CPhill

We have that

P  = n * s

Mean  :  X^2 found the mean to  be   : Sum of the data  / 24 =  5262 / 24  = 219.25

Median ...order the data from  low to high

138,152, 164, 172, 176, 182, 186, 186, 190, 190,  207, 213, 216, 233, 236, 240, 242, 259, 268, 274, 274, 285, 288, 291

We have 24 values...the median will come from the average of the 12th and 13th terms =  [ 213 + 216 ] / 2 = 214.5

The mode is/are the value(s) that appear(s) most often  = 186, 190 and 274  [ this data  is "tri-modal" ]

The range is  just the greatest weight  - the lightest weight =  291 - 138  = 153

\(x(x-3)=1\)

\($\frac{a+\sqrt{b}}{c}$ and $\frac{a-\sqrt{b}}{c}$\)

x( x - 3)  = 1

x^2 - 3x   = 1     subtract 1 from  both sides

x^2  - 3x  + 1    = 0  

Using the quadratic formula...   we have

x  =  [3 ±√ [9 - 4(1)(1) ]  / 2   =  [ 3 ±√ 5 ] / 2

So  abc  =  3 * 5 * 2    =  30

(a)

C  = 90 t        where t is the number of hours and  C is the  customers served

(b)

t is the independent variable

C is the dependent variable

(c)

C  = 90(11)   =  990 customers

I'll do  (a)...you can try  b

Slope  =  [ subtract the y coordinates  in some order ] / [  subtract the x coordinates in the same order ]

[Note...the order does not matter as long as it's the same ] 

So we have for (a)

Slope =  [ 5 - 5] / [ 6-  -1 ]  =  0 / 7    =  0

The slope of a tangent line to the circle at any point is given by   -x / y   where  (x,y)  is the point

So...the slope of this line is  (-8/ 15)

And using the point....we have

y  =(-8/15) ( x -8)  + 15    simplify

y = (-8/15)x + 64/15 + 225/15

y = (-8/15)x + 289/15

The trird term is 13  and the fourth term is 18

So....the common difference  =  5

To find the first term, we have

13 - 2d  =   13 - 2(5)   = 13  - 10    =  3

So....the 50th term is

3 + 5 (50 - 1)  =

3 + 5(49)  =

248  ⇒ "A"

Let x be the number of  software programs to be produced and y  be the number of  video games to be produced

We have this system of constraints

x ≤ 200

y≤ 300

x + y ≤ 425

And we wish to maximize this objective function

50x  + 35y

Look at the graph of the constraints, here : https://www.desmos.com/calculator/bbbhypnku7

The possible values  of (x , y)  occur at the corner points of the feasible  region , namely at (125, 300)  or ( 200, 225)

Plugging these into the objective function, we get

50(125) + 35(300)  =   $16,750

50(200) + 35(225)  =  $17,875

Then....200 software programs should be produced and  225 video games should be produced

-5/2(3x+4)< 6-3x        multiply through by 2 to clear the fraction and we have

-5(3x + 4)  < 12 - 6x      distribute the -5 across the terms in the parentheses

-15x - 20 < 12 -  6x    add 15x to both sides, subtract 12 from both sides

-32 < 9x       divide both sides by 9

-32 / 9  <  x   which is the same as  x > - 32 / 9

OK....good....[ we ALL mess up here and there.....LOL!!! ]