Can you answer all of these?

PRACTICE - Cardinal Numbers and Surveys (Advanced Math Concepts) 1) Students at a university were surveyed and asked about whether they liked to study math (M), history (H), and physics (P). The Venn diagram summarizes the results ofthe survey. Use the given Venn diagram to answer the following questions. A 22 a) How many students were surveyed? b) How many of these students like math or physics? c] How many ofthese students didn't like any ofthe three subjects? d) How many ofthese students liked math and history but not physics? 2) Use the Cardinal Number Formula to answer the following. 3) Evaluate n(A F) B) ifn(A) = 19, n(B) = 13, and n(A B): 7 b) Evaluate n(A F) B) ifn[A) = 38, n(B) = 27 and n(A U B) = 51 c) Evaluate n(B) ifn(A) = 9, n(A ()8) = 3 and n(A U B) = 27 3) A survey of 132 people asking what sports they regularly watch yielded the following results: 88 watch football 20 watch football and baseball 70 watch baseball 25 watch baseball and hockey 32 watch hockey 3 like football and hockey 20 watch all three Construct a Venn diagram and indicate how many people fall in each region F, B, and H. Use the Venn diagram to answer the following questions a) How many people watch only football? b) How many people don't watch any of the sports? 4) A restaurant surveyed its breakfast patrons about their ages and their morning drink preferences. The patrons' responses are summarized in the following table. Coffee (C) Juice () Tea (T) Totals 18-25 (Y) 15 22 18 55 26-33 (M) 30 25 22 77 Over 33 (0) 45 22 24 91 Totals 90 69 64 223 Find the number of people in the following sets. a) 26-33 year old or prefer juice b) Not 18-25 and prefer juice. c) YUC d) Tho' 5) Jim Donahue was a section chief for an electric utility company. The employees in his section cut down tall trees (T), climbed poles (P), and spliced wire (W). Donahue told his manager that he had 100 employees and submitted the following report about the employees: n(7) = 45 n(POW) = 20 n(P) = 50 n(TnW) = 25 n(W) = 57 n(TOPOW) =11 n(TOP) = 28 n(T'nP'nW') = 11 After receiving the report, the manager demoted Donahue and reassigned him. Why? 6) Donahue's reassignment was to the home economics department of the electric utility company. He interviewed 140 people in a shopping center to find out some of their cooking habits. He obtained the following results. Should Donahue be reassigned again? 58 use microwave ovens 19 use microwave ovens and electric ranges 63 use electric ranges 17 use microwave ovens and gas ranges 58 use gas ranges 4 use both gas and electric ranges I uses all three 2 cook only with solar energyCardinal Number Formula Ninety people at a Superbowl party were surveyed to see what they ate while watching the game. The following data was collected: 48 had nachos 20 had both wings and potato skins Examples 1) Suppose n(A) - 220 and n(B) - 150. If n(AnB) - 75, 39 had wings 19 had both potato skins and nachos then find n(AUB) 35 had potato skins 22 had both wings and nachos 10 had nachos, wings and potato skins 2) Suppose n(A) - 35 and n(B) = 22. If n(AUB) = 40, then find n(AnB) 3) Let D denote a standard deck of cards, n(D) = 52. If R is the set of all red cards and F is the set of all face cards, how many cards are in RUF ? How many had only nachos? How many had wings and nachos but not potato skins?Dwaine Tomlinson runs a basketball program in California. On the first day of the season, 60 young men showed up and were categorized by age level and by preferred basketball position, as shown in the following table. Position Guard Forward Center Totals G F (N Junior High 9 6 4 19 0 Senior High 12 5 9 26 (S College 5 2 15 C Totals 26 19 15 60 Using the set labels in the table, find the number of players in each of the following sets. a) JOG b) NU(SOF) c) s'n(GUN) d) (SAN')U(CNG')