What is the prime factorization of a b c d

ator Caucasus Mountains Apartheid Nationality Physical Map Relative Location Geography Human-Environment Interaction Region Absolute Location Movement Place 1. “What is it like there?” 2. What is 0 degrees’ latitude? 3. What is 0 degrees’ longitude? 4. What is the exact position of a place on the earth? 5. “Where is it?” 6. What are parallel lines that measure north and south? 7. What is the study of the earth and the people on it? 8. What kind of map shows mountains, rivers, plains, etc.? 9. “How does the environment affect man?” 10. What are lines that measure east and west? 11. What is the position of a place in relation to another place? 12. What is the mountain range that separates Europe and Asia? 13. “An area with similar characteristics.” 14. What kind of map shows boundaries and countries? 15. What is the term used to describe segregation of Blacks and Whites in South Africa? 16. “How are people and places connected?” 17. Belonging to a particular nation by origin, birth or naturalization: For 18-20 Please CIRCLE all Answers that Apply 18. Desert: a. Rainy b. Cold c. Hot d. Humid 19. Tundra: a. Rainy b. Cold c. Hot d. Humid 20. Rain Forest: a. Rainy b. Cold c. Hot d. Humid Multiple Choice For Questions 21-31 Please Choose the Letter of the Correct Response 21. What is the longest river in N. America? a. Mississippi b. Ohio c. Missouri d. Colorado 22. What is the longest mountain range in N. America? a. Appalachian b. Rocky 23. What are the oldest mountains in N. America? a. Appalachian b. Rocky 24. What mountain range is over 4,000 miles long? a. Rocky b. Himalayan c. Appalachian d. Andes 25. Where is the world’s largest rainforest? a. Africa b. North America c. South America d. Asia 26. Who colonized most of Africa? a. North America b. Asia c. Europe d. South America 27. What is the largest desert in the world? a. Sahara b. Arabian c. Mojave d. Kalahari 28. What is the longest river in the world? a. Rhine b. Amazon c. Mississippi d. Nile 29. What is the capital city of the U.S.? a. Atlanta b. Washington, D.C. c. Detroit d. Los Angeles 30. What is the largest continent? a. North America b. Africa c. Antarctica d. Asia 31. What is Asia’s most heavily populated country? a. China b. India c. Pakistan d. Thailand Map Practice For Questions 32-40 Please Use the Map Below to Match the Locations to their Letters on the Map. For Example: 32. Rocky Mountains = B 32. Rocky Mountains 33. Appalachian Mountains 34. Georgia 35. Washington, D.C. 36. Great Lakes 37. Mississippi River 38. Gulf of Mexico 39. Atlantic Ocean 40. Pacific Ocean

2,3,4,7). If it lands tails, a fair six-sided die is thrown (with values 3,4,5,6,7,9). Regardless of which die is used, Alice eats n grains of rice, where n is the largest prime factor of the die result (for example, the largest prime factor of 9 is 3). (a) What is the conditional probability that the coin lands heads, given that Alice eats three grains of rice? (b) Suppose that the entire experiment is conducted twice on the following day (starting with a new coin toss on the second run-through). What is the conditional probability that the coin lands heads on both run-throughs, given that Alice eats a total of five grains of rice during the two run-throughs? (Do not count the two grains from part (a) in part (b); we assume two brand new experiments, each with a new coin toss. Start your solution by defining a suitable partition of the sample space. Please use an appropriate notation and/or justification in words, for each value that you give as part of your solution.) Exercise 5) Alice and Bob throw an unfair coin repeatedly, with probability 2/5 of landing heads. Alice starts with £2 and Bob starts with £3 . Each time the unfair coin lands heads, Alice gives Bob £1 . Each time the unfair coin lands tails, Bob gives Alice £1 . The game ends when one player has £5 . (a) Draw a labelled Markov chain describing the problem, and write down a transition matrix P. Write down the communication classes, and classify them as either recurrent or transient. (b) Using the transition matrix, calculate the probability that Alice loses all of her money in exactly four tosses of the unfair coin. (c) Calculate the (total) probability that Alice loses all of her money (before Bob loses all of his). (d) Calculate the expected (mean) number of tosses of the unfair coin, for the game to end.