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How many first-stage pure-strategy Nash equilibria are present in this game?   

This game is dominance-solvable.   

Consider the following game between two players, A and B. Player A is endowed with $10 and is asked to transfer an amount between $0-$10 to player B (call this x). Whatever is transferred to player B is tripled (3x) – then player B can return any amount back between $0-$3x to player A. According to the subgame perfect equilibrium, player A will send $_____ to Player B.

Suppose 5 participants are asked to guess a discrete number from the interval 1 to 100 (inclusive). The winner is the person whose guess is closest to 5/3 times the mean of the choices of all players. The winner gets a fixed prize, and in case of a tie the prize is split amongst those who tie. In equilibrium, all players guess the winning number to be _______.

Suppose 5 participants are asked to guess a discrete number from the interval 1 to 100 (inclusive). The winner is the person whose guess is closest to the mean of the choices of all players. The winner gets a fixed prize, and in case of a tie the prize is split amongst those who tie. How many pure-strategy equilibria are present in this game?

How many Nash equilibria are present in this game?  

A 250 glass cup contains 535 grams of pure ethanol at 27.3˚C. How many grams of ice at -19.5˚C must be placed into the cup so that the final temperature of the mixture is 9.27˚C?

The greenhouse shown below is completely covered with ¼ inch glass panels having an R value of 0.91. The width W is 20.0 feet, the length L is 42.0 feet, the height of the sides H is 11.0 feet, and the sloped side of the roof S is 13.0 feet. If the outdoor temperature is 24.0 °F and we want to keep the inside of the greenhouse ata temperature of 67.0 °F, how many Watts of heating power will we need inside? You may assume that no heat flows through the floor of the greenhouse.  

The air tanks used by SCUBA divers are measured by how much air at atmospheric pressure can be squeezed into them under high pressure. If the tank is an “80.0 ft3 “ tank when filled to a pressure of 3300 PSI, what is the internal volume of the tank in LITERS? You can assume the tank stays at a temperature of 20.0 °C as it is being filled (they are usually immersed in a big tank of cold water while being filled). 

Name the PINK organelle (marked “A”) and in detail describe its function in the cell (a short paragraph).