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Drupady [299]
3 years ago
9

What is the expected number of female children in a family with three children?

Mathematics
2 answers:
Basile [38]3 years ago
4 0

Answer:

Option B is the correct answer.

Step-by-step explanation:

Expected value of female children= Probability of female children x Total number of children.

A child can be male or female, so there are 2 combinations, favorable outcome is female.

Probability of female children =\frac{1}{2}

Expected value of female children =\frac{1}{2}\times 3=1.5

Option B is the correct answer.

Paladinen [302]3 years ago
3 0
The answer is 1.5 females, one way to solve this is to multiply the probability of a female (50%) with the number of girls in total = 3 multiplied by (50%) = 1.5.
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Sam buys 4 tropical fish. Each fish is 5/8 of an inch long. Write an equation that represents 4 x 5/8 as a multiple of a unit fr
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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.

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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 :

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

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$\triangledown C$ 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 $\frac{dr}{dt}=\lambda \triangledown C$

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

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∴ 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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