The temperature of a cup of coffee t minutes after it has been poured is described by the function

1 answer:

5 0

A) You want to find t such that
.. C(t) = d
.. d = 20 +60*0.95^t
.. (d -20)/60 = 0.95^t
.. log((d -20)/60) = t*log(0.95)
.. t = log((d -20)/60)/log(0.95) . . . . . . time to cool to d degrees (d > 20)

b) C'(t) = 60*0.95^t*ln(0.95)
.. C'(1) = 60*0.95*ln(0.95) ≈ -2.924 °C/min

You might be interested in

Assume that the car lot contains 40 percent BMWs, 25 percent Volvos, and 35 percent Jaguars. Of the BMWs, 90 percent have naviga

sveticcg [70]

Answer:

The required probability is 0.4098.

Step-by-step explanation:

Consider the provided information.

According to conditional probability that A occurs , given B has occurred.

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

Assume that the car lot contains 40 percent BMWs, 25 percent Volvos, and 35 percent Jaguars.

Pr(BMWs)=0.40

Pr(Volvos)=0.25

Pr(Jaguars)=0.35

Of the BMWs, 90 percent have navigation systems, 30 percent of the Volvos have navigation systems, and 50 percent of the Jaguars have navigation systems.

Pr(Navigation | BMWs)=0. 90

Pr(Navigation l Volvos)=0.30

Pr(Navigation l Jaguars)=0.50

Total cars with navigation system = 0.40×0.90+0.25×0.30+0.35×0.50

=0.36+0.075+0.175=0.61

Pr(Not Bmw l Navigation system) = $\frac{0.25\times0.30+0.35\times0.50}{0.61}\approx0.4098$