Find the percent of decrease from 84 gallons to 45 gallons. Round to the nearest tenth of a percent if necessary.

The relationship between osmotic pressure and osmosis is closely linked. Osmotic pressure is the pressure exerted by a solvent to prevent the flow of water into a solution through a semipermeable membrane. It is directly proportional to the concentration of solute particles in the solution.

To calculate osmotic pressure, we can use the formula: Π = iRT(Cin - Cout)

- Π represents osmotic pressure in atmospheres.
- i represents the number of ions dissociated from each molecule in solution. For non-electrolytes like sugar, i is equal to 1.
- R is the gas constant, which is 0.082 atm/(K×M).
- T represents the temperature in Kelvin. For room temperature, it is 293 Kelvin.
- Cin represents the concentration of the solution inside the dialysis bag in moles per liter (M).
- Cout represents the concentration of the solution outside the dialysis bag.

Let's calculate the osmotic pressure for each of the given solutions:

1. Osmotic pressure of 70% Sucrose solution:
First, we need to calculate the molarity of the solution inside the bag (Cin). The molecular weight of sucrose is 342 g/mol. So, for a 70% sucrose solution, we have 700 g of sucrose in 1 L of solution. To convert this to moles, we divide by the molecular weight: (700 g / 342 g/mol) = 2.05 mol/L.

Now we can substitute the values into the formula:
Π = iRT(Cin - Cout)
Π = (1)(0.082 atm/(K×M))(293 K)(2.05 M - 0 M)
Π = 47.79 atm

Therefore, the osmotic pressure of the 70% Sucrose solution is 47.79 atm.

2. Osmotic pressure of 35% Sucrose solution:
Using the same process as above, we find that the molarity of the solution inside the bag (Cin) is 1.02 M.

Π = iRT(Cin - Cout)
Π = (1)(0.082 atm/(K×M))(293 K)(1.02 M - 0 M)
Π = 23.67 atm

Therefore, the osmotic pressure of the 35% Sucrose solution is 23.67 atm.

3. Osmotic pressure of water (control):
For water, the concentration of solute (Cin) is 0 M, as there is no solute present.

Π = iRT(Cin - Cout)
Π = (1)(0.082 atm/(K×M))(293 K)(0 M - 0 M)
Π = 0 atm

Therefore, the osmotic pressure of water is 0 atm.

The relationship between osmotic pressure and the rate of osmosis is that higher osmotic pressure leads to a faster rate of osmosis. Osmosis is the movement of solvent molecules from an area of lower solute concentration to an area of higher solute concentration through a semipermeable membrane. The higher the osmotic pressure, the greater the driving force for water molecules to move across the membrane.

If the dialysis membrane were impermeable to ions and NaCl was used instead of sucrose at the same molarity (2.05 M), the osmotic pressure would be different. NaCl dissociates into two ions in solution, so the value of i would be 2.

Π = iRT(Cin - Cout)
Π = (2)(0.082 atm/(K×M))(293 K)(2.05 M - 0 M)
Π = 97.98 atm

Therefore, if NaCl were used instead of sucrose, the osmotic pressure would be 97.98 atm. This is because NaCl generates more particles (ions) in solution, increasing the osmotic pressure compared to sucrose.

By understanding the relationship between osmotic pressure and the rate of osmosis, we can predict that a solution with higher osmotic pressure will have a faster rate of osmosis compared to a solution with lower osmotic pressure.

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Answer:

Simply apply the expression

Speed= distance/time

Step-by-step explanation:

The question is not complete, although, we can provide a solution to what it is trying to ask for

Step one:

given data

For Leo, let the distance that Leo covers be y meters

and let the distance that Juan covers be f meters

From speed = distance/time

for Leo, given that he traveled for x hours, his distance will be

d= y*x

for Juan, given that he traveled for h hours, his distance will be

d= f*h

Answer:

192/2= 96 g after 7h

96/2=48 g after 14h

48/2= 24 g after 21h

The side length measurements of 80 cm, 60 cm, and 100 cm form a right triangle.

In this question we need to determine whether the side length measurements of 80 cm, 60 cm, and 100 cm form a right triangle.

We know that any three integers a, b, c are Pythagorean triples if and only if a^2 + b^2 = c^2  where c > a, b

Consider c = 100 cm, a = 80 cm and b = 60 cm

Taking the square of each integer we get,

a^2 = 80^2

      = 6400

b^2 = 60^2

      = 3600

c^2 = 100^2

      = 10000

Consider a^2 + b^2

= 80^2 + 60^2

= 6400 + 3600

= 10000

= c^2

So, (80, 60, 100) is a Pythagorean triple.

Therefore, the given side length measurements form a right triangle

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Answer:

Scalene Triangle

Step-by-step explanation:

To classify the triangle we have to find the lengths of each side.

Side AB

d= √  (−1−(−3))2+(4−2)2√  

d= √  (2)2+(2)2

d= √  4+4

d=√  8

d=2.828427 approximately 2.8

Side BC

d= √  (3−(−1))2+(−4−4)2

d= √  (4)2+(−8)2

d= √  16+64

d=8–√0

d=8.944272 approximately 8.9

Side AC

d=  √  (3−(−3))2+(−4−2)2

d=  √  (6)2+(−6)2

d=  √  36+36

d=  √  7 2

d=8.485281 approximately 8.5

Since no sides are the same length, it is a scalene triangle.

I hope this helps!

Answer:

Step-by-step explanation:

Let's do this step by step!

The hyponteuse is 7.7 because it is the longest side of a 90 degree angle.

the formula for this would a^2 + b^2 = c^2

 3.3^2 + b ^2 = 7.7^2

 10.89 + b^2 = 59.29

- 10.89            - 10.89       subtract from both sides

  b^2 = 48.4

\(\sqrt{b} = \sqrt{48.4} \\\)

b = 6.95701085237

round to the nearest tenth ---> 7

Answer:

Step-by-step explanation:

∠a + 40 + 48 = 180   {Straight line angles}

∠a + 88         = 180

     ∠a           = 180 - 88

              ∠a  = 92°

92 + 47 + ∠x = 180 {angle sum property of triangle}

       139 + ∠x = 180

                ∠x = 180 - 139

∠x = 41°

I HOPE IT HELPED

In the eighth chapter of Animal Farm the horse named Boxer died due to overwork and fatigue.

Boxer was a hard working horse who lived by two mottos which were "Napoleon is always right" and "I should work harder". His fellow mare Clover warned him many times that he shouldn't overwork himself as he is not young anymore but Boxer never listened.

After he died he was sent to the butcher's store to be slaughtered but was told to the other animals that he died at a hospital and now is resting in peace. He was a true inspiration for the other animals at farm.

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Answer:

The answer is B. 60 boys

Step-by-step explanation:it would not let me put my reasoning but trust me its correct <3 brainliest please

The correct answer is: The benefits of the data should be weighed against the costs.

This is because the first step in evaluating change outcomes is to determine what data should be collected and how it will be collected.

While it is important to collect as much data as possible, it is also important to consider the costs of collecting and analyzing the data.

The data collected should be relevant to the outcomes being evaluated, and should be collected at regular intervals to track progress over time.

It is not productive to analyze change effects based on insignificant data, as this can lead to inaccurate conclusions.

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1.25 hours will it take them to paint a door.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Aaron can paint a door in 3 hours.

Anna can do the same job in 2 hours.

Since you have two painters for one door we can calculate the average of their combined times as

= (3 h + 2 h) /2

= ( 180 + 120) /2

= 300/ 2

= 150 minutes.

= 150/ 2

= 75 min

= 75/ 60

= 1.25 hours.

It would take nearly 1 hour and 25 minutes.

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Answer:

First Term = 6

Common Ratio = 3

Step-by-step explanation:

According to the Question,

Thus, \(S_{8} = 19680\) & \(S_{4} = 240\) .

Now, on solving  \(\frac{S_{8} }{S_{4} }\)  we get,

\(\frac{19680}{240} = \frac{\frac{a(r^{8-1)} }{r-1}}{\frac{a(r^{4-1)} }{r-1}}\)  

\(82 = \frac{r^{8}-1 }{r^{4}-1 }\)

\(82r^{4}-82 = r^{8}-1\\r^{8}-82r^{4}+81 = 0\\r^{8}-81r^{4}-r^{4}+81 = 0\\(r^{4}-81)( r^{4}-1) =0\)(r=1 is not possible so neglect \(( r^{4}-1) =0\) )

So, r=3 Now Put this value in \(S_{4} = {\frac{a(r^{4-1)} }{r-1}}\) We get a=6 .

These are the expressions that represent a perfect square monomial and its square root. A perfect square monomial is a term that can be written as the square of a binomial.

The expressions that represent a perfect square monomial and its square root are: \((x^2)\) - This is a perfect square monomial because it can be written as the square of the binomial (x).
\((4y^2)\) - This is a perfect square monomial because it can be written as the square of the binomial (2y).

The square root of a perfect square monomial is the binomial that was squared to get the monomial. So, the square roots of the above expressions are:

1.\(√(x^2) = x\)

2. \(√(4y^2) = 2y\)

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Expressions that represent perfect square monomials and their square roots include \(x^2\) and its square root x, as well as \(4y^4\) and its square root \(2y^2\).

A perfect square monomial is an expression that can be written as the square of a binomial. To determine if an expression represents a perfect square monomial, we can look for the following characteristics:

1. The expression must have only one variable.
2. The exponent of the variable must be even.
3. The coefficient must be a perfect square.

Let's consider some examples:

1. \(x^2\): This is a perfect square monomial because it satisfies all the conditions. The variable x has an even exponent of 2, and the coefficient 1 is a perfect square.

2. \(4y^4\): This is also a perfect square monomial. The variable y has an even exponent of 4, and the coefficient 4 is a perfect square.

3. \(3x^3\): This expression does not represent a perfect square monomial because the variable x has an odd exponent of 3.

To find the square root of a perfect square monomial, we take the square root of both the variable and the coefficient.

For example, the square root of \(x^2\) is x, and the square root of \(4y^4\) is \(2y^2\).

In conclusion, expressions that represent perfect square monomials and their square roots include \(x^2\) and its square root x, as well as \(4y^4\) and its square root \(2y^2\).

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Answer:

To calculate how many standard deviations away from the mean an ACT score of 31 is, we need to use the formula:

z = (x - μ) / σ

Where:

x = ACT score of 31

μ = mean of ACT scores (28)

σ = standard deviation of ACT scores (2)

z = number of standard deviations away from the mean

Substituting the values, we get:

z = (31 - 28) / 2

z = 1.5

Therefore, an ACT score of 31 is 1.5 standard deviations away from the mean.

Answer:

129

Step-by-step explanation:

Since,

AD = BC

AD = 3x + 24

BC = 4x - 11

3x + 24 = 4x - 11

4x - 11 = 3x + 24

4x - 3x = 24 + 11

x = 35

BC = 4x - 11

= 4 ( 35 ) - 11

= 140 - 11

BC = 129

Answer:

\(AB=BC\)

\(3x+24=4x-11\)

\(3x-4x=-11-24\)

\(x=35\)

\(BC=4\times 35-1\)

\(=140-11\)

\(=129\)

--------------------------

Hope it helps..

Have a great day!!

The height of the building is 12 feet.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c² = a² + b²

Given that:

Length of the ladder (hypotenuse) = 13 feet

Distance of the ladder's bottom from the house (base) = 5 feet

Let's denote the height of the house (vertical side) as 'b'.

Using the Pythagorean theorem, we have:

13² = 5² + b²

b² = 13² - 5²

b² = 169 - 25

b² = 144

Taking the square root of both sides:

b = √144

b = 12

Therefore, the value of b is 12 feets.

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Answer:

288 inches

Step-by-step explanation:

Just do 24 x 12 you will get the answer since 1ft=12 inches!

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Simple Random sampling  as each student is getting equal opportunity to get selected.

Describe random sampling.

A selection of participants from a community are chosen at random by the investigator using simple random sampling, a sort of sampling techniques. Every individual in the population has the same chance of being chosen. Then, information is gathered from as much of this randomly selected subgroup as possible.

Which four forms of random sampling are there?

Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are the four main random (probability) sampling techniques.

What benefit may simple random sampling provide?

The benefits of a simple random sample include its simplicity and accuracy of depiction. Simple random sampling is the easiest way to select a study sample from a bigger population.

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Answer:

D)

Step-by-step explanation:

The numerical value of the arc measure of UA is approximately 0.964 degrees.

We can use the relationship between the arc measure and the central angle subtended by the arc. Since angle ADU is the central angle that subtends arc UA, we can use the formula for the relationship between arc measure and central angle:

Arc measure = Central angle/360°

We are given the measure of angle ADU, so we can write:

Central angle ADU = (22x – 16)°

Now, we can use this to find the numerical value of the arc measure of UA.

Arc measure of UA = Central angle subtended by arc UA/360°

We know that angle ADU is a central angle that subtends arc UA, so:

Arc measure of UA = measure of angle ADU/360°

Substituting the given measures, we have:

(3x + 1)º = (22x – 16)°/360°

Multiplying both sides by 360°, we get:

360°(3x + 1)º = 22x – 16

Simplifying the left side by distributing, we have:

1080x + 360º = 22x – 16

Combining like terms, we get:

1102x = -344

Dividing both sides by 1102, we get:

x ≈ -0.312

Substituting this value back into the expression for the arc measure of UA, we have:

(3x + 1)º ≈ (3(-0.312) + 1)º ≈ 0.964º

Therefore, the numerical value of the arc measure of UA is approximately 0.964 degrees.

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Answer:

plsssssssssssssssssssssssssssssssssss

The z-score for a person who received a score of 62 is -2.1053.

To calculate the z-score, we use the formula:

z = (x - μ) / σ

Where:

x is the individual score,

μ is the mean of the distribution, and

σ is the standard deviation of the distribution.

In this case, the class mean (μ) is 71 and the standard deviation (σ) is 3.8. The individual score (x) is 62.

Plugging these values into the formula, we get:

z = (62 - 71) / 3.8

z = -9 / 3.8

z ≈ -2.3684

Rounding the z-score to four decimal places, we get -2.1053.

The negative z-score indicates that the person's score of 62 is below the class mean. A z-score measures the number of standard deviations an individual's score is above or below the mean. In this case, the score is approximately 2.1053 standard deviations below the mean.

The z-score allows us to compare the person's score to the rest of the class by standardizing it with respect to the mean and standard deviation. It provides a standardized measure of how far the person's score deviates from the average performance in the class.

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9514 1404 393

Answer:

  (b)  T(x, y) -> (x-3, y-6)

Step-by-step explanation:

Each image point is 3 left and 6 down from the corresponding pre-image point. That is -3 is added to each x-value, and -6 is added to each y-value. That transformation is represented by ...

   T(x, y) ⇒ (x-3, y-6)

Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).