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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.
A physician injects 5 mg of dye into a vein near the heart of a patient and by monitoring the concentration of dye in the blood over a 24-second period, determines that the concentration of dye leaving the heart after t seconds (o
what is the probability that each challenge will be won by a different camper? what is the Probability that Hank, one of the Seniors, will win at least one challenge?
At a 5 percent level of significance, test to see if there is a significant difference in the average amount spent at the two schools. Write your conclusion?
If the school cafeteria serves meat loaf, there is a 70% chance that they will serve peas. If they do not serve meat loaf, there is a 30% chance that they will serve peas anyway.
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?
Discrete Random Variable Defined on a Finite Sample Space. a) Prove that if X is a discrete random variable defined on a finite sample space, S, then we have E(X) = SUM X(a) P({a}).
A person is given 4 coins each with equal and independent probabilities of being a nickel , a penny, a dime or a quarter. What is the probability the person has been 37 cents
problem on percetanges
Explain why a point on the boundary line cannot be used as a test point when graphing a linear inequality in two variables. Provide an example.
Among U.S. cities with a population of more than 250,000 the mean one-way commute to work is 24.3 minutes. The longest one-way travel time is New York City, where the mean time is 37.9 minutes.
Hypothesis test for two differences between means
Find the natural domain of the given functions.
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