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4 years ago

(997)2 + 6 x 997 + 9

Mathematics

1 answer:

Igoryamba4 years ago

5 0

Answer: 1,000,000

Step-by-step explanation:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

997 times its self

994,009+6x997+9

994,009+5,982+9

994,009+5,982= 999,991

999,991+9= 1,000,000

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Each year, Monica deposits $200 into her savings that earns simple interest at an annual rate of 3.5%. What will her balance be

AURORKA [14]

Answer:

2,100

Step-by-step explanation:

$200 * 3.5= $700

$700 * 3= $2,100

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3 years ago

In ΔSTU, the measure of ∠U=90°, TU = 6.6 feet, and US = 2.3 feet. Find the measure of ∠S to the nearest tenth of a degree.

zimovet [89]

Answer:

70.8°

Step-by-step explanation:

The sides and angles are related in a right triangle such that ...

Tan = Opposite/Adjacent

tan(S) = UT/US = 6.6/2.3

The inverse tangent function is used to find the angle from its value:

∠S = arctan(6.6/23)

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3 years ago

Read 2 more answers

Are the square root of x squared minus one?

Delvig [45]

The roots of this equation are 1 and -1. You can get this by factoring to the version below.

(x + 1)(x - 1)

7 0

3 years ago

FOUR FRIENDS SHARE 3 SHEETS OF PAPER EQUALLY.

jenyasd209 [6]

Answer:

$\frac{3}{4}$ of a sheet of paper

Step-by-step explanation:

Hi!

This isn't the easiest to explain with numbers but I'll do it with an example instead.

If you had 60 cookies and had to split it equally with you and one of your other friends, how would you do it?

You would do $\frac{60}{2}$ , right? Because you have 60 cookies and you're dividing it amongst 2 people.

It's the same idea here!

We take the number of sheets of paper, and we divide it by the number of people we have to share it with.

so we do $\frac{3}{4}$ . You don't even have to simplify in this case because this is a fraction and this is the simplest form of this fraction as well

I hope this made sense, let me know if you have any questions

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3 years ago

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If X is a r.v. such that E(X^n)=n! Find the m.g.f. of X,Mx(t). Also find the ch.f. of X,and from this deduce the distribution of

astraxan [27]

$M_X(t)=\mathbb E(e^{Xt})$
$M_X(t)=\mathbb E\left(1+Xt+\dfrac{t^2}{2!}X^2+\dfrac{t^3}{3!}X^3+\cdots\right)$
$M_X(t)=\mathbb E(1)+t\mathbb E(X)+\dfrac{t^2}{2!}\mathbb E(X^2)+\dfrac{t^3}{3!}\mathbb E(X^3)+\cdots$
$M_X(t)=1+t+t^2+t^3+\cdots$
$M_X(t)=\displaystyle\sum_{k\ge0}t^k=\frac1{1-t}$

provided that $|t|$ .

Similarly,

$\varphi_X(t)=\mathbb E(e^{iXt})$
$\varphi_X(t)=1+it+(it)^2+(it)^3+\cdots$
$\varphi_X(t)=(1-t^2+t^4-t^6+\cdots)+it(1-t^2+t^4-t^6+\cdots)$
$\varphi_X(t)=(1+it)(1-t^2+t^4-t^6+\cdots)$
$\varphi_X(t)=\dfrac{1+it}{1+t^2}=\dfrac1{1-it}$

You can find the CDF/PDF using any of the various inversion formulas. One way would be to compute

$F_X(x)=\displaystyle\frac12+\frac1{2\pi}\int_0^\infty\frac{e^{itx}\varphi_X(-t)-e^{-itx}\varphi_X(t)}{it}\,\mathrm dt$

The integral can be rewritten as

$\displaystyle\int_0^\infty\frac{2i\sin(tx)-2it\cos(tx)}{it(1+t^2)}\,\mathrm dt$

so that

$F_X(x)=\displaystyle\frac12+\frac1{2\pi}\int_0^\infty\frac{\sin(tx)-t\cos(tx)}{t(1+t^2)}\,\mathrm dt$

There are lots of ways to compute this integral. For instance, you can take the Laplace transform with respect to $x$ , which gives

$\displaystyle\mathcal L_s\left\{\int_0^\infty\frac{\sin(tx)-t\cos(tx)}{t(1+t^2)}\,\mathrm dt\right\}=\int_0^\infty\frac{1-s}{(1+t^2)(s^2+t^2)}\,\mathrm dt$
$=\displaystyle\frac{\pi(1-s)}{2s(1+s)}$

and taking the inverse transform returns

$F_X(x)=\dfrac12+\dfrac1\pi\left(\dfrac\pi2-\pi e^{-x}\right)=1-e^{-x}$

which describes an exponential distribution with parameter $\lambda=1$ .

6 0

3 years ago

(997)2 + 6 x 997 + 9​

(997)2 + 6 x 997 + 9