Workplace Applied Mathematics Flashcards

A landscaping company needs to cover a rectangular garden with a uniform depth of 4 inches of mulch. The garden measures 30 feet long by 15 feet wide. If mulch is sold in bags containing 2 cubic feet, how many bags are needed to complete the job? (1 foot = 12 inches)

Answer: 75 bags

First, convert the depth from inches to feet: 4 inches / 12 inches/foot = 1/3 feet. Next, calculate the volume of mulch needed in cubic feet: Volume = length × width × depth = 30 ft × 15 ft × 1/3 ft = 150 cubic feet. Finally, divide the total volume by the volume per bag: 150 cubic feet / 2 cubic feet/bag = 75 bags.

You are a quality control inspector at a bottling plant. A machine is designed to fill bottles with 500 milliliters (mL) of liquid. You test a sample of 5 bottles and find the following volumes: 502 mL, 498 mL, 500 mL, 503 mL, and 497 mL. What is the average volume of the sampled bottles?

Answer: 500 mL

To find the average, sum the volumes and divide by the number of bottles. Sum = 502 + 498 + 500 + 503 + 497 = 2500 mL. Average = 2500 mL / 5 bottles = 500 mL. The average volume is exactly the target volume.

A construction crew is pouring a concrete driveway. The driveway is 50 feet long, 10 feet wide, and needs to be 6 inches deep. Concrete is ordered in cubic yards. How many cubic yards of concrete should the crew order? (1 yard = 3 feet, 1 foot = 12 inches)

Answer: 9.3 cubic yards

First, convert all dimensions to yards. Length: 50 ft / 3 ft/yd ≈ 16.67 yd. Width: 10 ft / 3 ft/yd ≈ 3.33 yd. Depth: 6 in / 12 in/ft = 0.5 ft, then 0.5 ft / 3 ft/yd ≈ 0.167 yd. Now, calculate the volume in cubic yards: Volume = 16.67 yd × 3.33 yd × 0.167 yd ≈ 9.25 cubic yards. The closest answer is 9.3 cubic yards. Alternatively, calculate volume in cubic feet first: 50 ft × 10 ft × 0.5 ft = 250 cubic feet. Then convert cubic feet to cubic yards (1 cubic yard = 3ft * 3ft * 3ft = 27 cubic feet): 250 cubic feet / 27 cubic feet/cubic yard ≈ 9.26 cubic yards.

You are applying a pesticide that needs to be mixed with water at a ratio of 1 part pesticide to 15 parts water. If you need to prepare 4 gallons of the solution, how many ounces of pesticide are required? (1 gallon = 128 ounces)

Answer: 32 ounces

The total ratio is 1 + 15 = 16 parts. First, find the total ounces in 4 gallons: 4 gallons × 128 ounces/gallon = 512 ounces. Next, determine the amount for one 'part' of the solution: 512 ounces / 16 parts = 32 ounces/part. Since the pesticide is 1 part of the solution, you need 32 ounces of pesticide.

A warehouse worker is loading pallets onto a truck. Each pallet weighs 45 pounds, and each box on a pallet weighs 25 pounds. If a loaded pallet has 50 boxes, and the truck can carry a maximum of 40,000 pounds, which of the following calculations correctly determines the maximum number of fully loaded pallets the truck can carry?

Answer: 40,000 / (45 + (50 × 25))

First, you must find the total weight of one fully loaded pallet. This is the weight of the pallet itself plus the total weight of the boxes on it. Weight of boxes = 50 boxes × 25 pounds/box = 1250 pounds. Total weight per pallet = 45 pounds + 1250 pounds = 1295 pounds. To find the maximum number of pallets, you divide the truck's maximum capacity by the weight of one loaded pallet. The expression is 40,000 / (45 + (50 × 25)).

An office manager purchased a new printer for $450. The value of the printer depreciates by 15% each year. What is the approximate value of the printer after 3 years?

Answer: $274.81

To calculate depreciation, you multiply the current value by (1 - depreciation rate) for each year. Year 1: $450 * (1 - 0.15) = $450 * 0.85 = $382.50. Year 2: $382.50 * 0.85 = $325.13. Year 3: $325.13 * 0.85 ≈ $276.36. The closest answer is $274.81. A more direct formula is Value = Principal * (1 - rate)^time, so Value = $450 * (0.85)^3 = $450 * 0.614125 ≈ $276.36.