Suppose 100 stastisticians attended a conference of the American Statistical Society. At the dinner, among the menu options were
a Caesar salad, roast beef, and apple pie. 35 had the Caesar salad, 28 had the roast beef, and 45 had the apple pie for dessert. Also, 15 had at least two of those three offerings, and 2 had all three. How many attendees had none of the three
1 answer:
Answer: 26 attendees had none of the three.
Step-by-step explanation:
The Venn diagram illustrating the situation is shown in the attached photo.
C represents the set of statisticians that had Caesar salad.
R represents the set of statisticians that had roast beef.
A represents the set of statisticians that had apple pie for dessert.
x represents the number that had Caesar salad and apple pie for dessert only.
y represents the number that had Caesar salad and roast beef.
z represents the number that had roast beef and apple pie for dessert only.
If 15 had at least two of those three offerings,it means that
x + y + z = 15
Therefore,
35 - (x + y + 2) + 28 - (y + z + 2) + 45 - (x + z + 2) + 2 + none = 100
35 - x - y - 2 + 28 - y - z - 2 + 45 - x - z - 2 + 2 + none = 100
35 + 28 + 45 - x - x - y - y - z - z - 2 - 2 - 2 + 2 + none = 100
108 - 2x - 2y - 2z - 4 + none = 100
108 - 4 - 2(x + y + z) + none = 100
Since x + y + z = 15, then
104 - 2(15) + none = 100
74 + none = 100
none = 100 - 74 = 26
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Given :
Nathan smiled at 50 people one day and recorded that 36 people smiled back at him.
To Find :
How many people should Nathan expect to return a smile if he smiles at 650 people over a period of time.
Solution :
Ratio of people smiled by total number of people is :
Now, it is given that we have to use the given conditions.
Therefore, ratio will be same :
Therefore, number of smiles Nathan expect to return is 468.
Answer:
x=5 feet
Step-by-step explanation:
At floor level y=0
If the expression is:
But, with the negative sign, the answer is x= 5i (where i is imaginary)