Answer:
Base Side Length =1.59m
Height = 3.16 m
Step-by-step explanation:
Volume of the box =
Let the base dimensions = x and y
Let the height of the box =h
<em>However, for any optimal configuration, Width = Length as varying the length and width to be other than equal reduces the volume for the same total(w+l)</em>
Volume, V=xyh=8
Since x=y
Surface Area of the box
The material for the top and bottom costs twice as much as the material for the sides.
Let the cost of the sides =$1 per square meter
Cost of the material for the sides = 4xh
Cost of the material for the top and bottom =
Therefore:
Total Cost,
Substitution of into C
To minimize C(x), we find its derivative and solve for the critical points.
To verify if it is a minimum, we use the second derivative test
Since C''(x) is greater than zero, it is a minimum point.
Recall:
Therefore, the dimensions that minimizes the cost are:
Base Side Lengths of 1.59m; and
Height of 3.16 m
The value of x in the expression is 3.
The distance between Madison's house and Jamie's house is 13 units
<h3>How to find the distance between Madison house and Jamie's house?</h3>
Madison lives between Ana and Jamie as depicted on the line segment.
The distance between Ana's house and Madison's house is represented by 3x+2 miles, the distance between Madison's house and Jamie's house is represented by 3x+4 miles, and the distance between Ana's house and Jamie's house is represented by 9x-3 miles.
Therefore,
(3x + 2) + (3x + 4) = 9x - 3
open the brackets
3x + 2 + 3x + 4 = 9x - 3
combine like terms
3x + 3x + 2 + 4 = 9x - 3
6x + 6 = 9x - 3
6x - 9x = -3 - 6
-3x = - 9
divide both sides by -3
x = -9 / -3
x = 3
Therefore, the value of x in the expression is 3
distance between Madison's house and Jamie's house = 3(3) + 4 = 9 + 4 = 13
learn more on distance here:brainly.com/question/24432432
#SPJ1
Answer:
Step-by-step explanation:
y=x+6
Answer:
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
From the central limit theorem we know that the distribution for the sample mean is given by:
Part a
The mean is
Part b
And the deviation:
Step-by-step explanation:
Assuming this complete info: Suppose a random variable xx is normally distributed with μ=17 and σ=5.6. According to the Central Limit Theorem, for samples of size 13:
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 central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
From the central limit theorem we know that the distribution for the sample mean is given by:
Part a
The mean is
Part b
And the deviation:
Y=-3x-3 that is your answer