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A builder is covering the floor of a rectangular room that is 23 feet by 25 feet with tiles that are 1 foot by 1 foot. The tiles are sold in boxes of 12 .

Diego says 59 boxes are needed to cover the floor, and that there will be a few leftover tiles.
a. Is Diego's answer reasonable? Explain or show your reasoning.

$4$ . A builder is covering the floor of a rectangular room that is $23$ feet by $25$ feet with tiles that are $1$ foot by $1$ foot. The tiles are sold in boxes of $12$ . $\newline$ Diego says $59$ boxes are needed to cover the floor, and that there will be a few leftover tiles. $\newline$ a. Is Diego's answer reasonable? Explain or show your reasoning.

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Find probabilities using the binomial distribution

Full solution

Q.

4

. A builder is covering the floor of a rectangular room that is

23

feet by

25

feet with tiles that are

1

foot by

1

foot. The tiles are sold in boxes of

12

.

\newline

Diego says

59

boxes are needed to cover the floor, and that there will be a few leftover tiles.

\newline

a. Is Diego's answer reasonable? Explain or show your reasoning.

Calculate Total Area: First, let's find out how many tiles are needed to cover the floor. Since the room is $23$ feet by $25$ feet, we multiply the two dimensions to get the total area in square feet. $\newline$ $23 \text{ feet} \times 25 \text{ feet} = 575 \text{ square feet}.$
Determine Number of Tiles: Now, since each tile covers $1$ square foot, we need the same number of tiles as the area of the floor, which is $575$ tiles.
Calculate Boxes Needed: Next, we need to figure out how many boxes of tiles are needed. Each box contains $12$ tiles. So we divide the total number of tiles by the number of tiles per box. $\newline$ $575$ tiles $/$ $12$ tiles per box $= 47.9167$ boxes.
Round Up to Nearest Box: Since we can't buy a fraction of a box, we'll need to round up to the nearest whole box. That means we need $48$ boxes to cover the floor.
Compare with Diego's Answer: Diego said $59$ boxes are needed, but we calculated that only $48$ boxes are required. Therefore, Diego's answer is not reasonable.

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