CPhill

C(4,1)  =   1 , 5 , 10 , 25    cents

C(4,2)  =  ( 1 + 5)    (1 + 10)  (1 + 25) (  5 + 10) ( 5 + 25)  (10 + 25)  =

                      6           11           26          15          30            35    cents

C(4,3)           ( 1 + 5  + 10)    (1 + 5 + 25)      (1 +10  + 25)  (  5 + 10 +  25)

                           16                     31                  36                      40       cents

C( 4, 4)  = ( 1 + 5 +  10   +  25)   =  41 cents

So     15   different amounts

Note  that this  is   the  sum of the entries  on Row 4  of Pascal's Triangle  -  1  =   2^4  - 1   = 15

The women can enter in   5!  =  120 ways

And the  men can enter   is 4!  = 24  ways

So    (120) (24)   =  2880  ways

Hey, jugoslav.....could you show how you solved this  ???

I couldn't figure  out  any way to solve it  

Here are two answers  : https://web2.0calc.com/questions/a-researcher-observes-and-records-the-height-of-a

The first one  is exactly the same problem as yours

The second  is a little different.....the numbers  are just changed a  little

Let me know if you get stuck  .....

Cost  for 5 lbs =  

5.75 ( 5)  -  3.25  =  $25.50

To buy  p  pounds  of  coffee

C (p)   = 5.75 (p)  - 3.25

Put the  0   in any  one of the trailing  four positions

And the  rest of the digits can be arranged in  4!/2!  identifiable ways  =   24/2 =  12  ways

So  4 * 12  =   48.....just as the guest found  !!!!

See here :

The  greatest  distance   is  just   BA + AD  =  BD  =  33 +  37   =  70

I don't really have  a tuttorial on desmos

You  can download it from  their  site.....you can log in by supplying an email and password  so you  can share your graphs   (I believe these are "saved" so  it makes  logging in each time easy )

Just  type whatever equation , points, etc.,   you want  in the   boxes on the  left

If you  check  the label box  under each entry  it  will  display point coordinates.....you can also  customize this by typing  some identifier  on the  line  by the  label box   (for ex :   A = (1,0)  ).....you can add anything  on this  label line 

I like desmos  OK,  but I tend to use Geogebra  more.....it is  a little harder to  use, but  it is ideal  for  drawing segments, etc......you  might explore  it, as well

Good job geoNewbie  !!!

See the graph here : https://www.desmos.com/calculator/6wrak7ngnw

Notice that a cricle centered at (8, -2)    with a radius of  sqrt (68)   will go through  both the  origin and  (10-10)

So  PA  = PO   =  sqrt (68)

 One x intercept is   x = 8

Because of symmetry, the  other x intercept  will  be   2 - (8 - 2) = 2  -6  = -4

And the point  (2, -54)  is on the graph so we  can solve  for "a"  thusly

-54 =  a ( 2 - - 4)  ( 2 - 8)

-54  = a  ( 6)(-6)

-54  = a ( -36)

a  =  54/36   =  3/2

Here's a graph   :  https://www.desmos.com/calculator/48496ve0xe