Step-by-step explanation:
length of the box is a = 25 -2x
width of the box is b =13 -2x
height of the box is x
and x < 6,5
so the volume of the box V=f(x) = x.(25-2x)(13-2x)= 4x^3 -76x^2 +325x
f'(x) = 12x^2 - 152x + 325
to maximize the volume of the box ( f(x) max ) then f'(x) = 0 --> x ≈ 2,72 and x ≈ 9,94
so x = 2,72 inches
Answer:
= ( 82.90, 85.10) points
Therefore at 90% confidence interval (a,b)= ( 82.90, 85.10) points
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 84
Standard deviation r = 4.5
Number of samples n = 45
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
84+/-1.645(4.5/√45)
84+/-1.645(0.670820393249)
84+/-1.10
= ( 82.90, 85.10) points
Therefore at 90% confidence interval (a,b)= ( 82.90, 85.10) points
Answer:
12700
Step-by-step explanation:
45 + .05x = 680
.05x = 635
x = 12700