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oksano4ka [1.4K]
2 years ago
13

At the BlueBird Cinema you can select

Mathematics
1 answer:
lara31 [8.8K]2 years ago
6 0

Using the Fundamental Counting Theorem, there are 400 ways to see a movie, have a drink and choose a type of candy.

<h3>What is the Fundamental Counting Theorem?</h3>

It is a theorem that states that if there are n things, each with n_1, n_2, \cdots, n_n ways to be done, each thing independent of the other, the number of ways they can be done is:

N = n_1 \times n_2 \times \cdots \times n_n

Considering the number of movies, drinks and candies, the parameters are given as follows:

n_1 = 10, n_2 = 5, n_3 = 8

Hence the number of ways is given by:

N = 10 x 5 x 8 = 400.

There are 400 ways to see a movie, have a drink and choose a type of candy.

More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866

#SPJ1

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I just need some help solving this question, i’m not sure what to do
KonstantinChe [14]

From the double-angle identity,

cos2x=2*sinx*cosx

we can rewritte our given equation as:

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By factoring 2cosx on the left hand side, we have

2cosx(2sinx-1)=0

This equation has 2 solutions when

\begin{gathered} cosx=0\text{ ...\lparen A\rparen} \\ and \\ 2sinx-1=0\text{ ...\lparen B\rparen} \end{gathered}

From equation (A), we obtain

x=\frac{\pi}{2}\text{ or }\frac{3\pi}{2}

and from equation (B), we have

\begin{gathered} sinx=\frac{1}{2} \\ which\text{ gives} \\ x=\frac{\pi}{6}\text{ or }\frac{5\pi}{6} \end{gathered}

On the other hand, we can find one more solution from the original equation by substituting x=0, that is,

\begin{gathered} 2ccos(2\times0)-2cos0=0 \\ which\text{ gives} \\ 2\times1-2\times1=0 \\ so\text{ 0=0} \end{gathered}

then, x=0 is another solution. In summary, we have obtained the following solutions:

\begin{gathered} x=0 \\ x=\frac{\pi}{2}\text{or}\frac{3\pi}{2}\text{ and } \\ x=\frac{\pi}{6}\text{or}\frac{5\pi}{6} \end{gathered}

However, the intersection of the last set is empty. So the unique solution is x=0 as we can corroborate on the following picture:

Therefore, the solution set is: {0}

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Answer: THE ANSWER IS C

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THE ANSWER IS C I TOOK THE TEST

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