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zysi [14]
2 years ago
9

Eliminate the parameter,t, in the parametric equation, x=6cos t, and y =3 sin t

Mathematics
1 answer:
german2 years ago
6 0
X = 6 cos(t) 
y = 3 sin(t)

we can rewrite these equations as:

\frac{x}{6}=cost(t) \\ \\ \frac{y}{3} =sin(t)

Taking squares of both equations we get:

( \frac{x}{6})^{2}=sin^{2} (t) \\  \\ 
( \frac{y}{3})^{2}=cos^{2}(t)

Adding both the equations, we get:

\frac{ x^{2} }{36}+ \frac{ x^{2} }{9}=sin^{2}(t)+cos^{2}(t)   \\  \\ 
 \frac{ x^{2} }{36}+ \frac{ x^{2} }{9}=1
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3 years ago
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final c
Black_prince [1.1K]

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<em>The test statistic value Z = 4.64 > 1.96 at 0.05 level of significance</em>

<em>Null hypothesis is rejected </em>

<em>Alternative hypothesis is accepted</em>

<em>Test the claim that the proportion of all children in the town who suffer not from asthma is 11%</em>

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given sample size 'n' = 167

Given data In a sample of 167 children selected randomly from one town, it is found that 37 of them suffer from asthma.

<em>Sample proportion </em>

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<em>Given Population proportion 'P'</em> = 11% = 0.11

<u><em>Step(ii) </em></u>:-

<em>Null Hypothesis : H₀ : p = 11</em>

<em>Alternative Hypothesis H₁: p≠11</em>

<u><em>Test statistic</em></u>

               Z = \frac{p^{-} -P }{\sqrt{\frac{P Q}{n} } }

              Z = \frac{0.2215 -0.11 }{\sqrt{\frac{0.11 X 0.89}{167} } }

             Z =   4.64

<u><em>step(iii)</em></u>

<em> Critical value Z = 1.96 </em>

<em>The calculated value Z = 4.64 > 1.96 at 0.05 level of significance</em>

<em>Null hypothesis is rejected </em>

<em>Alternative hypothesis is accepted</em>

<u><em>Conclusion:-</em></u>

<em>Test the claim that the proportion of all children in the town who suffer not from asthma is 11%</em>

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If a number is not a natural number then it is not a whole number
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