A linear function that represents the number of hot dogs purchased at a football game is compared to a different linear function that represents the time left in the game. Describe the key features of the functions that are needed to determine if these lines intersect.

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 8 y is greater than or equal to negative 5 over 2 times x plus 5 part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points) part b: is the point (5, −8) included in the solution area for the system? justify your answer mathematically. (4 points)

Amachine part consists of a half sphere and a cylinder, as shown in the figure. the total volume of the part is π cubic inches.

How many heads would you expect if you flipped a coin twice? first, fill in the table below with the correct probabilities. hint: the sample space for flipping a coin twice is {hh, ht, th, tt}. a = b = c = f