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question:The cost of 3 pens and 5 pencils is Rs. 260. Also, the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens?
answer:Let the cost of one pen be 5x and the cost of one pencil be x. According to the given information, we can set up the following equation: 3(5x) + 5(x) = 260 Solving for x: 15x + 5x = 260 20x = 260 x = 260 / 20 x = 13 Now that we have the value of x, we can find the cost of one pen: Cost of one pen = 5x = 5 * 13 = Rs. 65 To find the cost of one dozen pens, we multiply the cost of one pen by 12: Cost of one dozen pens = 65 * 12 = Rs. 780 Therefore, the cost of one dozen pens is Rs. boxed{780} .
question:Many calculators have a reciprocal key boxed{frac{1}{x}} that replaces the current number displayed with its reciprocal. For example, if the display is boxed{00050} and the boxed{frac{1}{x}} key is depressed, then the display becomes boxed{0.02}. If boxed{00050} is currently displayed, what is the fewest number of times you must depress the boxed{frac{1}{x}} key so the display again reads boxed{00050}? A) 1 B) 2 C) 3 D) 4 E) 5
answer:1. **Define the function**: Let f(x) = frac{1}{x} represent the operation of the reciprocal key on the calculator. 2. **Apply the function**: We need to determine how many times we must apply f(x) to return to the original number. Start by applying f(x) to the number 50: [ f(50) = frac{1}{50} ] 3. **Apply the function again**: Now apply f(x) to the result from step 2: [ fleft(frac{1}{50}right) = frac{1}{frac{1}{50}} = 50 ] 4. **Conclusion**: We see that applying f(x) twice returns us to the original number 50. Therefore, the fewest number of times you must depress the frac{1{x}} key to return the display to 00050 is 2. Thus, the correct answer is 2. The final answer is boxed{B}.
question:The diagonals of a rhombus are equal, a square is a rhombus, so the diagonals of a square are equal. In the reasoning of the above syllogism: A: The major premise is wrong B: The minor premise is wrong C: The form of reasoning is wrong D: The conclusion is wrong
answer:Solution: Since a rhombus has four equal sides and its diagonals are perpendicular, but the diagonals are not necessarily equal, therefore, regarding the reasoning that the diagonals of a rhombus are equal, a square is a rhombus, so the diagonals of a square are equal, the first error is in the major premise, thus, the correct choice is: boxed{A} Based on the method of deductive reasoning, we first judge the correctness of the major premise. If it is correct, we proceed step by step; if it is wrong, there is no need to proceed further. This question examines the basic method of deductive reasoning, where the correctness of the premise directly affects the conclusion. This question is relatively simple.
question:Given the universal set U={1,2,3,4,5,6}, and M={1,3,5}, then complement_U M= （ ） A: {2,4,6} B: {1,3,5} C: {1,2,3,4,5,6} D: emptyset
answer:Since the universal set U={1,2,3,4,5,6}, and M={1,3,5}, Therefore, complement_U M={2,4,6}. Hence, the correct option is boxed{A}.