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I am solving the test sheet from my previous math exam and there s an exercise i can t figure out


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2.Hi! I need help in solving a mathematical pattern problem. I am a teacher, and I am chagrined to admit ...

it that I am in the weeds with these. I can solve it up to completing the table. It's finding the rule that is a pain.
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5.Hello there! I'm struggling with group solubility/solvability, Sylow subgroups, and nilpotency (university maths). I would like some assistance as soon ...

ersity maths). I would like some assistance as soon as possible (in the next few hours), so if you are unavailable, I would love it if another tutor could help. These are the questions that are similar to, but are not exactly the ones I am struggling with. Solving these would give me a better chance of solving my assignment. I don't know where to begin with these: Provide a non-solvable finite group G with solvable subgroups L, K, M such that G = LK = LM, M \neq K , and show that it fits the criteria. ///// Define G, a finite p -group, such that G isn't abelian. Let K \le G such that |G:K| = p , where K is abelian. Prove that there are either 1 or p + 1 such abelian subgroups, and if there are p + 1 , then the index of Z(G) in G is p^2 ///// Define N normal subgroup, G finite group, O the intersection of all maximal subgroups of G . Prove that G = ON and N \cap O is nilpotent. ///// Define p a prime number, G a finite group, K a Sylow p -subgroup of G . Assume M \le K and g^{-1}Mg \le K , where g \in G . Prove that g = km for some k \in N_G(K) (normaliser of K in G ) and some m \in C_G(M) (centraliser of K in G)
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6.I'm checking my answers for a practice ACT exam I did, and I am confused by this question on probability... "As ...

lity... "As part of a probability experiment, Elliott is to answer 4 multiple-choice questions. For each question, there are 3 possible answers, only 1 of which is correct. If Elliott randomly and independently answers each question, what is the probability that he will answer the 4 questions correctly?" Solving the question I keep getting 1/256. My reasoning is that each question has a 1/4 chance of being right if you guessed, so 1/4 x 1/4 x 1/4 x 1/4 = 1/256. But my answer choices are as follows, with the correct answer being E: A. 27/81 B. 12/81 C. 4/81 D. 3/81 E. 1/81 Am I missing something? Or am I just completely solving this wrong?
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7.I am studying for my Cal 1 Final and I am having trouble with solving a problem. I would ask ...

her for help but they are not available on the weekends and my final is this Monday, so I thought I'd try my luck out here. I've included a photo of the problem I am trying to solve. Thank you!
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

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