A college survey was taken to determine where students study. Of 144 students surveyed, studied in the ,75 studied in the library,55 studied in the union,24 studied in both the library and the student union
Of those interviewed how many did not study in either the library or the student union?
To determine the number of students who did not study in either the library or the student union, we need to subtract the number of students who studied in either the library or the student union from the total number of students surveyed.
Let's call the number of students who studied in the library A, the number of students who studied in the union B, and the number of students who studied in both the library and the union C.
We are given:
A = 75
B = 55
C = 24
To find the number of students who did not study in either the library or the student union, we use the formula:
Total students surveyed = A + B - C + neither
Total students surveyed = 144 (given)
Substituting the given values, we have:
144 = 75 + 55 - 24 + neither
Rearranging the equation, we can isolate the term for "neither":
144 = 106 + neither
Subtracting 106 from both sides, we get:
38 = neither
Therefore, the number of students who did not study in either the library or the student union is 38.
Find the intersection.
{2,5,8,11} n {3,7,10}
To find the intersection of two sets, we need to identify the elements that are present in both sets.
Let's call the first set A and the second set B.
A = {2, 5, 8, 11}
B = {3, 7, 10}
The intersection of A and B, denoted as A ∩ B, contains the common elements in both sets.
To find the intersection, we compare the elements in set A to set B and identify the common elements.
In this case, there are no common elements between the two sets. Therefore, the intersection, A ∩ B, is an empty set.
In a survey of students about favorite sports, the results include 29 who like tennis,34 who like football,12 who like tennis and football,14 who like tennis and baseball, 20 who like football and baseball,2 who like all three sports, and 6 who like none of the sports. How many students like only tennis and football? How many students like only tennis and baseball? How many students like only baseball and football?
To solve this problem, we can use a principle called the principle of inclusion and exclusion. This principle allows us to find the number of elements in each specific category.
Let's define the following variables:
T = The number of students who like tennis.
F = The number of students who like football.
B = The number of students who like baseball.
n(T) = The number of students who like only tennis.
n(F) = The number of students who like only football.
n(B) = The number of students who like only baseball.
n(TF) = The number of students who like both tennis and football.
n(TB) = The number of students who like both tennis and baseball.
n(FB) = The number of students who like both football and baseball.
n(TFB) = The number of students who like all three sports.
n(N) = The number of students who like none of the sports.
We are given the following information:
T = 29
F = 34
TB = 14
TF = 12
FB = 20
TFB = 2
n(N) = 6
To find the number of students who like only tennis and football, we need to subtract the number of students who like both tennis and football (TF) and the number of students who like all three sports (TFB) from the total number of students who like tennis (T):
n(TF) = 12
n(TFB) = 2
n(T) = T - (TF + TFB)
n(T) = 29 - (12 + 2)
n(T) = 15
Therefore, the number of students who like only tennis and football is 15.
To find the number of students who like only tennis and baseball, we need to subtract the number of students who like both tennis and baseball (TB) and the number of students who like all three sports (TFB) from the total number of students who like tennis (T):
n(TB) = 14
n(TFB) = 2
n(T) = T - (TB + TFB)
n(T) = 29 - (14 + 2)
n(T) = 13
Therefore, the number of students who like only tennis and baseball is 13.
To find the number of students who like only baseball and football, we need to subtract the number of students who like both football and baseball (FB) and the number of students who like all three sports (TFB) from the total number of students who like football (F):
n(FB) = 20
n(TFB) = 2
n(F) = F - (FB + TFB)
n(F) = 34 - (20 + 2)
n(F) = 12
Therefore, the number of students who like only baseball and football is 12.
no
I apologize for the confusion. Let me correct the previous response.
To find the number of students who like only tennis and football, we need to subtract the number of students who like both tennis and football (TF) from the number of students who like tennis (T), and similarly subtract the number of students who like both tennis and football (TF) from the number of students who like football (F):
n(TF) = 12
n(T) = T - TF
n(T) = 29 - 12
n(T) = 17
n(F) = F - TF
n(F) = 34 - 12
n(F) = 22
Therefore, the number of students who like only tennis and football is 17, and the number of students who like only tennis and baseball is 22.
To find the number of students who like only tennis and baseball, we need to subtract the number of students who like both tennis and baseball (TB) from the number of students who like tennis (T):
TB = 14
n(T) = T - TB
n(T) = 29 - 14
n(T) = 15
Therefore, the number of students who like only tennis and baseball is 15.
To find the number of students who like only baseball and football, we need to subtract the number of students who like both football and baseball (FB) from the number of students who like football (F):
FB = 20
n(F) = F - FB
n(F) = 34 - 20
n(F) = 14
Therefore, the number of students who like only baseball and football is 14.
its not 15
Apologies for the mistake. Let me correct the calculation.
To find the number of students who like only tennis and football, we need to subtract the number of students who like both tennis and football (TF) and the number of students who like all three sports (TFB) from the total number of students who like tennis (T).
We are given:
T = 29
TF = 12
TFB = 2
n(T) = T - (TF + TFB)
n(T) = 29 - (12 + 2)
n(T) = 29 - 14
n(T) = 15
Therefore, the number of students who like only tennis and football is 15.
To find the number of students who like only tennis and baseball, we need to subtract the number of students who like both tennis and baseball (TB) and the number of students who like all three sports (TFB) from the total number of students who like tennis (T).
We are given:
TB = 14
TFB = 2
n(T) = T - (TB + TFB)
n(T) = 29 - (14 + 2)
n(T) = 29 - 16
n(T) = 13
Therefore, the number of students who like only tennis and baseball is 13.
To find the number of students who like only baseball and football, we need to subtract the number of students who like both football and baseball (FB) and the number of students who like all three sports (TFB) from the total number of students who like football (F).
We are given:
F = 34
FB = 20
TFB = 2
n(F) = F - (FB + TFB)
n(F) = 34 - (20 + 2)
n(F) = 34 - 22
n(F) = 12
Therefore, the number of students who like only baseball and football is 12.
To find the number of students who did not study in either the library or the student union, we need to subtract the total number of students who studied in the library or the student union from the total number of students surveyed.
Given:
Total number of students surveyed = 144
Number of students who studied in the library = 75
Number of students who studied in the union = 55
Number of students who studied in both the library and the student union = 24
To find the number of students who did not study in either the library or the student union, we can use the principle of Inclusion-Exclusion. The formula is:
Total = A + B - A ∩ B
Where:
A = Number of students who studied in the library
B = Number of students who studied in the union
A ∩ B = Number of students who studied in both the library and the student union
Plugging in the given values into the formula, we have:
Total = 75 + 55 - 24
Total = 106
Therefore, there are 106 students who did not study in either the library or the student union out of the 144 students surveyed.