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1. Let A ⊆ R be a set, let f, g: A ?R be functions and let k ∈ R. Suppose that f and g are uniformly continuous. Prove that f + g are uniformly continuous.
2. Let [a, b] ⊆R be a closed bounded interval, and let f : [a, b] ?[a, b] be a function. Suppose that f is continuous. Prove that there is some c ∈ [a, b] such that f(c) = c. The number c is call a fixed point of f.
A motel cleark counts his 1 dollar bills and his 10 dollar bills at the end of a day. He finds that he has a total of 64 bills, having a combined monetary value of $190. Find the number of bills of each denomination that he has.
Suppose that g: Y-->R is a function which is differentiable at y_0. Then the function g o f: X-->R is differentiable at x_0, and (g o f)' (x_0) = g'(y_0)f '(x_0)
You have a rectangular piece of cardboard that you want to fold into a box. It occurs to you that you can cut out an equal square from each corner of the rectangle, make a crease along each side and fold them up.
HIV Death Rates, which contains the death rates per 100,000 people for HIV related diseases in the US. a. Make a scatter graph of the data with a trendline. Copy and paste the graph here.
An explosion causes debris to rise vertically with an initial speed of 72 feet per second. The formula h = -16t2+ 72t describes the height of the debris above the ground, h, in feet, t seconds after the explosion. How long will it take for the debris..
Calculate the mean, median, and standard deviation for ounces in the bottles. Construct a 95% Confidence Interval for the ounces in the bottles. Conduct a hypothesis test to verify if the claim that a bottle contains less than sixteen (16) ounces is ..
Suppose you have 3 nickels, 2 dimes, and 6 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that
a large study involving over 20000 individuals shows that the mean percentage intake of kilocalories from fat was 39
In 35 of their stores they sold on the average 430 suits per year with a population standard deviation of 40. What is the test value for their claim?
How much can be saved by borrowing the funds for 30 days to take advantage of the cash discount? (Remember, Suite Dreams must borrow only the net amount due after the cash discount is taken.)
Find a linear model for the cost, of waste collection as a function of the number of kilograms.
Explain the importance of Euclid's parallel postulate in the development of hyperbolic and spherical geometry.
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