C. 5/6
30 people with soda + 45 people with lemonade = 75/90 people
simplifies to 5/6.
The correct option is (B) yes because all the elements of set R are in set A.
<h3>
What is an element?</h3>
- In mathematics, an element (or member) of a set is any of the distinct things that belong to that set.
Given sets:
- U = {x | x is a real number}
- A = {x | x is an odd integer}
- R = {x | x = 3, 7, 11, 27}
So,
- A = 1, 3, 5, 7, 9, 11... are the elements of set A.
- R ⊂ A can be understood as R being a subset of A, i.e. all of R's elements can be found in A.
- Because all of the elements of R are odd integers and can be found in A, R ⊂ A is TRUE.
Therefore, the correct option is (B) yes because all the elements of set R are in set A.
Know more about sets here:
brainly.com/question/2166579
#SPJ4
The complete question is given below:
Consider the sets below. U = {x | x is a real number} A = {x | x is an odd integer} R = {x | x = 3, 7, 11, 27} Is R ⊂ A?
(A) yes, because all the elements of set A are in set R
(B) yes, because all the elements of set R are in set A
(C) no because each element in set A is not represented in set R
(D) no, because each element in set R is not represented in set A
Answer: 3.712 hours or more
Step-by-step explanation:
Let X be the random variable that denotes the time required to complete a product.
X is normally distributed.
Let x be the times it takes to complete a random unit in order to be in the top 10% (right tail) of the time distribution.
Then, 
![P(z>\dfrac{x-3.2}{\sigma})=0.10\ \ \ [z=\dfrac{x-\mu}{\sigma}]](https://tex.z-dn.net/?f=P%28z%3E%5Cdfrac%7Bx-3.2%7D%7B%5Csigma%7D%29%3D0.10%5C%20%5C%20%5C%20%5Bz%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5D)
As, 
[By z-table]
Then,
So, it will take 3.712 hours or more to complete a random unit in order to be in the top 10% (right tail) of the time distribution.
Answer:
P = 0.4812
Step-by-step explanation:
First, we need to use here two expressions and then do the calculations.
The first one is the conditional probability which is:
P(B|A) = P(A∩B)/P(A) (1)
The second expression to use has relation with the Bayes's theorem which is the following:
P(D|C) = P(C|D)*P(D) / P(C|D)*P(D) + P(C|d)*P(d) (2)
Now, the expression (2) is the one that we will use to calculate the probability of a selected random bicyclist who tests positive for steroids.
So, in this case, we will call C for positive and D that is using steroids and d is the opposite of d, which means do not use steroids.
Then, the probabilities are the following:
P(D) = 8% or 0.08
P(C|D) = 96% or 0.96
P(C|d) = 9% or 0.09
P(d) = 1 - 0.08 = 0.92
With these data, let's replace in expression 2
P(D|C) = 0.96 * 0.08 /0.96 * 0.08 + 0.09*0.92
P(D|C) = 0.0768 / 0.1596
P(D|C) = 0.4812 or 48.12%
