Represent the following situation using Venn diagrams and answer the questions that follow. In a survey of 100 students in the i
1 answer:
There are 80 students studying at least one language
<h3>The Venn Diagram</h3>The given parameters are:
- Italian = 28
- German = 30
- French = 42
- Italian and French = 10
- Italian and German = 8
- German and French = 5
- Three languages = 3
Using the above parameters, we have:
German and French only = 5 - 3 = 2
Italian and French only = 10 - 3 = 7
Italian and German only = 8 - 3 = 5
French only = 42 - 7 - 2 - 3 = 30
German only = 30 - 2 - 5 - 3 = 20
Italian only = 28 - 7 - 5 - 3 = 13
See attachment for the Venn diagram
<h3>Students studying none of the languages</h3>This is calculated as:
None + At least one = Total
Using the Venn diagram, we have:
None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100
This gives
None + 80 = 100
Subtract 80 from both sides
None = 20
Hence, there are 20 students studying none of the languages
<h3>Students studying French only</h3>This is calculated as
French only = French - French and Italian - French and German + All three
So, we have:
French only = 42 - 10 - 5 + 3
Evaluate
French only = 30
Hence, there are 30 students studying French only
<h3>Students studying at least one</h3>In (b), we have:
None + At least one = Total ⇒ None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100
By comparing both equations, we have
At least one = 3 + 2 + 5 + 7 + 13 + 20 + 30
This gives
At least one = 80
Hence, there are 80 students studying at least one language
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We are provided the general forms of parabola according to its opening if:
it opens upward: (x - h)<span>² = 4a(y - k)
</span>it opens downward: (x - h)<span>² = -4a(y - k)
where "h" and "k" are the coordinates of the vertex, and "a" is the focal length from the focus to the vertex.
As you plot, the directrix y = 9 is a horizontal line, and the focus at (0,-9) is below that directrix. So, it means that the parabola opens downward (and not upward because the parabola must not touch to the directrix).</span> Next, identity the vertex (h,k). Note that the vertex is the midpoint between the focus and the point of the directrix. So the vertex is (0,0). Then, the focal length "a" is 9.
Hence, the equation is
(x - 0)<span>² = -4(9)(y - 0)
x</span><span>² = -36y</span>