Your swimming pool containing 65,000 gal of water has been contaminated by 7 kg of a nontoxic dye that leaves a swimmer's skin an unattractive green. The pool's filtering system can take water from the pool, remove the dye, and return the water to the pool at a flow rate of 200 gal/min. Assume that the dye is uniformly distributed throughout the pool.
(a) What is the initial value problem for the filtering process?
(b) You have invited several dozen friends to a pool party that is scheduled to begin in 4 h. You have determined that the effect of the dye is imperceptible if its concentration is less than 0.03 g/gal. Is your filtering system capable of reducing the dye
concentration to this level within 4 h?

Answers

Answer 1

Answer:

a) [tex]a(t)=7e^{\frac{-t}{325} }[/tex]

b) it is noticeable

Step-by-step explanation:

a) Let a(t) be the amount of die at time t. a is in kg and t is in minutes. Therefore:

[tex]\frac{da}{dt} =\frac{-a(t)}{65000}*\frac{200gal}{1 min}=\frac{-a}{325}\\\frac{da}{a} =\frac{-1}{325} dt\\\int\limits{\frac{1}{a} } \, da =\int\limits{\frac{-1}{325} } \, dt\\ln(a)=\frac{-1}{325} t+c\\a=ce^{\frac{-t}{325} }\\at\ t=0, a=7\\ 7=ce^0\\c=7\\a(t)=7e^{\frac{-t}{325} }[/tex]

b) 4 hrs = (4 * 60) min = 240 min

[tex]a(t)=7e^{\frac{-t}{325} }\\a(240)=7e^\frac{-240}{325} = 3.345kg[/tex]

3.345 kg = (3.345 * 1000 / 60000) g/gal = 0.0557 g/gal

0.0557 g/gal > 0.03 g/gal, therefore it is noticeable


Related Questions

Find the balance earned on an account that has $60,000 deposited for 6 years at 1.125% interest compounded continuously? Please help

Answers

Answer:

The balance of the account is $64,190.

Step-by-step explanation:

The amount of money after t years of continous compounding is given by the following equation:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial deposit and r is the interest rate, as a decimal.

$60,000 deposited for 6 years at 1.125% interest compounded continuously.

This means that [tex]P = 60000, r = 0.01125, t = 6[/tex]

So

[tex]P(6) = 60000e^{0.01125*6} = 64190[/tex]

The balance of the account is $64,190.

What is the length of the diagonal in a rectangular prism that measures 8mm by 14mm by 6m? Round your answer to the nearest tenth

Answers

Answer:

17.2

Step-by-step explanation:

It's kinda like the pythagorean theorem where you square the sides, add them, and then square root the answer. I hope this is correct

Write equations for the horizontal and vertical lines passing through the point , (4,5).

Answers

Answer:

Answer is below

Step-by-step explanation:

The equation for the horizontal line is x = 4. The equation for the vertical line is y = 5.

I graphed the lines on the graph below to show you that they intersect at the point (4,5).

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If 15+3x=3(2−2x), then x= [blank]

Answers

Answer:

x = -1

Step-by-step explanation:

15+3x=3(2−2x)

Distribute

15+3x = 6 -6x

Add 6x to each side

15+3x+6x = 6-6x+6x

15+9x = 6

Subtract 15 from each side

15-15+9x = 6-15

9x = -9

Divide by 9

9x/9 = -9/9

x = -1

A crime is committed by one of two suspects, A and B. Initially, there is equal evidence against both of the suspects. After further investigation, it is determined that the guilty party has a blood type found in only 10% of the population at large. Suspect A does have this blood type; the blood type of Suspect B is unknown.
Define the following 3 events A, M and C.
A: "A is guilty" (Thus ° denotes "B is guilty')
M: "A’s blood type matches that of the guilty party"
C: "B's blood type matches that of the guilty party"
A. The police reported that suspect A is not a relative of suspect B. Is it reasonable to set P( MA)=P(C|A)=10%? Why?
B. Assume that P(MAC)=P(C|A)=10%. Given the information from the further investigation of the crime scene, what is the probability that A is the guilty party?
C. Assume that P( MA)=P(C/A)=10%. Given the information from the further investigation of the crime scene, what is the probability that B’s blood type matches that of the guilty party?

Answers

Answer:

a) MA conditional with C can be interpreted as A which is known and C which is unknown match

b) 10/11

c) 2/11

Step-by-step explanation:

A={A is the guilty party}

[tex]M_A[/tex] = {A blood type matches that of the guilty party}

C = {B is the guilty party}

[tex]M_C[/tex] = {B blood type matches that of the guilty party}

a) The chance is 10% because MA conditional with C can be interpreted as A which is known and C which is unknown match

b) the probability that A is the guilty party is given by [tex]P(A/M_A)[/tex]. Using bayes theorem:

[tex]P(A/M_A)=\frac{P(M_A/A)P(A)}{P(M_A/A)P(A)+P(M_C/C)P(C)} =\frac{1*1/2}{(1*1/2)+(1/10*1/2)} =\frac{10}{11}[/tex]

c) the probability that B’s blood type matches that of the guilty party is given as [tex]P(M_C/M_A)[/tex]. Using LOTS Therefore:

[tex]P(M_C/M_A)=P(M_C/M_A,A)P(A/M_A)+P(M_C/M_A,A)P(C/M_A)=\frac{1}{10}*\frac{10}{11} +1*\frac{1}{11} =\frac{2}{11}[/tex]

is (1,3) a solution to this system of equations?
4x + 5y = 19
x + 5y = 16

Answers

Answer:

Yes

Step-by-step explanation:

I graphed both of the equations on the graph below to show you that they intersect at the point (1,3), making it the solution to the system.

If this answer is correct, please make me Brainliest!

Answer: Yes

Step-by-step explanation:

If G is the midpoint of
FH,
find FG.

Answers

Answer:

15

Step-by-step explanation:

15 is the answer because i looked it up

The required value of segment FG is 67 if G is the midpoint of FH.

What is a Line Segment?

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure given below shows a line segment FH, where the length of line segment FHrefers to the distance between its endpoints, F and H.

Given that G is the midpoint of FH

FG = 14x + 25 and  GH= 73 - 2x,

To determine the value of FG

F______________G______________H

⇒ FH= FG+ GH

Since G is the midpoint of FH, SoFG = GH

⇒  FH = FG+ GH

⇒ FH = 2FG

⇒ FG = GH

Substitute the values of FG = 14x + 25 and  GH = 73 - 2x,

⇒ 14x + 25 = 73 - 2x

⇒ 14x + 2x = 73 - 25

⇒ 16x = 48

⇒ x = 48/16

⇒ x = 3

Substitute the value of x = 3 in FG,

⇒ FG = 14x + 25

⇒ FG = 14(3) +25

⇒ FG = 67

Hence, the required value of segment FG is 67 if G is the midpoint of FH.

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The question seems to be incomplete the correct question would be

If G is the midpoint of FH,

find FG.

Where FG = 14x + 25 and  GH= 73 - 2x,

PLEASE HELP ITS FOR MATH

Answers

infinite, the line goes on forever indicated by the arrows at the end of each line

The answer is b. none. This is because the lines are parallel and therefore do not intersect at a point, meaning that there are no solutions.

A vertical pole stands in the sea. A mark, X, on the pole is 1.6m above sea level at low tide, the sea level is 3.9m higher than at
low tide.
(a) Find the distance of x below sea level at high tide.
(b) What is the position of x from sea level at the time when the sea level is exacly half way between high tide and low tide?​

Answers

Answer:

ummm I would say a angle of 7.65

Step-by-step explanation:

Answer:

7.65

Step-by-step explanation:

In a restaurant there are 8 starter 15 main dishes 9 dessert Jane is going to choose one of the following how many different ways are there for her to choose

Answers

Answer:

1335

Step-by-step explanation:

Starter + Main = 8 x 15 = 120

Main + Dessert = 15 x 9 = 135

Starter + Main + Dessert = 8 x 15 x 9 = 1080

120 + 135 + 1080 = 1335 possibilities

Answer:

Step-by-step explanation:

STARTER + MAIN:

8 x 15 = 120

MAIN + DESSERT:

15 x 9 = 135

STARTER + MAIN + DESSERT:

8 x 15 x 9 = 1080

120 + 135 + 1080 = 1335 possibilites

There are seven black socks, eight blue socks, 10 white socks, and five patterned socks in the drawer. What is the probability of pulling a blue sock, replacing it, and then drawing a patterned sock out of the drawer?

Answers

Answer:

2/45

Step-by-step explanation:

Total socks:

7 + 8 + 10 + 5 = 30

P(blue) × P(patterned)

8/30 × 5/30

4/15 × 1/6

2/45

Answer:

2/45

Step-by-step explanation:

The total number of socks is 7+8+10 +5

30

P(blue) = number of blue socks / total

           = 8/30 = 4/15

Then we replace it so we have the same number of socks

P(patterned) = number of patterned socks / total

                     = 5/30 = 1/6

P(blue, replace/patterned) = 4/15*1/6

                                             =2/45

PLEASEeEeEeEeEeEeeEeEeEeEeEeEeEeEeEeEeeeEeEeEeEeEeEeEeEeEEEeee
ANSWER NOW

Answers

Answer:

a

Step-by-step explanation:

Anyone can solve this

Let a, b, and c be real numbers where ab*C0. Which of the following functions could represent the graph below?
AN

Answers

Answer:

A on ed

Step-by-step explanation:

Which ordered pair would form a proportional relationship with the points in the graph? (4, 4) (6, 9) (9, 6) (8, 5)

Answers

Answer:the answer is 9,6

Step-by-step explanation:

I JUST TOOK THE QUIZ

Answer:

C (9,6) did it on edge

If the triangle's sides are a base that is 4 inches, a height that is 3 inches, and the other side that is 5 inches, what is the area of that triangle?

Answers

Answer:

6 in ^2

Step-by-step explanation:

divide side lengths by two and add those numbers

What is the slope and the y-intercept of the line on the graph below?​

Answers

Answer:

I love you sweetheart I want to look and love you

Answer:

slope- 1/4

y intercept- 1

A hiker is told to carry 2 cups of water for every 10 minutes spent walking. The hiker plans to hike for 60 minutes. How many cups of water should the hiker carry?

Answers

Answer:

12

Step-by-step explanation:

2 x 6 = 12

The number of cups of water the hiker should carry is 12 cups.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, a hiker is told to carry 2 cups of water for every 10 minutes spent walking.

Now, number of cups of water carry for 1 minute

= 2/10

= 0.2 cups

The number of cups of water carry for 60 minutes

= 0.2×60

= 12 cups

Therefore, the number of cups of water the hiker should carry is 12 cups.

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a is 100% more than b.
Which of these shows the ratio a:b?
2:1
100:1 1:100
1:2
A
B
C
D

Answers

Answer:

2-1=1 so A. is 100% more than B because A is 2 times bigger than B.

A. is the answer 2:1

Hope this helps

Step-by-step explanation:

The option that shows the ration A: B is Option C - 1:2. See the rationale below.

How to compute the above

If A is 100% more than B, it means that A is equal to B plus 100% of B. In other words, A is twice the value of B.

Therefore, the ratio of A to B is 1:2, indicating that A is twice as much as B.

Recall that a ratio is a quantitative relationship between two or more quantities, indicating how many times one quantity is contained or repeated in relation to another quantity.

It is expressed as a fraction or with a colon (:), representing the relative comparison of the quantities.

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Mary walks the 3 day breast cancer walk. They break the 62 miles evenly for each day. How
4
many miles does she walk in one day?

Answers

Answer:

she would walk at least those 62 miles

Step-by-step explanation:

We are told that in the 3 days of the walk to fight cancer, Mary breaks the 62 mile barrier every day, that is to say that every day she travels 62 miles or more.

You ask us how much she walks in a single day, considering what the statement that goes at least 62 miles each day says, she would walk at least those 62 miles on a normal day.

Seemas little sister is now 5 years old.if Her age is 2 years more than 1/4 of seemas age, how old is seems

Answers

Answer:

12

Step-by-step explanation:

Seema’s little sister is 2 years more than ¼ of Seema’s age, so you should subtract 2 from 5 to find ¼ of Seema’s age. If 3 is ¼ of Seema’s age, all you do is multiply it by 4 to get the original number. 3x4 is 12, so the final answer is that Seema is 12.

The jar shown below is 2/5 filled with water. If 750 ml more water is poured into the jar, it becomes full. What is the capacity of the jar?


2/5 is the fraction 2/5

Plz answer fast with easy explanation

Answers

Answer:

1250 ml

Step-by-step explanation:

Answer:

I’m glad you asked!

Step-by-step explanation:

2/5 + 750 ml equals the full jar amount or capacity.750/ 3 equals 250.That makes 150 the denominator.Now we just need to multiply 250 by 5.

[tex]250 x 5 = 1250.[/tex]

In a new experimental teaching method, when students have questions in class, they send them to the instructor via a laptop computer. From time to time, the instructor pauses to read the questions and to provide the answers, without revealing the identities of the students who are asking the questions. This new method is supposed to eliminate the reluctance of students to ask questions for fear of revealing their lack of understanding in public. In a study of this new method, 69 male students and 73 female students participated. Treat these as if they were simple random samples. Of the male students, 38 said that they liked the new method better than the traditional one in which students raise their hands to ask questions. Of the female students, only 20 said they liked the new method better
(a) Construct a 95% confidence interval for the difference between the proportions of male and female students who like the new method better. Let p1, denote the proportion of male students who like the new method better and let p2 denote the proportion of female students who like the new method better.
(b) A 95% confidence interval for the difference between the proportions of male and female students who like the new method better is __________.

Answers

Answer:

a)  (0.124, 0.435)

b) I am 95% confident that the proportion difference is between 0.124 and 0.435

Step-by-step explanation:

Given that:

For male students: number of male students ([tex]n_m[/tex]) = 69, number who liked the new method (x) = 38

For female students: number of female students ([tex]n_f[/tex]) = 73, number who liked the new method (x) = 20

a) The probability that a male student like the new method ([tex]P_1[/tex]) is given as:

[tex]P_1=\frac{38}{69} =0.55[/tex]

The probability that a female student like the new method ([tex]P_2[/tex]) is given as:

[tex]P_2=\frac{20}{73} =0.27[/tex]

c = 95%, α = 1 -c = 0.05

[tex]z_{\frac{\alpha }{2} }=1.96[/tex]

the difference between the proportions of male and female students who like the new method better = [tex]P_1-P_2[/tex] ± [tex]z_{\frac{\alpha }{2} }\sqrt{\frac{P_1(1-P_1)}{n_m} +\frac{P_2(1-P_2)}{n_f}}[/tex] =  [tex]0.55-0.27[/tex] ± [tex]1.96\sqrt{\frac{0.55(1-0.55)}{69} +\frac{0.27(1-0.27)}{73}}[/tex]  = (0.124, 0.435)

b) I am 95% confident that the proportion difference is between 0.124 and 0.435

How much wood will Moritz need to create his ramp?
Moritz is creating a wooden ramp with the given
dimensions. The ramp will not need a bottom face.
ft2
5 ft
3 ft
4 ft
6 ft
5 ft
6 ft
3 ft
4 ft​

Answers

Answer:

60 ft

Step-by-step explanation:

got it right

Answer:

60

Step-by-step explanation:

A rectangular room is 12 1/2 feet long and 10 1/3 feet wide. What is the area of the room?

Answers

Answer:120 1/6 feet sq.

Step-by-step explanation: Area of a rect. = length×breadth(width)

Area=12 1/2× 10 1/3

Area= 120 1/6

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A recipe calls for 33 teaspoons orange juice. A can of orange juice is 17 fluid ounces. How many teaspoons of juice are in the​ can?

Answers

Answer:

102

Step-by-step explanation:

1 fluid ounce = 6 teaspoons

Rearrange the equation so u is the independent variable.

-12u + 13 = 8w - 3

w = __

Answers

Answer: w = -3u/2  +  2

Step-by-step explanation:

-12u + 13 = 8w - 3

-12u + 13 + 3 = 8w -3 + 3

-12u + 16 = 8w

w = -3u/2   +   2

Which choice is equivalent to the expression below?
28.24
O A. 28 + 22/10 + 24/100
O B. 28+ 2/10 + 4/10
O C. 28. 22/10. 24/100
O D. 28. 224/10

Answers

Answer:

C

Step-by-step explanation:

Kelly contracts with Raphael for Raphael to bring a pony to her daughter's birthday party in exchange for $100. Kelly later learns her daughter is frightened of ponies. She contacts Raphael and Raphael agrees to bring a donkey to the party for $50 instead. What is true of the original agreement involving the pony and the $100?

Answers

Answer:

It was discharged by substituted contract

Step-by-step explanation:

In this situation, instead of simply canceling their original contract and terminating their interaction, Raphael and Kelly reached another agreement and stablished a substituted contract in place of the original one.

Therefore, the original agreement involving the pony and the $100 was discharged by substituted contract .

Complete parts ​(a) through ​(c) below. ​(a) Determine the critical​ value(s) for a​ right-tailed test of a population mean at the alphaequals0.05 level of significance with 15 degrees of freedom. ​(b) Determine the critical​ value(s) for a​ left-tailed test of a population mean at the alphaequals0.10 level of significance based on a sample size of nequals10. ​(c) Determine the critical​ value(s) for a​ two-tailed test of a population mean at the alphaequals0.05 level of significance based on a sample size of nequals13.

Answers

Answer:

a) [tex] t_{\alpha}= 1.753[/tex]

b) [tex] t_{\alpha}= -1.383[/tex]

c) [tex] t_{\alpha/2}= \pm 2.179[/tex]

Step-by-step explanation:

Part a

For this case we know that the degrees of freedom are:

[tex] df = 15[/tex]

And we want a right tailed test so then we need to find in the t distribution with degrees of freedom =15 a critical value who accumulate 0.05 of the area in the right and we got:

[tex] t_{\alpha}= 1.753[/tex]

Part b

For this case the significance is [tex]\alpha=0.1[/tex] the degrees of freedom are:

[tex] df = n-1= 10-1=9[/tex]

And since is a left tailed test the critical value for this case would be:

[tex] t_{\alpha}= -1.383[/tex]

Part c

For this case the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2=0.025[/tex] the degrees of freedom are:

[tex] df = n-1= 13-1=12[/tex]

And since is a two tailed test the critical values for this case would be:

[tex] t_{\alpha/2}= \pm 2.179[/tex]

Pip and Sara win some money and share it in the ratio 7:5. Pip gets £30 more than Sara. How much did Sara get?

Answers

Answer:

75 sweets.

Step-by-step explanation:

Pip gets 7/(7+5) = 7/12 .

Let Sara get x sweets so Pip gets 7/5 x sweets.

7/5 x = x + 30

2/5 x = 30

x = 5/2 * 30 =  75.

Sara gets 75 sweets.

Answer:

Sara has £75

Step-by-step explanation:

Pip : Sara

7   :    5

If Pip gets £30 more than Sara, then

5x+30=7x

Where x is £?

Subtract 5x from both sides

30=2x

Divide both sides by 2

x=£15

£15

Pip : Sara

105:  75

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Rosario donde estaEl ventilador (fan) est _____________________________________ . 1. la lmpara est ______________________________la mesa 2. El espejo esta ________________________________de la 3. La ventana esta ______________________la cama4, La alfombra (rug) esta __________________de la cama5. La cortina esta ____________________ventana6. la mesa de noche esta ______________________de la cama7. El armario esta _________________de la puerta Who settled in America colonies and why Why do you think sound travels faster in steel than it does in wood? (Hint: Think about the densities of the two materials, and how the particles might be arranged.) which of the following are exterior angles? check all that apply Please dont reportPLEASE DONT REPORTOK so Im a really bad kid and I yell,push,curse at my mom dont ask why I dont wanna explain itBasically I just need help on how to not get in trouble for things I doDont try to convince me not to do things Im going to do it either way. Consider the function represented by the following table.The function is increasinglinear quadratically exponentially Solve the system of equations. Byrd Company produces one product, a putter called GO-Putter. Byrd uses a standard cost system and determines that it should take one hour of direct labor to produce one GO-Putter. The normal production capacity for this putter is 120,000 units per year. The total budgeted overhead at normal capacity is $1,080,000 comprised of $420,000 of variable costs and $660,000 of fixed costs. Byrd applies overhead on the basis of direct labor hours. During the current year, Byrd produced 74,000 putters, worked 98,300 direct labor hours, and incurred variable overhead costs of $133,200 and fixed overhead costs of $612,000.Required:a. Compute the predetermined variable overhead rate and the predetermined fixed overhead rate.b. Compute the applied overhead for Byrd for the year.c. Compute the total overhead variance. Joey sells cars at Orange City Ford. He earns $350 a week plus $200 per car he sells. If he earned $1550 last week, how many cars did he sell? Write an equation and solve. PLSHURRY What planet rotates from top to bottom? Looking at the box plot below what was the median score 55 60 65 70 75 80 85 90 95 200. A97. B- 90. C66. D78 please help The algebraic expression 4x2 + 3Vx+5 is a polynomialPlease select the best answer from the choices providedTF -4.41666666667 as fraction help A longitudinal wave moves energy that is to the direction of the waves movement. Which of these terms is applicable in a discussion of accretion?OrbitQuasar 3-dimensionalDiameter Find the pH of HCl with a concentration of 0.00006MRound to the nearest whole number BRAINLIEST!!!19. Solve Michael enjoys his granddaughters positive attitude. Which characteristic of a healthy relationship does this describe? Saddle Inc. has two types of handbags: standard and custom. The controller has decided to use a plantwide overhead rate based on direct labor costs. The president has heard of activity-based costing and wants to see how the results would differ if this system were used. Two activity cost pools were developed: machining and machine setup. Presented below is information related to the companys operations. Standard Custom Direct labor costs $60,000 $103,000 Machine hours 1,400 1,290 Setup hours 96 400 Total estimated overhead costs are $300,000. Overhead cost allocated to the machining activity cost pool is $195,000, and $105,000 is allocated to the machine setup activity cost pool.Compute the overhead rate using the traditional (plantwide) approach. The art appreciation society operates a museum for the benefit and enjoyment of the community. During hours when the museum is open to the public, two clerks who are positioned at the entrance collect a $5.00 admission fee from each nonmember patron. Members of the Art Appreciation Society are permitted to enter free of charge upon presentation of their membership cards. At the end of the day, one of the clerks delivers the proceeds to the treasurer. The treasurer counts the cash in the presence of the clerk and places it in a safe. Each Friday afternoon the treasurer and one of the clerks deliver all cash held in the safe to the bank, and receive an authenticated deposit slip which provides the basis for the weekly entry in the cash receipts journal.The Board of Directors of the Art Appreciation Society has identified a need to improve their control procedures for cash admission fees. The board has determined that the cost of installing turnstiles, sales booths, or otherwise altering the physical layout of the museum will greatly exceed any benefits which may be derived. However, the board has agreed that the sale of admission tickets must be an integral part of its improvement efforts.Required: Identify three internal control weaknesses and suggest a solution for each. Be as specific as possible.