Will mark brainliest! a turkey is taken out of the oven with an internal temperature of 167∘f, and is placed on a kitchen counter where the temperature is 64∘f. after 46 minutes, the internal temperature has cooled to 123∘f. determine the amount of time it would take for the turkey to cool to 91∘f. round your answer 4 decimal places.

  110.5348 minutes

Step-by-step explanation:

The difference from room temperature changes from 103 to 59 in 46 minutes, so that difference can be modeled by the exponential equation ...

  Δt = 103×(59/103)^(t/46)

We want to find t for the temperature difference Δt = 91 -64 = 27.

  27 = 103×(59/103)^(t/46)

  27/103 = (59/103)^(t/46) . . . . . divide by 103

Taking logs gives the linear equation ...

  log(27/103) = (t/46)log(59/103)

Multiplying by the inverse of the coefficient of t, we get ...

  t = 46·log(27/103)/log(59/103) ≈ 46·(-0.58147346)/(-0.24198521)

  ≈ 110.5347

It will take about 110.5347 minutes for the turkey to cool to 91 °F internally.

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Comment on 4 decimal places

An answer correct to 4 decimal places (7 significant digits) is a pretty good indication that the problem was worked correctly. However, that level of precision in the timing makes little sense in this context. Most thermometers will take at least a few seconds to register the temperature to within a tenth of a degree or so. This problem is asking for an answer that is within 6 milliseconds and 30 micro-degrees. Neither of these is anywhere near realistic for a kitchen meat thermometer.

More realistic would be an answer to 4 significant figures, a tenth of a minute and a few hundredths of a degree.

(The rate of change at the time of interest is about -0.33 degrees per minute.)

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step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.