An ellipse has a vertex at (14, –1). The focus of the ellipse nearest that vertex is located at (8, –1). If the center of the el
lipse is located at (–1, –1), what is the equation of the directrix on that side of the ellipse?
x =
x =
2 answers:
Refer to the diagram shown below.
The right vertex is at (14, -1), and the center is at (-1, -1).
Therefore the semi-major axis is
a = 14 - (-1) = 15
The right focus is at (8, -1).
Therefore
c = 8 - (-1) = 9.
The distance of the directrix from the center is
d = c²/a = 9²/15 = 81/15 = 27/5.
Therefore the equation for the left directrix is
x = -1 - 27/5 = -32/5
Answer: x = -27/5
The right vertex is at (14, -1), and the center is at (-1, -1).
Therefore the semi-major axis is
a = 14 - (-1) = 15
The right focus is at (8, -1).
Therefore
c = 8 - (-1) = 9.
The distance of the directrix from the center is
d = c²/a = 9²/15 = 81/15 = 27/5.
Therefore the equation for the left directrix is
x = -1 - 27/5 = -32/5
Answer: x = -27/5
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Answer:
C. H0 : p = 0.8 H 1 : p ≠ 0.8
The test is:_____.
c. two-tailed
The test statistic is:______p ± z (base alpha by 2)
The p-value is:_____. 0.09887
Based on this we:_____.
B. Reject the null hypothesis.
Step-by-step explanation:
We formulate null and alternative hypotheses as proportion of people who own cats is significantly different than 80%.
H0 : p = 0.8 H 1 : p ≠ 0.8
The alternative hypothesis H1 is that the 80% of the proportion is different and null hypothesis is , it is same.
For a two tailed test for significance level = 0.2 we have critical value ± 1.28.
We have alpha equal to 0.2 for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28
The test statistic is
p ± z (base alpha by 2)
Where p = 0.8 , q = 1-p= 1-0.8= 0.2
n= 200
Putting the values
0.8 ± 1.28
0.8 ± 0.03620
0.8362, 0.7638
As the calculated value of z lies within the critical region we reject the null hypothesis.