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In a T-maze, a rate is given food if it turns left and an electric shock if it turns right. On the rst trial there is a 50-50 chance that a rat will turn either way; then, if it receives food on a given trial the probability that it will turn left on the next trial is 0.72, and if it receives a shock on a given trial the probability that it will turn left on the next trial is 0.84.
1. What is the probability that the rat will turn left on the second trial?2. Assuming the probability of a rat turning left on any given trials depends only on what it did in the preceding trial, nd the probability that a rate will turn left on the third trial.3. Removing the assumption in 2, calculate the expected number of trials that need to be made until the rat turns right.4. Removing the assumption from 2 again, calculate the expected number of trials needed until the rat turns right two times in a row.
Augmented matrices to solve the word problem
How many permutations are there of 12 objects taken five at a time? How is this answer related to answers in 1 and 2?
A set A is call a partially-ordered set if there is a relation R on A such that R is reflexive and transitive. If A is any set, prove that the power set P(A) is a partially ordered set under the relation "is a subset of".
Profit for each big shelf is $85 and for each medium shelf is $75. What is the constraint on money to invest?
Suppose a retiree wants to buy an ordinary annuity that pays her $2,000 per month for 20 years. If the annuity earns interest at 3.5% interest compounded monthly, what is the present value of this annuity?
Four people select a main dish from a menu of 7 items. How many choices are possible: If a record is kept of who selected which choice (as a waiter would)
How many solution sets do systems of linear inequalities have? Must solutions to systems of linear inequalities satisfy both inequalities? In what case might they not? Use an example for discussion.
Matrix Representation of a Linear Transformation, For the problem, refer to the linear transformation T
Harold operates a hot dog stand at the Jugulars football games. He pays $2000 per game to rent the space. Each hot dog (with bun and condiments) costs him $0.33, and he sells hot dogs for $3 each.
One of the most famous unsolved problems in mathematics is a conjecture made by Christian Goldbach in a letter to Leonhard Euler in 1742. The conjecture made in this letter is now known as Goldbach's Conjecture. The conjecture is as follows:
Use 4 point bins 96 to 99, 92 to 95 etc. to make a frequency table for the set of exam scores. Include columns for relative frequency and cumulative frequency.
Find the directrix, focus and roots of the parabola from the given data and sketching the graph of given equation
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