Riley finds a recipe for bubble solution that uses 1 cup water, 1/4 cup dish soap, and 1 tablespoon corn syrup. She uses 2 cups of dish soap. How much water
should she use?

Find the gradient of f(x,y,z)equals=left parenthesis x squared plus y squared plus z squared right parenthesis superscript negative 1 divided by 2 baseline plus ln left parenthesis x right parenthesis x2+y2+z2−1/2+ln(xyz) at the point left parenthesis negative 2 comma 1 comma negative 2 right parenthesis(−2,1,−2).

Arestaurant gives out a scratch-off card to every customer. the probability that a customer will win a prize from a scratch-off card is 25%. design and conduct a simulation using random numbers to find the experimental probability that a customer will need more than 3 cards in order to win a prize. justify the model for your simulation, and conduct at least 10 trials.

Select all expressions that are equivalent to 2(3x + 7y). question 1 options: 6x + 14y 6x + 7y 1(6x + 14y)