CPhill

You're welcome.....!!!!!

We have these data points   (3,17 )   and  (5, 15)  =  (t, h)

Find the slope, m

[  15 - 17] /   [ 5 - 3]  =    -2  /  2   =  -1

So remember, NSS.....to write a linear equation we have

 h = slope (t - x coordinate of one point)  +  (y coordinate of that point )

So we have

h  = -1 ( t - 3) +  17     simplify

h = -t + 3 + 17

h = -t + 20

So.....after 8 hours, the candle will be

h  = -8 + 20   

h =  12 inches tall

Let C be the cost without the discount

And the amount of the discount is 5% of this  =  .05C

So

Full Price  - Discount  = Final  cost

C  - .05C   =   12

.95C  = 12        divide both sides by ,95

C  = 12/ .95  ≈  $12.63

If f(x)  is  x^2.......translating up 2 units produces

x^2  +  2

Translating this to the left 8  units produces

(x + 8)^2  +  2   = g(x)

Convert   m  to cm

10.6m  =  1060 cm

So....we have the following proportion

Shortest side  of actual piece                   Shortest side of model piece        

----------------------------------------        =        ---------------------------------------

 Longest side of actual piece                    Longest side of model piece

Shortest side  of actual piece                   7cm

________________________   =          _______     

1060 cm                                                   20 cm

Multiply both sides by 1060

Shortest side  of actual piece  =     7 * 1060 /  20   =  371 cm 

Find  a possible k  using the first data set

11  =  7k      divide both sides by 7

11/ 7  = k

So....uisng the second data set we sould have that

13  = (11/7) 8    ????

13  = 88/7     this is not true.....so......no direct variation exists

-10 -10x = -30       add 10  to both sides

-10x  =  -20          divide both sides by -10

x  =  -20 / -10  =   2   

I am solving for x and y

nx+my = a

-nx+my = b        add the two equations  and we get

2my  =  a + b        divide both sides by 2m

y  =  (a + b) / (2m)

Put this back into the first equation for y

nx  +  m [ (a + b) / (2m)]  = a      simplify

nx +  (a + b) / 2    = a           subtract (a + b) / 2   from both sides

nx  =  a  -  (a + b) / 2         we can write this as

nx  =   [ 2a  - a - b ]  / 2

nx =  [ a - b] / 2       divide both sides by n

x =  ( a - b ) / (2n)

(-tan^2(x)-1)/(sec^2(x))  =

-(tan^2 (x) + 1) (sec^2(x) )  =

-  (sec^2 (x) )(sec^2 (x)  =

-sec^4(x)

Probability of 6 girls  =   (1/2)^6

Probability of 5 girls, 1 boy =   C(6,5)(1/2)^6

Probability of 4 girls, 2 boys  = C(6,4) (1/2)^6

Total probability  =  (1/2)^6 +  C(6,5)(1/2)^6 +   C(6,4) (1/2)^6  =  11/32 ≈ 34.4%