Problem. A man made lake initially contains 200 gal of water with 50 lb of a chemical dissolved into it. A solution containing 3 lb/gal of the chemical runs into the lake at a rate of 4 gal/min and the well mixed solution runs out of the lake at a rate of 4 gal/min. What is the maximum amount of chemical ever in the lake? A. Set up a differential equation modeling the amount of chemical in the lake at any time. (Choose your own notation, and clearly indicate meaning) B. Solve the differential equation. C. Based on the solution, answer the following: What is the maximum amount of chemical ever in the lake?

Question 1 (3 points) saved what is the solution for the following system of equations? use any method to solve. y = -x +4 y = x - 2 question 1 options: ( 4 , -2) (2, 1) (3, 1) (3, -2) question 2 (3 points) saved the solution to a system of equations is where the lines intersect. question 2 options: true false question 3 (3 points) which ordered pair is the best estimate for the solution of the system of equations? the graph of the system of equations : y = 3/2x +6 and y=1/4x - 2 question 3 options: (-6, -3) (-6.5, -3.5) (-7, -4) (-7, -3.5) question 4 (3 points) what is the solution for the following system of equations? use any method to solve. 2x + 8y = 4 x = -3y + 5 question 4 options: x = 14, y= -3 x = 2, y = -3 x = -3, y = -3 x = 12, y = 5 question 5 (3 points) solve the following system using any method. 8a - 4b = 20 5a - 8b = 62 question 5 options: a = 5, b = -4 a = 8, b = 4 a = -5, b = -8 a = -2, b = -9 question 6 (3 points) breana is selling tickets to a choral performance. on the first day of ticket sales, she sold 3 senior citizen tickets and 1 child ticket for a total of $38. breana took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. what is the price of a senior citizen ticket? question 6 options: question 7 (3 points) a farmer has 5 times as many cows as pigs. the farmer only has cows and pigs, and he has 168 animals. how many cows does he have? question 7 options: 140 cows 120 cows 50 cows 28 cows question 8 (3 points) how many solutions does the system have? question 8 options: zero one infinitely many question 9 (3 points) what is the solution to the system of equations? graph of x+2y = 6 and y = x question 9 options: (1 , -2) (2, 2) (3, 5) (-2, 2)

Which situation is an example of an observational study?

Evaluate f(x) when x = 3. f(x) = 16x? +2 if 6 < x < 9 112 if 9 x < 13 a: 110 b: 56 c: 74 d: 12