CPhill

Happy Birthday.......!!!!

y > x^2

y < -2(x + 2)^2 + 6

Instead of inequalities, let's just set these equal and see if we can find the correct solutions

x^2  = -2(x + 2)^2  + 6

x^2 = -2(x^2 + 4x + 4) + 6

x^2 = -2x^2 -8x - 8  + 6   

x^2 = - 2x^2 - 8x - 2      rearrange as

3x^2 + 8x + 2  =   0

Solving this with the Quadratic Formula,  we get the solutions :

x = ( -4 - √10 )  / 3  ≈   -2.387

x = (-4 + √10 ) / 3  ≈ -0.279

We have  three possible intervals  for solutions

(-infinity, ≈ -2.87 )    U ( ≈-2.87, ≈ -0.279) U  (≈ -0.279, infinity)

The way these usually work is that either the two outside intervals work or the middle interval does

Here's a graph to prove that the middle interval is correct  :

https://www.desmos.com/calculator/uvqnynvqym

The solution area is where both graphs overlap

Numbr divisible by 9  =  1000 / 9  =  111

So....number not divisible by 9   =   

1000 -  111  =

889

These are binomial probabilites

First one

C(22,7) (.092)^7* (.908)^15  = .00236  ≈  .22% 

Second one  : At  most 5   =   1 - P(7 have colorblindness) - P(6 have colorblindness)  =

1 - .00236  - C(22,6)(.092)^6 (.908)^16  = .9879  

Last one :  At least 3  =  1  - P(0) - P(1) - P(2)  =

1 - C(22,0)(.908)^22  - C(22,1)(.092)(.908)^21 - C(22,2)(.092)^2(.908)^20  = .3299

1.

Area  =   (1/2) (14.2) (8) sin (99° )   ≈   56.1 in^2

2.

Area  =  (1/2) (14) (12) sin (20°)  ≈  28.7 ft^2

3.

Area   = (1/2)(5) (4)sin(79°)  ≈ 9.8 ft^2

4. 

Area  =   (1/2) (40)(25) sin (80 ° )  =  492.4 m^2 

1.  Remember we have to convert feet to inches

5 ft  = 60 in        2 ft   =  24 in       1ft  = 12 in

Volume of tub   =  60 * 24 * 12  =  17280 in ^3 

Volume of mug  =  pi * (1.5)^2 * 4  ≈  28. 3 in^3

Note  1 * 10^4  =  10,000

So....the correct answer is  "D"

2.  B is correct

Area of the base  =  36

Area of sides

We have 4 equal triangles.....each  has a base of 6  and a height of 3....so the area of the sides  =

4 * (1/2) (6) (3)   =    2 * 6 * 3    =  36

So....the toal area  is  [ 36 + 36 ]  =    72  ft^2 

You are correct  Agent    !!!!!

1.

x  - 120

_______   =  -0.25

  4.3  

x - 120  =  -1.075

120 - x  =  1.075

x =  118.925 ≈  119 g

Here's another way

We have 9 ways to select the first digit  and 10  ways to select the second digit

So.....the number of 4 digit palindromes is  just

9 * 10   =

90

Notice that we can figure the area of this triangle in two ways

One of the bases  = 20....and the height to this base = 12

So the area  is  (1/2) 20 * 12  =   120  units^2

Also.....the other base  = 30  and the height of this base   = h

So

Area  of triangle  = (1/2) * 30 * h

120  =  15 * h        divide both sides by  15

8 ft   =  h