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## MGF 1106

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**MGF 1106**Test 1 Review and Practice Solutions**You will need to have your own calculator for the test.**• You may not share calculators or use any type of communication device in place of a calculator. • Tests may not be made up for any reason other than a mandatory school – sponsored activity for which you must miss class. • If you miss one test for any other reason, your final exam score will be substituted for that test. A second missed test is a zero. No homework bonuses are awarded on a test when the final exam is substituted or you receive a zero on a missed test.**Be sure to complete each assignment with a score of at least**80% to receive the 10 point bonus.**1) Find the next number in the sequence.**a) 7, 10, 13, 16, ?**2) Round 7.899157 to the nearest:**a) tenths: 7.9 b) thousandths: c) hundred – thousandths: 7.89916**3) John has a vending route. He’s paid $450 per week to**service the vending machines. Kent’s company pays him $1750 per month to do the same job. In a single year, who makes more money? What is the difference between the two annual salaries? Assume 12 months in a year and 52 weeks in a year. John: Kent: John makes more money. His annual salary exceeds Kent’s by $2400.**4) If you spend $9.74, in how many ways can you receive**change from a ten-dollar bill. Use a table and show all possibilities. $ 13 ways**5) Trent, Riley, Susan, Doug, and Betty competed in a race.**Betty finished 11 seconds after Doug. Betty finished 24 seconds after Riley. Susan finished 8 seconds after Riley. Doug finished 18 seconds before Trent. In which order did the runners finish the race? How many seconds difference was there between first and last place? (First is on the right) 11 B D 11 13 B D R 11 5 8 B D S R 7 11 5 8 T B D S R Order: Riley, Susan, Doug, Betty, Trent. 31 seconds between first and last.**7) Use the symbols ∈ and ∉ to make the statement true.**a) 3 _____ {3, 4, 5, 6} 3 __ ___ {3, 4, 5, 6} b) {7} ______ {} {7} __ ∉ ____ {} c) 9 ______ {} 9 __ ∉ ____ {}**9) Determine if each statement is true or false.**a) {1, 2} ⊆ {0, 1, 2, 3, 4, 5} True {1, 2} is a subset of {0, 1, 2, 3, 4, 5} b) {1, 2, 3} ⊂ {} False c) { } ⊂ {1, 2, 3} True The empty set is a proper subset of every set other than itself. d) 1 ⊈ {1, 2, 3, 4} True 1 is an element, not a subset.**10) List the subsets of{cake, pie, cookie}**No elements: { } One element: {cake}, {pie}, {cookie} Two elements: {cake, pie}, {cake, cookie}, {pie, cookie} Three elements: {cake, pie, cookie}**11) Suppose S is the set How many subsets does S have?**How many proper subsets does S have?**12) Suppose**Find A’. Find B’.**13) Suppose .**Find the following. a) b) c) d)**14) Suppose**Find the following. a) b) c)**15) Use the Venn diagram below to list the members of each**set.**16) A survey of 180 high school students was taken to**determine participation in various college activities. 43 were in a service club. 52 were in the band. 35 were on an athletic team. 13 were in a service club and the band. 14 were in the band and on an athletic team. 12 were in a service club and an athletic team. Five students participated in all three activities.**17) Negate each statement.**a) Hayley is going to see the sequel. Hayley is not going to see the sequel. b) Grant does not like apples. Grant likes apples.**18) Negate each statement.**a) All whales are mammals. Some whales are not mammals. b) No blue clouds are in the sky. Some blue clouds are in the sky. c) Some pianists are not proficient. All pianists are proficient. d) Some children like video games. No children like video games.**19) Let p, q, and r represent the following statements.**p: Jim likes oranges q: Mike likes strawberries r: Katie likes mangoes Translate each statement to symbolic form. a) Jim likes oranges and Katie does not like mangoes. p ∧ ~r b) Katie likes mangoes if and only if Mike likes strawberries. r ↔ q c) If Jim does not like oranges, then Mike likes strawberries or Katie does not like mangoes. ~p→(q ∨ ~r)**20) Let p, q, and r represent the statements in question**19. p: Jim likes oranges q: Mike likes strawberries r: Katie likes mangoes Translate each symbolic form to English. a) p ∨ q Jim likes oranges or Mike likes strawberries. b) q ∧ (~p →~r) Mike likes strawberries, and if Jim does not like oranges then Katie does not like mangoes.**MGF 1106**Extra Practice Problems**1) Find the next number in the sequence.**Each number is the sum of the two previous.**3) Rayna works as a math tutor and earns $2,495 each month.**Her sister Jeanine gives private piano lessons and charges $45 per hour. If Jeanine gave piano lessons for 57 hours last month, who made more money? How much more?**3) Rayna works as a math tutor and earns $2,495 each month.**Her sister Jeanine gives private piano lessons and charges $45 per hour. If Jeanine gave piano lessons for 57 hours last month, who made more money? How much more? Rayna: Jeanine Jeanine made more money. She earned 70 more dollars.**4) If you spend $9.68, in how many ways can you receive**change from a ten-dollar bill?Use a table and show all possibilities.**4) If you spend $9.68, in how many ways can you receive**change from a ten-dollar bill?Use a table and show all possibilities. $ 18 ways**5) Four mascots competed in a race at a baseball game. The**dancing bear finished eight seconds ahead of the chicken. The chicken finished 3 seconds behind the penguin. The ostrich finished 12 seconds ahead of the penguin. Who finished first? What was the difference between first place and last?**5) Four mascots competed in a race at a baseball game. The**dancing bear finished eight seconds ahead of the chicken. The chicken finished 3 seconds behind the penguin. The ostrich finished 12 seconds ahead of the penguin. Who finished first? What was the difference between first place and last? (First is on the right) 8 C B 3 5 C P B 3 5 7 C PB O Order: Ostrich, Bear, Penguin, Chicken 15 seconds between first and last.**7) Use the symbols ∈ and ∉ to make the statement true.**c_____ {}**7) Use the symbols ∈ and ∉ to make the statement true.**c ___ ∈ _ {}**10) List the subsets of {tea, milk, water, soda}**No elements: { } One element: {tea}, {milk}, {water}, {soda} Two elements: {tea, milk}, {tea, water}, {tea, soda}, {milk, water}, {milk, soda}, {water, soda} Three elements: {tea, milk, water}, {tea, milk, soda}, {tea, water, soda}, {milk, water, soda} Four elements: {tea, milk, water, soda}**11) How many subsets of {tea, milk, water, soda} should you**have found? Proper subsets?**11) How many subsets of {tea, milk, water, soda} should you**have found? Proper subsets?