The sample space of an event is the list of possible elements of the event.
The set elements are:
- Ac = {x : 0, 5 ≤ x ≤ 10}
- A n B = {x : 3 ≤ x ≤ 4}
- A ∪ B = {x : 0 < x ≤ 7}
- A∩Bc = {x : 1 ≤ x ≤ 2}
- A^c ∪ B = {x : 0, 3 ≤ x ≤ 10}
<h3>How to determine the intervals of the subsets</h3>
The given parameters are:
S = {x : 0 ≤ x ≤ 10}
A = {x : 0 < x < 5}
B = {x : 3 ≤ x ≤ 7}
<u>(a) Ac </u>
This represents the list of elements in the universal set not in set A.
So, we have:
Ac = {x : 0, 5 ≤ x ≤ 10}
<u>(b) A ∩ B </u>
This represents the list of common elements in sets A and set B.
So, we have:
A n B = {x : 3 ≤ x ≤ 4}
<u>(c) A ∪ B </u>
This represents the list of all elements in sets A and set B, without repetition.
So, we have:
A ∪ B = {x : 0 < x ≤ 7}
<u>d) A∩Bc </u>
Given that:
B = {x : 3 ≤ x ≤ 7}
So, we start by calculating B^c i.e. the list of elements in the universal set not in set B.
So, we have:
Bc = {x : 1, 2, 8 ≤ x ≤ 10}
A∩Bc would then represent the list of common elements in sets A and set Bc
So, we have:
A∩Bc = {x : 1 ≤ x ≤ 2}
<u>(e) A^c ∪ B</u>
In (a), we have:
Ac = {x : 0, 5 ≤ x ≤ 10}
Given that:
B = {x : 3 ≤ x ≤ 7}
A^c ∪ B would then represent the list of all elements in sets Ac and set B
So, we have:
A^c ∪ B = {x : 0, 3 ≤ x ≤ 10}
Read more about sets are:
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The question is incomplete. Here is the complete question:
Suppose your school is having a talent show to raise money for new music supplies. You estimate that 200 students and 150 adults will attend. You estimate $200 in expenses. Write an equation to find what ticket prices you should set to raise $1000.
Answer:
Step-by-step explanation:
Let 'x' be price per student ticket and 'y' be the price per adult ticket.
Given:
Number of students = 200
Number of adults = 150
Total fund to be raised = $1000
Expenses cost = $200
Now, price of ticket for 1 student = 'x'
Therefore, price of tickets of 200 students =
Price of ticket of 1 adult = 'y'.
Therefore, price of tickets of 150 adults =
Now, total fund raised will be equal to the total money obtained from selling the tickets minus the expenses estimated.
∴ Total fund raised = Total money from tickets - Expenses.
⇒
⇒
⇒
Therefore, the equation to find what ticket prices you should set to raise $1000 is given as:
If the function is h(t)=-16t^2+24, where h(t) is the height of the coconut in feet, then we can figure out the initial height (in feet) based on something called initial conditions. Initially, time is 0 seconds. Plugging that number into the equation results in:
h(0)=-16(0)^2+24 = 24 feet. Therefore, the initial height of the coconut is 24 feet
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