given f)x) then
- f(x) represents a reflection in the x-axis
f(x + 4 ) represents a shift of 4 units horizontally to the left
f(x) + 12 represents a vertical shift of 12 units down
thus h(x) = f(x + 4 ) - 12
is the graph of f(x), moved 4 units left, 12 units down and reflected in the x- axis
we are given

where
F is the number of board feet
d is the diameter (in inches) of the log
Since, we have to minimize F
so, firstly we will find it's derivative


now, we can set it to 0
and then we can solve for d


so, we get diameter as
..............Answer
Answer:
For a data set of N elements:
{x₁, x₂, ..., xₙ}
The mean is:

The mean absolute deviation is:

And the population standard deviation is:

In this case, our set has 5 elements, and the set is:
{2, 4, 6, 9, 14}
The mean of this set is:

The mean absolute deviation is:

And the population standard deviation is:

Answer: 68
Step-by-step explanation:
Formula for sample size when prior estimate of population proportion (p) is available: 
, where z*= critical-value.
E= Margin of error.
Let p be the population proportion of trees are infected with the citrus red mite.
As per given , we have

E= ± 0.08
The critical z-value corresponding to 90% confidence level = z*=1.645
Substitute all the values in the above formula , we get
Required sample size :

[Rounded to next integer.]
Thus, the minimum sample size should be taken =68
If d₁ and d₂ are the lengths of the diagonals, the area is given by
.. A = (1/2)*d₁*d₂
.. A = (1/2)*(12 in)*(16 in)
.. A = 96 in²
If b is the base and h is the height, the area is given by
.. A = b*h
We know the values of A and b, so
.. 96 in² = (10 in)*h
.. (96 in²)/(10 in) = h = 9.6 in
The height is 9.6 in.