Relations expressed as ordered pairs are?
1 answer:
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Answer:
Margin of Error = 1.96 7.75 = 15.19
Step-by-step explanation:
i) Margin of Error of a population with a standard deviation of 7.75?
ii) Let us assume a two tailed test with a 95% confidence interval
iii)
iv) therefore Margin of Error = 1.96 7.75 = 15.19
With the provided vertices and the focus point, the hyperbola will look like the one in the picture below.
notice the "c" distance from the center to the focus point.
since it's a vertical hyperbola, the positive fraction will be the one with the "y" in it, its center is clearly half-way between the vertices at -5, 5.
its major axis or traverse axis goes from -2 up to 12, so is 14 units long, therefore the "a" component is half that, or 7.
![\bf \begin{cases} h=-5\\ k=5\\ a=7\\ c=25 \end{cases}\implies \cfrac{(y-5)^2}{7^2}-\cfrac{[x-(-5)]^2}{b}=1 \\\\\\ \cfrac{(y-5)^2}{7^2}-\cfrac{(x+5)^2}{b}=1\\\\ -------------------------------\\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b\implies \sqrt{25^2-7^2}=b \\\\\\ \sqrt{625-49}=b\implies \sqrt{576}=b\implies 24=b\\\\ -------------------------------\\\\ \cfrac{(y-5)^2}{7^2}-\cfrac{(x+5)^2}{24^2}=1\implies \cfrac{(y-5)^2}{49}-\cfrac{(x+5)^2}{576}=1](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Ah%3D-5%5C%5C%0Ak%3D5%5C%5C%0Aa%3D7%5C%5C%0Ac%3D25%0A%5Cend%7Bcases%7D%5Cimplies%20%5Ccfrac%7B%28y-5%29%5E2%7D%7B7%5E2%7D-%5Ccfrac%7B%5Bx-%28-5%29%5D%5E2%7D%7Bb%7D%3D1%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B%28y-5%29%5E2%7D%7B7%5E2%7D-%5Ccfrac%7B%28x%2B5%29%5E2%7D%7Bb%7D%3D1%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0Ac%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20%5Csqrt%7Bc%5E2-a%5E2%7D%3Db%5Cimplies%20%5Csqrt%7B25%5E2-7%5E2%7D%3Db%0A%5C%5C%5C%5C%5C%5C%0A%5Csqrt%7B625-49%7D%3Db%5Cimplies%20%5Csqrt%7B576%7D%3Db%5Cimplies%2024%3Db%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%5Ccfrac%7B%28y-5%29%5E2%7D%7B7%5E2%7D-%5Ccfrac%7B%28x%2B5%29%5E2%7D%7B24%5E2%7D%3D1%5Cimplies%20%5Ccfrac%7B%28y-5%29%5E2%7D%7B49%7D-%5Ccfrac%7B%28x%2B5%29%5E2%7D%7B576%7D%3D1)
notice the "c" distance from the center to the focus point.
since it's a vertical hyperbola, the positive fraction will be the one with the "y" in it, its center is clearly half-way between the vertices at -5, 5.
its major axis or traverse axis goes from -2 up to 12, so is 14 units long, therefore the "a" component is half that, or 7.