Let f(x)f(x) and g(x)g(x) be functions with antiderivatives F(x)F(x) and G(x)G(x) respectively. Given that F(3)=3F(3)=3, G(3)=5G(3)=5, F(6)=1F(6)=1, and G(6)=6G(6)=6, evaluate the following integral ∫63(3f(x)−4g(x)) dx

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Acaterer charges $500 plus $30 per guest to cater a wedding. walt and traci don't want to spend more than $8000 on catering. write and solve an inequality in terms of the number of guests, g, that can be invited. a) 30g ? 8000; g ? 267 b) 500g < 8000; g < 16 c) 500 + 30g < 8000; g < 250 d) 500 + 30g ? 8000; g ? 250

You work for a landscape company that just got a contract to re-mulch a park. the area that needs mulching is 30 feet by 60 feet. they want a 3 inch layer of much on the area. the company has bags of mulch that cover 2 cubic yards that cost $4.00 per bag. how much will it cost the consumer just in materials to re-mulch the area (round to the nearest dollar)?