CPhill

Circumference  =   2 pi * radius

11 pi  = 2 pi (radius)         [   divide out pi    ]

11 = 2 * radius                 [ divide  both sides  by  2

11/2  = radius  =    5.5

Area of  circle  =

pi * (radius)^2  =

pi (5.5)^ 2  =

[ 30.25 pi ]   ft^2   ≈  [ 95.03  ]  ft^2  

A.   Ellipse

A. cylinder

Let the side of the square  = x

So.....the height of the  box will be x

And the base  area is   (12 -2x) (1- 2x)

So....the area is

Base area * height  =

(12 - 2x) (10 - 2x) *x   ⇒     "B"

The max area will be a circle

To find the radius....we have that...

Circumference   = 2pi * radius

40  = 2p  * radius        [ divide  both sids  by  2 pi]

40 / (2 pi)   = radius    =   20 /pi

And the area of the  circle is

pi * (radius)^2  =

pi * ( 20/pi)^2  =

400/pi    m^2  ≈   127.32 m^2

Next smaller text size  =

(1.772) / ( 1.21) =  1.464    ( rounded to  the  nearest thousandth )

The next larger size  =  (1.333) (1.777)  = 2.368741 ≈  2.369   (rounded to  3 decimal places )

1.

[ Sarah's point total -  17 ]

____________________     =    2.8       multiply  both sides by 4

           4

Sarah's point total  -   17 =     11.2        add 17 to both sides

Sarah's point total   =    28.2

2.  A z-score of  2.8 means that she scored more points than about  99.74%  of  the participants.....this would be  considered very unusual

First one looks good

Second.....

[ 6 -  8 ]/  3.2  =   -2 / 3.2  =   -0.625    ......Correct   !!!!!

The centroid of a triangle will divide the  triangle into  3  equal  areas

The coordinates of the  centroid are  given  by

;

 (  [sum of the  x coordinates of  the  vertex points ] / 3 , [ sum of the  y coordinates of the vertex points ] / 3 ) =

( [5 + 3 + 6 ]  /  3  , [ 8 + -2 + 1 ] / 3  )  =  (  14/3, 7/3)

So

10m + n   =

10 ( 14/3) + (7/3) =   140/3  +  7/3   = 147/3   =   49