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1. All the survivors who live in a certain a post-apocalyptic settlement spend their miserable days hunting mutant buffalo or growing broccoli, and some do both. If, in total, 45 survivors grow broccoli, 30 hunt, and 37 of them perform only one of those tasks, how many perform both tasks?
2. At the Biltmore Hotel, 86 guests are in rooms with king size beds and 57 guests are in rooms with bathtubs. If 83 of the guests are in rooms with only a bathtub OR a king size bed, how many guests are in rooms with both features?
3. The equation of a certain parabola is y = ax^2 + bx + c. If a>0 and c<0, which of the following could be the graph of the parabola? (I don't have pics so I'll describe them)
(A) vertex in 3rd quadrant, opens upward
(B) vertex in 4th quadrant, opens upward
(C) same as (A) but vertex is slightly moved over closer to the y-axis
(D) vertex in 1st quadrant, opens downward
(E) vertex in 2nd quadrant, opens downward
Please help me with these problems and explain your solutions. Thank you!