There are 4 quarts in a quart and 4 quarts in a gallon. A baker needs 1 cup of milk for each batch of muffins he makes. He has 3 gallons of milk and wants to make as many batches as possible. How many batches of muffins will the baker make?

Work Shown:

4 cups = 1 quart given info

4*(4 cups) = 4*(1 quart) ... multiply both sides by 4

16 cups = 4 quarts

4 quarts = 1 gallon given info

16 cups = 1 gallon replace "4 quarts" with "16 cups"

3*(16 cups) = 3*(1 gallon) ... multiply both sides by 3

48 cups = 3 gallons

The baker will get 48 cups out of 3 gallons of milk. Since each batch needs 1 cup of milk, this means the baker will be able to make 48 batches of muffins.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

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step-by-step explanation: