A large tank is partially filled with a solution. The tank has a faucet that allows solution to enter the tank at a rate of 16 3/4 liters per minute. The tank also has a drain that allows solution to leave the tank at a rate of 19 4/5 liters per minute. (a) What expression represents the change in volume of solution in the tank in 1 minute? (b) Simplify and give your answer as a simplified mixed number. (c) What is the change in volume of the solution after 10 minutes? Show necessary work. Give your answer as a simplified mixed number.

Answers

Answer 1

The change in volume per minute and the total change in the volume of the solution after 10 minutes will be [tex] - 3 \frac {1}{20} \: litres [/tex] and [tex]- 30 \frac {1}{2} \: litres [/tex] respectively.

Entry rate = [tex] 16 \frac{3}{4} [/tex] per minute

Discharge rate = [tex] 19 \frac{4}{5} [/tex] per minute

Change in the volume of solution in the tank per minute can be calculated thus :

Change in volume = (Entry rate - Discharge rate) × time

[tex] 16 \frac{3}{4} - 19 \frac{4}{5} = \frac{67}{4} - \frac{99}{5} = \frac{(335 - 396)}{20} = \frac{-61}{20} = - 3\frac{1}{20} \: litres \: per \: minute [/tex]

The total change in the volume of solution in the tank after 10 minutes can be calculated thus :

Change in volume per minute × time

[tex] - \frac{61}{20} \times 10 = - \frac{610}{20} = - 30 \frac {1}{2} \: litres [/tex]

Therefore, the solution in the tank decreases by [tex] 30 \frac {1}{2} \: litres [/tex] after 10 minutes

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Related Questions

HELPPPPPPP
which relationship shows a quadratic variation?​

Answers

Answer:

The first option

Step-by-step explanation:

The first option:

f(x) = 4(x^2)

Each time x is squared and then multiplied by 4.

___

f(1) = 4(1^2) = 4

f(2) = 4(2^2) = 16

f(3) = 4(3^2) = 36

f(4) = 4(4^2) = 64

Answer:

The first one

Step-by-step explanation:

This is because the function of it is f(x) =  4x^2. Additionally, this can be seen as there is not a perfect difference between the values.

Hope this helps... Feel free to mark this as brainliest! :D

What is the length of the line segment with endpoints (12.7, −6.5) and (−13.5, −6.5) ?

Answers

Answer:

Its 26.2

Step-by-step explanation:

I just took the test

Yw :DD

Answer:

The answer is 26.2

Step-by-step explanation:

I took this test, got it wrong, then it explained it so that I could completely understand the question.

Suppose a standard​ six-sided die is rolled and you receive ​$6.50 for every dot showing on the top of the die. What should the cost of playing the game be in order to make it a fair​ game?
The cost of playing the game should be?

Answers

6÷6.50=$1.08. 1.08 ×6= $6.48 + 2 =6.50

A letter use to represent a number value is called

Answers

Answer:

A variable

Step-by-step explanation:

HELP! Which expression is equivalent to a^b/c

Answers

Answer:

[tex]{ \rm{ {a}^{ \frac{b}{c} } \: \dashrightarrow \: ( {a}^{b}) {}^{ \frac{1}{c} } }} \\ \\ { \boxed{ \rm{ \boxed{} \: \: \sqrt[c]{ {a}^{b} } }}} \\ [/tex]

Dan and Brian have played 51 tennis matches.
Dan has won 29 times.
Brian won the rest.
a) Estimate the probability that Dan wins.
b) Estimate the probability that Brian wins.

Answers

Answer:

A = 29/51   B = 22/51

Step-by-step explanation:

(E) =  number of favorable outcomes/ total number of possible outcomes

- number of possible outcomes= 51

- number of favorable outcomes= 29

therefore, P(E) = 29/51

- number of possible outcomes= 51

- number of favourable outcomes = 51 - 29 = 22

therefore, P(E)= 22/51

Víctor has 2 times as many trophies as Dean. Together ,víctor and Dean have 27 trophies does víctor have?

Answers

Answer:

Victor has 18 trophies

Step-by-step explanation:

Let's set up "let statements"

Let d = Dean's trophies

Since Victor has 2 times as many trophies as Dean, we can set up a let statement for Victor like this...

Let 2d = Victor's trophies

Now we can set up an equation! Since we know Dean and Victor have 27 trophies altogether...our equation has to involve addition...

2d + d = 27

Combine like terms...(2d and d)

3d = 27

Divide 3 on both sides to isolate the variable "d"

3d ÷ 3 = d

27 ÷ 3 = 9

So...

d = 9

That means Dean has 9 trophies. But we are not done yet because we need to figure out how many trophies Victor has. Since Victor has 2 times the number of trophies as Dean we can do...

2 · 9 = 18

Therefore, Victor has 18 trophies!

Hope this helps :)

A loan is payed off in 15 years with a total of 250,000. It had 4% interest

Answers

Answer:

5.2%po joke Lang Hahahahahahah

Answer:

$137,339.88

Step-by-step explanation:

Use the compound interest formula and substitute the values given:

$250,000=P(1+0.0412)12(15)

Simplify using order of operations:

$250,000=P(301/300)180

Solve for P:

P=$250,000(301/300)180≈$137,339.88

Solve using a proportion . 5) If it costs $2.85 for 5 cookies, how much would 8 cookies cost?​

Answers

Answer:

$4.56

Step-by-step explanation:

2.85:5

multiply each side by 8/5

4.56:8

so it is $4.56 for 8 cookies

Find the perimeter of the triangle whose vertices are (−4,4), (−4,1), and (−8,−4). Write the exact answer. Do not round.

Answers

Answer:

Step-by-step explanation:

The perimeter of the triangle is [tex]3 + \sqrt{41} + 5\sqrt{5}[/tex] units

How to determine the perimeter?

The coordinates are given as:

(−4,4), (−4,1), and (−8,−4).

Calculate the distance between the vertices using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(-4 + 4)^2 + (4-1)^2} = 3[/tex]

[tex]BC = \sqrt{(-4 + 8)^2 + (1+4)^2} = \sqrt{41[/tex]

[tex]AC = \sqrt{(-4 + 8)^2 + (4+4)^2} = \sqrt{80[/tex]

The perimeter is the sum of the side lengths.

So, we have:

[tex]P = 3 + \sqrt{41} + \sqrt{80}[/tex]

Expand

[tex]P = 3 + \sqrt{41} + 4\sqrt{5}[/tex]

Hence, the perimeter of the triangle is [tex]3 + \sqrt{41} + 5\sqrt{5}[/tex] units

Read more about perimeter at:

https://brainly.com/question/24571594

#SPJ6

12 + 4[5% - 4(x + 5)] = 7 - 5x

Answers

Answer:

https://brainly.com/question/24983242 help

Step-by-step explanation:

12 + 4[5% - 4(x + 5)] = 7 - 5x

12 + 4•(5% - 4•(x + 5)) = 7 - 5•x

11x = -55

x = -5

Answer:

[tex]x = - \frac{34}{5} [/tex]

Step-by-step explanation:

12 + 4 (5% - 4(x + 5)) = 7 - 5x

12 + 4 (5/100 - 4x - 20) = 7 - 5x

12 + 4 (-399/20 - 4x) = 7 - 5x

12 - 399/5 - 16x = 7 - 5x

-399/5 - 16x = 7 - 5x

-16x + 5x = 7 + 339/5

-11x = 374/5

x = -34/5

What is 11,885 as a percentage (round to 2 decimal places X.XX)?

Answers

Answer:

9.25

Step-by-step explanation:

if sn = 1395 a = 3 and d = 3 find and =?​

Answers

Answer:

Simplify:=-1

Step-by-step explanation:

4x^2 times what equals -5x^2

Answers

Answer:

-1.25

Step-by-step explanation:

-5/4=

-1.25

check answer

4*-1.25= -5

Evaluate -c when c = 12

Answers

Answer: [tex]-12[/tex]

Step-by-step explanation:

[tex]-c=-(12)=\boxed{-12}[/tex]

Trigonometry prove that LHS=RHS​

Answers

Answer:

bc cot 0

Step-by-step explanation:

For each equation, determine if Y as a function of X.

Answers

Answer:

Not a function

Step-by-step explanation:

If you were to graph it, these would fail the vertical line test.

Will give brainliest.

Your cousin is selling cookies. He borrowed $10.82 from you for supplies and plans to sell each cookie for $0.75. If he sells an average of 12 cookies a day, how long will it take him to repay what he owes you AND make $25 in profit? (Round to the most reasonable number.)

Question 1 options:

3 days


4 days


5 days


6 days.

Show and explain your thought process for the question above. How did you reach your conclusion? What did you do to find that number?

Answers

Answer:

4 days

Step-by-step explanation:

Shaniqua is taking a test. After 20 minutes she has 35 questions left. After 40 minutes she has 15 questions left. If Shaniqua takes the same amount of time for each question how many questions are on the test

Answers

There were 55 questions in the test.

Answer:

55

Step-by-step explanation:

Suppose the sum of two integers is negative. Must both be negative

Answers

No, because -5+3=-2 This is the same as 3-5=-2.

Answer: Not necessarily. There are many ways to write a basic equation with a negative answer. For example, -3-4 = -7.

Step-by-step explanation:

Determine the value of x.
X 1
X 1.5

A)x=1
B)x=2.5
C)x=2
D)x=2.9​

Answers

Answer:

The correct option is C. (x=2)

Step-by-step explanation:

Given

Length of the hypotenuse of the right angled triangle (h) = 2.5 cm

Length of one of the side (a) = 1.5 cm

Let the length third side be 'b' cm

By Pythagoras theorem

h² = a² + b²

Adding Values on both sides

⇒ (2.5)² = (1.5)² + b²

⇒ 6.25 = 2.25 + b²

⇒ 6.25 - 2.25 = b²

⇒ 4 = b²

⇒ √4 = b

⇒ 2 = b

b = 2

please help!
The freezing point of seawater is -2 °C. The freezing
point of nitric acid is -42 °C. How much greater is the freezing
point of seawater than the freezing point of nitric acid?

Answers

Answer:

Express concentrations of solution components using mole fraction and molality

Describe the effect of solute concentration on various solution properties (vapor pressure, boiling point, freezing point, and osmotic pressure)

Perform calculations using the mathematical equations that describe these various colligative effects

Describe the process of distillation and its practical applications

Explain the process of osmosis and describe how it is applied industrially and in nature

Step-by-step explanation:

i helped

A piece of wire 3/7 m long as we cut into six pieces of the same length what is the length of each piece

Answers

Answer:

Each piece is 1/7 m long

Step-by-step explanation:

Wire length = 3/7 m

Pieces = 6

1 piece = 3/7 ÷ 6

= 3/7 ÷ 6/1

= 3/7 × 1/6

= 1/7 m

-1, -2, -4, -8….
What is the 8th term for this geometric sequence!

Answers

-4....................just took the quiz..........

Answer:

-128

Step-by-step explanation:

-1, -2, -4, -8, -16, -32, -64, -128

you are multiplying the previous number in the sequence by 2

hope this helped :)

What is the product of -4.6 and 3.2?

Steps to get there would be helpful too!

Answers

Answer:-14.72

Step-by-step explanation:

Answer:

The answer is negative 14.72

Step-by-step explanation:

this is because if you multiply negative 4.6 and 3.2

You might need:
Find one value of x that is a solution to the equation:
(x2 – 6)2 = -3x2 + 18

X=

Answers

Answer:

[tex]x = \sqrt{6} [/tex]

Step-by-step explanation:

2(x^2 - 6) = - 3x^2 + 18

2x^2 - 12 = - 3x^2 + 18

5x^2 - 12 = 18

5x^2 = 30

x^2 = 6

x = square root (6)

Look at the pictuse below i would copy and paste but I can't copy a picture

Answers

Answer:

15

Step-by-step explanation:

The constant of proportionality is 15 books per shelf.

If you look at the graph, you can see that for every 1 shelf, there are 15 books. For 1 shelf, there are 15 books, and for 2 shelves, there are 30. And the pattern continues.

Let me know if you have any questions, thanks!

Jaliyah wants to play a prank on her older sister at her birthday party. She has two bags of blue glitter that she's planning on filling a birthday hat with. To figure out how much glitter she needs to use, Jaliyah must first find the volume of the party hat. Find the volume of the party hat in cubic inches.

Height = 8.4 inches

Length = 5.3 inches

Answers

Answer:

44.52

Step-by-step explanation:

Volume = b * h

base times height

The height is 8.4 inches so 8.4 *

Length is the same as base so 5.4

8.4 * 5.4

Helloooo could someone plz help me on this ?

Answers

Answer:

15 cubic units

Step-by-step explanation:

If you add up the blocks you get 15

Model and Solve the problem.
5x1/2 Please hurry!!

Answers

2.5

please make me brainiest if helped!

Answer:

2.5

Step-by-step explanation:

i just did 5 times 0.5 hope this helped.

and 2.5 is greater then 2.05

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