CPhill

We need to find the height of both objects   and the radius of the cylinder

For the rectangular prism, we have

2.5  = (base area)(height

2.5 = (2 *1) * height

2.5 = 2 * height         divide both sides by  2

1.25  =  height

The surface area  = base area + side area  =   

(2* 1) +   2 * (1.25)( 2 + 1)  =   2 + 2.5 ( 3)   =  9.5 sq ft

So.....the total cost  = 9.5 * 1.30   =  $12.35 

For the cylinder we have that

2.5  =  base area * height

2.5 =   2.5 * height         divide both sides by 2.5

1  =  height

The radius can be found as

2.5 = pi * radius^2   

2.5 = 3.14 * radius^2      divide both side by   3.14

2.5 /3.14 =  radius^2      take the square root

√[2.5 / 3.14 ]  =  radius   

The total surface area =   base area  + side area  =   2.5 + 2 * pi * radius * height =

2.5 + 2 * 3.14 * √[2.5/3.14) * 1 =

2.5 + 2*3.14√[2.5/3.14]

So....the total cost for the cylinder =

1.30  ( 2.5  + 2* 3.14√[2.5/3.14]   )   =   $10.54 

So....the cylinder is cheaper

The height of the rectangular pack  =  6r   =   h1

The  height of the parallelogram  =  2r  + the height of two equilateral triangles with a side of 2r

The height of  one equilateral triangle  with a side of 2r  = (side)/ 2 * √3  = (2r) / 2 * √3  =   r√3

So....the height of two of these is   2r√3

So... the height of the parallelogram =  2r  +  2r√3   =   2  ( 1 + √3   )   =   h2

So.....the ratio  of    h1   to h2   =  

6 :  2 ( 1 + √3)   =        {  divide by  2 }

3 :   1 + √3

Mass  =  volume * density  =   pi * (radius)^2 (height) (density )

A.   pi * (2)^2 (2) ( 50)  ≈  1257   no

B.   pi * ( 3)^2 ( 2) ( 26)  ≈ 1470     yes

C .  pi * ( 2)^2 ( 3) ( 33)  ≈  1244   no

D.  pi * ( 3)^2 ( 1) * (47)  ≈ 1329  no

E.  pi * ( 4)^2 ( 1) ( 40)   ≈ 2011    yes

"B"  and "E" will incur additional shipping costs

a_n  =  (2/5) (5)  ^{n - 1}

a₁  = (2/5)(5)^{1 - 1}   =   (2/5)(5)⁰  =  2/5

a_n  =  5* a_{n - 1}

I don't see any densities listed......????

Last one

First term  =  -2(3) + 5  =  -1

Last term = -2(6) + 5 =  -7

Sum

[ first term + last term ] * number of terms  / 2  =

[ -1 + -7 ] *  4  / 2  =

-8 * 4  / 2  =

-16

Second one...not arithmetic or geometric......probably easiest to just list the terms

First term  ( 2 * 1)^2  =  4

Second term  = (2 * 2)^2  =  16

Thirs term = (2 * 3)^2  = 36

Fourth term  (2 * 4)^2 = 64

Sum  = 120

First one

First term  = 2(1)  = 2

Fifth term  = 2(5)  = 10

Sum of series  =

[ first term + last term ] *  number of terms  /  2    =

[ 2 + 10 ] * [ 5] / 2  =

12 * 5 / 2  =

60 / 2  =

30

The common difference is 5

The first term is -7   =  a1

Notice that, the jth term is given by :

aj  =  a1  + 5(j - 1) 

aj  =  -7  + 5j -  5

aj  =  -12  +  5j

aj =  5j - 12

Do you see the correct answer, based on this ????

The z score closest to 16% appears to be ≈  -.99

So....we have that

raw scores -   mean

________________  <     -.99

  std. dev.

raw scores - 73

____________   <   -.99      multiply both sides by  4     

     4

raw scores - 73  <  -3.96       add 73 to both sides

raw scores <   69.04  ≈   70%  =  scores below 70