How many people must be in the group so that the probability of any two people sharing the same birthday is ~50%?

Work out the angle of elevation from the

insens350 [35]

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \:Angle \:\: of \:\: elevation= 30°$

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$\large \tt Solution \: :$

Let the angle of elevation be " x "

$\qquad \tt \rightarrow \: \cos(x) = \dfrac{9 \sqrt{3} }{18}$

$\qquad \tt \rightarrow \: \cos(x) = \dfrac{ \sqrt{3} }{2}$

$\qquad \tt \rightarrow \: x = \cos {}^{ - 1} \bigg( \cfrac{ \sqrt{3} }{2} \bigg )$

$\qquad \tt \rightarrow \: x = 30 \degree \: \: or \: \: \cfrac{ \pi}{6} \: \: rad$

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

8 0

2 years ago

Read 2 more answers

Joseph is pouring concrete for his new patio. The area of the patio is 25.2 square feet

lidiya [134]

Answer:

3.5ft

Step-by-step explanation:

A = L(W)

25.2 = 7.2(W)

3.5 = W

5 0

2 years ago

2/3 - 1/5 as a fraction

Goryan [66]

Answer:

Step-by-step explanation:

8 0

3 years ago

F(x) = x2 + 1<br> g(x) = 5-x<br> (f+g)(x) =<br> O x2 + x-4<br> x²+x+4<br> O x2-x+6<br> O x2 + x + 6

charle [14.2K]

Answer:

$\boxed{(f + g)(x) = {x}^{2} - x + 6}$

Given:

$f(x) = {x}^{2} + 1 \\ \\ g(x) = 5 - x$

To Find:

$(f + g)(x) = f(x) + g(x)$

Step-by-step explanation:

$= > f(x) + g(x) = ({x}^{2} + 1) + (5 - x) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 1 + 5 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 6 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} - x + 6$

5 0

3 years ago

What is the value of the sum of all the terms of the geometric series 300, 60, 12, …?

ruslelena [56]

<h3>Answer: 375</h3>

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Work Shown:

a = 300 = first term

r = 60/300 = 0.2 = common ratio

We multiply each term by 0.2, aka 1/5, to get the next term.

Since -1 < r < 1 is true, we can use the infinite geometric sum formula below

S = a/(1-r)

S = 300/(1-0.2)

S = 300/0.8

S = 375

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As a sort of "check", we can add up partial sums like so

300+60 = 360
300+60+12 = 360+12 = 372
300+60+12+2.4 = 372+2.4 = 374.4
300+60+12+2.4+0.48 = 374.4+0.48 = 374.88

and so on. The idea is that each time we add on a new term, we should be getting closer and closer to 375. I put "check" in quotation marks because it's probably not the rigorous of checks possible. But it may give a good idea of what's going on.

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Side note: If the common ratio r was either r < -1 or r > 1, then the terms we add on would get larger and larger. This would mean we don't approach a single finite value with the infinite sum.

3 0

3 years ago