CPhill

I agree.....very nice, jfan  !!!!!

Let n be  the  number  and we have that

n  +  5/n  =  4.5       multiply  through by  n

n^2  + 5  = 4.5n      rearrange as

n^2  - 4.5n  + 5  =   0

Using the quad formula  we have

n =  4.5 + √ [ 4.5^2 - 4*1*5 ]              4.5  + √[20.25 - 20]          4.5  + √ .25       4.5 + .5

      ___________________   =        ________________  =   __________  =  _______ =

                    2                                              2                                 2                      2

5/2  =  2.5

And  the  other solution is        4.5 - .5

                                               _______  =    4/2   =   2

                                                      2

Very nice, CTG   !!!!!!

The  time  she  spends stationary  will  be  represented by  the  length (in time)  of the horizontal line segments on the graph

The  first one  is from 3 PM to 3:30PM    = 30 min

The second one is from  4PM to 5PM  =  1  hr

The third oneis from 6:30 PM to 7:30 PM  = 1  hr

So....the time stationary  =   2 hrs 30 min

identify the centere and radius. then sketch the graph

1. x^2+y^2-4x-14=0

Cmplete the square on x   and  we have that

(x^2  -4x  + 4)  + y^2  =  14  + 4

(x - 2)^2  + (y - 0)^2  = 18

The center  is  ( 2, 0)

The radius  =  √18

Here's a couple  :

1. If the  ends of a diameter  are  11,-6)  and (1,14)   then the  midpoint  is the  center of the circle

So   we  have that     [ (11 + 1) / 2  , (14 - 6)/2 ]  =  [ 12/2, 8/2 ]  = (6, 4)  is the  center

And  the  radius^2 can be computed as    [ ( 1 -6)^2  + (14 -4)^2 ] =   [ 5^2  + 10^2]  = 125

So...the  equation of the  circle  is

( x - 6)^2  + (y - 4)^2  =125

x^2  - 12x + 36  + y^2  - 8y  + 16   =   125

x^2  + y^2  - 12x  - 8y  - 73    = 0

(a)   longer than 11 inches

[ 11 - 10]

________  =      1/4  = .25

      4

The  percentage associaed with this z score  is   .5987

So approx   1 - .5987  =  .4013  ≈  40.13%   fish are longer than 11 inches

(b)  shorter than 8 inches

[ 8 - 10]

_______  = -1/2  = -.50

      4

The percentage associated with this z score is  .3085

So.....the   number of  fish  out of 400  that  are shorter than 8 inches =

400 (.3085)  ≈   123  

Go ahead  and give your answer, ZBB....your method may be better than mine !!!!

Here  are  the possible  outcomes

2 2 2      4 4 2 

2 2 4      4 2 4

2 4 2      2 4 4

4 2 2      4 4 4

Note  that the probability  of a sum of a 10  =   3  / 8

Good job, GM  !!!!