A flat rate shipping box is in the shape of a rectangular prism. You estimate that the volume of the box is 350 cubic inches. You measure the box and find that it has a length of 10 inches, a width of 9 inches, and a helght of 4.5 inches. Find the percent error. Round your answer to the nearest tenth of a percent.
The percent error is about %.

13.6%

Step-by-step explanation:

Step 1

Find the actual volume of the box

Volume = Length × Width × Height

You measure the box and find that it has a length of 10 inches, a width of 9 inches, and a helght of 4.5 inches.

Volume = 10 inches × 9 inches × 4.5 inches

Volume of the box = 405 cubic inches

Step 2

Calculate the percent error

|Estimated value - Actual value|/Actual value ×100

Estimated value= 350 cubic inches

Actual value = 405 cubic inches

= |350 - 405|/405 × 100

= |-55|/405 × 100

= 55/405 × 100

= 13.580246914%

Approximately = 13.6%

The Percent error is 13.6%

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt