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3 years ago

Given the parent functions f(x) = log10 x and g(x) = 3x - 1, what is f(x) g(x)?

Mathematics

1 answer:

Rudiy273 years ago

7 0

Answer:

Option (b) is correct.

The value of $f(x)g(x)=log_{10}x(3x-1)$

Step-by-step explanation:

Given functions $f(x)=log_{10}x$ and $g(x)=3x-1$

We have to find $f(x)g(x)$

We know $f(x)g(x)=f(x) \cdot g(x)$

Thus, $f(x) \cdot g(x)=log_{10}x \cdot (3x-1)$

Thus, solving further we get,

$log_{10}x \cdot (3x-1)=log_{10}x(3x-1)$

Thus, the value of $f(x)g(x)=log_{10}x(3x-1)$

Thus, Option (b) is correct.

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Answer:

$P(X \geq 7) = P(X=7) +P(X=8)$

And we can find the individual probabilities using the probability mass function

$P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826$

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And replacing we got:

$P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131$

Step-by-step explanation:

Previous concepts

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Solution to the problem

Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:

$X \sim Binom(n=8, p=0.9)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And for this case we want to find this probability:

$P(X \geq 7) = P(X=7) +P(X=8)$

And we can find the individual probabilities using the probability mass function

$P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826$

$P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305$

And replacing we got:

$P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131$

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