Chris claims that for any given values of x, the gradient of the curve y=2x^3 + 6x ^2 - 12x +3 is always greater than the gradient of the curve y=1 + 60x - 6x^2 ". show that chris is wrong by finding all the values of x for which his claim is 'not' true.

The number if marbles of different colors stored in a hat is listed below: 4 red marbles 10 green marbles 7 blue marbles. without looking in the hat, dan takes out a marble at random. he replaces the marble and then takes out another marble from the hat. what is the probability that dan takes out a blue marble in both draws?

Can someone check if i did this correct. it’s number 4 if you’re wondering.

At the county fair, the baxter family bought 6 hot dogs and 4 juice drinks for $12.90. the farley family bought 3 hot dogs and 4 juice drinks for $8.55. find the price of a hot dog and the price of a juice drink.