1) In a ballroom dance competition, each couple is identified by a number worn on the leader's back. At a recent competition, forty couples competed. Their numbers are listed below: 107 109 116 120 121 126 130 134 143 151 158 163 169 174 180 182 186 188 191 197 200 203 208 | 211 215 220 228 231 234| 241 | 246 253 256 262| 268 271 279 285 250 274 Dances at the competition are organized into heats, with each heat consisting of a particular group of dancers doing a particular dance. A portion of the Heat Schedule is given below, with the couples listed for twelve heats of Waltz, Foxtrot, and Quickstep: Heat 46 Waltz Heat 47 Foxtrot Heat 48 Quickstep 107 Heat 49 Waltz Heat 50 Heat 51 Foxtrot Quickstep 120 107 107 126 121 121 120 121 134 126 126 134 163 188 151 158 163 182 134 143 174 174 220 186 180 228 174 197 151 191 215 241 203 203 158 182 253 211 220 231 262 256 231 211 250 262 274 241 231 246 262 262 262 268 274 279 268 253 279 Heat 57 Heat 52 Waltz Heat 53 Foxtrot Heat 54 Heat 55 Waltz Heat 56 Quickstep Foxtrot Quickstep 109 109 109 109 109 109 143 180 188 126 134 120 191 121 116 116 134 163 126 180 174 186 158 211 191 180 220 200 200 228 200 215 231 211 211 231 231 231 253 241 231 215 250 250 253 250 228 274 256 262 268 256 231 279 262 274 285 262 246 285

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c) How many leaders competed in all three dances?


d) How many leaders competed in Foxtrot, but not Waltz?


e) How many leaders didn't compete in Quickstep or did compete in Quickstep and Waltz?


f) How many leaders competed in Waltz, Foxtrot, or Quickstep?


g) How many leaders competed in Waltz and Quickstep or competed in Foxtrot and Quickstep, but did not compete in all three?


h) How many leaders did not compete in Waltz?


i) How many leaders didn't compete in any of the three dances?


j) How many leaders competed in exactly one of the three dances?

 

b) Now, complete the simplified survey Venn diagram below, indicating only the cardinality of each region:
Waltz
Foxtrot
II.
III.
V.
IV.
VI.
VII.
VIII.
Quickstep
Using the Venn diagram with cardinality, answer the following questions:
Notice we are asking for how many leaders danced a particular dance, not their leader number, or even how many times
one leader danced a particular dance.
c) How many leaders competed in all three dances?
d) How many leaders competed in Foxtrot, but not Waltz?
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Transcribed Image Text:b) Now, complete the simplified survey Venn diagram below, indicating only the cardinality of each region: Waltz Foxtrot II. III. V. IV. VI. VII. VIII. Quickstep Using the Venn diagram with cardinality, answer the following questions: Notice we are asking for how many leaders danced a particular dance, not their leader number, or even how many times one leader danced a particular dance. c) How many leaders competed in all three dances? d) How many leaders competed in Foxtrot, but not Waltz? 10:13 PM O Type here to search 99+ 2/19/2021 25
1) In a ballroom dance competition, each couple is identified by a number worn on the leader's back. At a
recent competition, forty couples competed. Their numbers are listed below:
174
256
107
109
116
120
121
126
130
134
143
151
158
163
169
180
182
186
188
191
197
200
203
208
211
215
220
228
231
234
241
246
250
253
262
268
271
274
279
285
Dances at the competition are organized into heats, with each heat consisting of a particular group of
dancers doing a particular dance. A portion of the Heat Schedule is given below, with the couples listed for
twelve heats of Waltz, Foxtrot, and Quickstep:
Heat 46
Heat 47
Heat 48
Heat 49
Heat 50
Heat 51
Waltz
Foxtrot
Quickstep
Waltz
Foxtrot
Quickstep
107
107
107
126
121
120
121
120
121
134
126
126
134
163
188
151
163
134
174
174
220
158
182
143
186
180
228
174
197
151
191
215
241
203
203
158
211
220
256
231
211
182
250
231
262
241
231
253
262
262
274
262
246
262
268
274
279
268
253
279
Heat 54
Heat 55
Waltz
Heat 52
Heat 53
Heat 56
Heat 57
Waltz
Foxtrot
Quickstep
Foxtrot
Quickstep
109
109
109
109
109
109
121
116
143
126
116
120
134
163
180
134
126
191
180
174
188
186
158
211
191
180
220
200
200
228
200
215
231
211
211
231
231
231
241
231
215
250
250
253
253
250
228
274
256
262
268
256
231
279
262
274
285
262
246
285
a) Using the information from the Heat Schedule provided, complete the following Venn diagram by listing
the competitors' numbers as elements within the appropriate regions based on which dances the competitor
L...L..
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2:
Transcribed Image Text:1) In a ballroom dance competition, each couple is identified by a number worn on the leader's back. At a recent competition, forty couples competed. Their numbers are listed below: 174 256 107 109 116 120 121 126 130 134 143 151 158 163 169 180 182 186 188 191 197 200 203 208 211 215 220 228 231 234 241 246 250 253 262 268 271 274 279 285 Dances at the competition are organized into heats, with each heat consisting of a particular group of dancers doing a particular dance. A portion of the Heat Schedule is given below, with the couples listed for twelve heats of Waltz, Foxtrot, and Quickstep: Heat 46 Heat 47 Heat 48 Heat 49 Heat 50 Heat 51 Waltz Foxtrot Quickstep Waltz Foxtrot Quickstep 107 107 107 126 121 120 121 120 121 134 126 126 134 163 188 151 163 134 174 174 220 158 182 143 186 180 228 174 197 151 191 215 241 203 203 158 211 220 256 231 211 182 250 231 262 241 231 253 262 262 274 262 246 262 268 274 279 268 253 279 Heat 54 Heat 55 Waltz Heat 52 Heat 53 Heat 56 Heat 57 Waltz Foxtrot Quickstep Foxtrot Quickstep 109 109 109 109 109 109 121 116 143 126 116 120 134 163 180 134 126 191 180 174 188 186 158 211 191 180 220 200 200 228 200 215 231 211 211 231 231 231 241 231 215 250 250 253 253 250 228 274 256 262 268 256 231 279 262 274 285 262 246 285 a) Using the information from the Heat Schedule provided, complete the following Venn diagram by listing the competitors' numbers as elements within the appropriate regions based on which dances the competitor L...L.. 6:38 PM O Type here to search 日 99+ 2/19/2021 125 2:
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