The line: y = (3/8)x + 6 has a slope of 3/8.
Any line perpendicular to this line will have a slope that is the negative reciprocal of 3/8. Ignore whatever is the y-intercept; that number has no effect upon whether or not two lines are perpendicular.
The negative reciprocal of 3/8 is -8/3.
So, the correct choice is: y =(-8/3)x + 3.
I have no idea why there is a '(-1,2)' within this equation.
Since there are only two envelopes, as an example, let's assume that the number in the first envelope is $100.00.
Now, the number in the second envelope will be either $50.00 or $200.00.
The probability that it will be $50.00 is ½. Also, the probability that it will be $200.00 is ½.
From the $100.00 you now have, there is a ½ probability of losing $50.00 (going from $100.00 down to $50.00) and there is a ½ probability of gaining $100.00 (going from $100.00 up to $200.00).
So, the expected value is: ½(-$50.00) + ½(+$100.00) = -$25.00 + $50.00 = +$25.00.
Therefore, switch! (The same analysis works for any amount in the first envlope.)
That's my mathematical answer.
My psychological answer is this:
-- Obviously, you would sooner gain than lose; but gains don't necessarily balance losses; that is, it takes more than one gain to offset just one loss.
-- If the number in the first envelope is sufficiently large so that losing one-half of it would cause you to be mad at yourself, take the first envelope and don't even check to see what's in the second envelope ...
It depends........the "normal" function modeling this is given by....
P = √(c and y ) * Π(rounded)
Where c = lbs. of chocolate, y = "nutty" factor (this may apply to actual ingredients or just to the number of people consuming the fudge who exhibit tendencies towards "CDD")
"pi" is normally "rounded" (but it could be "squared" under special circumstances)
Sometimes, the formula is written more compactly as
√(Candy) * pie
Remember, your mileage may vary during the Holiday Season.......