answer:Scarlet saved 80. She bought a pair of earrings for 23, so her savings decreased by 23. She then bought a necklace that cost x, so her savings decreased by x. The amount of savings she has left is the difference between her original savings and the amount she spent: 80 - 23 - x. We are given that the amount of savings left is 9, so we can write: 80 - 23 - x = 9. Simplifying the left side, we get: 57 - x = 9. Subtracting 57 from both sides, we get: -x = -48. Multiplying both sides by -1, we get: x = 48. The value of x is 48. 48 The answer is: 48

answer:We want to find the value of X in the given situation. We are given that the value of the quarters is X, the value of the nickels is 10.00, and the value of the pennies is 10.00. To find the probability of choosing a quarter, we need to determine the total value of all the coins in the jar and the value of the quarters. The total value of all the coins can be calculated by adding the value of the quarters, nickels, and pennies: Total value = Value of quarters + Value of nickels + Value of pennies Total value = X + 10.00 + 10.00 Total value = X + 20.00 To find the probability of choosing a quarter, we need to divide the value of the quarters by the total value of the coins: Probability = Value of quarters / Total value Probability = X / (X + 20.00) Given that the probability is 1/31, we can write: 1/31 = X / (X + 20.00) Multiplying both sides of the equation by (X + 20.00) to eliminate the fraction, we get: (X + 20.00) / 31 = X Expanding the equation, we have: 20.00 = 31X - X^2 Rearranging the equation, we get: X^2 - 31X + 20.00 = 0 This is a quadratic equation that can be solved using factoring, completing the square, or the quadratic formula. However, since we are given that the value of X is a positive number representing the value of the quarters, we can eliminate the negative solution. Therefore, the value of X is 10.00. The answer is: 10.00

answer:Jack purchased 3 books every month for a year, so he purchased a total of 3 x 12 = 36 books. Each book cost 20, so Jack spent a total of 20 x 36 = 720 on books. At the end of the year, Jack sold all the books back for 500. To find out how much money he lost, we need to subtract the amount he received from the amount he spent. So, the amount of money Jack lost is 720 - 500 = 220. 220 The answer is: 220

answer:To solve this problem, we need to determine the value of x, which represents the number of players in the tournament. We know that each game is between two players, and only the winner advances to the next round. This means that in each game, one player is eliminated. To determine the total number of games played, we need to find the number of rounds in the tournament. Each round reduces the number of players by half. Let's start by finding the number of rounds: Number of rounds = log2(x) Next, we can calculate the total number of games played: Total number of games = Number of rounds - 1 Since 255 games must be played to determine the champion, we can set up the equation as follows: 255 = log2(x) - 1 Let's simplify and solve for x: log2(x) - 1 = 255 log2(x) = 256 To isolate x, we take the exponent of both sides of the equation: 2^(log2(x)) = 2^256 x = 2^256 The value of x is 2^256. The answer is: 256