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A publishing company has just published a new college textbook. Before the company decides the price at which to sell this textbook, it wants to know the average price of all such textbooks in the market. The research department at the company took a sample of 25 comparable textbooks and collected information on their prices. This information produced a mean price of $145 for this sample. It is known that the standard deviation of the prices of all such textbooks is $35 and the population of such prices is normal.

What is the point estimate of the mean price of all such college textbooks?
(b) Construct a 90% confidence interval for the mean price of all such college textbooks
X ∼ Gam(3, 1) and Y |(X = x) ∼ Exp(x); find (a) E [Y ]; (b) Var [Y ];
(c) Cov [X, Y ]
The random variables X and Y have a density of
fXY (x, y) = x + y for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, and fXY (x, y) = 0 elsewhere. Evaluate
E [X] and E [XY ].
1. A trucking company has a contract to move 115 truckloads of sand per week between three sand-washing plants W, X, and Y, and three destinations A, B and C. cost and volume information is given below. Compute the optimal transportation cost.
To

From
Project A
Project B
Project C
Supply
Plant W 5 10 10 35
Plant X 20 30 20 40
Plant Y 5 8 12 40
Demand 45 50 20

a. Formulate the transportation problem.
b. Set up the initial transportation tableau from the minimum-entry method.
c. Using the Northwest Corner rule, find the initial allocation.
d. Find the optimal solution using Stepping-stone method.
e. Compare the optimal solution obtained in e. using Modified Distribution Method.
2. A manufacturing company operates plants P1, P2, and P3 in different regions. The weekly production of these plants are as follow:

Plant Weekly Production (Box)
P1 1000
P2 850
P3 550

The total supply of the company is absorbed by warehouse W1, W2, and W3. Their weekly requirement is as follows:

Warehouse Weekly Requirement
W1 1000
W2 700
W3 850

The transportation cost (in peso) from each plant to each warehouse in given below:
To

From W1 W2 W3
P1 90 110 70
P2 80 50 100
P3 140 130 90

a. Formulate the transformation problem.
b. Set up the initial transportation tableau from the minimum-entry method.
c. Using the Northwest Corner Rule, find the initial allocation.
d. Determine the shipment from each plant to each warehouse that minimizes the delivery cost using Stepping-Stone Method.
Compare the optimal solution obtained in e. using Modified Distribution Method
what is the length of the conjugate axis? (y-2)^2/16-(x+1)^2/144=1
how many degrees are in a right angle
Suppose that a company's sales were $5,000,000 three years ago. Since that time sales have grown at annual rates of 10 percent, – 10 percent, and 25 percent.

Find the exact values of the trigonometric functions of a/2 and 2a by using half-angle and double angle formulas.



1) sin(a) = 4/5, and a in quadrant 1


Sketch the region below the curve y=2x−x^2 and above the x-axis and find its area.
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