A certain board game uses two standard six-sided dice. Each player rolls the dice and advances a number of squares equal to the sum of the values on the dice. If the player rolls doubles (two dice with the same value) on the first roll, the player is allowed to roll again. Similarly, if he rolls doubles on the second roll, he is allowed a third roll. If he rolls doubles on the third roll, he receives a penalty. What is the probability that a player will receive such a penalty on any given turn?

What is the standard form of -5x^2+2x^4-11+x^3+3x

The distance of a chord from the centre of a circle is 12cm and the lenght of the chord is 10cm. find the radius of the circle

Ascientist places 24 cells in a petri dish. she knows the cells grow at an exponential rate, doubling in number every hour. how long will it take (in hours) for there to be 1100 cells in the dish? time to 1100 cells: 5.51832530 hours how long will it take to reach 110 cells? time to 110 cells : 2.1963972 hours what is the average rate of change in the number of cells between 9 hours and 11 hours? average rate of change: cells per hour what is the instantaneous rate of change after 7 hours? instantaneous rate of change: cells per hour note: you can earn partial credit on this problem.