Answer:
x = - 
Step-by-step explanation:
To find f(g(x)) substitute x = g(x) into f(x), that is
f(g(x))
= f(x + 1)
= 2(x + 1)² ← expand using FOIL
= 2(x² + 2x + 1) ← distribute
= 2x² + 4x + 2
To find g(f(x)) substitute x = f(x) into g(x), that is
g(f(x))
= g(2x²)
= 2x² + 1
----------------------------------------------------------
Equating gives
2x² + 4x + 2 = 2x² + 1 ( subtract 2x² + 1 from both sides )
4x + 1 = 0 ( subtract 1 from both sides )
4x = - 1 ( divide both sides by 4 )
x = - 
i would start by simplifying the equation to get y by itself, you don't need to do this, but it makes it a little easier
y + 2 = 3 ( x + 4) distribute the 3 through the parenthesis
y + 2 = 3x + 12. subtract 2 from both sides
y = 3x +10
now to fill in the chart simply plug in the value of x to see what value of y it produces
y = 3(-2) +10
y = -6+10
y = 4
(-2,4)
y = 3(0) + 10
y = 0 + 10
y = 10
(0,10)
y = 3(2)+10
y = 6 + 10
y = 16
(2,16)
y = 3(4) + 10
y = 12 + 10
y = 22
(4,22)
Answer:
And using a calculator, excel or the normal standard table we have that:
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 weigths of a population, and for this case we know the distribution for X is given by:
Where
and
Since the distribution for X is normal then we know that the distribution for the sample mean
is given by:
We can find the probability required with the following z score formula:

And replacing we got:
And using a calculator, excel or the normal standard table we have that: