Please help with this question

9514 1404 393

  4. (d) 4.38 in³

  5. (b) 19 gallons

  6. (a) 6.4 yd³

Step-by-step 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.

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