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Dovator [93]
3 years ago
10

Sketch the graph of the given function. The state the functions domain and rangef(x)=-2{1/4}^x​

Mathematics
1 answer:
Karolina [17]3 years ago
4 0

Answer:

Domain: -∞ < x < ∞

Range: f(x) < 0

Step-by-step explanation:

f(x)=-2(\frac{1}{4})^x

We need to sketch the graph and identify domain and range of the function f(x).

The graph is attached in the figure below.

Domain:

The domain of the function is all the values of x that gives the real values for f(x).

So, in our case all values of x gives real values for f(x). So domain is:

-∞ < x < ∞

Range:

The range of the function is the resulting f(x) values when we put all the values of x.

In our case the value of f(x) will always be less than zero because of the negative sign.

Range is:

f(x) < 0

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A couple plans to have children until they get a​ girl, but they agree they will not have more than three​ children, even if all
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Answer:

a)Let X be number of children

X=1,2,3

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c) 1.6232

Step-by-step explanation:

The complete question is:

A couple plans to have children until they get a​ girl, but they agree they will not have more than three​ children, even if all are boys. Assume that the probability of having a girl is 47.00​%. ​

a) Create a probability model for the number of children​ they'll have.

X=1,2,3

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P(X=30=???

​(Round to four decimal places as​ needed

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E(X)= ???

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Expected number of boys= ???

Solution:

Probability of a girl= 0.47

Probability of a boy= 0.53

a) P(X=1)= 0.47

P(X=2) = 0.47× 0.53= 0.2491

P(X=3)= 0.47× 0.53× 0.53 + 0.53× 0.53× 0.53

             = 0.942923

b) E(number of children)= 1× P(X=1) + 2 ×P(X=2) + 3 × (PX=3)

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c) Y: number of boys

P(Y=1)= 0.53×0.47= 0.2491

P(Y=2) = 0.53×0.53×0.47=0.46375

P(Y=3)= 0.53× 0.53× 0.53= 0.148875

E(Y)= P(Y=1)×1 + P(Y=2)×2 + P(Y=3)×3

       = 0.148875×3 +0.46375×2+0.2491 ×1

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