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3 years ago

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In a CBS News survey done in 2009, 95% of n=346 randomly sampled married men said that they would marry their spouse again if th

ey had it to do all over again. In the same survey, 85% of n=522 married women said that they would marry their spouses if they had to do it over again. a. Calculate a 95% confidence interval that estimates the difference in proportions of married women and men who would marry their spouse again if they had it to do all over again. b. On the basis of the confidence interval determined in part a, can we infer that the population proporti

1 answer:

Nitella [24]3 years ago

5 0

Answer:

456

Step-by-step explanation:

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Ms. Clint is comparing the sales of sweaters and gloves at her store for the past ten winter weeks. Select the true statement ba

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Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.

$r(t)=x(t)i+y(t)j$ is a parametrization of the most $\text{rapid increase curve}$ , then

$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$ is a tangent to the curve.

So then we have that $\frac{dr}{dt}=\lambda \triangledown C$

$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4}$

∴ $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$

Using separation of variables,

$\frac{dy}{y}=2\frac{dx}{x}$

$\int\frac{dy}{y}=2\int \frac{dx}{x}$

$\ln y=2 \ln x$

⇒ y = kx^2 for some constant k

but we know that $y(x_0)=y_0$

$\Rightarrow kx_0^2=y_0$

$\Rightarrow k =\frac{y_0}{x_0^2}$

∴ The path of the shark will follow is along the parabola

$y=\frac{y_0}{x_0^2}x^2$

$y=y_0\left(\frac{x}{x_0}\right)^2$

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2 years ago

Find the value of the variable plz help

Naddika [18.5K]

Answer:

Step-by-step explanation:

Vertically opposite angles are equal.

8y + 36 = 14y -24 Subtract 36 to both sides

8y = 14y - 24 - 36 Combine

8y = 14y - 60 Subtract 14y from both sides

8y - 14y = - 60

-6y = -60 Divide by - 6

-6y/-6 = -60/-6

y = 10

===========================

x +48 = 64 Subtract 48 from both sides

x +48 - 48 = 64-16

x = 16

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I need help on this

Marina CMI [18]

I think it's answer choice a

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