What are all of the real roots of the following polynomial? f(x) = x5 + 3x4 + 5x3 + 15x2 + 4x + 12

Carson has only $20 bills and $10 bill in her wallet. the total value of the bills is $50. she has 1 more $20 bill than $10 bills. how many each kind of bill does carson have? a. one $20 and two $10 bills b. two $20 bills and one $10 bill c. one $20 bills and three $10 bills d. two $20 bills and two $10 bills

Abag contains 3 red marbles, 2 blue marbles, and 2 green marbles. one marble is picked, then another marble. assume that the selections are made with replacement. a) find the probability of picking two red marbles with replacement. b) find the probability of picking a red marble and a blue marble. assume the selections are made without replacement. c) find the probability of picking two red marbles without replacement. d) find the probability of picking a red marble and a blue marble without replacement.

In each of the cases that follow, the magnitude of a vector is given along with the counterclockwise angle it makes with the +x axis. use trigonometry to find the x and y components of the vector. also, sketch each vector approximately to scale to see if your calculated answers seem reasonable. (a) 50.0 n at 60.0°, (b) 75 m/ s at 5π/ 6 rad, (c) 254 lb at 325°, (d) 69 km at 1.1π rad.