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1. Let f: [a,b] ----> R and suppose f is integrable with respect to alpha. Prove that for any c in the real numbers, cf is integrable with respect to alpha and the integral from a to b of cf d(alpha) = c times integral from a to b of f d(alpha).
Give an example of a function f : [0,1] ----> R such that f is Riemann integrable and f is discontinuous on a dense subset of [0,1].
I cannot find the famous distribution that describes the frequency of the number of times a number comes up in a series of dice rolls?
Prove that if f is continuous at all values of x then so is kf where k is a constant. Give an example of a function that is continuous at all non-integer values but is discontinuous at all integer values.
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
Show that the curve with parametric equations x=sin(t), y=cos(t), and z=sin^2(t) is the curve of the surfaces z=x^2 and x^2 + y^2=1. Use this fact to help sketch the curve.
Math: Linear Transformation of the Space of Polynomials, Which of the following is a linear transformation T of the space of polynomials? Circle the letters corresponding to correct answers.
A cooler at a picnic contains 100 cans of soda covered by ice. There are 30 cans of cola, 40 cans of orange soda, 10 cans of ginger ale
Using the Quotient rule, find the gradient of the function:
Recurrence relations with complex characteristic roots
Examples of Probability and Statistics in Real Life, Can you think of situations in the business world or other real life situations where you would need to calculate or estimate probabilities?
A tank in the shape of an inverted right circular cone has height 6 meters and radius 4 meters. It is filled with 5 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank.
show that A is an ideal of R and describe the cosets in R/A
Simple linear regression model
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