Stiffness Matrix

Please see attached file. How do i equate the mass spring system?

Venn diagrams.

The records of Midwestern University show that in one semester, 38% of the students failed mathematics, 27% of the students failed physics, and 9% of the students failed mathematics and physics. A student is selected at random. a.) If a student failed physics, what is the probability that he or she failed mathematics? b.) If a student failed mathematics, what is the probability that he or she failed physics? c.) What is the probability that he or she fails mathematics or physics?

Linear Progamming: Graphical Methods

Please see the attached file for the fully formatted problem(s). Use graphical methods to solve the linear programming problems Minimize subject to: z = x + 3y x + y 10 5x+2y 20 -x +2y 0 x 0 y 0 Maximize subject to: z = 4x + 5y 10x - 5y 100 20x+10y 150 -x + y 12 x 0 y 0

Finite Math - Probability

If the probability that a women is rich is 0.4, the probability that she is beautiful is 0.3 and the probability that she is either rich or beautiful is 0.5, what is the probability that she is both rich AND beautiful? Please show "all" steps to solution. Thank you,

Finite Math - Sets Counting Techniques

The problem I am working is the following; please provide step-by-step to obtain solution's. I am unable to figure (c) out the ANSWER IS ... 7805 There are 5 rotten plums in a crate of 25 plums, How many samples of 4 of the 25 plums contain at least one rotten plum?