small pkgs

x+10  = # lge pkgs

20(x+10) = wt of lge pkgs

10x + 20(x+10) = 950 pounds

30x + 200 = 950

30x = 750

x = 25 small packages        x+10 = 35 large packages

Here's an easy way to determine even and odd

If I put  (-x) in for  x and I  come back to what I started with....then the function is even

If I put (-x) in for x and  all the original signs switch....the function is odd

So...first one

x^2 - 2x + 1

(-x)^2 - 2(-x) + 1   =   x^2 + 2x + 1

I don't come back with what I started with and all the signs are not switched...so...neither

Second one

x^2 + 1

(-x)^2 + 1   =  x^2 + 1 ....I end up with what I started with....so....even

Last one

-2x + 1

-2(-x) + 1  =    2x + 1.....I don't come back with what I started with and the signs are not all switched either....so.....neither!!!!