4/9 + (x-1) = 28/9 - (x-7x) + 1
4/9 + x - 1 = 28/9 - x + 7x + 1
-5/9 + x = 37/9 + 6x
-5x = 42/9
-5x = 4.6 (repeating 6)
x = -0.93 (repeating 3)
Hope this helps! ;)
Pangaea is the answer I had the same question.
Answer:
Step-by-step explanation:
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 t distribution or Student’s t-distribution is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
Data given
Confidence =0.99 or 99%
represent the significance level
n =16 represent the sample size
We don't know the population deviation 
Solution for the problem
For this case since we don't know the population deviation and our sample size is <30 we can't use the normal distribution. We neeed to use on this case the t distribution, first we need to calculate the degrees of freedom given by:
We know that 
so then 
and we can find on the t distribution with 15 degrees of freedom a value that accumulates 0.005 of the area on the left tail. We can use the following excel code to find it:
"=T.INV(0.005;15)" and we got 
on this case since the distribution is symmetric we know that the other critical value is 
Hmm, the 2nd derivitve is good for finding concavity
let's find the max and min points
that is where the first derivitive is equal to 0
remember the difference quotient
so
f'(x)=(x^2-2x)/(x^2-2x+1)
find where it equals 0
set numerator equal to 0
0=x^2-2x
0=x(x-2)
0=x
0=x-2
2=x
so at 0 and 2 are the min and max
find if the signs go from negative to positive (min) or from positive to negative (max) at those points
f'(-1)>0
f'(1.5)<0
f'(3)>0
so at x=0, the sign go from positive to negative (local maximum)
at x=2, the sign go from negative to positive (local minimum)
we can take the 2nd derivitive to see the inflection points
f''(x)=2/((x-1)^3)
where does it equal 0?
it doesn't
so no inflection point
but, we can test it at x=0 and x=2
at x=0, we get f''(0)<0 so it is concave down. that means that x=0 being a max makes sense
at x=2, we get f''(2)>0 so it is concave up. that means that x=2 being a max make sense
local max is at x=0 (the point (0,0))
local min is at x=2 (the point (2,4))
