Suppose that the random variables x, y, and z have the following joint probability distribution. xyz(x, y, z) 1 1 1 0.05 1 1 2 0.10 1 2 1 0.15 1 2 2 0.20 2 1 1 0.20 2 1 2 0.15 2 2 1 0.10 2 2 2 0.05 determine the following: a. p(x = 2) b. p(x = 1, y = 2) c. p(z < 1.5) d. p(x = 1 or z = 2) e. e(x) f. p(x = 1 | y = 1) g. p(x = 1, y = 1 | z = 2) h. p(x = 1 | y = 1, z = 2) i. conditional probability distribution of x given that y = 1 and z = 2

Frank has $66.50 in his account on sunday. over the next week, he makes the following changes to his balance via deposits and purchases: day debit ($) credit ($) monday 60.33 80.75 tuesday 54.45 wednesday 49.20 15.00 thursday 35.40 friday 16.85 75.00 saturday 80.56 on what day does frank first get charged an overdraft fee? a. wednesday b. thursday c. friday d. saturday select the best answer from the choices provided a b c d

5.(04.07) two different plants grow each year at different rates, which are represented by the functions f(x) = 4* and g(x) = 5x + 2. what is the first year the f(x) height is greater than the g(x) height? year 3 year 0 year 2 year 1

You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function.how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions