CPhill

The  volume of the ice box  is   12 * 24 * 16  =  4608  in^3   (1)

The  volume  of each cone  is    [ pi (1.5)^2 * 5  / 3 ]     in^3    (2)

So.....the number of cups that can be filled is  (1)  / (2)  =

      4608 

    _______                      =   about 391  cups

[  pi (1.5)^2 * 5  / 3 ] 

1)   P(3 yellow)

We have 20    marbles in total

The number  of sets that can be made  is  by choosing any 3 of the 20=  C(20, 3)  = 1140

The set  we are interested in  is the one where we choose any 3  of the 6 yellow marbles  =

C(6,3)  =  20

So.....the probability  is    20 / 1140   =  2/114  =   1/57  ≈ .0175

2)  P ( 1  brown and 2 orange)

We  have 5 ways to choose a brown one  

And we have only 1 way of selecting both orange marbles

So...the probability  is

[ 5 * 1  ] /  1140  =  5/1140  =  1/228  ≈  .0044

3) P( 1 green)   =  3/20  =  .15

We have  these   relationships

 ΔABC   similar  to  ΔBDC    similar   to   ΔADB

Look  at  the first two triangles....note that....

AC            BC

___   =      ___

BC            DC

So   "B"  is true

The first one is a little tricky

If  ABC  is similar to FDE...then

AB            BC                AC

__     =     ___     =        ___

FD            DE                FE

Notice that DE  is 1/2   of   BC

DE  =  2

BC  =  4   

FE  is  1/2  of AC

AC  =  8

So....FE   =  4

And  note that   (2,1)  is  4  units from E

So   (2,1)   =  F

Each side  of   P'Q'R'  is twice that of its corresponding side  of PQR

So

P'R'

___  =   2    is true

PR

Also

P'Q'

____  =  2               multiply both sides by PQ

PQ

P'Q'  =  2PQ     subtract  2PQ  from both sides

P'Q' - 2PQ   =  0     is also true

You are correct   !!!!

P'Q'         12 units             3

___   =     _______   =     __   =    3

PQ            4  units            1

Note that   (a,b) *scale factor  =   (a * scale factor,    b * scale factor )

P  =  (12, 6)

So  P'  =  (12, 6) * scale Factor  =  (12, 6) * (1/3)  = (4, 2 )

Q = ( -9, 15)

So Q'  =  (-9. 15) * Scale Factor  = (-9, 15) * (1/3)  = (-3, 5)

To find the cale factor....we just need to compare the lengths of similar sides of Figure 2 and Figure 1

Look  at  the base  of Figure  2..its length   = 2

Look at the base of Figure 1.....its length  =  4

So....the scale factor  is

Length  of  base  of Figure 2           2              1

_______________________  =  _____  =   _____

Length  of base  of figure 1             4              2

The scalle factor is given by :

    RG'                       12                  12                    4

_________   =     _______    =    _______    =    ____ 

RG' + G'G           12  +  3                15                    5

LOL, Jakesplace....!!!

I'd say that hectictar is as "correct"  as I am......!!!!!