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3 years ago

Solve for x 3x - (8-x) = 47

Mathematics

2 answers:

DedPeter [7]3 years ago

5 0

Answer:

x = 55/ 4

Step-by-step explanation:

3x - (8-x) = 47

3x - 8 + x=47

3x + x= 47 + 8

4x = 55

x = 55/ 4

Hope this helps

Keep Smiling :)

DIA [1.3K]3 years ago

3 0

X=13.75 in decimal form

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PLEASE HELP 35 POINTS<br> Find the value of x in the triangle shown below.

BartSMP [9]

Answer:

B sqrt(17)

Step-by-step explanation:

Using pythagoras theorem

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3 years ago

What are the numbers that are divisible by three

faust18 [17]

The numbers divisible by 3 are multiples of 3.

6 0

2 years ago

If X and Y are independent continuous positive random

Leni [432]

a) $Z=\frac XY$ has CDF

$F_Z(z)=P(Z\le z)=P(X\le Yz)=\displaystyle\int_{\mathrm{supp}(Y)}P(X\le yz\mid Y=y)P(Y=y)\,\mathrm dy$

$F_Z(z)\displaystyle=\int_{\mathrm{supp}(Y)}P(X\le yz)P(Y=y)\,\mathrm dy$

where the last equality follows from independence of $X,Y$ . In terms of the distribution and density functions of $X,Y$ , this is

$F_Z(z)=\displaystyle\int_{\mathrm{supp}(Y)}F_X(yz)f_Y(y)\,\mathrm dy$

Then the density is obtained by differentiating with respect to $z$ ,

$f_Z(z)=\displaystyle\frac{\mathrm d}{\mathrm dz}\int_{\mathrm{supp}(Y)}F_X(yz)f_Y(y)\,\mathrm dy=\int_{\mathrm{supp}(Y)}yf_X(yz)f_Y(y)\,\mathrm dy$

b) $Z=XY$ can be computed in the same way; it has CDF

$F_Z(z)=P\left(X\le\dfrac zY\right)=\displaystyle\int_{\mathrm{supp}(Y)}P\left(X\le\frac zy\right)P(Y=y)\,\mathrm dy$

$F_Z(z)\displaystyle=\int_{\mathrm{supp}(Y)}F_X\left(\frac zy\right)f_Y(y)\,\mathrm dy$

Differentiating gives the associated PDF,

$f_Z(z)=\displaystyle\int_{\mathrm{supp}(Y)}\frac1yf_X\left(\frac zy\right)f_Y(y)\,\mathrm dy$

Assuming $X\sim\mathrm{Exp}(\lambda_x)$ and $Y\sim\mathrm{Exp}(\lambda_y)$ , we have

$f_{Z=\frac XY}(z)=\displaystyle\int_0^\infty y(\lambda_xe^{-\lambda_xyz})(\lambda_ye^{\lambda_yz})\,\mathrm dy$

$\implies f_{Z=\frac XY}(z)=\begin{cases}\frac{\lambda_x\lambda_y}{(\lambda_xz+\lambda_y)^2}&\text{for }z\ge0\\0&\text{otherwise}\end{cases}$

and

$f_{Z=XY}(z)=\displaystyle\int_0^\infty\frac1y(\lambda_xe^{-\lambda_xyz})(\lambda_ye^{\lambda_yz})\,\mathrm dy$

$\implies f_{Z=XY}(z)=\lambda_x\lambda_y\displaystyle\int_0^\infty\frac{e^{-\lambda_x\frac zy-\lambda_yy}}y\,\mathrm dy$

I wouldn't worry about evaluating this integral any further unless you know about the Bessel functions.

6 0

3 years ago

How much smaller is the sum of the first 1000 natural numbers than the sum of the first 1001 natural numbers?

aleksandr82 [10.1K]

ANSWER

1001

EXPLANATION

The sum of the first n - natural numbers is

$S_n= \frac{n}{2} (2a + d(n - 1))$

The sum of the first 1000 terms is

$S_{1000}= \frac{1000}{2} (2(1) + 1(1000 - 1))$

$S_{1000}=500 (1001)$

$S_{1000}=500500$

The sum of the first 1001 terms is

$S_{1001}= \frac{1001}{2} (2(1) + 1(1001 - 1))$

$S_{1001}= 1001 \times (501)$

$= 501501$

The difference is

$501501 - 500500= 1001$

5 0

2 years ago

Read 2 more answers

A local restaurant owner can purchase tea for $16 per pound and coffee for $8 per pound. His budget does not allow him to spend

sergiy2304 [10]

Answer:

answer is 152

Step-by-step explanation:

i mutiplied $16 and $8 and got 128 the subtracted 128 and 280 and final answer is 152

5 0

2 years ago