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3 years ago

2. If f(x) = x – 5 and g(x) = x2 + 3, find f[g(-2)].

Mathematics

2 answers:

nata0808 [166]3 years ago

7 0

Answer: 2

Step-by-step explanation:

F(x)= X-5

G(x) =X2 +3

Find F(g(-2))

G(x)= x2 +3

G(x)=G(-2);

X= -2

Substitute for x in g equation

G(-2)= (-2)^2+3

=4+3

Therefore G(-2)= 7

F(g(-2))= x-5

Substitute for g(-2)= 7

F(7) = 7-5

irina [24]3 years ago

3 0

Answer:

= 2

Step-by-step explanation:

# g(x) = x^2 + 3 hence g(-2) = (−2)2+3=4+3=7

and so f(g(-2)) = f(7) = 7 - 5 = 2

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Answer:

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If we find the expected value of Y we got:

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And the deviation $Sd(Y) = \sqrt{0.005}=0.0707$

So then our random variable Y have the following distribution:

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And we want to find this probability:

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And we can use the z score formula given by:

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And if we use the z score formula we got:

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the lenghts of a population, and for this case we know the distribution for X is given by:

$X \sim N(3.25,0.05)$

Where $\mu=3.25$ and $\sigma=0.05$

We slect two observations $X_1, X_2$

And let denote the combined lenght as:

$Y = X_1 + X_2$

If we find the expected value of Y we got:

$E(Y) = E(X_1) + E(X_2) = 3.25 + 3.25 =6.5$

And for the variance we assume that we have independent random variables for X1 and X2 so then we have:

$Var(Y) = Var(X_1) + Var(X_2) = \sigma^2 + \sigma^2 = 2 \sigma^2 = 2*(0.05^2) = 0.005$

And the deviation $Sd(Y) = \sqrt{0.005}=0.0707$

So then our random variable Y have the following distribution:

$Y \sim N (\mu =6,5 , \sigma = 0.0707)$

And we want to find this probability:

$P(Y$

And we can use the z score formula given by:

$z=\frac{y -\mu_y}{\sigma_y}$

And if we use the z score formula we got:

$P(Y$

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