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1. Prove that if n is any integer, then 3n3 + n+ 5 is odd. (Suggestion: do one case for n odd and one case for n even.)
2. A cold-footed centipede has a drawer filled with many, many socks. And yes, that centipede does have 100 feet. If the centipede only owns green and brown socks, how many must it pull from the drawer in the dark of the morning to be assured that it has a matching set for all of its feet? What if the centipede also owns polka-dotted socks? What if the centipede's drawer has many, many socks of k different colors?
One card is selected from the box at random, and the color on one side is observed. If this side is green, what is the probability that the other side of the card is also green?
How do teachers really make a difference to an effective program?
The base of an aquarium with volume V = 330 is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.
Find the classes and the limiting probabilities of the Markova chain transition probability matrix.
1. Show that big-Theta notation (Θ) defines an equivalence relation on the set of functions. 2. Give the best lower bound that you can for the following code fragment, as a function of the initial value of n.
On the other hand, the interest earned during that year was 22% rather than 20%. What is the total per contract gain for this year?
Find the maximum or minimum value of the function and then state the domain and range of the function y=8-3x-4x2.
describe how it affects the determinant.
the restaurant you are working at makes one massive batch of potato salad each day. if yourun out before the end of the
What are the information that must appear labels of containers holding hazardous chemicals?
How can you identify the Dependent and independent variables in a real world situation modeled by a graph?
Find the area of the region bounded by the parabola y = 3x2, the tangent line to this parabola at (1, 3), and the x-axis.
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