3 years ago

Turma:

Mathematics

1 answer:

Roman55 [17]3 years ago

3 0

E porque ya lo use y es facil

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Find the exact value of cos 120° in simplest form with a rational<br> denominator.

IRINA_888 [86]

Given:

cos 120°

To find:

The exact value of cos 120° in simplest form with a rational denominator.

Solution:

We have,

$\cos 120^\circ$

It can be written as

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$\cos 120^\circ=-\sin 30^\circ$ $[\because \cos (90^\circ-\theta)=-\sin \theta]$

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3 years ago

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 58.

Yanka [14]

Answer: 0.025

Step-by-step explanation:

Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between the interval [48.0 minutes, 58.0 minutes].

The probability density function :-

$f(x)=\dfrac{1}{58-48}=\dfrac{1}{10}$

Now, the probability that a given class period runs between 50.25 and 50.5 minutes is given by :-

$\int^{50.5}_{50.25}\ f(x)\ dx\\\\=\int^{50.5}_{50.25}\ \dfrac{1}{10}\ dx\\\\=\dfrac{1}{10}|x|^{50.5}_{50.25}\\\\=\dfrac{1}{10}\ [50.5-50.25]=\dfrac{1}{10}\times(0.25)=0.025$

Hence, the probability that a given class period runs between 50.25 and 50.5 minutes =0.025

Similarly , the probability of selecting a class that runs between 50.25 and 50.5 minutes = 0.025

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3 years ago