Let x be a set and let aç be a set for each a in a nonempty index set i. prove the distributive properties: xn (ua) = u(xna 1 ael and xu = n(xu ag). auaj lael ael y1. let a, b, and c be sets. prove that car ca x c).

Data for the height of a model rocket launch in the air over time are shown in the table. darryl predicted that the height of the rocket at 8 seconds would be about 93 meters. did darryl make a good prediction? yes, the data are best modeled by a quadratic function. the value of the function at 8 seconds is about 93 meters. yes, the data are best modeled by a linear function. the first differences are constant, so about 93 meters at 8 seconds is reasonable. no, the data are exponential. a better prediction is 150 meters. no, the data are best modeled by a cubic function. a better prediction is 100 meters.

Twice the sum of a number and 2 is equal to three times the difference of the number and 8. find the number.

Acafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or french fries. he used a computer program to randomly select three dishes for monday's lunch. what is the theoretical probability the applesauce and broccoli will both be offered monday?