Answer:
1. b ∈ B 2. ∀ a ∈ N; 2a ∈ Z 3. N ⊂ Z ⊂ Q ⊂ R 4. J ≤ J⁻¹ : J ∈ Z⁻
Step-by-step explanation:
1. Let b be the number and B be the set, so mathematically, it is written as
b ∈ B.
2. Let a be an element of natural number N and 2a be an even number. Since 2a is in the set of integers Z, we write
∀ a ∈ N; 2a ∈ Z
3. Let N represent the set of natural numbers, Z represent the set of integers, Q represent the set of rational numbers, and R represent the set of rational numbers.
Since each set is a subset of the latter set, we write
N ⊂ Z ⊂ Q ⊂ R .
4. Let J be the negative integer which is an element if negative integers. Let the set of negative integers be represented by Z⁻. Since J is less than or equal to its inverse, we write
J ≤ J⁻¹ : J ∈ Z⁻
Let x = # of tickets sold in advance
Let y = # of tickets sold the day of
Cost of the tickets & total sales: 6x & 10y = 6828
You also know y = x + 206
Take the equation mentioned above y = x + 206 and sub it in anywhere the variable y is in the other equations so you'll have this:
6x + 10(x+206) = 6828
Now solve for x to get x = 298
To finish the problem, you must now find the number of y tickets sold.
Sub your x value that you found back into the equation y = x + 206 and you'll get y = 504.
So, 298 tickets were sold in advance and 504 tickets were sold the day of
2500 * 0.9 = 2250
2250 * 0.9 = 2025 current stock
