If f(x)= 1/3x and g(x)=3x, then what are g * f (x) and g*f(1/2)

1 answer:

3 0

The correct answer is: 3) " x ; 1/2" .
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Explanation:
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Question 1)

g [ f(x) ] = ? ;

→ Given: " f(x) = 1/3 x " ;

→ Given: " g(x) = 3x " ;
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g [ f(x) ] = g(1/3 x) = 3(1/3 x) = 1x = "x" .
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Question 2)

g [ f(1/2) ] = ? ;
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→ Given: " f(x) = 1/3 x " ;

→ f(1/2) = (1/3) * (1/2) = (1*1) / (3*2) = (1/6) ;

→ g [ f(x) ] =

g(1/6) = 3* (1/6) = (3/1) * (1/6) = (3*1) / (1*6) = 3/6 = (3÷3) / (6÷3) = " 1/2 " .
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 (6 pts) The average age of CEOs is 56 years. Assume the variable is normally distributed. If the SD is four years, find the pr

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Answer:

The probability that the age of a randomly selected CEO will be between 50 and 55 years old is 0.334.

Step-by-step explanation:

We have a normal distribution with mean=56 years and s.d.=4 years.

We have to calculate the probability that a randomly selected CEO have an age between 50 and 55.

We have to calculate the z-value for 50 and 55.

For x=50:

$z=\frac{x-\mu}{\sigma}=\frac{50-56}{4}=\frac{-6}{4}= -1.5$

For x=55:

$z=\frac{x-\mu}{\sigma}=\frac{55-56}{4}=\frac{-1}{4}=-0.25$

The probability of being between 50 and 55 years is equal to the difference between the probability of being under 55 years and the probability of being under 50 years:

$P(50$