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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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- RJ&M Company manufactures furniture such as sofas and tables. In theircurrent inventory, a total of 48 planks of wood are left. Each sofa needs four planks of wood to be made while each table needs two planks of wood to be made. The company earns a profit of P hundred pesos where P(x, y) = (6x^2)y for selling x units of sofas and y units of tables. With their current inventory of woods, how many sofas and tables are needed to be produced to maximize their profit?California Wine producer Chill Wines has in their line a mid-market chardonnay, of whichthey produce 200,000 bottles a year. They have been bottling their wines with natural corkclosures, which are known to have sealing issues resulting in the spoilage of wine, aproblem that is worse in their chardonnay than in the other wines they sell. This problem,which results in a 15% spoilage rate for their chardonnay, is both expensive and impactsthe company’s reputation. They have researched several other closure products on themarket and have decided to try using a new closure in a test run of 91 bottles theirchardonnay. After allowing the wine to stay in the bottles for the time it generally takes toget it from the winery to customers, they tested the run and found 16 spoiled bottles. As thecompany has a both an immediate financial and reputation risk, they want to be 90% surethat changing the closures will help limit wine spoilage. What do their results suggest? a)What is known? What…First order linear of 2x3y'=y(y2+3x2)
- (8y3sec22x + 4x3e-3y + 6csc23x)dx - (3x4e-3y - 12y2tan2x)dy = 0max p=10x+12y subject to: 3x+2y+s1=1500 2x+3y+s2=1500 x+y+s3=600A political mailing will have several pages on the economy, the military, and the environment. The total number of these pages in the booklet should not be greater than 110, including at most 20 pages on the economy. For the target group that will receive the booklet, market research suggests that there will be a positive impact proportional to 5 times the number of pages on the economy, a positive impact proportional to 3 times the number of pages on the military, and a positive impact proportional to 2 times the number of pages on the environment. The editor insists that the number of pages on the environment be at least twice as many as the number on the military. Find the number of pages that should be devoted to the economy, the military, and the environment. (Hint: Write the constraint involving environment and military pages in the form ≤0.)
- Find d2y/dx2 if 2x3-3y2=8In the environment of increased competition, a fitness club executive is considering the purchase of additional equipment. They are choosing between Acme, Standard and High Pro. With new equipment they can attract new clients and increase their overall profits. The profits are dependent on the markets demand for the new equipment and brand name recognition. If they go with the Acme equipment, there profit would be $375,000 in a favorable market or -$125,000 in an unfavorable market. If they go with the Standard equipment, there profit would be $250,000 in a favorable market or -$95,000 in an unfavorable market. If they go with the High Pro equipment, there profit would be $175,000 in a favorable market or -$50,000 in an unfavorable market. a) Create a decision table and a decision tree.Max Z = 6XI + 4X2 Subject to 7XI + 8 X2 ≤224 8XI + 12 X2 ≤192 15XI + 16X2 ≤480 Xi ≥ 0
- Dataware is trying to determine whether to give a $10 rebate, cut the price $6, or have no price change on a software product. Currently, 40,000 units of the product are sold each week for $45 apiece. The variable cost of the product is $5. The most likely case appears to be that a $10 rebate will increase sales 30%, and half of all people will claim the rebate. For the price cut, the most likely case is that sales will increase 20%. a. Given all other assumptions, what increase in sales from the rebate would make the rebate and price cut equally desirable? b. Dataware does not really know the increase in sales that will result from a rebate or price cut. However, the company is sure that the rebate will increase sales by between 15% and 40% and that the price cut will increase sales by between 10% and 30%. Perform a sensitivity analysis that could be used to help determine Dataware’s best decision.At the Blood Bank, they know that O+ blood is the most common blood type and that 40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6% of the people have A- blood. Half of the people have blood type A or B. Let: X= number of people who have blood type O+ Y= number of people who have blood type A- Z= number of people who have blood type A or B please answer a) b) and c)A production manager is trying to determine how many units of two types of products to produce each day. One of these is the Standard model, while the other is the Luxurious model. The profit per unit on the Standard model is R600, while the profit per unit on the Luxurious model is R400. The Standard model requires 20 minutes of assembly time, while the Luxurious model requires 35 minutes of assembly time. The Standard model requires 10 minutes of inspection time, while the Luxurious model requires 0.25 hour of inspection time. To meet a specific order, at least 6 Luxurious models must be produced. There are 450 minutes of assembly time and 3 hours of inspection time available each day. Make use of Linear programming graphical method to determine how many units of each product that should be manufactured to maximize profits?