Suppose that a six-sided die is "loaded" so that any particular even-numbered face is three times as likely to be observed as any particular odd-numbered face. (a) what are the probabilities of the six simple events? (hint: denote these events by o6. then p(o1) = p, p(o2) = 3p, p(o3) = p(o6)= 3p. now use a condition on the sum of these probabilities to determine p. answer as an exact fraction or round your answers to three decimal places.)

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

Someone answer asap for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =

In a column proof the right column states your reasons