Part A: Create a sample space and find the product of each combination. What is the probability that the person wins the game. Express your answer as a fraction in lowest terms and as a percent rounded to the nearest whole number. Part B: The sponsor of the booth determines that they are giving away too many prizes. Recommend a minimum winning number that lowers the chance of winning 25%. Explain your reasoning.

Part C: Participants achieving a winning score of 70 or higher in a four consecutive attempts will receive a large stuffed animal. What is the probability of this occurring?

Part D: After Changing the game rules, patron and onlookers are disappointed when the first five games yield products of 12, 21, 32, 35, and 12. Recommend a statement that the sponsor can use to reassure customers that the game is fair.

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.

How do you write y-10=2 (x-8) in standard form

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24