The following year, as a result of the Cherry Mine disaster, the Illinois legislature established stronger mine safety regulations and in 1911, Illinois passed a separate law, which would later develop into the Illinois Workmen's Compensation Act.
A monument to those who lost their lives was erected May 15, 1971, by the Illinois Department of Transportation and the Illinois State Historical Society.
The centennial commemoration of the Cherry Mine disaster was held in Cherry, November 14–15, 2009. A new monument, located at the Cherry Village Hall, was dedicated to the miners who lost their lives in the disaster.
3x - 2y = 5
-3x. -3x
-2y= -3x + 5
/-2. /-2. /-2
Y= -3/2x - 5/2
Hi,
Answer: 7/27
<u>My work:</u> For this problem is already simplified to its simplest terms.
I Hoped I Helped!
Answer: (a) 0.344578
(b) 0.211855
Step-by-step explanation: Let X represent Jill's score and Let Y represent Jack's score.
Jill's scores are approximately normally distributed with mean 170 and standard deviation 20 implies :
X ≈(170 , )
Also , since Jack's scores are approximately normally distributed with mean 160 and standard deviation, it implies
Y ≈ ( 160 , ).
It is given that their scores are independent which means that the outcome one one will not affect the outcome of the other, we the have:
Y - X ≈ N(-10 ,+ )
Y - X ≈ N(-10 ,625 )
Also , Y + X ≈ N ( 330 , 625 )
(a) We need to find the approximate probability that Jack's score is higher , that is
P ( Y > X)
=P(Y - X >0)
= P ( >
= 1 - Ф()
= 1 - Ф()
= 1 - Ф ( 0.4)
= 1 - 0.655422
= 0.344578
P ( Y > X) ≈ 0.345
(b) We need to calculate the approximate probability that their total score is above 350 , that is
P ( X + Y > 350)
= P ( > )
= 1 - Ф()
= 1 - Ф ( 0.8)
= 1 - 0.788145
= 0.211855
P ( X + Y > 350)≈ 0.212
Answer:
a) Minimize
subject to
b) Attached
c) The optimum value that minimizes cost is x1=28 and x2=8.
Step-by-step explanation:
The objective function is the cost of extraction and needs to be minimized.
The cost of extraction is the sum of the cost of extraction of ore type 1 and the cost of extraction of ore type 2:
Being x1 the tons of ore type 1 extracted and x2 the tons of ore type 2.
The constraints are the amount of minerals that need to be in the final mix
Copper:
Zinc
Magnesium
Of course, x1 and x2 has to be positive numbers.
The feasible region can be seen in the attached graph.
The orange line is the magnesium constraint. The red line is the copper constraint. The green line is the zinc constraint.
The optimal solution is found in one of the intersection points between two constraints that belong to the limits of the feasible region.
In this case, the cost can be calculated for the 3 points that satisfies the conditions.
The optimum value that minimizes cost is x1=28 and x2=8.