An individual consumes products X and Y and spends $36 per time period. The prices of the two goods are $3 per unit for X and $2 per unit for Y. The consumer in this case has a utility function expressed as: U(X, Y) = .5XY a. Express the budget equation mathematically by plugging in the given information. Use capital letters and a single space between operators.

Pick the expression that matches this description: a polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 (choice a) 7x^5+2x^2+6 (choice b) 7x^6−6x^4+5 (choice c) 6x^7−x^5+5 (choice d) 6x^5+x^4+7

The architect's side view drawing of a saltbox-style house shows a post that supports the roof ridge. the support post is 8 ft tall. the distance from the front of the house to the support post is less than the distance from the post to the back of the house. how far from the front of the house is the support post positioned?

The height of a birch tree, f(x), in inches, after x months is shown in the graph below. how much does the birch tree grow per month, and what will be the height of the birch tree after 10 months? a. the birch tree grows 1 inch per month. the height of the birch tree will be 16 inches after 10 months. b. the birch tree grows 2 inches per month. the height of the birch tree will be 26 inches after 10 months. c. the birch tree grows 3 inches per month. the height of the birch tree will be 36 inches after 10 months. d. the birch tree grows 2 inches per month. the height of the birch tree will be 24 inches after 10 months.