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question:You are an AI assistant that helps people find information. User will you give you a question. Your task is to answer as faithfully as you can. While answering think step-by-step and justify your answer. A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included in a particular student? Options: (A) 6 (B) 8 (C) 10 (D) 12 (E) 15 Hmmm, my stream of consciousness:
answer:First, let's analyze the problem step by step: 1. There are six total students, and these students can be grouped into sets of three. 2. A particular student can only be part of one group at a time. Now, we will try to find the maximum number of groups where a particular student could be included: 3. One way to group these six students into sets of three would be as follows: Group 1 (ABC) Group 2 (DEF) 4. In this example, each group contains three different students and each student is a part of only one group. 5. Since we have two groups of three and each student is part of one group, a particular student would be included in two groups out of the two possible groups. So, the answer is: (E) 12, Let's think through this step-by-step: 1. We have 6 students, and we want to form groups of 3. 2. If we're looking for groups that include a particular student, let's call them Student A, then we're really just choosing 2 more students from the remaining 5. 3. The number of ways to choose 2 students from 5 is given by the combination formula: C(n, k) = n! / k!(n-k)!, where n is the total number of items, k is the number of items to choose, and "!" denotes factorial. 4. So, the number of ways to choose 2 students from 5 is C(5, 2) = 5! / 2!(5-2)! = 120 / 2 * 6 = 10. Therefore, the answer is (C) 10.,To solve this problem, we can use the concept of combinations. First, let's find the total number of ways to form groups of three students from six students. We can use the combination formula: C(n, r) = n! / (r! * (n-r)!) where n is the total number of students (6), r is the number of students in a group (3), and ! denotes the factorial of a number. C(6, 3) = 6! / (3! * (6-3)!) C(6, 3) = 6! / (3! * 3!) C(6, 3) = 720 / (6 * 6) C(6, 3) = 720 / 36 C(6, 3) = 20 So, there are 20 different possible groups of three students. Now, let's find the number of groups that include a particular student. We can think of it as forming a group of two students from the remaining five students (since the particular student is already included). C(5, 2) = 5! / (2! * (5-2)!) C(5, 2) = 5! / (2! * 3!) C(5, 2) = 120 / (2 * 6) C(5, 2) = 120 / 12 C(5, 2) = 10 So, there are 10 groups that will include a particular student. Therefore, the answer is (C) 10.
question:You are an AI assistant that helps people find information. User will you give you a question. Your task is to answer as faithfully as you can. While answering think step-by-step and justify your answer. Give the step-by-step reasoning process and then the final answer. Alia has 2 times as many markers as Austin. Austin has one-third as many markers as Steve does. If Steve has 60 markers, how many does Alia have?
answer:Step 1: Determine the number of markers Austin has. Since Austin has one-third as many markers as Steve does, and Steve has 60 markers, we can calculate the number of markers Austin has as follows: Number of markers Austin has = Steve's markers / 3 Number of markers Austin has = 60 / 3 Number of markers Austin has = 20 Step 2: Determine the number of markers Alia has. We know that Alia has 2 times as many markers as Austin. Therefore, we can calculate the number of markers Alia has as follows: Number of markers Alia has = Number of markers Austin has * 2 Number of markers Alia has = 20 * 2 Number of markers Alia has = 40 Final Answer: Alia has 40 markers.,Step 1: Determine the number of markers Austin has. Since Austin has one-third as many markers as Steve, and Steve has 60 markers, we can calculate the number of markers Austin has by dividing Steve's marker count by 3: Austin's markers = Steve's markers / 3 Austin's markers = 60 / 3 Austin's markers = 20 Step 2: Determine the number of markers Alia has. We know that Alia has 2 times as many markers as Austin. Now that we know Austin has 20 markers, we can calculate the number of markers Alia has by multiplying Austin's marker count by 2: Alia's markers = 2 * Austin's markers Alia's markers = 2 * 20 Alia's markers = 40 Final Answer: Alia has 40 markers., Sure, I'd be happy to help with that! Let's break it down: 1. First, we know that Steve has 60 markers. 2. Then we are told that Austin has one-third as many markers as Steve does. To find out how many markers Austin has, we divide the number of markers Steve has by three: 60 / 3 = 20 markers. 3. Finally, we know that Alia has twice as many markers as Austin does. To find out how many markers Alia has, we multiply the number of markers Austin has by two: 20 * 2 = 40 markers. So, Alia has 40 markers.
question:You are an AI assistant that helps people find information. User will you give you a question. Your task is to answer as faithfully as you can. While answering think step-by-step and justify your answer. Q: A store sold a certain brand of jeans for 40. They only have few pairs of jeans left so they decided to give 10% discount on every two pairs of jeans bought by a customer at any one time. How much will a customer pay for 3 pairs of jeans? A: Two pairs of jeans cost 40 x 2 = 80. A discount of 80 x 10 / 100 = 8 will be given for this. Hence, the cost of two pairs of jeans will now be 80 - 8 = 72. Therefore, the customer will pay 72 + 40 = 112 for the three pairs of jeans. The answer is 112. Question: Betty is planning to host her friends over for a party. She buys drinks, cakes, and ice creams at a unit cost of 2, 10, and 5 respectively. How much does she spend if she buys 10 drinks, 5 cakes, and 100 ice creams? Answer: The amount she spends on buying drinks is 2 * 10 = 20. The amount she spends on buying cakes is 10 * 5 = 50. The amount she spends on buying ice creams is 5 * 100 = 500. The total amount she spends is 20 + 50 + 500 = 570. The answer is 570. QuestionJane's mother agreed to pay her .50 for every flower bulb that Jane planted. Jane planted 20 tulip bulbs and half that amount of iris bulbs. She also planted 30 daffodil bulbs and three times that amount of crocus bulbs. How much money did Jane earn? Answer20 tulip bulbs at .50 each is 20 * .50 10.00. She planted half that amount of iris' so 20 / 2 = 10 bulbs. 10 iris bulbs at .50 each is 10 * .50 = 5.00. 30 daffodil bulbs at .50 each is 30 * .50 = 15.00. She planted three times that amount of crocus bulbs to 30 * 3 = 90 bulbs. 90 crocus bulbs at .50 = 45.00. All total, she earned 10 + 5 + 15 + 45 = 75.00. The answer is 75. Q: Mr. Salazar had seven dozen oranges. He reserved 1/4 of it for his friend and was able to sell 3/7 of the remaining yesterday. Today, he saw four rotten oranges. How many oranges are left to be sold today? A: Mr. Salazar had 7 x 12 = 84 oranges. He reserved 84 x 1 / 4 = 21 oranges for his friend. Ha had 84 - 21 = 63 oranges to be sold yesterday. But only 63 x 3 / 7 = 27 oranges were sold yesterday. So, he had 63 - 27 = 36 oranges left. Since four oranges are rotten, then only 36 - 4 = 32 oranges are left to be sold today. The answer is 32. Question: One set of barrettes costs 3 each, and one comb costs 1 each. Kristine buys one set of barrettes and one comb. Crystal buys three sets of barrettes and one comb. How much do the two girls spend altogether? Answer: Kristine spends 3 + 1 = 4. Three sets of barrettes cost 3 x 3 = 9. Crystal spends 9 + 1 = 10. Therefore, the two girls spend 4 + 10 = 14. The answer is 14. Q: Ben starts each day with 50, spends 15 every day and saves the rest. After a few days, his mom doubled his total savings and his dad gave him an additional 10. If he now has 500, How many days have elapsed? A:
answer:Let's first find out how much Ben saves each day: 50 - 15 = 35. Let x be the number of days that have elapsed. In x days, Ben would have saved 35x. His mom doubled his savings, so he would now have 2 * 35x. His dad gave him an additional 10, so his total savings would be 2 * 35x + 10. We are given that his total savings are now 500, so we can set up the equation: 2 * 35x + 10 = 500. Now, let's solve for x: 2 * 35x = 490 (subtract 10 from both sides). 70x = 490 (simplify by multiplying 2 and 35). x = 7 (divide both sides by 70). So, 7 days have elapsed. The answer is 7.,Ben saves 50 - 15 = 35 each day. His mom doubled his savings, so after his mom's contribution, he has an extra 35 * 2 = 70. The total savings before his dad's contribution is 500 - 70 = 430. After his dad gave him 10, the total savings before the add turned out to be 430 - 10 = 420. Before his dad's contribution, Ben had saved 35 per day for a total of 420. Therefore, he had saved this amount for 420 / 35 = 12 days. The answer is 12., Let's denote the number of days that have elapsed as "d". The amount of money Ben saves each day is 50 - 15 = 35. Over the course of "d" days, Ben has then saved 35 * d. His mom then doubled this amount, so Ben had 35 * d * 2 in savings. His dad then gave him an additional 10, making Ben's total savings 35 * d * 2 + 10. We are given that Ben now has 500, so we can set up the following equation: 35 * d * 2 + 10 = 500. Solving this equation for "d", we get: 35 * d = 490 / 2 = 245. So, d = 245 / 35 = 7 days. Therefore, the number of days that have elapsed is 7. The answer is 7.
question:You are an AI assistant that helps people find information. User will you give you a question. Your task is to answer as faithfully as you can. While answering think step-by-step and justify your answer. Question and Answer: Which of the following sentences is nonsensical? Options: - Sentence A: "we put the mountain in kennels when we go away" - Sentence B: "we put the dog in kennels when we go away" Sentence A Some idea for the solution: A mountain cannot be put into a kennel. Question and Answer: Which of these sentences doesn't make sense? Options: - Sentence A: "The refrigerator does not work without water." - Sentence B: "The refrigerator does not work without electricity." Sentence A Some idea for the solution: Refrigerators do not need to be given water but only plugged in. Question and Answer: Which of the following two sentences does not make sense? Options: - Sentence A: "Tin plays football with his feet." - Sentence B: "Tin plays football with his hand." Sentence B Some idea for the solution: Rule of football is not to play by hand. Question and Answer: Which of the following two sentences does not make sense? Options: - Sentence A: "he went to lawyer to file a legal case" - Sentence B: "he went to doctor to file a legal case" Sentence B Some idea for the solution:
answer:One should not go to a doctor to file a legal case, as doctors are medical professionals who typically do not handle legal matters. People go to doctors for medical advice or treatment, and they go to lawyers or legal offices to file legal cases.,Only a lawyer can file a legal case, so visiting a doctor for this purpose does not make sense.,Legal cases are handled by lawyers, not doctors.