Consider the monty hall problem. in the case that the door you initially chose hid the valuable prize, suppose that monty opens one of the other two doors for you not uniformly at random, but rather opens the second door with probability p and the third door with probability 1 − p, for some p ∈ [0, 1]. how does this affect your chances of getting the prize when switching?

Use the x-intercept method to find all real solutions of the equation.x^3-10x^2+27x-18=0

Brady has a 20 year fixed rate mortgage for $215,500 with monthly payments of 1,305.89.the annual interest rate is 4%. what is the total cost of the principal and interest for this loan rounded to the nearest dollar

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