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question:According to statistics, the prices (unit: Yuan) of two types of vegetables, (A) and (B), over consecutive (n) days are (a_1), (a_2), (a_3), ..., (a_n) and (b_1), (b_2), (b_3), ..., (b_n), respectively. Let (M = {m | a_m < b_m, m = 1, 2, …, n}). If the number of elements in (M) is greater than (dfrac{3}{4}n), then it is said that the price of vegetable (A) is lower than that of vegetable (B) over these (n) days, denoted as (A ≺ B). Now, given three types of vegetables (A), (B), and (C), the correct statement is       (     ) A: If (A ≺ B) and (B ≺ C), then (A ≺ C) B: If neither (A ≺ B) nor (B ≺ C) holds, then (A ≺ C) does not hold C: (A ≺ B) and (B ≺ A) can both not hold simultaneously D: (A ≺ B) and (B ≺ A) can both hold simultaneously

answer:**Analysis** This question tests simple logical reasoning and is considered a basic question. By using a specific example, we can determine that option C is correct. **Solution** For example, if the prices of vegetable (A) over consecutive (10) days are (1), (2), (3), (4), ..., (10), and the prices of vegetable (B) over consecutive (10) days are (10), (9), ..., (1), then neither (A ≺ B) nor (B ≺ A) holds simultaneously, Therefore, the correct choice is boxed{text{C}}.

question:mer scored 400 points on the first try in a Candy crush game, 70 points fewer on the second try, and a certain multiple of the number of points she scored on the second try on the third try. The total number of points that she scored in all tries is 1390. What is the ratio of the points she scored on the third try to the points she scored on the second try?

answer:Let's break down the information given: 1. Homer scored 400 points on the first try. 2. On the second try, she scored 70 points fewer than the first try, so she scored 400 - 70 = 330 points. 3. On the third try, she scored a certain multiple of the points she scored on the second try. Let's call this multiple "m". So, the points she scored on the third try would be 330m. 4. The total number of points she scored in all tries is 1390. Now, we can set up an equation to find the value of "m": First try + Second try + Third try = Total points 400 + 330 + 330m = 1390 Now, let's solve for "m": 730 + 330m = 1390 330m = 1390 - 730 330m = 660 Now, divide both sides by 330 to find "m": m = 660 / 330 m = 2 So, the multiple "m" is 2, which means Homer scored twice as many points on the third try as she did on the second try. The ratio of the points she scored on the third try to the points she scored on the second try is therefore boxed{2:1} (since she scored twice as many points on the third try).

question:Given a sequence {a_n} that satisfies a_{n+1} = a_n a_{n1} (n in N^*, n geqslant 2), with a_1 = 2018 and a_2 = 2017. Let S_n be the sum of the first n terms of the sequence {a_n}. The value of S_{100} is ______.

answer:Since the sequence {a_n} satisfies a_{n+1} = a_n - a_{n-1}, with initial terms a_1 = 2018 and a_2 = 2017, we can proceed to find the next few terms: a_3 = a_2 - a_1 = 2017 - 2018 = -1, Continuing in this way, we find: begin{align*} a_4 &= a_3 - a_2 = -1 - 2017 = -2018, a_5 &= a_4 - a_3 = -2018 + 1 = -2017, a_6 &= a_5 - a_4 = -2017 + 2018 = 1, a_7 &= a_6 - a_5 = 1 - (-2017) = 2018, a_8 &= a_7 - a_6 = 2018 - 1 = 2017. end{align*} We notice that the sequence repeats every 6 terms, that is, a_{n+6} = a_n. Thus, the sequence is periodic with period 6. To find S_{100}, the sum of the first 100 terms, we note that since the sequence repeats every 6 terms, we will have 16 complete cycles of this repeating pattern within the first 96 terms, plus the first 4 terms as the remainder: S_{100} = (a_1 + a_2 + a_3 + a_4) + 16 times (a_5 + a_6 + a_7 + a_8 + a_9 + a_{10}). Given the sequence values we computed, and the fact that each complete cycle sums to zero (since a_5 to a_{10} cancel each other out), we have: begin{align*} S_{100} &= (2018 + 2017 - 1 - 2018) + 16 times 0 &= 2016. end{align*} Thus, the answer is boxed{2016}.

question:Javier uses 5 pounds of meat to make 10 hamburgers for his family gathering. How many pounds of meat does he need to make 40 hamburgers for a community event? textbf{(A)}hspace{.05in}15 qquad textbf{(B)}hspace{.05in}18 qquad textbf{(C)}hspace{.05in}20 qquad textbf{(D)}hspace{.05in}22 qquad textbf{(E)}hspace{.05in}25

answer:1. **Determine the amount of meat per hamburger**: Javier uses 5 pounds of meat to make 10 hamburgers. Therefore, the amount of meat required for one hamburger is calculated by dividing the total pounds of meat by the number of hamburgers: [ text{Meat per hamburger} = frac{5 text{ pounds}}{10 text{ hamburgers}} = frac{1}{2} text{ pounds per hamburger} ] 2. **Calculate the total meat needed for 40 hamburgers**: To find out how much meat is needed for 40 hamburgers, multiply the amount of meat needed for one hamburger by 40: [ text{Total meat needed} = frac{1}{2} text{ pounds per hamburger} times 40 text{ hamburgers} = 20 text{ pounds} ] 3. **Conclusion**: Javier needs 20 pounds of meat to make 40 hamburgers. The final answer is 20 pounds. The final answer is boxed{textbf{(C)} 20}

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