CPhill

Call the radius  of the cylinder and sphere, r

And the height  of the cylinder  = 2r

So

60  =  pi * r^2 * 2r

30 =  pi * r^3

30/pi  =  r^3

[30/pi]^1/3  =  r

So...the volume of the sphere is

(4/3)pi [ (30/pi)^1/3 ]^3  =

(4/3) pi * 30/pi  =

40 cm^3

We could  also  see this by the forllowing ratio

Vsphere      =   (4/3)pi *r^3              (4/3)                4                 2            40

_______          __________    =      _____  =     ______  =      __    =    ___

V cylinder         pi * r^2 * 2r                2                  6                  3            60

\(2\log{(a -2b)} = \log{a} + \log{b} \)

We can write

log (a - 2b)^2  = log ( a * b)

And we can solve

(a - 2b)^2  =  ab

a^2 - 4ab + 4b^2  = ab

a^2 - 5ab + 4b^2  = 0     factor

(a - 4b) ( a - b)  =  0

Setting  each factor to 0  and solving we have that

a  = 4b         and  a  = b

Assuming  a, b   are both positive, the first solution is the only one where all logs are defined for real numbers

So

a  / b  =

[4b]/ b  =

4

First one....the scale factor is  2

Second one

n/6  =  5/3    multiply both sides by 6

n  =  6 * 5/3

n = 30/3

n  = 10

Assuming a quadratic, we have that

y  = ax^2 + bx + c  

Since (0,5) is on the graph, c  =5

And we have the remaining  system

a(9)^2 + b(9)  + 5  =  -11

a(6)^2  + b(6) + 5  =  13     simplify

81a + 9b  =  -16     multiply through by  6 ⇒  486a  + 54b  =  - 96   (1)

36a + 6b   =   8      multiply through by  -9 ⇒  -324a  -54b  =  -72     (2)

Add (1)  and (2)

162a  =  -168

a  = -28/27

To  find b we have

36 (-28/27) + 6b  =  8   

-112/3 + 6b  = 8 

⇒  b  =  68/9

The function is

y  =  - (28/27)x^2  + (68/9)x  + 5

Here's a graph  with the included points  :

https://www.desmos.com/calculator/z4qpjyxpic

N(Spanish or History)  = N(Spanish)  + N(History)  - N(Spanish and History)

N(Spanish or History) =       26          +    38              -   16

N(Spanish or History )  =    48

Prob  =  (48  / 88)      =   6 / 11

Number that liked movie  =  26

Of these.....12  are in the 18-34 age group

So

12 /26   =   6/13  ≈  46%

OK...RP!!!!

24 use text messaging

Of these, 17  also use  e-mail....so....

The probability is  17/24 =   70.83   ≈    71%

2x^2 - mx + n

The sum of the roots is given by

m / 2  = 6   multiply both sides by 2

m  = 12

The product of the roots  is given by

n/2  = 10      multiply both sides by 2

n  =  20

So....

m + n  =  12  + 20   = 32

EDIT TO CORRECT AN ERROR.....

5^x  = 80

Log Form

log₅ 80   = x

b   = 5

x  = x

n  = 80

a) Not replaced

Yelllow marker First - Then Blue Marker  =

(1/10)(1/9)  =  1/90

b) Replaced

(1/10) (1/10)  = 1/100

Answer   "C"