ElectricPavlov

I will assume you can have 1 letter words like   'M'  'A'  'T'  and 'H'  

4 p 1  +   4 p 2 +  4 p 3  +  4 p 4=

4                12        24           24        = 64 'words'

1.815 x 10^11 / 8.67 x 10^22 = .20934x 10^-11 = e^-20000/1.987T

                                             -26.892 =- 20000/1.987T

                                              T = -20000/(1.987(-26.892)     T =374.29

All you have given is an expression.....  T can be any value....

if you have an EQUATION    like     4500 = e^(-20000/(1.987T)      take the ln of both sides of the equation and you have

                                                     ln 4500 = -20000/(1.987T)      then re-arrange

                                                          1.987T = -2000/4500       then divide both sides by 1.987

                                                                   T = -20000/(4500(1.987)) 

18 24 30 is a possibility.  (a multiple of 3-4-5 common rt triangle)   Hypotenuse = 30

18-12 = 6         6 / 4 = + 1.5

20 would be 2 S.D. away from the mean     12 + 2 S.D. = 12 + 2(4) = 20

Here is my take:

Generally, you  have ASSETS and LIABITIES.....

Assets are positives and are weighed against negative LIABILITIES to calculate your NET WORTH

Borrowing money increases your LIABILITY

.Her LIABILITY went up 20    liabilities are a negative......she now OWES 20 to her dad.,,,,,,

JUst use a graphing calculator or website to graph the two fxns..... where the graphs intersect is the solutions to the system of equations

Here is desmos:

-x^2+3x+8 = 2x+2    rearrange

0 = x^2 -x-6     factor

(x-3)(x+2) = 0    means x = 3 and -2

Sub into one of the equations to find the y values    x = 3  y = 8        x = -2  y= -2     (using equation  y = 2x+2)

(always good to commit to memory the values of the standard bell curve...as shown above)

Similar Q has been posted multiple times.    One standard deviation ABOVE 76 = 84    and has a z-score .8413   so approx 16% of the population is ABOVE this score  ....but that does not fit the answers......so look at the NEGATIVE z-score table for the value nearest .16  

Between -1.- and - 0.9 standard deviations represents this 16%  ...I'll just use -1.0

76 - 1.0(8) = 68        scores below 68 represent 16% of the scores

I think it is D   the probabilities should add to no more than 1.0 if all of the Px's are included in the table