Some hydrogen gas is collected over water at 20 c. the levels of water inside and outside the gas collection bottle are the same. the partial pressure of hydrogen is 538.1 torr. what is the barometric pressure at the time the gas is collected. answer of units of torr.

Answers

Answer 1

To find the barometric pressure when hydrogen gas is collected over water at 20°C, we need to consider the partial pressure of water vapor at that temperature.

1. Look up the vapor pressure of water at 20°C: From a reference table, the vapor pressure of water at 20°C is 17.5 torr.

2. Apply Dalton's Law of partial pressures: According to Dalton's Law, the total pressure is the sum of the partial pressures of all the gases present.

Total pressure (barometric pressure) = Partial pressure of hydrogen + Partial pressure of water vapor

3. Calculate the total pressure: Given that the partial pressure of hydrogen is 538.1 torr,

Total pressure = 538.1 torr (hydrogen) + 17.5 torr (water vapor)
Total pressure = 555.6 torr

The barometric pressure at the time the gas is collected is 555.6 torr.

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Related Questions

How did participation in other reform movements help strengthen the women's movement? women's struggles in other groups made them want to have a group where they could be in charge. women's success in reform movements made them question the limitations placed on them in society. the success of other reform programs led to the transcendentalism movement. the experience gained working on reform programs made women qualified to create the women's rights movement.

Answers

Answer:

Women's success in reform movements made them question the limitations placed on them in society

• women’s success in reform movements made them question the limitations placed on them in society.

Explanation:I took the test

the graph shows the ratio of (Federal) Debt to GDP (gray bars indicate a recession)


Based on the graph, explain how the country's rate of GDP growth has compared to its debt growth over time and what the implication is for the debt/gdp ratio.

(Answer must be 200 words max)

the graph shows the ratio of (Federal) Debt to GDP (gray bars indicate a recession)Based on the graph,

Answers

The growth rate of GDP determines a direct relation between debt growth over time and this relation reveals that a 1% point increase in the ratio of government debt to GDP would reduce real GDP growth by about 0.01 percentage point.

What is the Debt-to-GDP ratio?

The debt-to-GDP ratio is the metric comparing a country's public debt to its gross domestic product (GDP). By comparing what a country owes with what it produces, the debt-to-GDP ratio reliably indicates that particular country's ability to pay back its debts.

According to the context of this question, a 1% point increase in the ratio of government consumption to GDP leads to a decline in the real economic growth of about 0.1 percentage points, on average. This ratio is useful for investors, leaders, and economists. It allows them to gauge a country's ability to pay off its debt.

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What symbols represent James in James and the Giant peach?

Answers

In "James and the Giant Peach," James is not represented by a single symbol. However, there are several recurring motifs and themes associated with James throughout the book. For example, James is often associated with the color green, which represents growth, renewal, and hope. Additionally, James is associated with insects, such as the grasshopper and the centipede, which represent his connection to the natural world and his own personal growth and transformation. Finally, the peach itself can be seen as a symbol of James, as it represents his journey from a lonely and unhappy life to a world of adventure and new experiences.

what is a three column cash book​

Answers

Answer:

Blank 3 Column Cash Book Get Your Copy Today! Large Size 8.5 inches by 11 inches Include Sections for: Debit and Credit side Date Particulars Reference Discount Cash and Bank Buy one Today and have a safe record of your accounts

Explanation:

The Cash Book that has three columns for discount received and paid, cash transactions and bank transactions is called Three Column Cash Book.

Explanation

The three column cash book (also known as triple column cash book) has three money columns on both debit and credit side – one on each side for recording discount, cash and bank amounts. If a business keeps a bank account and receipts and payments are frequently made through bank account than it is useful to maintain a three column cash book rather than a single column cash book or a double column cash book.

It is the custom of the business houses that discount is allowed and received for early payments of dues. If cash is paid early, creditors may allow a discount. On the other hand, if debtors pay early, a discount may be allowed to them. It may be noted that cash and discount are related to each other that’s why discount columns are also provided in Cash Book.

Thus in three column cash book, three columns for amount are provided on each side. One column is used to record cash receipts and payments, the second column is provided to record banking transactions and in third column discount received and discount allowed are recorded.

Where, the single and double column cash books are alternatives to a cash account, the three column cash book serves the purpose of cash as well as bank account.

Which of the following demonstrates how Earth systems interact over large periods of time and different-sized spaces?

Answers

Plate tectonics is an example that demonstrates how Earth systems interact over large periods of time and different-sized spaces. (Option A)

How is this so?

It involves the   movement and interaction of Earth's lithospheric plates,which cover the planet's surface.

Plate tectonics influences   various geological processes, such as the formation of mountains,earthquakes, and volcanic activity.

These interactions occur over long periods,shaping the Earth's surface and affecting regions across   different spatial scales, from local to global.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Which of the following demonstrates how Earth systems interact over large periods of time and different-sized spaces?

A) Plate tectonics

B) Geographic Entities

C) Astronomy

D) Biochemical cycles

Rank the following in terms of size, from largest to smallest:
Planet, comet, dwarf planet, universe, moon, asteroid, meteoroid, star,
galaxy

Answers

Answer:

Universe, galaxy, star, planet, dwarf planet, moon, comet, asteroid, meteoroid.

during a college visit, you should be sure to

Answers

Answer:

Explanation:

During a college visit you should be sure to ask questions of current students. Community colleges have smaller campuses than four-year institutions do; as such, you'll likely have much more direct access to students than at larger schools where students are spread across multiple buildings or even campuses.

What is a goal of the mission of the James Webb Space Telescope?

to find evidence of life on Mars

to study how solar flares of our sun affect Earth

to find evidence of events in the history of the universe

to study how Venus and Earth diverged as planets

(33 points)

Answers

Answer:

to find evidence of events in the history of the universe

Explanation:

A goal of the mission of the James Webb Space Telescope is to find evidence of events in the history of the universe.

The correct answer to the given question is option C.

The James Webb Space Telescope has several objectives and goals, with the primary aim of its mission being to identify the events that led to the formation of the universe.

In addition, it aims to collect data on various galaxies, stars, and planets that will help scientists determine the evolution of these entities.The primary objective of the James Webb Space Telescope is to identify the early universe's formation by collecting data on the stars, galaxies, and planets.

It is also aimed at gathering data on various celestial objects such as exoplanets and black holes.The James Webb Space Telescope aims to collect data that will allow astronomers to determine the events that led to the formation of the universe.

It will collect data on distant galaxies, stars, and planets to provide insights into the evolution of these entities. The telescope will have advanced capabilities such as infrared vision that will allow it to collect data on some of the universe's earliest structures.

Additionally, the James Webb Space Telescope aims to collect data on exoplanets, which could provide insights into how life in the universe developed. The telescope's ability to identify the atmospheric composition of exoplanets will be crucial in determining their habitability.

Ultimately, the telescope's primary goal is to contribute to the advancement of our understanding of the universe.

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Ignore 3/4 can someone please explain

Ignore 3/4 can someone please explain

Answers

Answer: 1/6

Explanation:

The question is asking how much of the whole circumference is arc AB given that it's central angle is 60°. We can see that the angle is \(\frac{60}{360}\) of the whole. This means that if there were 360 equal sectors, or slices, of the circle, then this angle would take 60 of them.

From this, we can see that if the circumference was divided into 360 equal parts, then the arc would also take up 60 of them, making the arc \(\frac{60}{360}\), or \(\frac{1}{6}\).

We could have alternatively seen that the ratio of arc length to the whole circumference would be the same as the ratio of the central angle to the "whole angle" or 360°.

\(\frac{Arc\hspace{0.1cm}Length}{Circumference}=\frac{Central\hspace{0.1cm}Angle}{360}\)

Putting in 60 for the central angle, we get

\(\frac{Arc\hspace{0.1cm}Length}{Circumference}=\frac{6}{360}=\frac{1}{6}\)

The question is asking what fraction of the circumference is the arc length, so let's isolate the arc length by multiplying the circumference to both sides

\(Arc\hspace{0.1cm}Length=\frac{1}{6}*Circumference\)

This equation in words says that the arc length is one sixth of the circumference, which is exactly what the question is asking.

Read the excerpt from "He Lion, Br.uh Bear, and Br.uh Rabbit” from The People Could Fly

"Listen," said he Lion, and then he roared: "ME AND MYSELF. ME AND MYSELF. Nobody tell me what not to do," he said. "I'm the king of the forest, me and myself."

"Better had let me tell you somethin,"br.uh Rabbit said, "for I've seen Man, and I know him the real king of the forest."

He Lion was quiet awhile. He looked straight through that scrawny lil Rabbit like he was nothin atall.

Rabbits are shown in this excerpt as

A. confident and stubborn.
B. powerful and strong.
C. wise and self-assured.
D. weak and polite.

Answers

Answer:

C. wise and self-assured.

The correct answer is C !

C4Lcademy
Answer
I need to past plz

Answers

What are you trying to ask there is not question

How is the temperature of a substance related to the kinetic energy of its molecules? select all that apply.

Answers

The kinetic energy is proportional to the temperature.

What is the relation between temperature and kinetic energy?

So first, we know that the kinetic energy of an object is given by:

K = (1/2)*m*v^2

Where v is the velocity and m is the mass.

We know that substances are made of molecules, and these molecules are tiny objects that move. As the temperature increases, you should see that the speed of motion of these particles increases (this is why dilation happens). So, if the velocity increases, then also increases the kinetic energy of the molecules in the substance.

The thermal velocity is approximated by:

\(v = \sqrt{(k/m)*T}\)

Where (k/m) is a constant, now, if you replace that in the kinetic energy equation, you can see that the kinetic energy is proportional to the temperature.

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Please help! The problem is attached below. I was told to simplify the expression and then create an If-Then scenario. Meaning I need to find the domain of the expression. I have already simplified the expression correctly, which is also attached below. 20 Points if u help and give a step-by-step explanation!

Please help! The problem is attached below. I was told to simplify the expression and then create an
Please help! The problem is attached below. I was told to simplify the expression and then create an

Answers

The domain of the simplified expression a/(bxy) is given as follows:

b ≠ 0, x ≠ 0, y ≠ 0.

The scenario is then an inverse proportional relationship, with a constant of a/b, and inverse to the variables x and y.

How to define the domain of an expression?

The domain of a function is given by the set that contains all the possible input values for the function.

The expression in this problem is given as follows:

a/(bxy).

It is a fractional expression, meaning that the denominator cannot assume a value of zero, and hence the domain is given as follows:

b ≠ 0, x ≠ 0, y ≠ 0.

An inverse proportional relationship is defined as follows, as a function of one variable:

y = k/x.

In which k is the constant of proportionality.

Hence, in this problem, the expression f(x,y) = a/(bxy) represents a multi-variable inverse proportional relationship, with constant of a/b.

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A light source is shining on a vertical surface or a slanted surface as shown 3 points
below. Which statement is correct?
Surface is vertical
Surface is tilted
The light energy that hits the vertical surface is stronger because it is concentrated on
a smaller area.
The light energy that hits the vertical surface is weaker because it is concentrated on
a smaller area.
The light energy that hits the slanted surface is stronger because it is concentrated on
a larger area.
The light energy that hits the slanted surface is stronger because it is concentrated on
a smaller area

Answers

Answer:

The light energy that hits the vertical surface is stronger because it is concentrated on a smaller area.

Explanation:

One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal. Define the random variable X in words

Answers

The random variable X represents the number of hours Americans spend watching television each month.

In the given scenario, 108 Americans were surveyed, and it was found that they watched an average of 151 hours each month, with a standard deviation of 32 hours. The random variable X helps us quantify and describe the distribution of this data. By defining X as the number of hours spent watching television, we can analyze and make inferences about the population's television viewing habits. The random variable X in this scenario represents the number of hours an individual American spends watching television each month. Each survey respondent's value of X corresponds to the number of hours they reported watching TV. The random variable X allows us to quantify and analyze the variability in TV viewing habits among the surveyed American population.

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3. List at least 5 ideas for a company name. (Complete sentences are not necessary. 2. 0 points) 4. Decide which name you will use for your company, and explain why you chose this name. (3. 0 points) 5. Will your company need a DBA name? Why or why not? (1-2 sentences. 3. 0 points) 6. Will you register your company name as a trademark with the state or USPTO, or both? Explain why or why not. (2-4 sentences. 3. 0 points) 7. List at least 3 places where you can look for information about licenses and permits. (3. 0 points) 8. If your business grows large, which type of business organization would you prefer to use (function, product, location, process, or customer)? Explain why. (2-3 sentences. 2. 0 points) 9. Will your business keep inventory? If so, list some of the types of inventory you will store. If not, explain why you won't need to have inventory. (2-3 sentences. 2. 0 points)

Answers

Five company name ideas: LightCraft, TechBuddies, EcoInnovate, ZenMind, FreshHarvest.

What is the reason for choosing this name?

I choose EcoInnovate because it implies a focus on ecological sustainability and innovation, which are current market trends.

My company won't need a DBA name, as EcoInnovate clearly reflects the company's values and mission.

I will register EcoInnovate as a trademark with USPTO for nationwide protection. State registration isn’t as comprehensive.

For licenses and permits, check the Small Business Administration (SBA) website, your local Chamber of Commerce, and state government websites.

If my business grows large, I’d prefer a product-based organization to focus on specialized innovations.

My business will keep inventory including raw materials for product development and finished goods for customer orders.

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95% confidence, within 5 percentage points, and a previous estimate of
0. 25

Answers

Answer: 1

Explanation: 1

What does the speaker observe in london's summer morning?
a peaceful moming in a park in london
the work of a shop owner in london
a busy moming in a london market
the rising of the sun over an empty london

Answers

The speaker observes in "London's summer morning" is a busy morning in a London market. This allows Robinson to make a Romanticized version of the summer morning in London, but cheekily throw in that it is all a "busy dream".

In Islam, who is prophet Muhammad (peace be upon him) ?

Answers

the prophet Muhammad is called Allah

In Islam, Prophet Muhammad (peace be upon him) is considered the last and final prophet sent by God (Allah) to guide humanity. He is revered as the messenger of Allah and is considered the seal of the prophets, meaning that no prophet will come after him.

Prophet Muhammad (pbuh) was born in the city of Mecca, in present-day Saudi Arabia, in the year 570 CE. At the age of 40, he received the first revelation from Allah through the Angel Gabriel, which marked the beginning of his prophethood. The revelations continued over a period of 23 years, and they were later compiled into the holy book of Islam, the Quran.

Prophet Muhammad (pbuh) preached monotheism (the belief in one God) and called people to worship Allah alone and follow His guidance. He taught the importance of faith, prayer, charity, fasting, and pilgrimage, among other teachings and principles that form the foundation of Islam.

Muslims regard Prophet Muhammad (pbuh) as a role model and strive to follow his example in their personal and communal lives. They hold great love, respect, and reverence for him and frequently use the phrase "peace be upon him" (pbuh) as a sign of honor and respect when mentioning his name.

4. Look at the stanza of the poem where the word "hear!" is repeated before th
bleeding drops of red." What does the speaker emphasize when he repeats
kind of mood does this repetition create?

Answers

The speaker emphasizes the sound of the drops hitting the ground, creating a sense of impact and finality.

How does he use repetition?

By repeating "hear!" twice, the speaker draws attention to the sound of the drops hitting the ground, as if urging the listener to really listen to and understand the gravity of the situation.

This creates a sense of impact and finality as if each drop is a definitive end to something and thus we can see that the thing which this does in the grand scheme of things is that it emphasizes the sound of the drops hitting the ground, creating a sense of impact and finality.

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Hear! Hear! the mournful cry,

Of bleeding drops of red,

As they fall and drip and die,

On the ground where brave men tread.

1. PART A: Which of the following best identifies
a theme of the excerpt?

Answers

Answer:

soeone who is good at all they do

Explanation:

Someone who is good in everything

Who should you NOT contact of you think you are the victim of identity theft or fraud? (Everfi)
1) credit card companies
2)your financial institution
3)your local elected official like the mayor
4) the credit bureaus

Answers

3) your local official
Priority would be credit companies or insurance companies

If 4x² + 4 = 8, which two could be the value of x?

Answers

Answer:

+/- 1

Explanation:

4x² = 4          Subtract 4 from both sides

x² = 1         Divide 4 from both sides

x = Negative/ positive 1         Square root

Hope this helps! :)


How does the conflict "character versus nature" tie into the theme of the story? The Grasshopper and The Ant

Answers

The conflict of character versus nature is an external conflict in literature. It is frequently represented as a person battling the environment, including natural disasters, wild animals, or the natural world's destructive side.

In The Grasshopper and The Ant, this conflict ties into the story's theme in a variety of ways.

To begin with, the narrative depicts how nature, in this case, the environment, can have an impact on our lives. Throughout the story, the grasshopper avoids the ant's attempts to prepare for the winter, preferring to sing and dance.

When the winter arrives, the grasshopper is caught unprepared and ends up hungry and freezing. The story's moral teaches readers that being ill-prepared can be disastrous, especially when it comes to nature. It also highlights the importance of being proactive in preparing for the worst.

Another way the character versus nature conflict ties into the story's theme is by highlighting the ant's perseverance and hard work. Despite the harsh circumstances, the ant remains determined and dedicated to his goal of preparing for the winter. This serves as an inspiration to readers to persevere even in the most challenging situations.

Furthermore, the story shows how nature can be both harsh and benevolent. The grasshopper suffers due to the harsh winter, but the ant's hard work also pays off in the end when he can enjoy the fruits of his labor. This teaches readers that nature can both give and take away.

Finally, the conflict of character versus nature in The Grasshopper and The Ant serves to teach readers about the importance of balance. The ant's hard work and preparation are admirable, but the grasshopper's love of life and music is also crucial. This emphasizes that while it's essential to be prepared, it's also necessary to enjoy life and not take it for granted.

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is anyone having trouble with brainly.

Answers

Answer:

yes. very much so.

Explanation:

Yea im having trouble with brainly too

Which of the following is the cheapest route to visit each city using the nearest neighbor route starting from a and ending at a.

Answers

Is this a multiple Choice question?

Water is boiled to make steam to turn a generator to send power to a house. the energy conversions involved include ___________________

Answers

girk the water bacially uses ifye oh ar head because he’s bald

The average age of a breed of dog is 19. 5 years. If the distribution of their ages is normal and 20% of dogs are older than 22. 6 years, find the standard deviation

Answers

The standard deviation of the ages of this breed of dog is approximately 4.4 years.

To find the standard deviation, we can use the concept of z-scores and the cumulative distribution function (CDF) of a standard normal distribution. Let's denote the average age as μ (mu) and the standard deviation as σ (sigma).

Given that the average age of the breed is 19.5 years, we can set μ = 19.5. We are also given that 20% of the dogs are older than 22.6 years. Using the z-score formula, we can calculate the z-score corresponding to this percentile:

z = (x - μ) / σ

Where x is the given value (22.6 years) and z is the z-score. Rearranging the formula, we can solve for σ:

σ = (x - μ) / z

Plugging in the values, we have:

σ = (22.6 - 19.5) / z

To find the z-score corresponding to the 20th percentile, we can use the inverse CDF of the standard normal distribution. Using statistical software or a z-table, we find that the z-score corresponding to the 20th percentile is approximately -0.84.

Substituting the values, we get:

σ = (22.6 - 19.5) / -0.84 ≈ 3.7 / -0.84 ≈ -4.4

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The average age of a breed of dog \(= μ = 19.5\) yearsThe percentage of dogs that are older than 22.6 years = 20%Let's calculate the z-score of the given percentage\(:z = (x - μ) / σ20 = (22.6 - 19.5) / σσ = (22.6 - 19.5) / 0.84σ = 3.69 / 0.84σ = 4.39\) (approximately)

Therefore, the standard deviation is approximately 4.39 years.Explanation:Given, the average age of a breed of dog\(= μ = 19.5\)yearsThe percentage of dogs that are older than 22.6 years = 20%Let's calculate the z-score of the given percentage:z = (x - μ) / σ

Where\(,x = 22.6μ = 19.5σ =\)Standard deviationThen,\(20 = (22.6 - 19.5) / σσ = (22.6 - 19.5) / 0.84σ = 3.69 / 0.84σ = 4.39\)(approximately)Therefore, the standard deviation is approximately 4.39 years.

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Which planets are the OUTER planets? Where did they form in the nebula disk? Why did they form where they did? (discuss temperature and density differences of the nebula disk)

Answers

The outer planets are Jupiter, Saturn, Uranus, and Neptune. Each planet began as microscopic dust and held in the accretion disk. The atoms and molecules began to stick together and formed into larger molecules. And the last one I dont know

fill in the blanks to describe nicolas and santi day at the beach

fill in the blanks to describe nicolas and santi day at the beach

Answers

The completed sentence is;

Nicolas feels like he is having a wonderful day at the beach.

Meanwhile, Santi thinks about how he has visited the beach often

Now he wishes he could go to the mountains.

What is the explanation for the above?

In the above text, one  person  - Nicholas rarely visits the beach while Santi  if a frequent visitor.

For Nicholas, he is having a great experience while Santi is sated and wish to explore more leisurely locations.

Hence it is correct to state that:

Nicolas feels like he is having a wonderful day at the beach.

Meanwhile, Santi thinks about how he has visited the beach often

Now he wishes he could go to the mountains.

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Other Questions
Please help!!! Question 6!!! ppppppllllllleeeeeaaaassssseeeeeee How are scientific theories and laws developed? what is a civilization? question 2 options: movies, television shows, radio programs, music, fads, types of hobbies, and books an advanced culture that has highly developed social, economic, and political structures a culture judged according to its unique traditions and customs a group of people who live close to one another and often work toward common goals One of the primary costs of evolving large brains is O a they evolved inte in evolutionary history. Ob they are associated with population increases, which increases evolutionary pressures O c. they are more subject to mutations than small brains, slowing evolution Od large brains require a lot of energy and nutrients relative to their size ES Choose the answer to the following math problem. quatre-vingt-neuf + un = cent quatre-vingt-dix quatre-vingt-quinze quatre-vingts claire opened claire's beauty parlor in her home. she solicited funds to begin the business from jack, who believed that the business was incorporated. claire had, in fact, never filed the papers. one day, claire fell asleep while giving a customer a permanent and the solution caused her customer severe burns. the customer sued the beauty parlor for $500,000, an amount enormously in excess of the business assets. under the revised act, what would be the result? What is a difference quotient in math? What was the speaker doing and what his state of mind when his encounter with the raven occurred? Cite evidence from the text in support of your answer. Research on environmental influences on gender typing shows that teacherstend to negotiate more when boys misbehave, coming up with a joint plan to improve behavior.use more disapproval and controlling discipline with girls than with boys.seem to expect girls to misbehave more often than boys.give girls more encouragement than boys to participate in adult-structured activities. Imagine a world where every bag of skittles ever made contains exactly 100 pieces of candy. The colors for skittles are the colors of the rainbow: red, orange, yellow, green, blue, and purple. The latest data analysis on bags of skittles has told us the following: About 20 percent of them have an equal number of candies of each color. About 40 percent of them have a 2-1-1-3-1-1 ratio of the colors red, orange, yellow, green, blue, and purple. The remaining 40 percent of them have only red candies. What is the average distribution of colors in a bag of skittles a put is an option that gives its owner the right to do which of the following? sell a specific security at a fixed price for an indefinite time period. buy a specific security at fixed conditions of price and time. sell a specific security at fixed conditions of price and time. buy a specific security at a fixed price for an indefinite time period. Which two shades did odysseus speak to before encountering tiresias in the land of the dead? Problem id PRABER4K some distinguished philosophers have tried to develop probability without measure theory. one of the reasons for difficulty is the following. -2=2+v/4 two step equations Your client has been given a trust fund valued at $1.55 million. She cannot access the money until she turns 65 years old, which is in 20 years. At that time, she can withdraw $22,500 per month.If the trust fund is invested at a 4.5 percent rate, how many months will it last your client once she starts to withdraw the money? (Do not round intermediate calculations and round your final answer to 2 decimal places.)Number of months: Acetic acid (Hac) solution was prepared by dissolving 0.05 moles of acetic acid (Hac pKa = 4.8) in water to give 1 liter. What is the initial pH of the solution. 50 ml of 1.00 of NaOH was added to the acetic acid solution from a previous question to neutralize it. What is the new pH of the solution A nurse is reinforcing teaching about breastfeeding with a client who is postpartum. Which of the following statements by the client indicates an understanding of the teaching?A. "I will apply vitamin E oil to my nipples after each feeding."B. "I will nurse my baby for 5 to 10 minutes on each breast."C. "I will lay my baby on a pillow at the level of my breast."D. "I will make sure that just the nipple is in my baby's mouth." 2 - Choisissez Complete this conversation with the correct prepositions or articles