Answer:
Step-by-step explanation:
1) The given inequality is
![|\sqrt{n} \frac{(\bar R_n-p)}{\sqrt{p(1-p)} } |](https://tex.z-dn.net/?f=%7C%5Csqrt%7Bn%7D%20%5Cfrac%7B%28%5Cbar%20R_n-p%29%7D%7B%5Csqrt%7Bp%281-p%29%7D%20%7D%20%7C%3Cq_%7B%5Calpha%20%2F2%7D%7C%20%5C%5C%5C%5C%20%5Cto%28%5Cfrac%7B%28%5Csqrt%7Bn%7D%20%5Cbar%20R_n-p%29%7D%7B%5Csqrt%7Bp%281-p%29%7D%20%7D%29%3Cq%5E2_%7B%5Calpha%20%2F2%7D)
![\to n( \bar R _n - p)^2](https://tex.z-dn.net/?f=%5Cto%20n%28%20%5Cbar%20R%20_n%20-%20p%29%5E2%3Cp%281-p%29q%5E2_%7B%5Calpha%20%2F2%7D)
![\to n\bar R +np^2-2nR_np](https://tex.z-dn.net/?f=%5Cto%20n%5Cbar%20R%20%2Bnp%5E2-2nR_np%3Cq%5E2_%7B%5Calpha%20%2F2%20p-%20q%5E2_%7B%5Calpha%20%2F2%7Dp%5E2)
Arranging the terms with p² and p, we get
![p^2(n+q^2_{\alpha /2)-p(2n \bar R _n+q^2_{\alpha / 2})+n \bar R ^2 _n](https://tex.z-dn.net/?f=p%5E2%28n%2Bq%5E2_%7B%5Calpha%20%2F2%29-p%282n%20%5Cbar%20R%20_n%2Bq%5E2_%7B%5Calpha%20%2F%202%7D%29%2Bn%20%5Cbar%20R%20%5E2%20_n%20%3C0)
Hence, the inequality is of the form
Ap² + Bp + c < 0
2. A quadratic equation of the form
Ap² + Bp + c < 0 with A > 0 looks like
<u>Check the attached image</u>
The region where the values are negative lies between p₁ and p₂ ...
The p₁ < p < p₂
Answer:
136 degrees
Step-by-step explanation:
From the above question, we are told that:
The measure of a tangent chord angle = 68 degrees
From circle theorems, we know that:
The measure of an angle formed by a tangent and chord(Tangent-chord angles ) is equal to half the measure of the intercepted arc.
Hence,
68° = 1/2 (measure of the intercepted arc.)
Let the Measure of the intercepted arc = x
68° = 1/2x
Divide both sides by 1/2
Measure of the Intercepted arc(x) = 68° ÷ 1/2
Measure of the Intercepted arc = 68° × 2
Measure of the Intercepted are = 136°
Therefore, the measure of the intercepted arc inside the angle is 136°
All you do is add both equations up
that simple
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