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3 years ago

The point P(8, 6) is on the terminal side of θ. Evaluate sin θ.

1 answer:

3 0

$\bf P(\stackrel{a}{8}~,~\stackrel{b}{6})\impliedby \textit{let's find the hypotenuse}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
c=\sqrt{8^2+6^2}\implies c=\sqrt{64+36}\implies c=\sqrt{100}\implies c=10
\\\\\\
sin(\theta)=\cfrac{\stackrel{b}{opposite}}{\stackrel{c}{hypotenuse}}\implies sin(\theta )=\cfrac{6}{10}\implies sin(\theta )=\cfrac{3}{5}$

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Step-by-step explanation:

From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let $p_1$ be the probability that a bearing meets the specification.

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So, $X\geq 440.$

Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.

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Denote the probability od acceptance of a shipment by $p_2$ .