answer：First, I need to determine the ratio in which the two types of rice should be mixed. The given ratio is 3, which means for every 3 parts of the Rs. 16/kg rice, there is 1 part of the Rs. 24/kg rice.Next, I'll assign variables to represent the quantities of each type of rice. Let’s denote the quantity of Rs. 16/kg rice as 3x and the quantity of Rs. 24/kg rice as x, where x is a common measure of quantity.Calculating the total cost of each type of rice:- The total cost of the Rs. 16/kg rice is 3x multiplied by Rs. 16, which equals Rs. 48x.- The total cost of the Rs. 24/kg rice is x multiplied by Rs. 24, which equals Rs. 24x.Adding these together gives the total cost of the mixture:Total Cost = Rs. 48x + Rs. 24x = Rs. 72x.The total quantity of the mixture is the sum of the quantities of both types of rice:Total Quantity = 3x + x = 4x kg.Finally, to find the price of the mixture per kg (P), I'll divide the total cost by the total quantity:P = Total Cost / Total Quantity = Rs. 72x / 4x = Rs. 18/kg.

answer：Okay, so Anne has 15 Sweettarts, and she wants to give them equally to her 3 friends. I need to figure out how many Sweettarts each friend gets. Hmm, let's see. First, I should understand what the problem is asking. Anne has a total of 15 Sweettarts, and she wants to distribute them equally among her 3 friends. That means each friend should get the same number of Sweettarts. So, I need to divide the total number of Sweettarts by the number of friends to find out how many each one gets.Alright, so the total number of Sweettarts is 15, and there are 3 friends. To find out how many each friend gets, I can use division. Division is the operation that tells us how many times one number fits into another. In this case, I want to know how many times 3 fits into 15.Let me write that down: 15 divided by 3. So, 15 ÷ 3. I know that 3 times 5 is 15, so 15 divided by 3 should be 5. That means each friend gets 5 Sweettarts.Wait, let me double-check to make sure I didn't make a mistake. If each friend gets 5 Sweettarts, and there are 3 friends, then 5 times 3 equals 15. Yes, that matches the total number of Sweettarts Anne has. So, that makes sense.Is there another way to think about this? Maybe using multiplication. If I consider that each friend gets the same number of Sweettarts, and I want to find that number, I can set up an equation. Let's say each friend gets 'x' Sweettarts. Then, 3 friends would get 3 times x Sweettarts in total. So, 3x = 15.To find x, I can divide both sides of the equation by 3. So, x = 15 ÷ 3, which again gives me x = 5. That confirms my earlier answer.Another way to visualize this is by using objects. Imagine Anne has 15 candies, and she wants to distribute them equally into 3 groups. She can give one candy to each friend one by one until all candies are distributed. After giving out all 15 candies, each friend would have received 5 candies. This hands-on method also leads to the same conclusion.I could also think about it in terms of real-life scenarios. For example, if I have 15 apples and I want to share them equally among 3 people, each person would get 5 apples. It's the same principle here with Sweettarts.Just to ensure there's no confusion, let's clarify the question again. It says Anne gave equal numbers of Sweettarts to her 3 friends. It doesn't mention anything about Anne keeping any Sweettarts for herself, so we can assume she gave all 15 to her friends. If she had kept some, the calculation would be different, but since she gave them all away, the division is straightforward.Also, it's important to note that the number of Sweettarts each friend receives must be a whole number because you can't give a fraction of a Sweettart in this context. Since 15 divided by 3 is exactly 5, there's no remainder, and everything works out evenly.In summary, by dividing the total number of Sweettarts (15) by the number of friends (3), we find that each friend receives 5 Sweettarts. This is confirmed through multiple methods: basic division, setting up an equation, visualizing the distribution, and considering real-life analogies. All these approaches lead to the same answer, which reinforces its correctness.

answer：First, I need to determine the weight of the elephant in pounds. Since 1 ton equals 2000 pounds, a 3-ton elephant weighs:3 tons * 2000 pounds/ton = 6000 poundsNext, I need to find out the weight of the donkey. The donkey weighs 90% less than the elephant, which means it weighs 10% of the elephant's weight. To calculate 10% of the elephant's weight:10% of 6000 pounds = 0.10 * 6000 pounds = 600 poundsFinally, to find the combined weight of the elephant and the donkey, I add their individual weights together:6000 pounds (elephant) + 600 pounds (donkey) = 6600 poundsTherefore, the combined weight of the elephant and the donkey is 6600 pounds.

answer：Okay, so I need to find out how many moles of urea are formed when I combine 1 mole of carbon dioxide (CO₂) with 2 moles of ammonia (NH₃). Hmm, I remember that urea is produced from these two substances, but I'm not exactly sure about the chemical reaction involved. Maybe I should start by writing down the balanced chemical equation for this reaction.Alright, urea has the formula (NH₂)₂CO, right? So, I think the reaction involves CO₂ and NH₃ combining to form urea and some other product, probably water (H₂O). Let me try to write that out:CO₂ + NH₃ → (NH₂)₂CO + H₂ONow, I need to balance this equation to make sure the number of atoms of each element is the same on both sides. Let's count the atoms:On the left side:- Carbon (C): 1 (from CO₂)- Oxygen (O): 2 (from CO₂) + 1 (from H₂O) = 3- Nitrogen (N): 1 (from NH₃)- Hydrogen (H): 3 (from NH₃)On the right side:- Carbon (C): 1 (from urea)- Oxygen (O): 1 (from urea) + 1 (from H₂O) = 2- Nitrogen (N): 2 (from urea)- Hydrogen (H): 4 (from urea) + 2 (from H₂O) = 6Hmm, the numbers don't match up. I need to adjust the coefficients to balance the equation. Let's try adding a coefficient of 2 in front of NH₃:CO₂ + 2NH₃ → (NH₂)₂CO + H₂ONow, let's recount the atoms:Left side:- Carbon: 1- Oxygen: 2 (from CO₂) + 1 (from H₂O) = 3- Nitrogen: 2 (from 2 NH₃)- Hydrogen: 6 (from 2 NH₃)Right side:- Carbon: 1- Oxygen: 1 (from urea) + 1 (from H₂O) = 2- Nitrogen: 2 (from urea)- Hydrogen: 4 (from urea) + 2 (from H₂O) = 6Okay, now the nitrogen and hydrogen are balanced, but oxygen is still off. On the left, there are 3 oxygen atoms, and on the right, there are 2. I need to balance the oxygen. Maybe I can add another H₂O molecule on the right side:CO₂ + 2NH₃ → (NH₂)₂CO + 2H₂OLet's check again:Left side:- Carbon: 1- Oxygen: 2 (from CO₂) + 2 (from 2 H₂O) = 4- Nitrogen: 2- Hydrogen: 6Right side:- Carbon: 1- Oxygen: 1 (from urea) + 2 (from 2 H₂O) = 3- Nitrogen: 2- Hydrogen: 4 (from urea) + 4 (from 2 H₂O) = 8Hmm, now oxygen is still not balanced. I have 4 on the left and 3 on the right. Maybe I need to adjust the coefficients differently. Let's try increasing the coefficient of CO₂ to 2:2CO₂ + 2NH₃ → (NH₂)₂CO + 2H₂ONow, let's count:Left side:- Carbon: 2- Oxygen: 4 (from 2 CO₂) + 2 (from 2 H₂O) = 6- Nitrogen: 2- Hydrogen: 6Right side:- Carbon: 1 (from urea)- Oxygen: 1 (from urea) + 2 (from 2 H₂O) = 3- Nitrogen: 2- Hydrogen: 4 (from urea) + 4 (from 2 H₂O) = 8This doesn't seem to help. Maybe I need to try a different approach. I recall that the balanced equation for urea synthesis is:CO₂ + 2NH₃ → (NH₂)₂CO + H₂OBut earlier, when I tried that, oxygen wasn't balanced. Wait, maybe I made a mistake in counting. Let me check again:Left side:- Carbon: 1- Oxygen: 2 (from CO₂) + 1 (from H₂O) = 3- Nitrogen: 2- Hydrogen: 6Right side:- Carbon: 1- Oxygen: 1 (from urea) + 1 (from H₂O) = 2- Nitrogen: 2- Hydrogen: 4 (from urea) + 2 (from H₂O) = 6Ah, I see now. The oxygen is still off by one. Maybe there's an error in the initial reaction. Perhaps the correct balanced equation is:CO₂ + 2NH₃ → (NH₂)₂CO + H₂OBut according to this, oxygen isn't balanced. Maybe the correct balanced equation is:CO₂ + 2NH₃ → (NH₂)₂CO + H₂OAnd I just have to accept that it's not perfectly balanced, or perhaps I'm missing something. Wait, let's try to balance it properly.Let me write the unbalanced equation:CO₂ + NH₃ → (NH₂)₂CO + H₂ONow, let's balance nitrogen first. On the left, there's 1 NH₃, which has 1 N. On the right, urea has 2 N. So, I need 2 NH₃ on the left:CO₂ + 2NH₃ → (NH₂)₂CO + H₂ONow, nitrogen is balanced (2 on each side). Next, let's balance hydrogen. On the left, 2 NH₃ have 6 H. On the right, urea has 4 H and H₂O has 2 H, totaling 6 H. So, hydrogen is balanced.Now, let's balance carbon. On the left, there's 1 C from CO₂. On the right, there's 1 C from urea. So, carbon is balanced.Finally, oxygen. On the left, there's 2 O from CO₂. On the right, there's 1 O from urea and 1 O from H₂O, totaling 2 O. So, oxygen is balanced.Wait, earlier I thought oxygen wasn't balanced, but now it seems it is. Maybe I made a mistake in my initial counting. Let me double-check:Left side:- CO₂: 1 C, 2 O- 2 NH₃: 2 N, 6 HRight side:- (NH₂)₂CO: 2 N, 4 H, 1 C, 1 O- H₂O: 2 H, 1 OTotal on right:- C: 1- O: 1 (urea) + 1 (H₂O) = 2- N: 2- H: 4 (urea) + 2 (H₂O) = 6Left side:- C: 1- O: 2- N: 2- H: 6Yes, everything balances now. So, the balanced equation is:CO₂ + 2NH₃ → (NH₂)₂CO + H₂OGreat, now that I have the balanced equation, I can use stoichiometry to find out how many moles of urea are formed.From the equation, 1 mole of CO₂ reacts with 2 moles of NH₃ to produce 1 mole of urea and 1 mole of H₂O.Given that I have 1 mole of CO₂ and 2 moles of NH₃, they are in the exact stoichiometric ratio required for the reaction. This means that all the CO₂ and NH₃ will react completely without any excess.Therefore, the number of moles of urea formed should be equal to the number of moles of CO₂ used, which is 1 mole.Wait, but let me make sure I'm not missing anything. Is there any possibility of a limiting reactant here? Since the mole ratio of CO₂ to NH₃ is 1:2, and I have exactly 1 mole of CO₂ and 2 moles of NH₃, neither is in excess. So, both reactants will be fully consumed, and the reaction will proceed to completion.Hence, the number of moles of urea produced is indeed 1 mole.

answer：Okay, so I have this problem here about angles in the coordinate plane. Let me try to understand it step by step. The question is about whether the statement "the terminal side of angle α passes through the point (-1, 2)" is a sufficient and necessary condition, necessary but not sufficient, sufficient but not necessary, or neither sufficient nor necessary.First, I need to recall what a sufficient and necessary condition means. A sufficient condition means that if the condition is met, then the statement must be true. A necessary condition means that for the statement to be true, the condition must be met. If it's both, then the condition and the statement imply each other. If it's neither, then the condition doesn't necessarily lead to the statement, nor is it required for the statement to be true.So, in this case, the statement is about the terminal side passing through (-1, 2). The question is whether this is a sufficient and/or necessary condition for something. Wait, the original problem doesn't specify what the condition is for. Hmm, maybe I need to look back at the problem.Wait, the problem is in the context of angle α with Ox as its initial side. So, I think the condition is related to the tangent of α. Because in the coordinate plane, if you have a point (x, y) on the terminal side of an angle, then tan α = y/x. So, if the terminal side passes through (-1, 2), then tan α = 2/(-1) = -2.So, maybe the problem is asking about the condition for tan α = -2. Is the statement "the terminal side passes through (-1, 2)" a sufficient and necessary condition for tan α = -2?Let me think. If the terminal side passes through (-1, 2), then tan α = -2. So, that would make it a sufficient condition because it guarantees that tan α is -2. But is it necessary? That is, is tan α = -2 only if the terminal side passes through (-1, 2)? No, because tan α = -2 could also be achieved by other points on the same line. For example, if the terminal side passes through (1, -2), that would also give tan α = -2. So, the condition is not necessary because there are other points that can satisfy tan α = -2 without passing through (-1, 2).Therefore, the statement is a sufficient condition but not a necessary one. So, the answer should be C: sufficient but not necessary condition.Wait, but in the initial analysis, the assistant concluded it was B: necessary but not sufficient. That seems contradictory. Let me double-check.If the terminal side passes through (-1, 2), then tan α = -2. So, passing through (-1, 2) is sufficient for tan α = -2. But tan α = -2 doesn't necessarily mean the terminal side passes through (-1, 2); it could pass through any point on that line with slope -2. So, the condition is sufficient but not necessary. Therefore, the correct answer should be C.But the assistant's initial thought process concluded B. Maybe there was a misunderstanding. Let me see.In the initial analysis, the assistant considered that tan α = -2 could be in the second or fourth quadrant. If it's in the fourth quadrant, the terminal side wouldn't pass through (-1, 2). So, the condition is not necessary because tan α = -2 can be achieved in another quadrant without passing through (-1, 2). Therefore, the statement is sufficient but not necessary.Yes, that aligns with my conclusion. So, the correct answer should be C: sufficient but not necessary condition.Wait, but the assistant initially concluded B. Maybe there was a mistake in the initial analysis. Let me go through it again.The assistant said that if the terminal side passes through (-1, 2), then tan α = -2, which is correct. So, that's sufficiency. Then, for necessity, the assistant said that tan α = -2 can be achieved in the fourth quadrant, so the terminal side doesn't have to pass through (-1, 2). Therefore, the condition is not necessary. So, the statement is sufficient but not necessary, which is C.But the assistant's final answer was B. That seems incorrect. So, perhaps the assistant made a mistake in the final conclusion.In summary, the statement "the terminal side of angle α passes through the point (-1, 2)" is sufficient to conclude that tan α = -2, but it's not necessary because tan α = -2 can be achieved by other points as well. Therefore, the correct answer is C: sufficient but not necessary condition.

answer：Okay, so I have this problem here about a bar of soap losing volume each time it's used. Every time you use it, it decreases by 10%. I need to figure out the minimum number of times you have to use a new bar so that less than half of its volume remains. The options are from 5 to 9, so I guess I need to figure out which one is the correct answer.Let me start by understanding the problem better. If the soap loses 10% of its volume each time it's used, that means after each use, it retains 90% of its previous volume. So, if I start with a volume V, after one use, it's 0.9V. After two uses, it's 0.9 times 0.9V, which is 0.81V. After three uses, it's 0.9 times 0.81V, which is 0.729V, and so on.I need to find the smallest number of uses, let's call it n, such that the remaining volume is less than half of the original volume. So, mathematically, I need to find the smallest integer n where 0.9^n < 0.5.Hmm, okay. So, I can write this inequality as 0.9^n < 0.5. To solve for n, I think I need to use logarithms because the variable is in the exponent. Let me recall the logarithm rules. If I take the natural logarithm of both sides, I can bring down the exponent.So, taking ln on both sides: ln(0.9^n) < ln(0.5). Using the power rule for logarithms, this becomes n * ln(0.9) < ln(0.5). Now, I need to solve for n. But wait, ln(0.9) is a negative number because 0.9 is less than 1. Similarly, ln(0.5) is also negative. So, when I divide both sides by ln(0.9), which is negative, the inequality sign will flip.So, n > ln(0.5) / ln(0.9). Let me compute this value. I remember that ln(0.5) is approximately -0.6931 and ln(0.9) is approximately -0.10536. So, plugging these in: n > (-0.6931) / (-0.10536). Calculating that gives me approximately 6.578.Since n has to be an integer and it's greater than 6.578, the smallest integer n is 7. So, after 7 uses, the volume remaining will be less than half of the original volume.But wait, let me double-check this because sometimes when dealing with percentages, it's easy to make a mistake. Maybe I should calculate the remaining volume after each use step by step to ensure that 7 is indeed the correct answer.Starting with V = 1 (for simplicity), after 1 use: 0.9After 2 uses: 0.81After 3 uses: 0.729After 4 uses: 0.6561After 5 uses: 0.59049After 6 uses: 0.531441After 7 uses: 0.4782969Okay, so after 7 uses, the volume is approximately 0.4783, which is less than 0.5. So, that confirms it. 7 uses are needed.I think that makes sense. Each time, it's decreasing by 10%, so it's a geometric sequence with a common ratio of 0.9. The volume decreases exponentially, so it takes a certain number of steps to get below half.I wonder if there's another way to think about this without using logarithms. Maybe using the rule of 72 or something? But that's more for doubling times or interest rates. Maybe not directly applicable here.Alternatively, I could use trial and error, plugging in the answer choices to see which one gives a volume less than 0.5. Let's try that.Option A: 5 uses. 0.9^5 = 0.59049, which is greater than 0.5. So, not enough.Option B: 6 uses. 0.9^6 = 0.531441, still greater than 0.5.Option C: 7 uses. 0.9^7 = 0.4782969, which is less than 0.5. So, 7 is the answer.Option D: 8 uses. 0.9^8 = 0.43046721, which is also less than 0.5, but since 7 already works, we don't need to go higher.Option E: 9 uses. 0.9^9 = 0.387420489, which is also less than 0.5, but again, 7 is the minimum.So, both methods confirm that 7 is the correct answer. I think I'm confident with that.I guess another way to look at it is to realize that each time you're multiplying by 0.9, so it's a geometric decay. The half-life in this context isn't a fixed number like in radioactive decay because the decay rate is percentage-based rather than exponential with a fixed half-life. But in this case, since it's a fixed percentage decrease each time, the number of steps needed to reach half the volume can be calculated as above.I think I've thought this through thoroughly. The answer should be 7.