9514 1404 393
Answer:
4. (d) 4.38 in³
5. (b) 19 gallons
6. (a) 6.4 yd³
Explanation:
4. The equation can be rearranged to find the compressed volume.
Multiply both sides by the compressed volume:
(compression ratio)×(compressed volume) = (expanded volume)
Divide both sides by the compression ratio:
(compressed volume) = (expanded volume)/(compression ratio)
Fill in the numbers and do the arithmetic.
compressed volume = 46.0 in³/(10.5/1) = 4.38 in³
The compressed volume is about 4.38 in³.
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5. The area to be covered is 3170 ft². We want to cover it twice, so the total area we want to cover is 2×3170 ft² = 6340 ft². One gallon of paint covers 350 ft². We want to find the smallest integer number of gallons n such that ...
n×(350 ft²) ≥ 6340 ft²
Dividing by the coefficient of n, we have ...
n ≥ 6340/350 ≈ 18.11
The smallest integer value of n is 19. 19 gallons of paint will be needed.
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6. The quantity of sand needed (q) is proportional to the area to be covered, so we have ...
q/(400 yd²) = (1.6 yd³)/(100 yd²)
Multiplying both sides of this equation by 400 yd² gives ...
q = (1.6 yd³)(400/100) = 6.4 yd³
6.4 yd³ of sand will be needed.