Billy has a von Neumann-Morgenstern utility function U(c) = c 1/2. If Billy is not injured this season, he will receive an income of 25 million dollars. If he is injured, his income will be only 10,000 dollars. The probability that he will be injured is .1 and the probability that he will not be injured is .9. His expected utility is

The expected utility is 0.59.

Step-by-step explanation:

Since we have given that

Probability that he will be injured = 0.1

Probability that he will not be injured = 0.9

If Billy is not injured this season, he will receive an income of 25 million dollars.

and

If he is injured, his income will be only 10,000 dollars.

According to question, the expected utility is given by

Hence, the expected utility is 0.59.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong