Math Answers

Solve (𝐷

2 − 3𝐷 + 2)𝑦 = 𝑥

2 + sin 𝑥 where 𝐷 =

𝑑

𝑑𝑥

Draw all possible random samples of size 3 with replacement from the 

population 15, 24 ,38 ,10 . all sample mean equal to population mean

DM. list the ordered pairs in the equivalence relations R induced by these partitions of p { {1} , {3} , { 2,4,5,6} rt he set of { 1,2,3,4,5,6}

LA. find the minimal polynomial of the linear operator t : R³ "- R³" define by t (x,y,z) =(x+2y+3z, 4y+5z,6 z).is t

A can of cat food, guaranteed by the manufacturer to contain at least 10 units of protein, 20 units of mineral matter, and 6 units of fat, consists of a mixture of four different ingredients. Ingredient A contains 10 units of protein, 2 units of mineral matter, and 1 2 unit of fat per 100g. Ingredient B contains 1 unit of protein, 40 units of mineral matter, and 3 units of fat per 100g. Ingredient C contains 1 unit of protein, 1 unit of mineral matter, and 6 units of fat per 100g. Ingredient D contains 5 units of protein, 10 units of mineral matter, and 3 units of fat per 100g. The cost of each ingredient is Birr 3, Birr 2, Birr 1, and Birr 4 per 100g, respectively. How many grams of each should be used to minimize the cost of the cat food, while still meeting the guaranteed composition? (Hint: Solve through simplex model)

Bedele Brewery produces Ale and Beer. Suppose that the productions are limited by scarce resources of Corn, Hops and Barely malt. To make Ale, 5 kg of Corn, 4 Kg of Hops and 35 Kg of Barely malt are required. To make Beer, 15 Kg of Corn, 4 Km of Hops and 20 Kg of Barely malt are required. Suppose that only 480 Kg of Corn, 160 Kg of Hops and 1190 Kg of Barely malt are available. The Brewery plans to enjoy a Profit of Birr 13 for each Kg of Ale and Birr 23 for each Kg of Beer.

Required:

Formulate the linear programming model

How many Ale and Beer should the Brewery Company produce in order to maximize the returns? Using the graphical method. 

What is the total profit? 

Is there any slack?

Suppose there are 10 male and 6 female professors to teach Discrete mathematics. In how

many ways a student can choose Discrete mathematics professor.

Suppose you have savings in the bank that you want to invest in stocks and bonds instead of setting up in a new business.

Write one to two paragraphs discussing what method you can use to make the investment and explain the reasons for your decision.

Copy Machine Use A store manager hypothesizes that the average number of pages a person copies on the store’s copy machine is less than 40. A sample of 50 customers’ orders is selected. At a _ 0.01, is there enough evidence to support the claim? Assume population standard deviation 30.9.

Use the composite trapezoidal rule to find approximations to 𝐼 = ∫ 𝐬𝐢𝐧𝒙 𝒅𝒙 𝝅

𝟎

with n = 1, 2, 4, and 8. Then perform Romberg extrapolation on the results.