A large tank is filled to capacity with 600 gallons of pure water. Brine containing 5 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is pumped out at a rate of 12 gallons/min. Find the number A(t) of pounds of salt in the tank at time t. A(t)

Answers

Answer 1
Answer:

Salt flows into the tank at a rate of

(5 lb/gal) * (6 gal/min) = 30 lb/min

The volume of solution in the tank after t min is

600 gal + (6 gal/min - 12 gal/min)*(t min) = 600 - 6t gal

which means salt flows out at a rate of

(A(t)/(600 - 6t) lb/gal) * (12 gal/min) = 2 A(t)/(100 - t) lb/min

Then the net rate of change of the salt content is modeled by the linear differential equation,

A'(t)=30-(2A(t))/(100-t)

Solve for A:

A'+(2A)/(100-t)=30

Multiply both sides by the integrating factor, \frac1{(100-t)^2}:

(A')/((100-t)^2)+(2A)/((100-t)^3)=(30)/((100-t)^2)

\left(\frac A{(100-t)^2}\right)'=(30)/((100-t)^2)

Integrate both sides:

\frac A{(100-t)^2}=(30)/(100-t)+C

\implies A(t)=30(100-t)+C(100-t)^2

The tank starts with no salt, so A(0) = 0 lb. This means

0=30(100)+C(100)^2\implies C=-\frac3{10}

and the particular solution to the ODE is

A(t)=30(100-t)-\frac3{10}(100-t)^2=\frac3{10}t(100-t)


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Answers

Really, now, do you think it fair (or realistic) to hope that someone will do all your homework for you?  Please be thoughtful and courteous and post no more than one or two questions at a time.

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HOME Realty claims that it can sell a detached, residential house faster than any other realty company. With the aim of examining HOME's claim, you sample 20 customers who sold a detached, residential house through HOME and record the selling times (in days) of the houses. Your data are summarized below:Selling Time Frequency
0 10 3
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Find the proportion of selling times in the sample that are less than 20 days claims that it can sell a detached, residential house faster than any other realty company.

Answers

Answer:

0.35

Step-by-step explanation:

Given the data:

Selling Time___ Frequency

0 10____________3

10 20__________ 4

20 30__________ 6

30 40__________ 4

40 50__________ 3

Proportion of selling time in sample above that are less Than 20 days :

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R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}

Select all numbers that are in the domain.

Answers

Answer:

-3 -3 -1 1

Step-by-step explanation:

give me five stars and ill tell you

Answer: Answer: -3,-1, and 1.

Step-by-step explanation: You are given the relation R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} The domain of the relation are all possible inputs and the range of the relation are all possible outputs. So, the inputs are : -3,-1,1; and the outputs are : -2,0,2. As a result, the domain is : -3,-1,1; and the range is : -2,0,2.

I need to find an equation that hass an infinite number of solutions

Answers

Answer

2(7x + 3) - x

= 13x + 6

Explanation

2(7x + 3) - x

= 14x + 6 - x

= 14x - x + 6

= 13x + 6

Hope this Helps!!!

"India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the following probability distribution for the household size in India. Col1 Household Size 1 2 3 4 5 6 7 8 Col2 Probability 0.02 0.09 0.18 0.25 0.20 0.12 0.08 0.06 a. What is the probability that there are less than 5 members in a household in India"b. What is the probability that there are 5 or more members in a typical household in India? (Round your answer to 2 decimal places.)Probability
c. What is the probability that the number of members in a typical household in India is strictly between 2 and 5? (Round your answer to 2 decimal places.)

Probability

Answers

The probability that the number of members in a typical household in India is less than 5, greater than or equal to 5, and strictly between 2 and 5 are 0.54, 0.46, and 0.43 respectively

Probability distribution

Given the probability distribution for the household size in India as shown;

X       1      2     3        4      5       6        7      8       Total

P  0.02  0.09  0.18  0.25  0.20  0.12  0.08  0.06    1.00

a) The probability that the number of members in a typical household in India is strictly less than 5 is given as:

P(X < 5) = P(X=1) +  P(X=2) +  P(X=3) +  P(X=4)

P(X < 5) =  0.02+ 0.09 + 0.18 + 0.25

P(X < 5) = 0.54

b) The probability that the number of members in a typical household in India is greater or equal to 5 is given as:

P(X ≥ 5) = P(X=5) +  P(X=6) +  P(X=7) +  P(X=8)

P(X  ≥ 5) =  0.20 +  0.12 + 0.08 + 0.06

P(X  ≥ 5) = 0.46

c) The the probability that the number of members in a typical household in India is strictly between 2 and 5

P(2 < X < 5) = P(X=3) +  P(X=4)

P (2 < X < 5) =  0.18 + 0.25

P (2 < X < 5) = 0.43

Hence the probability that the number of members in a typical household in India is less than 5, greater than or equal to 5, and strictly between 2 and 5 are 0.54, 0.46, and 0.43 respectively

Learn more on probability distribution here: brainly.com/question/24756209

Answer:

0.54,0.46,0.43

Step-by-step explanation:

Given that India is the second most populous country in the world, with a population of over 1 billion people.

The pdf of household size say X in India varies from 1 to 8.

The distribution is shown as follows

X       1      2     3        4      5       6        7      8       Total

P  0.02  0.09  0.18  0.25  0.20  0.12  0.08  0.06    1.00

a) the probability that there are less than 5 members in a household in India

=P(X<5)

=P(1 to 4) = 0.54

b.  the probability that there are 5 or more members in a typical household

in India

=P(X\geq 5) = P(5 to 8)\n\n= =0.46

c) the probability that the number of members in a typical household in India is strictly between 2 and 5

=P(2<x<5) = P(3)+P(4)\n=0.43

The observation which occurs most frequently in a sample is the mean

Answers

Answer: That’s actually mode

Step-by-step explanation:

Mode- the value that appears most often in a set of data.

Median- the middle number in a list of numbers ordered from lowest to highest.

Mean- the total of all the values, divided by the number of values.

Range- the difference between the lowest value and the highest value.

Answer:

mode

Step-by-step explanation: