Find the expected value of the winnings from a game that has the following
payout probability distribution:

Which of the following is the graph of y= square root -x-3

How do you write a paragraph proof to prove that the corresponding angles shown are congruent

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.