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question:a board game, the spinner is divided into four regions: A, B, C, and D. The probability of the arrow stopping on region A is 3/8, the probability of it stopping on region B is 1/4, and the probability of it stopping on region C is the same as the probability of it stopping on region D. What is the probability of the arrow stopping on region C, expressed as a common fraction?
answer:Let the probability of stopping on region C be p. Since the sum of the probabilities of stopping on each region is 1, we have the equation frac{3}{8} + frac{1}{4} + p + p = 1. Combining like terms, we get frac{3}{8} + frac{1}{4} + 2p = 1. Finding a common denominator, we have frac{6}{16} + frac{4}{16} + 2p = 1. Simplifying, we get frac{10}{16} + 2p = 1. Subtracting frac{10}{16} from both sides, we get 2p = frac{6}{16}. Dividing both sides by 2, we get p = frac{3}{16}. Therefore, the probability of the arrow stopping on region C is boxed{frac{3}{16}}. The answer is: frac{3}{16}
question:Jack, who weighs 60 pounds, wants to play on the see-saw with his cousin Anna, who weighs 40 pounds. How many 4-pound rocks does Jack need to hold to make their weights equal?
answer:The difference in weight between Jack and Anna is 60 - 40 = 20 pounds. To make their weights equal, Jack needs to add 20 pounds to his side of the see-saw. Since each rock weighs 4 pounds, Jack needs 20 / 4 = 5 rocks to make their weights equal. 5 The answer is: 5
question:The math teacher would be happy if the class average test score was at least 85. There are 10 students in the class, 5 of which scored a 92 on the test and 4 of which scored an x. The last student would have to score at least 70 to make the teacher happy. What is the value of unknown variable x? What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the score of the remaining 4 students in the class. Let's break down the information given: Number of students who scored a 92: 5 Number of students who scored an x: 4 Score needed for the last student to make the teacher happy: 70 Total number of students in the class: 10 Class average test score needed: 85 We can set up the equation as follows: (Number of students who scored a 92 * Score of students who scored a 92) + (Number of students who scored an x * Score of students who scored an x) + (Score needed for the last student * 1) = (Class average test score needed * Total number of students in the class) (5 * 92) + (4 * x) + (70 * 1) = (85 * 10) Let's simplify and solve for x: 460 + 4x + 70 = 850 To isolate x, we subtract 530 from both sides of the equation: 460 + 4x + 70 - 530 = 850 - 530 4x = 320 To solve for x, we divide both sides of the equation by 4: x = 320 / 4 x = 80 The value of x is 80. 80 The answer is: 80
question:Tim decides to run a campaign for governor. He gets the maximum 1200 donation from x people, and three times as many people donated half this sum of money to his campaign. These donations together accounted for 40% of the total money that Tim raised. How much total money did he raise? If we know the answer to the above question is 3750000, what is the value of unknown variable x?
answer:Tim gets the maximum 1200 donation from x people, so the total amount of money from these donations is 1200 * x = 1200x. Three times as many people donated half this sum of money, so the number of people who donated is 3x and the amount of money from these donations is (1200/2) * 3x = 1800x. The total amount of money raised is the sum of the money from these two types of donations: 1200x + 1800x = 3000x. We are given that these donations account for 40% of the total money raised, so we can write: 3000x = 0.4 * total money raised. Simplifying the right side, we get: 3000x = 0.4 * total money raised. Dividing both sides by 0.4, we get: 7500x = total money raised. We are given that the total money raised is 3,750,000, so we can write: 7500x = 3,750,000. Dividing both sides by 7500, we get: x = 500. The value of x is 500. 500 The answer is: 500