For a school fundraiser, Percy bought a big box of rubber ducks and wrote prize amounts, in dollars, on the bottom of each rubber duck. The prize amounts were $5, $10, $20, $50, and $100. The number of ducks with each prize amount varied so that the total value for all the ducks with each prize amount was always $500. Percy then put all the rubber ducks in his school's swimming pool. At the fundraiser, participants used a long net to catch a duck from the pool. They won the amount written on the bottom of the rubber duck, and then they threw the duck back into the pool before the next person's turn. Since the ducks were returned to the pool after they were caught, the chances of winning any particular amount remained the same.

Amir paid $15 to play the game once. If we assume he randomly selected a duck, what is the probability that Amir won more money than he paid to play the game?

Jada has a meal in a restaurant she adds up the prices listed on the menu for everything they ordered and gets a subtotal of $42.00. after tax the total is 45.99. what percentage of the subtotal is the total?

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

In a small section of a stadium there are 40 spectators watching a game between the cook islands and fiji. they all support at least one of the two teams. 25 spectators support the cook islands and 16 of these support both teams. how many support only fiji?