If 40 percent of a movie ticket costs $5.00 what is 20 percent of the cost of two tickets
1 answer:
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First, lets determine 
(the number of elements in 
).
We can see that the negative even integers that are between -27 and 0 are: -24, -22, -20, -18, -16, -14, -12, -10, -8, -6, -4, and -2.
This means
.
A proper subset of is can't be itself, this means the a proper subset of can't have 13 elements.
Given that re-arranging the elements of any set doesn't yield a different set, we use combinations (binomial coefficients) to get the number of subsets in a particular set.
The number of subsets of with 1 element are given by 
(which means 13 combine 1), in the same way the number of subsets with 2 elements is given by 
and so forth until reaching the number of subsets with 12 elements.
The previous statement can be written as:
In the previous summation we also included the empty subset, which is always a proper subset of.
So is an acceptable answer, but we can simplify it.
The following statement is true (it can be easily proven):
From our previous discussion, this means that the number of subsets of any arbitrary set is equal to 
.
This means that the number of proper subsets (which is the number of subset minus the set itself, for finite subsets) is equal to
.
So, the answer is:
There are 8191 proper subsets of.
We can see that the negative even integers that are between -27 and 0 are: -24, -22, -20, -18, -16, -14, -12, -10, -8, -6, -4, and -2.
This means
A proper subset of
Given that re-arranging the elements of any set doesn't yield a different set, we use combinations (binomial coefficients) to get the number of subsets in a particular set.
The number of subsets of
The previous statement can be written as:
In the previous summation we also included the empty subset, which is always a proper subset of
So
The following statement is true (it can be easily proven):
From our previous discussion, this means that the number of subsets of any arbitrary set
This means that the number of proper subsets (which is the number of subset minus the set itself, for finite subsets) is equal to
So, the answer is:
There are 8191 proper subsets of
Answer:
The antenna should be place 0.75 inches above the vertex.
Step-by-step explanation:
We have the equation of the parabola:
(x-4)²=3(y-3)
The general equation of the parabola is:
(x-x₀)²=4p(y-y₀)
where:
(x₀,y₀) is the vertex of the parabola
p is the focus of the parabola
Hence,
The vertex of the parabola is (4,3)
The focus of the parabola is given by:
Then, we have to shift the antenna towards the focus point. The focus point would be:
(x₀,y₀+p)=(4,3+0.75)= (4,3.75)
The directrix of the parabola is:
y=y₀-p
y=3-.75=2.25
A graph of the parabola is attached, with its focus point (4.3.75) and its directrix (y = 2.25)
