Please use the symbol " ^ " to denote exponentiation: 9x^6 = (___)^2.
Note that 9x^6 = 3^2*(x^3)^2. Thus,
9x^6 = (___)^2 becomes (3x^3)^2.
Then <span>9x^6 – 16y^6 = (3x^3)^2 - (4y^3)^2 = ((3x^3) - (4y^3))[(3x^3) +(4y^3)]</span>
7.43: Let 
denote the random variable for height and 
for the sample mean. Then if 
is the mean of
So the probability that the difference between the sample and population means does not exceed 0.5 inch is
per the empirical or 68/95/99.7 rule.
7.44: For a sample of size <em>n</em>, the sample standard deviation would be 
. We want to find <em>n</em> such that
Comparing to the equation from the previous part, this means we would need
so a sample of at least 157 men would be sufficient.
Let
x------> the length side of the square base of the box
y-------> the height of the box
we know that
volume of the box=b²*h
b=x
h=y
volume=256 cm³
so
256=x²*y------>y=256/x²--------> equation 1
<span>The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.</span>
surface area of the cardboard=area of the base+perimeter of base*height
area of the base=x²
perimeter of the base=4*x
height=y
surface area=x²+4x*y-----> equation 2
substitute equation 1 in equation 2
SA=x²+4x*[256/x²]-----> SA=x²+1024/x
step 1
find the first derivative of SA and equate to zero
2x+1024*(-1)/x²=0------> 2x=1024/x²----> x³=512--------> x=8 cm
y=256/x²------> y=256/8²-----> y=4 cm
the answer is
the length side of the square base of the box is 8 cm
the height of the box is 4 cm
2)Negative linear association because the line is straight and it’s going down meaning it’s negative
