CPhill

P(two  are hearts)  =  C(3,2)(13/52)(12/51)(39/50) =  117/850

P(3 are hearts)  = (13/52)(12/51)(11/50)  = 11/850

So....the total probability  =  [ 117 + 11] / 850 =  128/850  = 64/425

This  known as the "pigeonhole principle"

By  taking  7 + 5 + 3  =  15  balls  you are guaranteed  to end up with 3 red balls......

6S +  5J  = 40    (1)

3S  + 2J  = 19  multiply through by  -2 ⇒    -6S - 4J  = -38   (2) 

Add (1)  and (2)

J =  2   (cents)

And

3S + 2(2)  =  19

3S +  4  =19

3S =15

S = 5 (cents)

Let  The  number  of delivery  men =  D

Then the  number  of chefs  =  (2/3)D + 24

So   we  have  this

(2/3)D + 24            5

_________  =     ____     cross-multiply

     D                      3

3 [ (2/3)D + 24  ]  = 5D      simplify

2D  + 72  =  5D     subtract  2D from both sides

72 =  3D      divide  both  sides  by  3

24  = D = number  of delivery  men

And  the  number of chefs =  (2/3)(24) + 24  = 16 + 24  =   40

The  balls  that  meet the  requirements  are

4   8    12   13   16    20   24

So.....the probability  is

7 / 25

We  have  this  equation

total wins                        [ 2  +  2n ]

_________     =             __________  =    .60    

total games                    [ 15  + 3n ]

Where n  is the  number of weeks  after  the  5th week

Multiply  both sides  by   15 + 3n  and we have that

2 + 2n   =   .60 [15 + 3n ]  

2 + 2n  =  9  + 1.8n      subtract  1.8n, 2  from both sides

.2n = 7      divide  both sides  by  .2

n =  35

So..it will take   5 + n =  5 + 35 =   40 weeks to reach a  60%  winning percentage

Proof:

After   40  weeks  we  have   2 + 2(35)  =   72 wins

And  15 + 3(35)  =  120  games will have been played

So

72  / 120    =   .60

First  one :

Coordinates  of  A '   =  (1,2)

Second one :

Coordinates of B '  = (2, 5)

Third  one :

Coordinates  of C'   = (4, -3)

Note  that the  rule for a 180°  rotation  seems to  be :

(x , y)  ⇒  ( -x, - y)

Jason jumped off a cliff into the ocean while vacationing with some friends. His height as a function of time could be modeled by the function h(t)= -16t^2 + 16t + 480, where t is the time in seconds and h is the height is feet.

a. How long did it take for Jason to reach his maximum height?

The  time  to  reach  the max  height is given by :

-16/ [ 2 * -16]  =  1 / 2  sec

b. What was the highest point that Jason reached?

Highest point  =  -16(1/2)^2  + 16 (1/2) + 480  =  -4 + 8 + 480  =  484  ft

c. Jason hit the water after how many seconds?

We need to solve  this :

-16t^2 + 16t  + 480  = 0         divide throug  by  - 16

t^2  -  t   -  30 =   0      factor

(t + 5) ( t - 6)    = 0

Seteting each factor to 0  and solving for  t  produces

t  =  - 5 sec  [ reject ]

or

t = 6 sec   [ accept ]

First  one  ⇒  point   L

Second  one ⇒  point B

Third one......  reflection over  the  x  axis rule  :  ( x , y)  ⇒  (  x ,-y) 

So

(2, 1)  ⇒ (2, - 1)

CORRECT   !!!