Discrete Mathematics

Discrete Mathematics Show work where space is provided. 1. Use RPM to multiply 15 by 42 2. Write 480 as a sum of powers of 2. 4. Give the absolute and relative error when converting 3/4 to a decimal rounded to the tenths 4 3. Is 9055 divisible by 9? 5. Write as a logarithm and vice versa: a) 3 4 = 81 b) log 5 x = 6. Given A = { 2, 4, 6, 8, 10 }, B = { 1, 3, 5, 8, }, C = { 1, 2 ,6, 7, 9} , find a) AUB b ) A U (B ∩ C) 7. P ( 9, 3 ) = ? 8. C ( 12, 4 ) = ? 9. Complete the truth tables P _Q_ _P˄Q 10. Given that 900 people are surveyed, 600 watch sports, 500 watch reality shows, and 320 watch both, how many a) watch only sports? b) watch neither sports nor Reality shows? (P˄Q) 11. How many 3 letter codes are possible if the first letter must be A or B, and letters can be repeated? 12. Given the graph below, a ) Is it simple? b ) Is it connected? Yes No Yes c ) Is there an Euler path? No Yes d) Is there a Hamiltonian circuit? 13. Find the 10th term of an arithmetic sequence … difference of 4. Find the 9th term. 15. Find the sum of the first 20 terms of the sequence 5, 9, 13, … 17. A pair of dice are rolled and the faces showing up are recorded and totaled. List the event that a sum of 7 is rolled. 19. You play a game where you pick a card from a deck of cards numbered 1 – 10. Should you pick a 7, you win $20. If you pick a 1, 5, or 10, you win $10. Pick any other numbered card, and you lose $4. What do you expect to win/lose after 20 attempts? Round answer to nearest dollar. No Yes No 14. Given the geometric sequence 1, -2, 4, with first term of 5, and common 16. Two different letters are chosen from the letters A, B, C, D without regard for order. List the Sample space. 18. A card is selected from a standard deck of cards. What is the probability of selecting a king, given that a red card has been chosen? 20. Three items are chosen at random from a bag containing 5 coins, and 4 washers. What is the probability that three coins are chosen