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3 years ago

10

Easy question

1 answer:

Leviafan [203]3 years ago

5 0

$\dfrac{\mathrm dy}{\mathrm dt}=ky\iff\dfrac{\mathrm dy}y=k\,\mathrm dt$

Integrating both sides, we get

$\ln|y|=kt+C$
$\implies y=e^{kt+C}=e^{kt}e^C=Ce^{kt}$

When $t=0$ , we have $y=10000$ , so that

$10000=Ce^{0k}\implies C=10000$

When $t=4$ , we have $y=8000$ , which means

$8000=10000e^{4k}\implies k=\dfrac14\ln\dfrac{8000}{10000}\approx-0.0558$

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Which is bigger: 3/8 or 7/20

umka21 [38]

$\rm ^{20)}\frac{3}{8}= \frac{60}{160} \\ \\ ^{8)}\frac{7}{20}= \frac{56}{160} \\ \\ So~ \frac{3}{80}~is~bigger~because~60\ \textgreater \ 56.$

4 0

3 years ago

Read 2 more answers

Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

kompoz [17]

a.

$f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}$

is a proper joint density function if, over its support, $f$ is non-negative and the integral of $f$ is 1. The first condition is easily met as long as $C\ge0$ . To meet the second condition, we require

$\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}$

b. Find the marginal joint density of $X$ and $Y$ by integrating the joint density with respect to $z$ :

$f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz$

$\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}$

Then

$\displaystyle P(X\le1.375,Y\le1.5)=\int_0^{1.5}\int_0^{1.375}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy$

$\approx\boxed{0.12886}$

c. This probability can be found by simply integrating the joint density:

$\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz$

$\approx\boxed{0.012262}$

7 0

3 years ago

A pancake recipe calls for 4 cups of flour and 3 cups of milk.Does a recipe calling for 2 cup of flour and 1.5 cups milk use the

kolbaska11 [484]

Yes, because if you divide 4 and 3 by 2, you get 2 and 1.5

5 0

3 years ago

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Let h = number of hours to bike 165 mi. Let m = number of miles biked in 7 hr. Which proportion can be used to determine the val

Drupady [299]

Answer:

$\frac{m}{h} = \frac{165}{7}$

5 0

2 years ago

Sasha invests $200 at 5% after 6 months

Umnica [9.8K]

5% of 200 is 10, after six months, so total of $60? not sure though.

8 0

3 years ago