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3 years ago

Need help asap pls !

Mathematics

1 answer:

matrenka [14]3 years ago

8 0

Answer:

L={∅}

Step-by-step explanation:

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Which of the events below is an example of a conditional probability?

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Statement 1 is an example of conditional probability.

Events with conditional probability always follow the format:

The probability of A happening, given that B has already happened.

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3 years ago

What is the product of 45,693*532?write you answer in words

AlekseyPX

24,308,676
Twenty-four million three hundred eight thousand six hundred seventy-six

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3 years ago

Find all solutions in the interval [0, 2π). <br> 2 sin2x = sin x

tester [92]

Answer:

The solutions on the given interval are :

$0$

$\pi$

$\cos^{-1}(\frac{1}{4})$

$-\cos^{-1}(\frac{1}{4})+2\pi$

Step-by-step explanation:

We will need the double angle identity $\sin(2x)=2\sin(x)\cos(x)$ .

Let's begin:

$2\sin(2x)=\sin(x)$

Use double angle identity mentioned on left hand side:

$2\cdot 2\sin(x)\cos(x)=\sin(x)$

Simplify a little bit on left side:

$4\sin(x)\cos(x)=\sin(x)$

Subtract $\sin(x)$ on both sides:

$4\sin(x)\cos(x)-\sin(x)=0$

Factor left hand side:

$\sin(x)[4\cos(x)-1]=0$

Set both factors equal to 0 because at least of them has to be 0 in order for the equation to be true:

$\sin(x)=0 \text{ or } 4\cos(x)-1=0$

The first is easy what angles $\theta$ are $y$ -coordinates on the unit circle 0. That happens at $0$ and $\pi$ on the given range of $x$ (this $x$ is not be confused with the $x$ -coordinate).