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We have defined space X to be contractible in two ways:
Definition 1: X is contractible if it is homotopy equivalent to a point; and
Definition 2: X is contractible if the identity map of X is null-homotopic.
Show that these two definitions are equivalent.
Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. Find the errors E_ k and relative errors R_k for the values p1 in parts b) and c).
Academic response to Binomial Distribution, Historical data shows 15% of the customers entering a store make a purchase. There are 50 customers in the store at the moment.
Find the distance of the ship from the lighthouse.
Let F be a forest. Add a vertex x to F and join x to each vertex of odd degree in F. Prove that the graph obtained in this way is randomly Eulerian from x
Important information about Find the indicated probability, Assume the geometric distribution applies. Use the given probability of success p to find the indicated probability.
Important information about Sets, Counting & Probability : Combinations, How many poker hands consist of four clubs and a card of a different suit?
Evaluate the area of the rectangle - Write a polynomial that represents the area.
Asymptotes of trigonometric functions and Graph y = csc( 0.5x + pi/2) and y = cos( 0.5x + pi/2) on one set of coordinate axes.
For the exponential function ex and logarithmic function log x, graphically show the effect if x is doubled.
Evaluate the function for the values of x given as 1,2,4,8,16. Describe the differences in the rate at which each function changes with the increasing values of x.
A computer store has 10 copies of a word processing program, 12 copies of a spreadsheet program, and 8 copies of a draw program. Three of the word processing, four of the spreadsheet and two of the draw programs are infected with a computer virus.
At a price of $1.90 per bushel, the annual U.S. supply and demand for barley are 410 million bushels and 455 million bushels, respectively. When the price rises to $2.70 per bushel
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