Define A = {x : 0 ≤ x ≤ 1}, B = {x : 0 ≤ x ≤ 3}, and C = {x : −1 ≤ x ≤ 2}. Draw diagrams showing each of the following sets of p
oints: (a) AC ∩ B ∩C (b) AC ∪(B ∩C) (c) A ∩ B ∩CC (d) [(A ∪ B)∩CC ] C
1 answer:
Answer: (a) {0,1}; (b) {0,1, 2}; (c) {0,1}; (d) {0, 1, 2}
Step-by-step explanation: Defining the sets A,B and C:
A = {0,1}; B = {0, 1, 2, 3}; C = {-1, 0, 1, 2}
(a) A ∩ B ∩ C = {0, 1}, because it represents the intersection of the sets, the items that appears in all the three sets.
(b) A ∪ (B ∩ C) = {0, 1} ∪ {0, 1, 2} = {0, 1, 2}. In this case, it represents the union of the sets A with the intersection of sets B and C.
The (c) and (d) are a combination between union and intersection of the sets.
The Venn Diagrams are the representations of the sets and their interactions and are represented in the attachments
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Step-by-step explanation:
Jaime is at point A and wants to get across the river to Point B.
They must head upstream towards Point C.
1. Calculate the net speed across the river.
∆ABC is a right triangle, so
2. Calculate the time to cross the river
Answer:
Axis of Symmetry: -6
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Given:
The probability of drawing a red candy at random from a bag of 25 candies is .
To find:
The probability of randomly drawing a red candy from the bag after removing 5 candies from the bag.
Solution:
Let n be the number of red candies in the bag. Then, the probability of getting a red candy is:
After removing the 5 candies from the bag, the number of remaining candies is and the number of remaining red candies is
.
Now, the probability of randomly drawing a red candy from the bag is:
Therefore, the required probability is .