Suppose that we are putting animals in a barn. there are three types of animals: horses, cows, and goats. the barn has a fixed number of stalls (partitions). these stalls are arranged in a single row, and are consecutive. horses and cows are big, and each need 2 stalls. a goat is small, and only needs 1 stall. stalls are not allowed to be empty. assume that all horses are equivalent, all cows are equivalent, and all goats are equivalent. for example, in a barn with only 1 stall, you can only place 1 goat (g). in a barn with 2 stalls, you could have one horse (h), or one cow (c), or two goats (gg). in a barn with 3 stalls, there are 5 possible sequences: ggg, gh, gc, hg, cg. find a recurrence relation that describes how many ways are there to arrange the animals into a barn with n stalls. hint: think about the last animal in the row of stalls.

Write a function balancechemical to balance chemical reactions by solving a linear set of equations. the inputs arguments are: reagents: symbols of reagents in string row array products: symbols of products in string row array elements: elements in the reaction in string row array elcmpreag: elemental composition of reactants in two dimensional numeric array elcmpprdcts: elemental composition of prducts in two dimensional numeric array hint: the first part of the problem is setting up the set of linear equations that should be solve. the second part of the problem is to find the integers from the solution. one way to do this is to mulitiply the rational basis for the nullspace by increasing larger integers until both the left-and right-side integers exist. for example, for the reaction that involves reacting with to produce and : reagents=["ch4", "o2"]; products =["co2", "h2o"]; elements =["c","h", "o"] elcmpreag=[1,4,0;

Assume a class window with accessor method getwidth that accepts no parameters and returns an integer. assume further an array of 3 window elements named winarr, has been declared and initialized. write a sequence of statements that prints out the width of the widest window in the array.

This assignment continues work on the online booking facility introduced at the end of chapter- 10. the work will be continued in the assignments for chapters 14 and 15 (a) assume that you will produce your online booking facility using an agile approach. i. suggest the kind of user research you would like to conduct for your product before iteration cycles begin. ii prioritize the requirements for your product according to business value, i.e which requirements are likely to provide the greatest business benefit, and sketch out the ux design work you would expect to undertake during the first four iteration cycles, i.e. cycle 0, and cycles 1 to 3. (b) using one of the mockup tools introduced above, generate a mockup of your product's landing page, as developed in the assignment for chapter-11 (c) using one of the patterns websites listed previously, identify suitable interaction patterns for elements of your product, and develop a software-based prototype that incorporates all the feedback and the results of the user experience mapping achieved at the end of chapter-11. if you do not have experience in using any of these, create a few html web pages to represent the basic structure of your website