CPhill

D is correct

Avg  =   (120 + 144 + 143 + 111  +  167 ) /  5 =    ????

There is an easier way to do this but I've forgotten the method.....here's a clumsier way  !!!!

Square  both sides

79 + 24sqrt (7) =   a^2  + 2absqrt (7)  + b^2 * c

This implies  that

c = 7  

 24 = 2ab

12  = ab

  Testing some values

       a           b                         a^2        b^2 * c              a^2 + b^2 * c =  79   ???

       1           12                        1           144 * 7                      No

       2            6                         4            36 * 7                       No

       3            4                         9            16 * 7                       No

       4            3                       16             9 * 7                       Yes

So     sqrt  [ 79 + 24sqrt 7 ]  =      sqrt  [ ( 4 + 3sqrt 7)^2 ]     =      4 + 3sqrt 7

So    a =  4   b = 3   and c = 7   

abc  =   4 * 3 * 7   =    84 

We can model this with the sine function

We have this form

y  =  Asin (Bx)

y = the displacement   at any time, x

A = the amplitude =  7 in

x= time in sec

The period =  8s

B =   2pi / 8  =  pi/4

The function  is     y =  7sin [ (pi / 4)  x ] 

Here's a graph  :   https://www.desmos.com/calculator/urhpnycwzv

I barely remember this but I'll take my best shot

Note  that    as  x approaches  6, the  function   12x - 36   =  12 (6) - 36  =   72  -36  =    approaches 36

And as x approaches 6, the function x^2  =  6^2 =  approaches  36

So.....by the Squeeze Theorem......f(x)  also approaches 36  as x approaches 6  [ i.e., the limit  =36 ] 

(x^2 - 4x + 2) + (x^2 - 5x + 2) = 1  simplify as

2x^2 - 9x + 3  =   0

This will  have two real roots

In the form    ax^2  + bx + c ,  the sum of these =    -b / a    =     9 /  2

Here's a similar problem  :

https://web2.0calc.com/questions/pls-help_10037

Call the amount that Adam had originally  =  A

Call the amount that Friday  had originaly = F

We  have these two  equations

(A - 9) / F  =   2/7

A / ( F - 9)  =  7/11

Cross-multiply in each case

7 (A - 9)  = 2F

11A  = 7 (F - 9)                 simplify  both

7A  - 63   = 2F                      (1)

11A =  7F - 63                  rearrange  both as

7A - 2F  =  63

11A - 7F  = - 63            multiply  the first equation by -7   and the second by 2

-49A  + 14F  = -441

22A  -   14F  =  -126           add these

-27A  = -567

A = -567 / -27   =   21     ( Adam originally had $21  )

And using (1)  to find F

7(21)  - 63  =  2F

147 - 63  =  2F

84  = 2F

84/2   = F =   42    (   Friday originally had $42 )  

They originally had  $63  dollars combined

g ( f(n) )   means  that we are putting the function f  into  g   (for n)

So we have

2 ( n^2 - 2)  +  2  =

2n^2  - 4  +  2   =

2n^2  - 2

Call the number of dimes  = D  = number of pennies    and the number of nickels = N 

So....we have these equations

Value of a  dime  * number of dimes  +  Value of a nickel * number of nickles =  6.10

.10D  +  .05N  =   6.10            (1)

And

Value of penny  *  number +  Value of a nickel * number = 3.49

.01 (D )  +  .05N  = 3.49             (2)

Subtract  (2)  from (1)

.09 D   = 2.61

D  = 2.61 / .09   =    29   = number of dimes = number of pennies

And to  find the number of nickels, use ( 1)

.10 (29) + .05N = 6.10

2.90 +.05N  = 6.10

.05N  =  6.10 - 2.90

.05N  = 3.20

N =  3.20 / .05 =   64 = number of nickels