You are ordering a new home theater system that consists of a tv, surround sound system, and dvd player. you can choose from 18 different tvs, 18 types of surround sound systems, and 4 types of dvd players. how many different home theater systems can you build?

To find the total different combinations, multiply the quantity of each item together.

18 TV's x 18 surround sound's x 4 DVD player's

= 1296 different combinations.

  5.7 cm or 2 1/4 in

Step-by-step explanation:

Your tape measure is not shown.

  On my tape measure, 5.7 cm is the closest mark. On the inch scale, 2 1/4 inches is the next-closest mark.

On a tape measure graduated in 1/32 inch between 2 and 3 inches, you can find the closest mark by rounding to the nearest 32nd:

  2.23607 × 32 ≈ 71.55 ≈ 72 --- 32nds of an inch

  72/32 = 2 1/4 . . . . the closest mark on an inch ruler graduated in 32nds

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For a ruler graduated in millimeters, you can find the closest millimeter in the same way. There are 25.4 mm to the inch.

  2.23607 in × 25.4 mm/in ≈ 56.80 mm ≈ 57 mm

  57 mm = 5.7 cm . . . closest mark on metric scale

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When we check the error, we find the metric mark is closer than the inch mark.

  5.7 cm ≈ 2.24409 in . . . . error of 0.00802 in

  2 1/2 in = 2.25000 in . . . error of 0.01393 in