All Answers 356736 Answers

1. The probability is 3/20.

2. The sum of the coordinates is 1 + 2 = 3.

That's not correct according to the answer key. Either way I'm looking for a solution, not the answer.

The maximum area is 16*pi.

Readng off the graph, f(2) = 4.

1. The expected value is 11/2.

2. The expected value is 17/3.

Note  that angle FHG = JHG   = 90 - 28  =   62°

Since  GJ  = GH, then  angles  JHG and GJH  are  equal

So  angle JGH   = 180  - 2(62)  =  180  -  124  =   56°

The remainder is 6.

The probability is 1/2.

Let  the  number of hot lunches =  H

Then  the number of cold lunches =  2H  - 1

So

3H  + 1.80  ( 2H - 1)  =  288.60

3H  + 3.60H  - 1.80  =  288.60

6.60H   =  288.60  +  1.80

6.60H  = 290.4      divide both sides  by  6.60

H =  290.4  / 6.60      =     44  hot lunches

2H - 1  =  2(44)  - 1  =    87  cold lunches

The remainder is 3.

oh thank you that was easier thn i though. Ty Mr. Cphill

* * * edited * * *    ( but answer does not change)

x^2 -2x       + y^2-9y     < = 22       then complete the square for x and y

(x-1)^2       + (y-4.5)^2  < = 22 + 1 + 20.25

                                    <  = 43.25                          43.25 is the radius squared

Note something, Choff

A 100%  increase means that something doubles  =  (1 + 1) =  2 times as much

A 200% increase means that  something triples = (2 + 1)   = 3 times as  much

So  an 800%  increase   means that sometning is  (8+1)  =    9 times as  much as  the  original amt

2003  = A   = the original number

2005  =  3A  =   200% increase  over  2003  = 3 times as  many

2007  =   3 (3A) =   9A  =   800% increase over 2003  = 9 times as  many

Since f(x) is divisible by x^3, f(x) is of the form ax^5 + bx^4 + cx^3.

You then want ax^5 + bx^4 + cx^3 + 2 to be divisible by (x + 1)^3.  Using long division, you get the equations

-10a  + 6b - 3c = 0

4a - 3b + 2c = 0

-a + b - c + 2 = 0

==> a = 6, b = 16, c = 12

So f(x) = 6x^5 + 16x^4 + 12x^3.

This will be the area inside of a circle...first simplify to

x^2 -2x       + y^2-9y      = 22       then complete the square for x and y

(x-1)^2       + (y-4.5)^2   = 22 + 1 + 20.25

                                      = 43.25                          43.25 is the radius squared

area = pi r^2   = 43.25 π

490  / 1400  =    49  / 140    =  .35  =   35 %

Let  the questions he answered correctly  =  x

Let  the one  he answered incorrectly  = 90 -  x

{ the ones he didn't answer don't matter  since they add  nothing to  the  total  points }

So

7x  -  2(90 - x)   =  495

7x  - 180  + 2x   = 495

9x - 180  =  495

9x =   495 + 180 

9x =  675

x  = 675 /  9    =   75   answered  correctly 

x^2 + y^2 =  - 7 =  2y  - 8x  + 1

x^2 + 8x + y^2 - 2y  =  7 + 1        complete the square on  x and y

x^2  + 8x  + 16   +  y^2  - 2y + 1  =  7 + 1 + 16  +  1

(x + 4)^2   + ( y - 1)^2  =  25

This is a  circle  centered at  ( -4, 1)   with a radius  of  5

The  area =  pi 5^2   =  25 pi

Makes sense now. Thanks!

Re-arrange:

x^2 +8x         +  y^2 - 2y      =    8                                   complete the squares for x and y

(x+4)^2         +   (y-1)^2      =     8   +  16     +1

(x+4)²             +  (y-1)²           = 5²                                              this is circle equation with radius = 5

pi r² = area of circle 

pi 5² =   25 pi   units²             ( 78.54  units²)

beat me to it. Good job 

lmao this guy cheatin on the aops exam

answer is 76

There are 28 students in the program

   the program has a debate team made of = seniors juniors

                   soooo   25% of the juniors = 10% of the seniors   

                                    .25j = .1s       and    j+s = 28

                                                                    s = 28-j

                                     .25 j = .1(28-j)

                                      .25j + .1j = 2.8

                                      .35j = 2.8

                                           j = 8                   8 juniors are in the program

Let the  number   of  15 cent stamps   = x

Let the number  of  25 cent stamps = 15   -  x

So

15x  +  25 ( 15  - x)   =  315

15x  +  375   - 25x =   315

15x  - 25x  =   315  - 375

-10x  =  - 60      divide  both sides by -10

x =  6   =   the number of 15 cent stamps sold

15  -  x  =   15  -  6  =   9    = the number  of 25 cent stamps sold

Not as tough as it seems

x^2 - 10x + y^2 - 10y + 25 = 8x + 4y + 16      simplify as

x^2  -10x - 8x + y^2 - 10y  -4y   + 25  - 16   =    0

x^2  - 18x  + y^2 - 14y  +  9  = 0

x^2  -18x  +  y^2  -14y    =  -9       complete the square on  x and  y

x^2  -18x  + 81  +  y^2 - 14y + 49  =   -9 + 81 + 49

(x - 9)^2   + ( y - 7)^2   = 121

To find the y intercept, let  x   = 0

(0 - 9)^2  + ( y -7)^2  = 121

81 +  ( y -7)^2   = 121

(y -7)^2   =   121  -81

(y - 7)^2   =40      take both roots

y - 7  = ± sqrt (40)   =  ± 2sqrt (10)

So ....two y intercepts

y = (0,  7  - 2sqrt (10)  )

And 

y =  (0, 7 + 2sqrt (10)  )