You and a friend are playing rock-paper-scissors.4 each of you throws rock with probability r, paper with probability p, and scissors with probability s. (you both use the
same probabilities because you are equally smart.)
a) use lagrange multipliers to show that your probability of winning is maximized if
you use r = p = s =1/3
.
b) for rock awareness month, it is decided that games won by throwing rock will earn
you $1.50, while games won by throwing paper or scissors will only earn you $1. find
the probabilities that maximize your expected winnings.
c) what happens if the payout for rock is raised to $2?

okay wait before i answer, is this for your points on a graph?

-232

step-by-step explanation:

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

answer: input the dimensions of the room to be painted. click the button to calculate the amount of paint and man-hours needed for this job.

interior paint coverage depends on the brand of paint used. the coverage amount is listed on the label of the paint can. use this to adjust the values in the paint coverage section below. paint usually is applied at 350 to 400 square feet per gallon (primer at 200 to 300 square feet per gallon).

step-by-step explanation: