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Elena L [17]
3 years ago
15

A cup of hot coffee has been left to cool in a room with an ambient temperature of 21°C.

Mathematics
1 answer:
ch4aika [34]3 years ago
4 0

Answer:

The temperature of the coffee after 10 minutes will be 21.27°C.

Step-by-step explanation:

The equation representing the elapsed time, <em>m</em>, in minutes, since the coffee was left to cool, and the  temperature of the coffee, <em>T</em>, measured in °C is:

T(m)=21+74.10^{-0.03 m}

Compute the temperature of the coffee after 10 minutes as follows:

T(10)=21+74.10^{-0.03 \times 10}

          =21+0.274824\\=21.274824\\\approx 21.27^{o}\ C

Thus, the temperature of the coffee after 10 minutes will be 21.27°C.

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Lara is a 50% partner. She is guaranteed payment of no less than 20,000. The partnership's income before deducting guaranteed pa
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Answer:

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Partnership's income = 50,000

Lara's guaranteed payment = 20,000

As the Income 50,000 is larger than Lara's guaranteed payment i.e 20,000. Since Lara is 50% partner so she will receive half the amount of the partnership's income.

Partnership's Income = 50,000  

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8 0
3 years ago
g If the economy improves, a certain stock stock will have a return of 23.4 percent. If the economy declines, the stock will hav
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Answer:

E(X) = 23.4* 0.67 -11.9*0.33= 11.759 \%

Now we can find the second central moment with this formula:

E(X^2) = \sum_{i=1}^n X^2_i P(X_i)

And replacing we got:

E(X^2) = (23.4)^2* 0.67 +(-11.9)^2*0.33= 413.5965

And the variance is given by:

Var(X) = E(X^2) - [E(X)]^2

And replacing we got:

Var(X) = 413.5965 -(11.759)^2 =275.5105

And finally the deviation would be:

Sd(X) = \sqrt{275.5105}= 16.599 \%

Step-by-step explanation:

We can define the random variable of interest X as the return from a stock and we know the following conditions:

X_1 = 23.4 , P(X_1) =0.67 represent the result if the economy improves

X_2 = -11.9 , P(X_1) =0.33 represent the result if we have a recession

We want to find the standard deviation for the returns on the stock. We need to begin finding the mean with this formula:

E(X) = \sum_{i=1}^n X_i P(X_i)

And replacing the data given we got:

E(X) = 23.4* 0.67 -11.9*0.33= 11.759 \%

Now we can find the second central moment with this formula:

E(X^2) = \sum_{i=1}^n X^2_i P(X_i)

And replacing we got:

E(X^2) = (23.4)^2* 0.67 +(-11.9)^2*0.33= 413.5965

And the variance is given by:

Var(X) = E(X^2) - [E(X)]^2

And replacing we got:

Var(X) = 413.5965 -(11.759)^2 =275.5105

And finally the deviation would be:

Sd(X) = \sqrt{275.5105}= 16.599 \%

7 0
3 years ago
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