Three players a, b, c play the following game. first, a picks a real number between 0 and 1 (both inclusive), then b picks a number in the same range (different from a’s choice) and finally c picks a number, also in the same range, (different from the two chosen numbers). we then pick a number in the range uniformly randomly. whoever's number is closest to this random number wins the game. assume that a, b and c all play optimally and their sole goal is to maximise their chances of winning. also assume that if one of them has several optimal choices, then that player will randomly pick one of the optimal choices.
questions:
(a) if a chooses 0, then what is the best choice for b?
(b) what is the best choice for a?
(c) what is the best choice for the first player when the game is played among four players?

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

the speed is   miles per hour > is false

step-by-step explanation:

we know that  

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

for the point

substitute the values of x and y

the linear equation is equal to

statements

case a) it takes hours to go miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct

case b) the speed is   miles per hour

the statement is false

because the speed is

case c) the unit rate for the trip is

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took minutes to go the first miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct

3

step-by-step explanation:

3