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question:The average age of the 40 members of a computer science camp is 17 years. There are X girls, 15 boys, and 5 adults. If the average age of the girls is 15 and the average age of the boys is 16, what is the average age of the adults? If we know the answer to the above question is 28, what is the value of unknown variable X?
answer:We are given the average age of the 40 members of the computer science camp is 17 years. We are also given that there are X girls, 15 boys, and 5 adults. The average age of the girls is 15 and the average age of the boys is 16. To find the average age of the adults, we can use the concept of weighted averages. The total age of the girls is X * 15. The total age of the boys is 15 * 16. The total age of the adults is 5 * average age of adults. The total age of all the members of the camp is (40 * 17). We can set up an equation using the given information: (X * 15) + (15 * 16) + (5 * average age of adults) = (40 * 17) Simplifying, we have: 15X + 240 + 5 * average age of adults = 680 15X + 5 * average age of adults = 440 We are given that the average age of the adults is 28, so we can substitute it into the equation: 15X + 5 * 28 = 440 15X + 140 = 440 Subtracting 140 from both sides of the equation, we find: 15X = 300 Dividing both sides of the equation by 15, we get: X = 20 The value of X is 20. The answer is: 20
question:Suppose the function f has all real numbers in its domain and range and is invertible. Some values of f are given by the following table: begin{array}{c || c | c | c | c | c} x & 1 & 2 & 3 & X & 5 hline f(x) & 2 & 3 & 5 & 7 & 8 end{array}What is the value of f(f(3)) + f(f^{-1}(4)) + f^{-1}(f^{-1}(5))? If there is not enough information to answer this question, enter "NEI". If we know the answer to the above question is 14, what is the value of unknown variable X?
answer:we can find the value of f(f(3)), f(f^{-1}(4)), and f^{-1}(f^{-1}(5)). From the table, we can see that f(3) = 5. Therefore, f(f(3)) = f(5) = 8. To find f^{-1}(4), we need to find the input value x such that f(x) = 4. From the table, we can see that f(2) = 3 and f(3) = 5. Since f is invertible, the output value of 4 must be between 3 and 5. Therefore, f^{-1}(4) does not exist and we cannot determine the value of f(f^{-1}(4)). To find f^{-1}(f^{-1}(5)), we need to find the input value x such that f^{-1}(x) = 5. From the table, we can see that f^{-1}(5) = 3. Therefore, the expression f(f(3)) + f(f^{-1}(4)) + f^{-1}(f^{-1}(5)) becomes 8 + NEI + 3. Since we cannot determine the value of f(f^{-1}(4)), the sum of the expression is "NEI". The answer is: 4
question:Seven distinct points are identified on the circumference of a circle. How many different triangles can be formed if each vertex must be one of these X points? If we know the answer to the above question is 35, what is the value of unknown variable X?
answer:We want to find the value of X in the given situation. To find the number of different triangles that can be formed, we can use the combination formula. The number of different triangles that can be formed with X points is given by: Number of triangles = X choose 3 We are given that the number of triangles is 35, so we can write: 35 = X choose 3 Using the combination formula, we have: 35 = frac{X!}{3!(X-3)!} To simplify the equation, we can expand the factorials: 35 = frac{X(X-1)(X-2)}{3!} Multiplying both sides of the equation by 3! to eliminate the fraction, we get: 35 * 6 = X(X-1)(X-2) 210 = X(X-1)(X-2) Now, we need to find the value of X that satisfies this equation. We can try different values of X and solve for the equation. Starting with X = 7: 210 = 7(7-1)(7-2) 210 = 7(6)(5) 210 = 210 The equation holds true for X = 7. Therefore, the value of X is 7. The answer is: 7
question:Mara has 40 crayons and 10 percent of her crayons are pink. Luna has 50 crayons and 20 percent of them are pink. In total how many pink crayons do Mara and Luna have?
answer:Mara has 10% of 40 crayons that are pink, so she has 0.10 x 40 = 4 pink crayons. Luna has 20% of 50 crayons that are pink, so she has 0.20 x 50 = 10 pink crayons. In total, Mara and Luna have 4 + 10 = 14 pink crayons. 14 The answer is: 14