CPhill

This is a 30-60-90 right triangle

The side opposite the 30 degree angle  = 5  = the base

The side opposite the 60 degree  =  sqrt(3)  *  the  side opposite the 30 degree angle  = 5*sqrt (3)....this is the height

So....tha area is   

(1/2)  base * height  = 

(1/2) 5  *  5sqrt(3)    =   

 ( sqrt (3) / 2) * 25  cm^2  ≈ 21.65 cm^2

A quarter has a diameter of  24.26  mm  ≈  .955 in

And the  height (thickness)  is 1.75 mm ≈  .0689   in

So....the volnme of one quarter  is the volume of a cylinder with a diameter of  955 in and a height of .0689 in  =

pi ( .955/2)^2  * ( .0689)    ≈  .04935 in^3

So  (theoretically), the number of quarters that would fit in the box is ≈  182.876 in^3  / .04935 in^3  ≈  3706 quarters

Arc length  =   2pi * radius  *  (given angle  / 360)     ...so we have

Arc length =  2pi * 6  *  (45  / 360) 

Arc length  = 12 pi * (1/8) 

Arc length  =  (12/8) * pi    =   (3/2)  pi   ( inches  )

P A l B )  =   .3 / .54  =  .55

P (B  l A )   = .3 / .55  = .54

P (A )  = .55

P(B)  = .54

Drinking  coffee and drinking water are independent events because  P(A l B)  = P(A)  and P (B lA)   = P(B)

We have this:

A  = 90 * (2)^(t/4)       where A is the amount present after  t hours

So...after 12 hours, we have

A  = 90 * (2) ^(12/4)

A = 90  *  (2)^3

A = 90 * 8

A =  720 pounds  =  "A"

[Time - 4.6]  / 1.1   =  -1.2  multiply both sides by 1.1

Time - 4.6  =  -1.32      add 4.6 to both sides

Time  =  3.28  hrs

If  f(3)  = 5   and    f(3x)  = f(x) + 2, then .....

f(3x)  = f(3) + 2     implies that x  = 3

So

f(3 * 3)  = f(3) + 2

f(9)  =  5 + 2

f(9)  = 7

And

f(3x)  = f(9) + 2   implies that  x  = 9...so.....

f(3*9) = f(9) + 2

f(27)  = 9

And

f(3x)  = f(27) + 2   implies that x  = 27

f(3 * 27)  = f(27) + 2

f(81)  = 9 + 2

f(81) = 11

And   (81, 11)  is on the original graph  .....so  (11, 81)  is on the inverse

So

f^-1(11)  =  81

LOL!!!!....I didn't see that second one...see my added answer [ in red ]  ....

We are looking for the z score that corresponds with [ 1 - .70]   =  .30.....the closest value [per table]  is about -.52

So...we are trying to solve this

[ x  -15  ]  / 5.2  =  -.52       multiply both sides by 5.

 x - 15  =  -2.704  add 15 to both sides

x  = 12.296  = 12.3 years of age

m minor arc BCD   =  2  (angle A)

                                                                      Inscribed Angle Theorem

2m (angle A)  + 2 m (angle C)  = 360°

                                                                        Division Property of Equality