Here is a slightly complicated version to the game we discuss in the class. Suppose there are four questions Q1, Q2, Q3 and Q1, which are associated with a reward of $100, $1,000, $10,000, and $50,000, respectively. 2 There is a challenger, denoted by CHI. The rule is as follows: (a) CII initially is at the state 21 and has $0 at hand;
(b) When presented a question, CII will have two choices, either to quit or to accept. If to quit, CHI will take all the money she has earned so far and game is over. If she accepts and passes the challenges, she will be presented by the next question; if she accepts but fails, she get $0 and game is over;
(c) The game will be over if CII passes the last question Q4 and in that case, CHI will earn all the rewards over the four questions. Assume that CHI knows in advance that she will pass Q1, Q2, Q3, and Q1 with respective probabilities 3/4, 1/2, 1/2, and 1/4.
1. Consider such a simple policy that always accepts the challenge. Please compute the value function V". Here you should explicitly state the values V* () for the four states s = Q1, Q2, Q3 and Q1.
2. Please compute an optimal policy r* and the value function V. Again, please explicitly state the values V**(*) for the four states s=Q1, Q2, Q3 and Q1.

Part one: measurements 1. measure your own height and arm span (from finger-tip to finger-tip) in inches. you will likely need some from a parent, guardian, or sibling to get accurate measurements. record your measurements on the "data record" document. use the "data record" to you complete part two of this project. name relationship to student x height in inches y arm span in inches archie dad 72 72 ginelle mom 65 66 sarah sister 64 65 meleah sister 66 3/4 67 rachel sister 53 1/2 53 emily auntie 66 1/2 66 hannah myself 66 1/2 69 part two: representation of data with plots 1. using graphing software of your choice, create a scatter plot of your data. predict the line of best fit, and sketch it on your graph. part three: the line of best fit include your scatter plot and the answers to the following questions in your word processing document 1. 1. which variable did you plot on the x-axis, and which variable did you plot on the y-axis? explain why you assigned the variables in that way. 2. write the equation of the line of best fit using the slope-intercept formula $y = mx + b$. show all your work, including the points used to determine the slope and how the equation was determined. 3. what does the slope of the line represent within the context of your graph? what does the y-intercept represent? 5. use the line of best fit to you to describe the data correlation.

Divide. write in the simplest form. 4 1/6 divided by 10

20 points 1. your friend, taylor, missed class today and needs some identifying solutions to systems. explain to taylor how to find the solution(s) of any system using its graph. 2. taylor graphs the system below on her graphing calculator and decides that f(x)=g(x) at x=0, x=1, and x=3. provide taylor some feedback that explains which part of her answer is incorrect and why it is incorrect. f(x)=2x+1 g(x)=2x^2+1