10. A statistics class has 24 students where students work in groups of 4 every week that are
randomly assigned
a. What is the probability a student will work in the same group of 4 this week that they did
last week?
b. If the class has 14 females and 10 males, how many groups can be made that have 2 males
and 2 females?

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Ответ:

isiahisiah799

20.01.2021

Mathematics

a. $\frac{dT}{dt}=k(T-Tm); T(0)=190$

b. $C_{0}=122$

c. k=-0.00259

d. $t=153.39838\\$ minutos

Step-by-step explanation:

a. Newton's law of cooling states that the speed with which a body is cooled is proportional to the difference between its temperature and that of the medium in which it is found. Then, the initial value problem is given by:

Tm=68

$\frac{dT}{dt}=k(T-Tm); T(0)=190$

b. The differential equation obtained is a differential equation of separable variables:

$\frac{dT}{T-Tm}=kdt\\\\\int {\frac{dT}{T-Tm}}=\int{kdt}\\\\Ln|T-Tm|=kt+C\\\\T(t)=C_{0}e^{kt}+Tm=C_{0}e^{kt}+68\\\\T(0)=C_{0}e^{k(0)}+68=190\\\\C_{0}=122$

c. After 33 minutes of serving the coffee has cooled to 180°:

$T(33)=122e^{33k}+68=180\\\\e^{33k}=\frac{112}{122}\\\\33k=Ln(\frac{112}{122})\\\\k=-0.00259$

$150=122e^{-0.00259t}+68\\\\Ln(\frac{150-68}{122})=-0.00259t\\\\t=153.39838\\\\$

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