CPhill

Call the  monthly  salary, S

Amount  left after  depositing  (1/2) of his salary in the bank  = (1/2)S

So

(1/3) *(1/2)S    -  15 * 8  = 720    simplify

(1/6)S  - 120  = 720      add 120  to both sides

(1/6)S=  840     multiply both sides by 6

S = $5040

Rearrange as

2x^2 - 12x + 2y^2 + 4y =  20          divide through by  2

x^2 - 6x  + y^2  + 2y  = 10      complete the square on x and  y

x^2 -6x + 9  + y^2 + 2y + 1  = 10 + 9 + 1      factor

(x - 3)^2  + (y +1)^2   =  20

This is a circle  with a center of  (3, -1)  and a radius of  √20

The  side of the square = twice the radius of the circle  =   2√20  = √80

So....the area of the square   =  side^2  =  (√80)^2 =   80  units^2

"Anchor" J  at any point on the  circumference

Proceeding in a clock-wise direction we could have the following possibilities for  the four points

JKLM

JKML

JLKM

JLMK

JMLK

JMKL

Note that the  two entries in red  are  the ones  where  chords JK  and LM  intersect

So.....the probability of intersecting chords  is   2 / 6    =     1 / 3

See here   : 

https://web2.0calc.com/questions/i-need-help_5754

The  vertex  is  ( 2,1)

The x coordinate  of the  vertex is given by

-b/ [2a] = 2

-b= 4a

b = -4a

And another point on the parabola  is   (0, 5)    so  c  =  5

So   we can solve this

a (2)^2  + b (2)^2 + c  = 1

a(2)^2   - 4a (2)  + 5  =1

4a  -8a  + 5  =1

-4a  = -4

a = 1

And b = -4(1)  =- 4

So....the function is

x^2  - 4x  + 5

So

a + b +  c  =

1  - 4  +  5  =

2

I = Prt

3940 = P * .06 * 5

3940  = P  *  .3       divide both sides by .3

13,133.33  =  P

This is impossible.....the  cosine only ranges between -1  and 1  inclusive.....so  63/10  = 6.3  which is outside that range

Yep....thanks, DragonLord....I realized my mistake later on.....16 is correct  !!!

(a)  The probability  is   5/16 * 3/16  =   15 / 256 ≈  .0586

(b)  The probability  is  5/16 * 3/15  =   5/16 * 1/5  =  1/16  = .0625

The  possible  rational  roots   is given by  

± All  the possible factors of  15   divided by  All the possible factors of  9

Factors  of  15 =   1, 3, 5, 15

Factors  of  9  =  1, 3 , 9

So...all  the possible rational roots  =    ± (  1 , 1/3 , 1/9 , 3,  5 , 5/3 , 5/9 , 15  )

So.....16  possible rational roots

Thanks to DragonLord for catching my earlier error   !!!!