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prisoha [69]
2 years ago
8

When 70,000 is written as 7.0 10^{n} what is the value of n ?

Mathematics
2 answers:
Lelechka [254]2 years ago
6 0
70 000=7\cdot10^4\\ \\840000000=8,4\cdot10^8\\ \\0,004=4\cdot10^{-3}\\ \\0,000000123=1,23\cdot10^{-7}
igor_vitrenko [27]2 years ago
5 0
I believe it's n=-4? It's a negative because the decimal moves to the right 4 times to get 70,000
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Critical points occur where the gradient is zero. This is guaranteed whenever x=0 and either y=0 or y=-2.

The Hessian matrix for this function looks like

H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}-18e^y&-18xe^y\\-18xe^y&9e^y(2-x^2+4y+y^2)\end{bmatrix}

and has determinant

|H(x,y)|=-162e^{2y}(2+x^2+4y+y^2)

Maxima occur whenever the determinant is positive and f_{xx}. Minima occur whenever both the determinant and f_{xx} are positive. Saddle points occur whenever the determinant is negative.

At (0,0), you have a saddle point since the determinant reduces to -324, so (0,0,0) is the saddle point.

At (0,-2), the determinant is \dfrac{324}{e^4}>0 and f_{xx}(0,-2)=-\dfrac{18}{e^2}, so \left(0,-2,\dfrac{36}{e^2}\right) is a local maximum.

No other critical points remain, so you're done.
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What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success​ p? C
charle [14.2K]

Answer:

(D)E[ X ] =np.

Step-by-step explanation:

Given a binomial experiment with n trials and probability of success​ p,

f(x)=\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}, 0\leq  x\leq n

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Since each term of the summation is multiplied by x, the value of the term corresponding to x = 0 will be 0. Therefore the expected value becomes:

E(X)=\sum_{x=1}^{n}x\left(\begin{array}{c}n\\x\end{array}\right)p^x(1-p)^{n-x}

Now,

x\left(\begin{array}{c}n\\x\end{array}\right)= \frac{xn!}{x!(n-x)!}=\frac{n!}{(x-)!(n-x)!}=\frac{n(n-1)!}{(x-1)!((n-1)-(x-1))!}=n\left(\begin{array}{c}n-1\\x-1\end{array}\right)

Substituting,

E(X)=\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^x(1-p)^{n-x}

Factoring out the n and one p from the above expression:

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Representing k=x-1 in the above gives us:

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This can then be written by the Binomial Formula as:

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