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Mademuasel [1]
3 years ago
8

A standard number cube is rolled 180 times predict how many times a 3 or a 5 will be the result

Mathematics
1 answer:
bazaltina [42]3 years ago
6 0
A number cube generally has 6 sides. If you wanted a 3 or a 5 out of one roll, the probablitility would be 2/6. Multiply 2/6 times 180. Your answer is 60 times.
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3x(x + 6) = -10 step by step equation
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Answer:

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Step-by-step explanation:

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A rectangular table has an area of 5/6 of a square meter. The length of a table is 2/3 of a meter. What is the width of the tabl
sergejj [24]

Answer:

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Step-by-step explanation:

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svetoff [14.1K]

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Step-by-step explanation:

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Step-by-step explanation:

4 0
3 years ago
Find all solutions of the equation on the interval [0,2π]
shtirl [24]
1)

\bf 3tan(x)-\sqrt{3}=0\implies 3tan(x)=\sqrt{3}\implies \boxed{tan(x)=\cfrac{\sqrt{3}}{3}}

now, let's take a peek at your Unit Circle, as you should have one, if you don't, this is a prime time to get one, you'll need it, you can find many online, or I can post one here for you, many good ones.  Anyhow, let's take a peek at π/6.

\bf \cfrac{\pi }{6}\quad 
\begin{cases}
sine=&\frac{1}{2}\\
cosine=&\frac{\sqrt{3}}{2}
\end{cases}\qquad tan\left(  \frac{\pi }{6}\right)=\cfrac{sin\left(  \frac{\pi }{6}\right)}{cos\left(  \frac{\pi }{6}\right)}\implies \cfrac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}

\bf \cfrac{1}{2}\cdot \cfrac{2}{\sqrt{3}}\implies \cfrac{1}{\sqrt{3}}\impliedby \textit{now, let's \underline{rationalize the denominator}}
\\\\\\
\cfrac{1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies \cfrac{1\sqrt{3}}{(\sqrt{3})^2}\implies \boxed{\cfrac{\sqrt{3}}{3}}

now, the tangent function is positive, if both the numerator and denominator have the same sign, that happens in the I Quadrant, as in π/6, but is also true in the III Quadrant, since both are negative.

\bf \measuredangle x=
\begin{cases}
\frac{\pi }{6}&I~Quadrant\\\\
\frac{7\pi }{6}&III~Quadrant
\end{cases}



2)

\bf 4cos^2(x)-1=0\implies 4cos^2(x)=1\implies cos^2(x)=\cfrac{1}{4}
\\\\\\
cos(x)=\pm\sqrt{\cfrac{1}{4}}\implies  cos(x)=\pm\cfrac{\sqrt{1}}{\sqrt{4}}\implies cos(x)=\pm\cfrac{1}{2}
\\\\\\
\measuredangle x=cos^{-1}\left( \pm\frac{1}{2} \right)\implies \measuredangle x=
\begin{cases}
\frac{\pi }{3}\\\\
\frac{2\pi }{3}\\\\
\frac{4\pi }{3}\\\\
\frac{5\pi }{3}
\end{cases}
4 0
4 years ago
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