{"id":4642,"date":"2020-04-21T00:19:14","date_gmt":"2020-04-21T00:19:14","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/assignment-general-problem-solving-problem-set\/"},"modified":"2021-03-25T01:00:23","modified_gmt":"2021-03-25T01:00:23","slug":"assignment-general-problem-solving-problem-set","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/chapter\/assignment-general-problem-solving-problem-set\/","title":{"raw":"Module 1 Problems","rendered":"Module 1 Problems"},"content":{"raw":"

Exercises<\/h2>\r\n

Set 1: State the pattern and then find the next number in the sequence.<\/h3>\r\n
    \r\n \t
  1. [latex]\\left\\{17,26,35,...\\right\\}[\/latex]<\/li>\r\n \t
  2. [latex]\\left\\{-1,5,-25,125,...\\right\\}[\/latex]<\/li>\r\n \t
  3. [latex]\\left\\{-1,2,5,...\\right\\}[\/latex]<\/li>\r\n \t
  4. [latex]\\left\\{-32,-16,-8,-4,...\\right\\}[\/latex]<\/li>\r\n \t
  5. [latex]\\left\\{40,60,80,...\\right\\}[\/latex]<\/li>\r\n \t
  6. [latex]\\left\\{12,17,22,...\\right\\}[\/latex]<\/span><\/li>\r\n \t
  7. [latex]\\left\\{10,-3,0.9,-0.27,...\\right\\}[\/latex]<\/span><\/li>\r\n \t
  8. [latex]\\left\\{-15,-7,1,...\\right\\}[\/latex]<\/span><\/li>\r\n \t
  9. [latex]\\left\\{0.61,1.83,5.49,16.47,...\\right\\}[\/latex]<\/span><\/li>\r\n \t
  10. [latex]\\left\\{8.9,10.3,11.7,...\\right\\}[\/latex]<\/span><\/li>\r\n \t
  11. [latex]\\left\\{-0.52,-1.02,-1.52,...\\right\\}[\/latex]<\/li>\r\n \t
  12. [latex]\\left\\{-32,-16,-8,-4,...\\right\\}[\/latex]<\/li>\r\n \t
  13. [latex]\\left\\{14,56,224,896,...\\right\\}[\/latex]<\/li>\r\n<\/ol>\r\n

    Set 2: Solve each problem.<\/h3>\r\n
      \r\n \t
    1. How many outcomes are possible from tossing a pair of coins?<\/li>\r\n \t
    2. How many outcomes are possible from tossing a coin and rolling a 6-sided die?<\/li>\r\n \t
    3. How many two-letter strings\u2014the first letter from [latex]A[\/latex] and the second letter from [latex]B-[\/latex] can be formed from the sets [latex]A=\\left\\{b,c,d\\right\\}[\/latex] and [latex]B=\\left\\{a,e,i,o,u\\right\\}?[\/latex]<\/li>\r\n \t
    4. How many ways are there to construct a string of 3 digits if numbers can be repeated?<\/li>\r\n \t
    5. How many ways are there to construct a string of 3 digits if numbers cannot be repeated?<\/li>\r\n \t
    6. Compute [latex]P\\left(5,2\\right)[\/latex]<\/li>\r\n \t
    7. Compute [latex]P\\left(8,4\\right)[\/latex]<\/li>\r\n \t
    8. Compute [latex]P\\left(3,3\\right)[\/latex]<\/li>\r\n \t
    9. Compute [latex]C\\left(8,5\\right)[\/latex]<\/li>\r\n \t
    10. Compute [latex]C\\left(12,4\\right)[\/latex]<\/li>\r\n \t
    11. Compute [latex]C\\left(26,3\\right)[\/latex]<\/li>\r\n \t
    12. In horse racing, a \u201ctrifecta\u201d occurs when a bettor wins by selecting the first three finishers in the exact order (1st place, 2nd place, and 3rd place). How many different trifectas are possible if there are 14 horses in a race?<\/li>\r\n \t
    13. A wholesale T-shirt company offers sizes small, medium, large, and extra-large in organic or non-organic cotton and colors white, black, gray, blue, and red. How many different T-shirts are there to choose from?<\/li>\r\n \t
    14. Hector wants to place billboard advertisements throughout the county for his new business. How many ways can Hector choose 15 neighborhoods to advertise in if there are 30 neighborhoods in the county?<\/li>\r\n \t
    15. An art store has 4 brands of paint pens in 12 different colors and 3 types of ink. How many paint pens are there to choose from?<\/li>\r\n \t
    16. How many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8\u00a0freshmen and 11\u00a0juniors?<\/li>\r\n \t
    17. How many ways can a baseball coach arrange the order of 9 batters if there are 15 players on the team?<\/li>\r\n \t
    18. A conductor needs 5 cellists and 5 violinists to play at a diplomatic event. To do this, he ranks the orchestra\u2019s 10 cellists and 16 violinists in order of musical proficiency. What is the ratio of the total cellist rankings possible to the total violinist rankings possible?<\/li>\r\n \t
    19. A motorcycle shop has 10 choppers, 6 bobbers, and 5 caf\u00e9 racers\u2014different types of vintage motorcycles. How many ways can the shop choose 3 choppers, 5 bobbers, and 2 caf\u00e9 racers for a weekend showcase?<\/li>\r\n \t
    20. A skateboard shop stocks 10 types of board decks, 3 types of trucks, and 4 types of wheels. How many different skateboards can be constructed?<\/li>\r\n<\/ol>\r\n

      Set 3: Solve each problem.<\/h3>\r\n
        \r\n \t
      1. Out of 230 racers who started the marathon, 212 completed the race, 14 gave up, and 4 were disqualified. What percentage did not complete the marathon?<\/li>\r\n \t
      2. Patrick left an $8 tip on a $50 restaurant bill. What percent tip is that?<\/li>\r\n \t
      3. Ireland has a 23% VAT (value-added tax, similar to a sales tax). How much will the VAT be on a purchase of a \u20ac250 item?<\/li>\r\n \t
      4. Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax), while employers paid another 6.2%. How much will someone earning $45,000 a year pay towards social security out of their gross wages?<\/li>\r\n \t
      5. A project on Kickstarter.com was aiming to raise $15,000 for a precision coffee press. They ended up with 714 supporters, raising 557% of their goal. How much did they raise?<\/li>\r\n \t
      6. Another project on Kickstarter for an iPad stylus raised 1,253% of their goal, raising a total of $313,490 from 7,511 supporters. What was their original goal?<\/li>\r\n \t
      7. A company wants to decrease their energy use by 15%.\r\n