(a) How many liters of wine can be held in a wine barrel whose capacity is 31 gal? (b) The recommended adult dose of Elixophyllin', a drug used to treat asthma, is 6 \(\mathrm{mg} / \mathrm{kg}\) of body mass. Calculate the dose in milligrams for a 185 -lb person. (c) If an automobile is able to travel 400 \(\mathrm{km}\) on 47.3 \(\mathrm{L}\) of gasoline, what is the gas mileage in miles per gallon?(d) When the coffee is brewed according to directions, a pound of coffee beans yields 50 cups of coffee \((4\) cups \(=1\) qt). How many kg of coffee are required to produce 200 cups of coffee?

We know that 1 gallon is approximately equal to 3.78541 liters. The formula to convert gallons to liters is: \[ Liters = Gallons \times 3.78541 \] Given that the capacity of the wine barrel is 31 gallons, apply the formula to find the liters of wine it can hold. \[ Liters = 31 \times 3.78541 \] \[ Liters ≈ 117.44771 \] Thus, the wine barrel can hold approximately 117.45 liters of wine.

First, we need to convert the person's weight from pounds to kilograms. We know that 1 pound is approximately equal to 0.453592 kg. The formula to convert pounds to kilograms is: \[ Kilograms = Pounds \times 0.453592 \] Given that the person's weight is 185 pounds, apply the formula to find the weight in kilograms. \[ Kilograms = 185 \times 0.453592 \] \[ Kilograms ≈ 83.91452 \] Next, we need to calculate the dose of Elixophyllin in milligrams. The recommended adult dose of Elixophyllin is 6 mg/kg of body mass. To find the dose for this person, use the formula: \[ Dose\,(mg) = Weight\,(kg) \times Dose\,(mg/kg) \] Plug in the calculated weight in kilograms and the given dose in mg/kg. \[ Dose\,(mg) = 83.91452 \times 6 \] \[ Dose\,(mg) ≈ 503.48712 \] Thus, the dose for a 185-lb person is approximately 503.49 mg.

First, we need to convert the distance from kilometers to miles. We know that 1 kilometer is approximately equal to 0.621371 miles. The formula to convert kilometers to miles is: \[ Miles = Kilometers \times 0.621371 \] Given that the automobile can travel 400 km, apply the formula to find the distance in miles. \[ Miles = 400 \times 0.621371 \] \[ Miles ≈ 248.548 \] Next, convert the fuel consumption from liters to gallons. We know that 1 liter is approximately equal to 0.264172 gallons. The formula to convert liters to gallons is: \[ Gallons = Liters \times 0.264172 \] Given that the automobile consumes 47.3 L of gasoline, apply the formula to find the fuel consumption in gallons. \[ Gallons = 47.3 \times 0.264172 \] \[ Gallons ≈ 12.4937196 \] Finally, to find the gas mileage in miles per gallon, divide the distance in miles by the fuel consumption in gallons. \[ Gas\,Mileage\,(mpg) = \frac{Miles}{Gallons} \] \[ Gas\,Mileage\,(mpg) = \frac{248.548}{12.4937196} \] \[ Gas\,Mileage\,(mpg) ≈ 19.884 \] Thus, the gas mileage is approximately 19.88 miles per gallon.

We first find out how many pounds of coffee are required to produce 200 cups of coffee. Given that 1 lb of coffee yields 50 cups, \[ \frac{1\,lb}{50\,cups} = \frac{x\,lb}{200\,cups} \] Solving for x (pounds of coffee required), \[ x = \frac{1\,lb \times 200\,cups}{50\,cups} \] \[ x = 4\,lb \] Now, we need to convert the required coffee amount from pounds to kilograms. We know that 1 pound is approximately equal to 0.453592 kg. The formula to convert pounds to kilograms is: \[ Kilograms = Pounds \times 0.453592 \] Given that we need 4 pounds of coffee, apply the formula to find the required coffee amount in kilograms. \[ Kilograms = 4 \times 0.453592 \] \[ Kilograms ≈ 1.814368 \] Thus, we need approximately 1.81 kg of coffee to produce 200 cups of coffee.