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Your first Q is missing some vital info.

2.  This is a bowl shaped parabola .....the minimum value for s   is      - b / 2a   = - (-8)/(2(1)) = 4   

                then subbing s = 4 into the eq   yields   2(4)^2-8(4)+19 = 19        4,19

3. This is a dome shaped parabola    max  is   -b/2a  = - (8)/(2(-1)) = 4 

                then subbing t=4 into the eq yields     -(4)^2 + 8t -4  = 12               4,12

7 / sec 50    =    7 / (1/cos 50) = 7 cos 50  = 7*cos(50) = 6.754762199444

Nice, Alan  !!!!

As follows:

\(\sigma = \text{With sample size of }N \text{ and population standard deviation }\sigma_p\\ \text{the standard error of the mean }= \dfrac{\sigma_p}{\sqrt{N}}\\ \text{A 95% confidence interval for the sample is that interval centered about}\\ \text{the sample mean that contains 95% of the probability mass}\\ \text{This turns out to be the interval }[\mu_s - 1.96 \sigma,~\mu_s + 1.96\sigma]\)

I'll let you plug and chug the numbers but it should be reasonably clear that Bob's sample does look fishy.

I think that if Rom's answer was not adequate for you that you should have had to ask for mor help yourself.

And you should have been as clear as possible about what you needed help with.

You are doing a course in English and so you need to learn the jargen that goes with it. 

Plus if you struggle a little with the English that is all the more reason why you need to ask further questions yourself.

You need to learn to use these words!

Hi, OP here. I do actually prefer CP "solving" the question. Seeing the steps and how he does it really does help me understand what he's doing so I can administer it to all my other problems that are like this. Not all students come here with their mind set on having other people solve their problems for their own gain, I come here to understand. My native language isn't English and mathematics isn't my forte at all so to be frank I do prefer seeing a simplified version. Thanks for the help though! I do appreciate it a lot :)

Ideal gas law  is  PV =nRT      since n is constant (# moles) for this experiment, we can say PV = kT

and then   P/k = T/V       Pressure in the balloon is constant for all three balloons    so we can say that for all three balloons  P/k is constant  

So initially

k = T/V    =

V₁/T_{1 = 600/285 =2.11=k    for all of the balloons}

_{Now for the second balloon ' k ' has to be the same}

_{630/T2 =2.11   T2 = 298.6 Kelvin}

_{For balloon 3}

_{k = 2.11    = V3/T3 = V3/265    yields   V3 = 559 ml}    

From the information about the first balloon, we can determine k 

k = V₁/T₁ = 600/285 = 2.1053 (this is rounded from 2.10526316)

Since k has now been determined, it's just arithmetic to solve for the second and third balloons.

k = V₂/T₂ 

2.1053 = 630/T₂

(2.1053)T₂ = 630

T₂ = 630/2.1053 = 299.24

You can use this same method to solve for V₃

.

Thanks!

\(f(x) = \frac{3x - 7}{x + 1}.\)

The domain is all values of x that don't make the denominator = 0

Thus x = - 1    is excluded from the domain

So....the domain  is    ( - inf, -1) U (-, inf )

\(f(x) = 3(x - 6)^2 + 1\)

This is a parbola that opens upward with a vertex of  (6, 1)

So....the range is    [ 1, inf )

Angle TAB =  105°

Using the Law of Sines

AB / sin ATB = AT/ sin CBA

AB / sin 105 = AT / sin 45

AB =  24 * sin 105 /sin 45 =  24 (1/2) ( 1 + sqrt(3) ) =  12 (1 + sqrt (3)  )

And using it again

AC / sin CBA = AB / sin ACB

AC / (sqrt (2) /2)  = 12 ( 1 + sqrt (3) )  

AC =  6sqrt (2) (1 + sqrt 3 )

So...the area of  ABC  =

(1/2) (AB) (AC) * sin (60) =

(1/2) 12 ( 1 + sqrt (3) ) * 6sqrt (2) (1 + sqrt (3) )  * sqrt (3) /2  =

18 sqrt (6) * ( 1 + sqrt 3)^2  =

18 sqrt (6)  ( 1 + 2sqrt(3) + 3) =

18sqrt (6) (4 + 2sqrt(3) ) =

72sqrt (6) + 108sqrt(2)  units ^2  =  

36sqrt(2) ( 2sqrt(3) + 3)   units^2

sqrt(1902 - sqrt(1902 + 907)) =43, where a=1902 and x=907

The number of identifiable arrangements is

   Number of letters!                                              6!                        720

   ______________________     =                 _________   =        _____    =     60

   repeats of B! * repeats of C !                         2!   *  3!                   12

Yep..thanks for catching that, guest....correction made !!!

We only need to consider one of the teams

On Alice's team .....we have 6 ways to choose the next person, 5 ways to choose the next one after that and 4 ways to choose the final person

So...we have  ( 6 * 5 * 4)  =  120 possible ways of choosing Alice's team  

And the other players on each of Andrew's  possible teams are the ones - by default - not chosen for Alice's team

So.....120 ways

Let's look at the vertex form of a parabola

th vertex   h, k  of this parabola is   (-3,0)

a (x-h)^2 +k  =  y         sub in h and k

a (x-(-3))^2 + 0 = y      now pick an easy point on the parabola.......like   -2,1 and sub it in to find 'a'

a (-2 +3)^2 = 1

a = 1

so:   (x+3)^2 = y    or   x^2 + 6x + 9 = y

Done, GM...under your post

The only hard part is the second part

f(x) =   x - 3

g(x) + f(x)  =    ( 2x^2 + 5x - 1)  + ( x - 3)   =   2x^2 + 6x - 4

So   [ g(x) + f(x) ]^2 = 

 [ 2x^2 + 6x - 4]^2   = 

[ 2 (x^2 + 3x - 2] ^2  =  

4 [  x^2 + 3x  - 2 ]  [x^2 + 3x - 2 ]  =

4      [  (x^4 + 3x^3 - 2x^2) + ( 3x^3 + 9x^2 - 6x ) -2x^2 - 6x + 4 ] =

4 [ x^4   + 6x^3  + 5x^2 - 12x + 4 ]  =

4x^4 + 24x^3  + 20x^2 - 48x + 16

So

f(x)  - [ g(x) + f(x) } ^ 2 =

(x - 3) - [ 4x^4 + 24x^3 + 20x^2 - 48x + 16 ] =

-4x^4 - 24x^3 - 20x^2 + 49x - 19

I think this question is MUCH easier than it first appears to be.

The little tirangle and the big one are similar triangles BUT you do not need to use this fact.

1) Mark everything that you know on the diagram.

2) let distance  MI=x and IN=y    that will make it easier

3) Find missing angles using facts about angles on a transversal through  parallel lines.  

4) use these angles to deduce facts about side lengths.

5) You should now have algebraic expressions for lengths AM and AN and MN

6) add those lengths together and see what you get :))

Please no one answer over the top of me, I am trying to teach.

If you get stuck you can ask specific questions.   :)

Possible pairs 

(Chicken, Donkey) =  5 * 4 =  20 possible pairs

(Chicken, Emu) = 5 * 7 =   35 possible pairs

(Donkey, Emu) = 4 * 7 = 28 possible pairs

Now...just add 'em up   !!!

Answered under your original post, GM.....