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Give examples to show that the finiteness of the collections in parts c and d is essential.
a) For any finite collection G1, G2, ...., Gn of open sets, intersection (at the top of the intersection sign is n and at the bottom is i=1) of Gi is open.
b) For any finite collection F1, F2, ...., Fn of closed sets, union sign (with n at the top of the sign and i=1 at the bottom) of Fi is closed.
For the exponential function ex and logarithmic function log x, graphically show the effect if x is doubled.
Suppose the spot and three-month forward rates for the yen are ¥79.85 and ¥79.16, respectively. What would you estimate is the difference between the annual inflation rates of the United States and Japan? (Negative amount should be indicated by a ..
A sample of 500 travelers who used the internet to book a trip were asked to which travel website they used. There responses are given in the table below. Use this information to construct a circle graph illustrating the percent of people who gave..
Find the hypothesis and the null hypothesis
A single line divides a plane into two regions. Two lines (by crossing) can divide a plane into four regions, three lines can divide it into seven regions.
Important information about Probability and combinations. Assume you have five cards are chosen from a standard deck of 52 playings cards. How many hands contain four aces?
Find the equation of parabola from the given data - Determine the equation of a parabola with vertex
Probability problems based on Poisson & Normal distribution
Prove the triangle inequality starting with: |V+W|^2. You must use Re (less than or equal to) | | and the Schwarz inequality.
How would you explain the difference between the method used for graphing a function from how to determine the domain and range from the graph of a function?
In each case make a conjecture about a possible generalisation, and explore it (i.e. attempt to prove your conjectures true or false).
Let G be a group (finite or infinite) and let a and b in G. Let o(a) represent the order of a. Suppose G is abelian and both a and b are of finite order. Show that ab is of finite order and o(ab) divides o(a)o(b).
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