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vichka [17]
3 years ago
6

Write the equation of a horizontal ellipse with a major axis of 30, a minor axis of 14, and a center at (-9, -7

Mathematics
1 answer:
erma4kov [3.2K]3 years ago
7 0
Recall that the major axis is "a + a" or 2a, whilst the minor axis is "b + b" or 2b.

so if the major axis is 30, then a = 15, and if the minor one is 14, b = 7.

\bf \textit{ellipse, horizontal major axis}
\\\\
\cfrac{(x-{{ h}})^2}{{{ a}}^2}+\cfrac{(y-{{ k}})^2}{{{ b}}^2}=1
\qquad 
\begin{cases}
center\ ({{ h}},{{ k}})\\
vertices\ ({{ h}}\pm a, {{ k}})
\end{cases}\\\\
-------------------------------\\\\
\textit{we know that }
\begin{cases}
a=\frac{30}{2}\\
b=\frac{14}{2}\\
h=-9\\
k=-7
\end{cases}\implies \cfrac{[x-(-9)]^2}{15^2}+\cfrac{[y-(-7)]^2}{7^2}=1
\\\\\\
\cfrac{(x+9)^2}{225}+\cfrac{(y+7)^2}{49}=1
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Answer:

The statistic for this case is given t =-1.68

The degrees of freedom are given by:

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Since is a one-side lower test the p value would given by:  

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Step-by-step explanation:

Data given and notation  

\bar X represent the sample mean  

s represent the sample standard deviation  

n=20 sample size  

\mu_o =350 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is lower than 350, the system of hypothesis are :  

Null hypothesis:\mu \geq 350  

Alternative hypothesis:\mu < 350  

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

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t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

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The statistic for this case is given t =-1.68

P-value  

The degrees of freedom are given by:

df =n-1= 20-1=19

Since is a one-side lower test the p value would given by:  

p_v =P(t_{19}  

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Step-by-step explanation:


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