120 students were surveyed about their food preferences. 62 liked pizza,75 liked burgers and 48 liked tacos. 15 liked all three. 93 liked pizza or burgers, 96 liked burgers or tacos, and 88 liked pizza or tacos.
a) construct a venn diagram that will display the above info (just tell me whats between all the circles and in them) [i also know 15 is in the middle]
b) state the number of people that liked none of the foods.
Jacob asked 30class mates weather they like pets 18class mates have dogs 12 have cats 10 have fish 5 class mates has all three pets 6 classmates only have cats and dogs 3 only have fish and cats no one has only cats and fish sOme classmates has no pets
a) The Venn diagram representing the given information would have the following:
- In the intersection of all three circles: 15
- In the intersection of the circle representing pizza and burgers: (62 - 15) = 47
- In the intersection of the circle representing burgers and tacos: (75 - 15) = 60
- In the intersection of the circle representing pizza and tacos: (48 - 15) = 33
- Outside all three circles: The number of people who liked none of the foods
b) To find the number of people who liked none of the foods, we need to subtract the total number of people who liked at least one food from the total number of students surveyed (120):
Number of people who liked none of the foods = Total surveyed - Total who liked at least one food
Number of people who liked none of the foods = 120 - (62 + 75 + 48 - 47 - 60 - 33 + 15)
Number of people who liked none of the foods = 120 - 80
Number of people who liked none of the foods = 40
a) To construct a Venn diagram that displays the given information, we can start by drawing three overlapping circles to represent pizza, burgers, and tacos. We know that 15 students liked all three, so we can place this number in the intersection of all three circles.
Next, we need to determine the number of students who liked only one type of food. To do this, we subtract the number of students who liked all three from the total number of students who liked each pairing of foods:
- For the pairing of pizza and burgers, 93 students liked either pizza or burgers. Since 15 students liked both, we subtract 15 from 93 to find that 78 students liked only pizza or burgers. We can place this number in the area of the diagram where the pizza and burger circles overlap (excluding the intersection with tacos).
- For the pairing of burgers and tacos, 96 students liked either burgers or tacos. Since 15 liked both, we subtract 15 from 96 to find that 81 students liked only burgers or tacos. We place this number in the area where the burger and taco circles overlap (excluding the intersection with pizza).
- For the pairing of pizza and tacos, 88 students liked either pizza or tacos. Since 15 liked both, we subtract 15 from 88 to find that 73 students liked only pizza or tacos. We place this number in the area of the diagram where the pizza and taco circles overlap (excluding the intersection with burgers).
Now, we can determine the remaining numbers to place in the circles. We add up the number of students who liked only one type of food and the number who liked all three:
- For the pizza circle, we have 62 students who liked pizza only (62 - 15 = 47 students) and 73 who liked both pizza and tacos (15 students overlap). Adding these numbers gives us 47 + 73 = 120 students.
- For the burger circle, we have 75 students who liked burgers only (75 - 15 = 60 students) and 78 who liked both pizza and burgers (15 students overlap). Adding these numbers gives us 60 + 78 = 138 students.
- For the taco circle, we have 48 students who liked tacos only (48 - 15 = 33 students) and 81 who liked both tacos and burgers (15 students overlap). Adding these numbers gives us 33 + 81 = 114 students.
b) To determine the number of people who liked none of the foods, we can subtract the total number of students who liked at least one food from the total number of students surveyed. In this case:
Total number of students = 120
Number of students who liked at least one food = 120 + 138 + 114 - (15 + 78 + 73) = 120 + 138 + 114 - 166 = 206
Number of students who liked none of the foods = Total number of students - Number of students who liked at least one food = 120 - 206 = -86
Since the result is negative, it means that there is an error in the given information or calculation. The number of students who liked none of the foods cannot be negative.