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We should use complemetary counting to solve this. 

So what's the probability that neither will be the ace of hearts. 

51/52*50/51 = 50/52 = 25/26

1-25/26 = 1/26

So the probability that at least one if the ace of hearts is 1/26. 

=^._.^=

There are 10 two-digit numbers with a tens digit of 3, and 10 two-digit numbers with a units digit of 3, so the answer is 10 + 10 = 20.

The roots can be (1,28) (2,14) (4,7) so that would mean 3.

Thanks

90°  counter-clockwise rotation rule     x, y   →   -y  ,  x

So

(1,  -1)  →   ( 1, 1)  = X'

(3 ,4)   →    (-4, 3)  = Y'

(5,  -1) →    ( 1  , 5) = Z'

Let  us  look at the number  of  ways in which  the ace  of  hearts   could  be  directly on the king of  hearts

These  two  cards  could occupy   51 positions.....and  for  each of  these, the other  cards  could  be  arranged in 50! ways

The total  number of  arrangements=  52!

So....the  number of ways  that  the  ace of hearts is not directly on the  king of hearts   =

52!  -  51 * 50!    =   52!  - 51!    =     EP's  answer    !!!!

Ashley has 36 coins totaling $4.20 in quarters and dimes. How many of each coin does she have?     

If all 36 coins were dimes, then Ashley would have 3.60  

However, Ashley has 4.20, so we have to raise the total by 0.60  

Every time you substitute a quarter for a dime, you gain 0.15   

If you substitute four quarters for four dimes, you gain 0.60  

So, Ashley has 4 quarters and 32 dimes  

_.

25 % off means you pay 75% of the original price    .75 ($40)

  then add tax     .75(40)(1.10) = $ .........     final price

We  only  need  the equations  of two lines  to do this

Find  the slope   between  AB  =   (1,2)  and (3,5)  =  (5-2)  /( 3 -1)  =  3/2

The equation  of  the line perpendicular  to segment  AB  through  ( 6,3)  is

y  = (-2/3)(x - 6) + 3

y = (-2/3)x + 4  +  3

y = (-2/3)x  + 7        (1)

Next

Find  the slope  between  AC  = ( 1,2)  and (6,3)  =  (3 -2) /( 6 - 1)  =  1/5

The equation of  the  line  perpendicular  to segment AC  through  B  is

y = -5 ( x -3)+  5

y = -5x + 20        (2)

Find  the  x coordinate  of the  orthocenter  by  setting  (1)   = (2)

(-2/3)x  +  7   =  - 5x  +  20     multiply through  by  3

-2x  + 21  = -15x  +  60

13x  =  39

x  = 3

And  the y coordinate  is   -5(3)  +  20  =   5

So....the orthocenter is  actually B    = (3,5)

Thanks!

The  difference  of  the  roots     = sqrt  ( b^2  - 4ac) =  sqrt   ( b^2  - 4c)

And   l b - 2c  l    can be written  as   sqrt [ (b - 2c)^2   ]

This implies that

b^2   - 4c  =   ( b  - 2c)^2

b^2  - 4c  = b^2  - 4bc  + 4c^2

-4c  =  -4bc + 4c^2

c  =  bc  - c^2

c^2  +  c  =  bc

c + 1    = b

c   =   b   - 1

Hi,

We have the question The equation 2x - 3/(x - 2) = 4- 3/(x - 2) has how many roots?,

first we can simplify the equation.,

2x-3/x-2 = 4x-11/x-2

if we cross multiply we get a quadratic equal to a quadratic..

So..

We can't have a degree higher than 2...

therefore there are 2 roots to the equation

p.s correct me if im wrong.

Would it be possible for you to put the equation

:)

Uhhhh.....    None?  ?  

q + d = 36

25q + 10d = 420

q = 36 - d

25 (36 - d) + 10d = 420

900 - 25d + 10d = 420

900 - 15d = 420

15d = 480

    d = 32

q + d = 36

q + (32) = 36

q = 4

There are 4 quarters and 32 dimes

d = dimes                     value = 10d

q = quarters = 36 -d     value = 25 (36-d)            the values summed = 420

10d      +        25(36-d)     =       420     solve for d =# dimes    then  # q = 36-d

97*2-90 = 104^o

Since they're similar, we can take the similar side that has actual values to find the ratio between the triangles.

7 : 3.5 = 2 : 1

This means:
2y = x + 4

2x = 3y

x - 2y = -4

2x - 3y = 0

2x - 4y = -8

2x - 3y = 0

----------------

y = 8

x - 2y = -4

x - 2(8) = -4

x = 12

Interest  amt after  2  years   =

Amt  after  two years -  Initial amt

70  ( 1.05)^2  - 70     ≈   $7.18

minor arc AD   = 360  - 96  -  100  -120   =  44°

Angle B =  (1/2)  measure  of  ( minor  arc AD  + minor arc DC)   = 

(1/2)  ( 44  +  120)    =

22  +  60    =  

82°

Area of a triangle =   1/2 base * height         base = 6 + h 

        140              =  1/2  (6+h) * h

         280 = h^2 + 6h

           h^2 + 6h - 280 = 0    Quadratic Formula or factoring shows   h = 14      so base = 20

       (h-14)(h+20) = 0      h =   14  or  -20 (throw out)

5cm is the radius. This means the circumference is 2 * 5π = 10π

6.28 is about 2π. This means the sector angle is 2π/10π * 360 = 72^o

Area of the sector = 5²π / 5

                              = 25π / 5

                              = 5π

                              ≈ 15.7cm², which is your answer :)

There are 52! ways to arrange the 52 cards of the deck

   there are only 51 ways to have the ace of hearts directly on top of the king of hearts in the shuffled deck positions

     but that leaves the other 50 cards to arrange in any order or  50!

52!  - 51 * 50!= 52!-51! =

        79107056417656496291436393839934463764226245720866291712000000000000 = 7.9107056417656496e67

 ( I think !)

..