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# Write the number using the number word million and then round to one decimal place

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q → r) and q → (p ∨ r). Q2. Write the converse, inverse and contrapositive of the statement: “I will score marks whenever I will study”. Q3. Convert the following compound propositions into English sentences for given p: It is below freezing. q: It is snowing. (i) ¬q → ¬p (ii) ¬q ∨ (¬p ∧ q ) (iii) p ↔ ¬q (iv) p ∨ q (v) ¬q ∧ ¬p Q4. Determine whether each of the statements is true or false. (i) If 1 + 1 = 2, then 2 + 2 = 5. (ii) If 1 + 1 = 3, then 2 + 2 = 4. (iii) If 1 + 1 = 3, then dogs can fly. (iv) Monkeys can fly if and only if 1 + 1 = 3. (v) A number is prime if and only if it is divisible by 1 and itself.
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s him about the same time to assemble. He figures he has time to make at most 18 pieces of furniture by this Saturday. The materials for each bookcase cost him \$20.00 and the materials for each TV stand cost him \$40.00. He has \$600.00 to spend on materials. Andrew makes a profit of \$60.00 on each bookcase and a profit of \$100.00 for each TV stand. Find how many of each piece of furniture Andrew should make so that he maximizes his profit. Using the information in the problem, write the constraints. Let x represent number of bookcases, and y represent number of TV stands.
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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.
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etween. * A B D 3. Which shows the following numbers in order from least to greatest? * B C D 4. Which is the best name for this group of numbers? * A B D 5. Which point on the number line best represents √3? * A B C For question 6 and 7, write each number in either scientific notation or standard notation. 6. The diameter of Mercury is 4879 kilometers. * 7. The diameter of a bacterial cell called a mycoplasma is about 2 x 10-7 meter. * 8. In which group are the numbers in order from greatest to least? * B C D 9. Greg found the length of a hypotenuse of a right triangle to be √90 feet. Between which two integers does √90 lie? * A B C 10. Which is the best name for this group of numbers? * A C D 11. The water levels of five Texas lakes were measured on the same day in 2010. The table below shows the number of feet above or below normal level for each lake. Which list shows the numbers in the table from greatest to least? * B C D 12. Which numbers from this list are less than -0.94? * B C D 13. The length of a micrometer is approximately 0.00003937 inch. How would you express this in scientific notation? * A B C 14. The National Park Service manages approximately 84,000,000 acres of federal land. How would you express this number using scientific notation? * B C D 15. Seismosaurus is the longest known dinosaur. It measured 1800 inches. How far would 3000 Seismosaurus dinosaurs span if they were placed head to tail? Write your answer in scientific notation. *
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