what is the percent yield of a reaction in which 200. g of phosphorus trichloride reacts with excess water to form 155 g of hcl and aqueous phosphorous acid (h3po3)?

Answers

Answer 1

The correct percent yield of the reaction is approximately 97.3%.

Given,

Mass of phosphorus trichloride = 200g

Mass of HCl = 155g

The theoretical yield of HCl using stoichiometry:

Moles of PCl3 = Mass of PCl3 / Molar mass of PCl3

= 200 g / 137.5 g/mol

= 1.455 moles

Theoretical yield of HCl = Moles of PCl3 x (3 moles HCl / 1 mole PCl3)

= 1.455 moles x (3 moles HCl / 1 mole PCl3)

= 4.365 moles

The molar mass of HCl:

HCl = 1.0 g/mol (H) + 35.5 g/mol (Cl)

= 36.5 g/mol

The theoretical mass of HCl:

Theoretical mass of HCl = Theoretical yield of HCl x Molar mass of HCl

= 4.365 moles x 36.5 g/mol

≈ 159.3025 g

Percent yield = (Actual yield / Theoretical yield) x 100

= (155 g / 159.3025 g) x 100

= 97.3%

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Related Questions

What are the products of the following reactions?

1) cyclopentanone + cyclohexylamine

2) 3-pentanone + butylamine

3) 3-pentanone + cyclohexylamine

Answers

Imines are the nitrogen analogues of aldehydes and ketones, containing a C=N bond instead of a C=O bond.

They are formed through the addition of a primary amine to an aldehyde or ketone, kicking out a molecule of water (H2O) in the process.

In this post we show some examples of the synthesis of imines, walk through the mechanism for their formation, provide a few of their reactions and compare their properties to those of aldehydes and ketones.

A primary amine is added nucleophilically to the carbonyl group of an aldehyde or ketone to begin the reversible process of amine production. After that, a proton transfer creates a carbinolamine, a neutral amino alcohol. The carbinolamine oxygen is acid protonated to create a better leaving group, which is then removed as water to create an iminium ion. The ultimate imine product is produced when nitrogen is deprotonated.

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What are the products of the following reactions?1) cyclopentanone + cyclohexylamine2) 3-pentanone +

More bushes of potatoes will be produced if the soil is fertilized more WHAT IS THE INDEPENDENT VAIRABLE AND THE DEPENDENT VARIABLE

Answers

Answer:

The dependent variable is the bushes of potatoes while the soil is an independent variable.

Explanation:

An experiment can be defined as an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).

This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.

Cause and effect can be defined as the relationship between two things or events in which an occurrence one (cause) leads to the occurrence of another (effect).

In an experiment , the variable being manipulated by an experimenter is known as an independent variable while the dependent variable is the event expected to change when the independent variable is manipulated.

Hence, the dependent variable is the bushes of potatoes while the soil is an independent variable.

please help asap in 10 mins
What are the conditions necessary for electro-chemical corrosion to occur?

Answers

Answer:

Presence of an Electrolyte

Metal Surface

Oxygen or Other Oxidizing Agent

Difference in Potential

Electrochemical Pathway

Explanation:

Which description is true of earth’s four layers?

Answers

Answer:

The astenosphere is located below the lithosphere

The mantle is composed of silicate material

Explanation:

The Earth has several different layers, and they can be presented in two different manners, depending on their chemical composition and their physical properties. According to the chemical composition the Earth has three layers, crust, mantle, and core, while in accordance to the physical properties it has five, lithosphere, astenosphere, mesosphere, outer core, and inner core.

The astenosphere is the second layer from the top, and it lies just below the lithosphere. It is also the upper part of the mantle. The mantle is a layer that is largely composed of silicate material, mostly silicate molten rock. It can easily be seen from the volcanic activities that this layer is composed of silicate material because the magma is rich in it, and the magma comes from this layer.

the major product of the given reaction has the molecular formula c10h16o3. draw its structure in the most stable tautomeric form. the starting material is a 7 carbon chain where carbon 1 is double bonded to oxygen and single bonded to o c h 2 c h 3. carbon 2 has a methyl substituent. carbon 7 is double bonded to oxygen and single bonded to o c h 2 c h 3. this reacts with n a o c h 2 c h 3, followed by an acidic aqueous workup.

Answers

The same atoms make up tautomers, which are isomers with various electrical and molecular configurations. The associated tautomeric form is the most reliable.

Describe tautomery.

Tautomery is a specific type of isomery caused by a shift in one or more atoms' positions inside the molecule. The molecule electronic distribution and, consequently, the molecular structure are altered by this shift in location.

Tautomerization, the constant interconversion, is what gives equilibrium to the isomeres known as tautomers in solution. The same kind and number of atoms are present in both molecules.

The item in the suggested example has the chemical formula C10H16O3. In isomeric molecules, 6C, 16H, and 3O are essential. The distribution of these atoms, however, fluctuates, changing the structure of the resultant molecule.

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URGENT! Please help! Hi, I have to do a titration lab report using the Royal Society of Chemistry online titration lab. Please help me answer the following questions using the observation table I think?

URGENT! Please help! Hi, I have to do a titration lab report using the Royal Society of Chemistry online
URGENT! Please help! Hi, I have to do a titration lab report using the Royal Society of Chemistry online

Answers

Answer:

I'm sorry, but I cannot see the observations or the data table you mentioned in your question. However, I can still provide you with some general guidance on how to approach the calculations and answer the questions based on the given information.

4. To calculate the concentration of the NaOH solution, you need to know the mass of NaOH used and the volume of the solution. The formula to calculate concentration is:

Concentration (in mol/L) = (Mass of NaOH (in grams) / molar mass of NaOH) / Volume of solution (in L)

Make sure to convert the mass of NaOH to moles by dividing it by the molar mass of NaOH. The molar mass of NaOH is the sum of the atomic masses of sodium (Na), oxygen (O), and hydrogen (H).

5. The balanced equation for the neutralization reaction between NaOH and HCl is:

NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l)

(aq) represents an aqueous solution, and (l) represents a liquid.

6a. To calculate the average concentration of HCl in the sample from site B, you need to know the volumes and concentrations of the NaOH and HCl solutions used in the titration. Use the formula:

Concentration of HCl (in mol/L) = (Volume of NaOH solution (in L) * Concentration of NaOH (in mol/L)) / Volume of HCl solution (in L)

Multiply the volume of NaOH solution used by its concentration to find the amount of NaOH used. Then, divide this amount by the volume of HCl solution used to find the concentration of HCl.

6b. To determine the pH of the water at site B, you need to know the concentration of HCl from the previous calculation. The pH can be calculated using the formula:

pH = -log10[H+]

Since HCl is a strong acid, it dissociates completely into H+ ions. Therefore, the concentration of H+ ions is equal to the concentration of HCl. Take the negative logarithm (base 10) of the H+ concentration to find the pH.

To check if the water is safe, compare the calculated pH value to the range provided (pH 4.5-7.5). If the pH falls within this range, the water is considered safe for plant and animal reproduction in an aquatic environment.

6c. Use a similar calculation as in 6a to determine the average concentration of HCl in the sample from site C.

6d. Use the concentration of HCl from 6c to calculate the pH using the formula in 6b. Follow the same procedure to check if the water is safe based on the pH range.

7. To find the most current pH value for the Grand River, you can search for the latest data from reliable sources such as environmental agencies, research institutions, or government websites. Compare this pH value to the pH values obtained in the experiment to assess the difference between them.

Remember, without the specific data and observations, the calculations and comparisons provided here are only general guidelines. It's important to use the actual data from your experiment to obtain accurate results and conclusions.

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w
In your own words, what does the law of
conservation of energy tell us? Hint: It is
VERY similar to the law of conservation
of matter (we studied that in the first
semester).

Answers

Answer:

The law of conservation of mass States that matter can never be created or destroyed during c

A 0.8612-g sample of a mixture of NaBr, NaI, and NaNO3 was analyzed by adding AgNO3 and precipitating a 1.0186-g mixture of AgBrand AgI. The precipitate was then heated in a stream of Cl2, convertingit to 0.7125 g of AgCl. Calculate the %w/w NaNO3 in the sample.

Answers

Percentage by weight of the NaNO₃, is given by the ratio of the mass of NaNO₃ to the mass of the sample

The percentage by weight of NaNO₃ in the sample is approximately 30.713 %

Reason:

Given parameters are;

Mass of sample of NaBr, NaI, and NaNO₃ mixture = 0.8612 g

Mass of AgNO₃ and AgI formed = 1.0186

Mass of AgCl formed = 0.7125

Required:

Percentage by weight of NaNO₃ in the sample

Solution:

Let A represent NaBr, let B represent NaI, and let C represent NaNO₃, we have;

Equation 1 A + B + C = 0.8612

The addition of AgNO₃, precipitates 1.0186 g mixture of AgBr and AgI, therefore, we have;

\(A \cdot\left(\dfrac{Molar \ mass \ of \ AgBr}{Molar \ mass \ of \ NaBr} \right) + B \cdot \left(\dfrac{Molar \ mass \ of \ AgI}{Molar \ mass \ of \ NaI} \right) = 1.0186\)

Molar mass of AgBr = 187.77 g/mol

Molar mass of NaBr = 102.894 g/mol

Molar mass of AgI = 234.77 g/mol

Molar mass of NaI = 149.89 g/mol

Which gives;

Equation 2 \(A \cdot\left(\dfrac{187.77}{102.894} \right) + B \cdot \left(\dfrac{234.77}{149.89} \right) = 1.0186\)

The forming of the precipitate by passing the compounds through a stream of chlorine gives;

\(A \cdot\left(\dfrac{Molar \ mass \ of \ AgCl}{Molar \ mass \ of \ NaBr} \right) + B \cdot \left(\dfrac{Molar \ mass \ of \ AgCl}{Molar \ mass \ of \ NaI} \right) = 0.7125\)

Molar mass of AgCl = 143.32 g/mol

Therefore, we get;

Equation 3 \(A \cdot\left(\dfrac{143.32}{102.894} \right) + B \cdot \left(\dfrac{143.32}{149.89} \right) = 0.7125\)

Solving equation (2), and (3) gives;

A ≈ 0.3252 g, B ≈ 0.2715 g

Plugging in the values of A, and B in equation (1), gives;

0.3252 + 0.2715 + C = 0.8612

C = 0.8612 - (0.3252 + 0.2715) ≈ 0.2645

The mass of NaNO₃ in the mixture, C ≈ 0.2645

\(The \ percent \ by \ weight \ of \ NaNO_3 = \dfrac{0.2645}{0.8612} \times 100 \approx \underline{30.713 \%}\)

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Help me Look at the pictures!!!! Past due!
Make an explanation of how my hypothesis is not supported.

Help me Look at the pictures!!!! Past due!Make an explanation of how my hypothesis is not supported.
Help me Look at the pictures!!!! Past due!Make an explanation of how my hypothesis is not supported.
Help me Look at the pictures!!!! Past due!Make an explanation of how my hypothesis is not supported.

Answers

Answer:

Explanation:

the temperture of the warmer water will make it have more space and have less density in the water.

Between the green skinned lime and the yellow skinned lime, which of these are more acidic.

Answers

Green limes are more acidic as they tend to be smaller than yellow skinned limes. Yellow skinned limes tend to be sweeter whereas green skinned limes tend to be more sour. Green skinned limes are most likely immature compared to a yellow skinned lime which is mature

What is SI unit of volume​

Answers

Answer:

The SI unit of volume is m³

Can someone please write this in y’all’s own words please and I’ll give you branly

Can someone please write this in yalls own words please and Ill give you branly

Answers

Answer: we can make our own water and not take any water from animal.

Explanation:

I would like to get some help on this

I would like to get some help on this

Answers

Compound          Type of IMFs                   Sublime at STP?

Carbon dioxide       London dispersion         Yes

Hydrogen fluoride  Hydrogen bonding   No

Calcium chloride     Ionic bonding                  No

Naphthalene        London dispersion         Yes

Iodine                      London dispersion        Yes

Sodium chloride        Ionic bonding                 No

Water                    Hydrogen bonding         No

What is a Compound?

A chemical compound is described as  a chemical substance composed of many identical molecules containing atoms from more than one chemical element held together by chemical bonds.

London dispersion forces are also described as a type of intermolecular force acting between atoms and molecules that are normally electrically symmetric.

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HELP ME ASAP

What is the frequency of an
orange light with a wavelength of
483 nm?
? ] × 10[²]
10
c = 3.0 x 108 m/s
Hint: Watch your units!
[?
Hz
Be sure to enter both the coefficient and the exponent.
Coefficient (green)
Exponent (yellow)

HELP ME ASAPWhat is the frequency of anorange light with a wavelength of483 nm?? ] 10[]10c = 3.0 x 108

Answers

Answer:

Explanation:

λν = c

Wavelength, λ (lambda), times frequency, ν (nu), equals the speed of light.

c = 3.0 x 108 m/s

===

We are given a wavelength of 483 nanometers.  1 nanometer = 1x10^-9 meter.   483nm = 4.83x10^-7 meters

---

λν = c

ν = c/λ

ν = (3.0x10^8 m/s)/(4.83x10^-7 m)

ν = 6.21x10^14 Hz  (1/s)

If the forces are balanced...
The net force is greater than zero
The net force is zero
The net force is less than zero

If the forces are balanced...The net force is greater than zeroThe net force is zeroThe net force is

Answers

Answer:

the net force us 0.............

Explanation:

please mark brain

Can someone help with these

Can someone help with these

Answers

I’m sorry I don’t know I just need some points
Answer:

One strategy is to incorporate a soil bacterium gene that produces a glyphosate tolerant form of EPSPS.

Another way is to incorporate a different soil bacterium gene that produces a glyphosate degrading enzyme.

how many grams of phosphorus are in 50-gram sample of aluminum phosphate

Answers

There are approximately 12.7 grams of phosphorus in a 50-gram sample of aluminum phosphate.

To determine the number of grams of phosphorus in a 50-gram sample of aluminum phosphate, we need to know the molar mass and the chemical formula of aluminum phosphate.

The chemical formula for aluminum phosphate is AlPO4. It indicates that each molecule of aluminum phosphate contains one aluminum atom (Al), one phosphorus atom (P), and four oxygen atoms (O).

To calculate the molar mass of aluminum phosphate, we can add up the atomic masses of its constituent elements based on their stoichiometric ratios:

Molar mass of AlPO4 = (molar mass of Al) + (molar mass of P) + (4 * molar mass of O)

Using the periodic table, we can find the atomic masses of the elements:

Molar mass of Al = 26.98 g/mol

Molar mass of P = 30.97 g/mol

Molar mass of O = 16.00 g/mol

Now, let's calculate the molar mass of aluminum phosphate:

Molar mass of AlPO4 = (26.98 g/mol) + (30.97 g/mol) + (4 * 16.00 g/mol)

= 121.95 g/mol

The molar mass of aluminum phosphate is 121.95 g/mol.

To determine the number of grams of phosphorus in a 50-gram sample of aluminum phosphate, we need to calculate the mass fraction of phosphorus in the compound. The mass fraction is the ratio of the molar mass of phosphorus to the molar mass of aluminum phosphate.

Mass fraction of phosphorus = (molar mass of P) / (molar mass of AlPO4)

= (30.97 g/mol) / (121.95 g/mol)

≈ 0.254

Multiplying the mass fraction by the mass of the sample gives us the grams of phosphorus:

Grams of phosphorus = (mass fraction of phosphorus) * (mass of the sample)

= 0.254 * 50 g

≈ 12.7 g

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Using the average atomic masses for each of the following elements calculate the mass in AMU of each of the following samples

Using the average atomic masses for each of the following elements calculate the mass in AMU of each

Answers

Calculate the mass, in amu, of 278 atoms of Li.

1) We need to find Li (Lithium) in the periodic table.

1) The atomic mass of Lithium is 6.94 u.

\(\text{The mass of Lithium sample=}\frac{6.94\text{ u of Lithium}}{1\text{ mole of Lithium}}\cdot\frac{1\text{ mole of Lithium}}{6.022\cdot10^{23}\text{ atoms of Lithium}}\)

2) We can cancel some units and rearrange the equation.

\(\text{Lithium sample = }\frac{6.94\text{ u of Lithium}}{6.022\cdot10^{23}\text{ atoms of Lithium}}\)

3) Multiply the equation above by the number of atoms

\(\text{Lithium Sample = }\frac{6.94\text{ u of Lithium}}{6.022\cdot10^{23}\text{ atoms of Lithium}}\cdot\frac{278\text{ atoms of Lithium}}{\square}\text{ = 3.20}\cdot10^{-21}\text{ u of Lithium}\)

The mass of 278 atoms of Lithium is 3.20*10^-21 u

what are the coefficients that will balance the skeleton equation​

Answers

Answer:

When the following equation is balanced, what is the coefficient for HCl? Mg(s) + HCl(aq) -> MgCl2(aq) + H2(g) . 2. What are the coefficients that will balance the skeleton equation below? AlCl3 + NaOH -> Al(OH)3 + NaCl.

which has more mass, a mole of ne gas or a mole of n2 gas?

Answers

A mole of N2 gas has more mass than a mole of Ne gas. To compare the mass of a mole of Ne gas and a mole of N2 gas, we need to consider their molar masses.


One mole of any substance contains the same number of particles, which is Avogadro's number (6.02 x 10^23). However, the masses of different substances can vary due to differences in their atomic or molecular weights.
The atomic weight of Ne is 20.18 g/mol, while the molecular weight of N2 is 28.01 g/mol. Therefore, a mole of N2 gas contains more mass than a mole of Ne gas.

The molar mass of Ne (neon) is approximately 20.18 g/mol, while the molar mass of N2 (molecular nitrogen) is approximately 28.02 g/mol. Since the molar mass of N2 is greater than the molar mass of Ne, a mole of N2 gas has more mass than a mole of Ne gas.

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What is the relationship between layering of fluids and density?

Answers

Density of a liquid determines how it will layer (heaviest to lightest). If the liquid is least dense it will float to the bottom. Layers will remain separated because each liquid is actually floating on top of the more dense liquid beneath it.

What is Decomposition Reaction

Answers

Answer:

Explanation:

Decomposition reaction, also known as analysis or dissociation, is a type of chemical reaction in which a compound breaks down into simpler substances or elements. In this reaction, a single reactant undergoes a chemical change and produces two or more products.

The decomposition reaction can be represented by the general equation:

AB → A + B

Where AB is the reactant, and A and B are the products. The reactant AB is usually a compound, and it breaks down into its constituent elements or simpler compounds.

There are different types of decomposition reactions, including:

Thermal decomposition: It occurs when a compound is heated, resulting in its decomposition into simpler substances. For example, the thermal decomposition of calcium carbonate (CaCO3) produces calcium oxide (CaO) and carbon dioxide (CO2):

CaCO3 → CaO + CO2

Electrolytic decomposition: It takes place when an electric current is passed through an electrolyte, causing it to break down into its component ions. For instance, the electrolysis of water (H2O) leads to the decomposition into hydrogen gas (H2) and oxygen gas (O2):

2H2O → 2H2 + O2

Photochemical decomposition: It occurs when a compound undergoes decomposition due to exposure to light energy. Chlorine gas (Cl2) can decompose into chlorine atoms (Cl) under the influence of light:

Cl2 → 2Cl

These are just a few examples of decomposition reactions. They are important in various chemical processes and are used in industries, laboratory experiments, and natural phenomena. By understanding and controlling decomposition reactions, scientists can gain insights into the behavior of different compounds and develop practical applications in fields such as chemistry, materials science, and environmental science.

Answer:

Explanation:

reaction in which a compound breaks down into simpler substances or elements

How bad of alcoholic do you have to be to have your brain affected​

Answers

Answer:

Alcohol in Your Body

Alcohol reaches your brain in only five minutes, and starts to affect you within 10 minutes. After 20 minutes, your liver starts processing alcohol. On average, the liver can metabolize 1 ounce of alcohol every hour.

Explanation:

hope that helps you i just love sharing glmv sorry

How bad of alcoholic do you have to be to have your brain affected

What is the representative particle for potassium chloride?

Answers

Nana a she’s a little while she’s in here a lot better lol I just don’t have her number I think she was just joking around that I didn’t know if she

the predominant intermolecular force found in na⁺(aq) is _____

Answers

The predominant intermolecular force found in Na⁺ (aq) is Ion-Dipole Interactions.

What are intermolecular forces?

Intermolecular forces can be defined as the attractive or repulsive forces that produce between the molecules or ions of a solution or substance. These forces are responsible for the physical properties and chemical properties of matter.

Forces that develop between the molecules themselves are intermolecular forces.  The intermolecular forces are Ion-Dipole Interactions, Dipole-Dipole Interactions, Ion-Induced Dipole Interactions, Dispersion Forces, and Dipole-Induced Dipole Interaction.

In the Na⁺ aqueous solution, sodium Na⁺ ions interact with the dipole of water molecules therefore, the predominant intermolecular forces in such solution are Ion-Dipole Interactions.

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What's the difference between a wax crayon and a plastic crayon?

Answers

Answer:

Crayons use wax and Oil pastels use non-drying oil and wax. Besides the composition of the colours, there is a huge difference in how a wax crayon and an oil pastel works. ... Crayons, don't colour your hands. Well, most crayons don't.

Explanation:

what's crayons are softer and they smudge because they have more oil pastels in them plastic crayons are harder and they don't intend to smudge.

The atomic mass of iron is 55.85, and oxygen is 16.0. What is the mass of 6.02 × 1023 molecules of Fe2O3?

Answers

Answer:159.7grams

Explanation:

(55.85)2+(16)3

159.7grams

Answer:

The correct answer for plato/edmentum is C (159.7g)

plzzzzzzzzzz help ASAP

plzzzzzzzzzz help ASAP

Answers

Answer:

i think the answer is c because it says that is all they care

What is a practically insignificant reaction?

Answers

Answer:

Practical significance refers to the magnitude of the difference, which is known as the effect size. Results are practically significant when the difference is large enough to be meaningful in real life. ... Very small differences will be statistically significant with a very large sample size.

Explanation:

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True or False. Star gazing is a pretty popular hobby in today's world.

Answers

Answer:

yes (true)

Explanation:

Star gazing has started to become a more popular hobby in todays world due to the pandemic

true

Absolutely everyone just wants to look up at them and wonder what’s beyond this world and just think by themselves or with others
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In a raffle where 9000 tickets are sold for $2 each, one prize of $2300 will be awarded. What is the expected value of a single ticket in the raffle?State your answer in terms of dollars rounded to the nearest cent (hundredth). pangngalan na panawag sa mga kongkreto at abstraktong bagay. Which is the largest of the followin fractions? 7/12, 2/3,5/6,3/4, 5/8, (a) 2/3 (b) 3/4 (c) 5/ 5 Cloward and Ohlin addressed the street hustler as a role model for youth and the methods used to earn easy money through a life of crime. What did they call this career path of delinquency 3. The table below shows the distances, in miles, from Craig's home to different locations in histown. Which statement comparing the distances, in miles, of two of the locations from Craig's home is correct?The park is closer to Craig's home than the library.The school is closer to Craig's home than the park.O The mall is farther from Craig's home than the school.O The library is farther from Craig's home than the mall. Amy and Jack have candies in a ratio of 1:3. Together, they have a total of 40 candies. How many candies does Amy have? 8. Find the slope. Make sure to reduce. Ixl HELP pLease get this done quick Jason Roberts has been part of a workgroup team for four months. The team's primary goal is to develop a marketingplan for a new product. Tami Wong, a marketing manager, typically assumes the leadership role in the team. However,the team has not formally identified a leader. The team members meet twice a month. They discuss ideas for how tosell and advertise the product. Team members have volunteered to do research or other tasks. Jason and two otherteam members have reported on their progress. Others have said they have not yet had time to do their part of theproject. The deadline for completing the marketing plan is only two months away, and much work remains to be done.Clearly, the team needs to evaluate its methods.1) What questions should Jason consider as part of a self-evaluationof his work with the team?2) What suggestions could Jason make to the team members for improving the way theteam functions? What is the correct version of this sentence?This is what I want to do today; nothing.What I want to do today is, nothing.This is what I want to do today: nothing. the l. a. scene is often overshadowed by san francisco and london during this time period. how does a band like the doors rise to prominence without being part of either scene? what separates them from their contemporaries? are they still influential today? name some examples. the market structure which is characterized by a high degree of interdependence between sellers is known as Learning Goal: To understand the concept of normal modes of oscillation and to derive some properties of normal modes of waves on a string. A normal mode of a closed system is an oscillation of the system in which all parts oscillate at a single frequency. In general there are an infinite number of such modes, each one with a distinctive frequency fi and associated pattern of oscillation. Consider an example of a system with normal modes: a string of length L held fixed at both ends, located at x=0 and x=L. Assume that waves on this string propagate with speed v. The string extends in the x direction, and the waves are transverse with displacement along the y direction. In this problem, you will investigate the shape of the normal modes and then their frequency. The normal modes of this system are products of trigonometric functions. (For linear systems, the time dependance of a normal mode is always sinusoidal, but the spatial dependence need not be.) Specifically, for this system a normal mode is described by yi(x,t)=Aisin(2xi)sin(2fit).a) Find the three longest wavelengths (call them 1, 2, and 3) that "fit" on the string, that is, those that satisfy the boundary conditions at x=0 and x=L. These longest wavelengths have the lowest frequencies.Express the three wavelengths in terms of L. List them in decreasing order of length, separated by commas.b) The frequency of each normal mode depends on the spatial part of the wave function, which is characterized by its wavelength i.Find the frequency fi of the ith normal mode.Express fi in terms of its particular wavelength i and the speed of propagation of the wave v.c) Find the three lowest normal mode frequencies f1, f2, and f3.Express the frequencies in terms of L, v, and any constants. List them in increasing order, separated by commas. Costs that tend to deter firms from changing their prices in response to changes in the market equilibrium price are referred to as A) burden costs. C) real menu costs. B) large menu costs D) small menu costs. In 1967 , an earner in the bottom fifth was earning 9% of a top-fifth earner's income. In dollar terms, the bottom-fifth worker was earning $9,850. By 2020 , the bottom fifth earner was earning 6% of the top-fifth earner and the bottom-fifth worker's income was 14,600. Find the top-fifth worker's income in 1967. In 1967, an earner in the bottom fifth was earning 9% of a top-fifth earner's income. In dollar terms, the bottom-fifth worker was earning $9,850. By 2020, the bottom fifth earner was earning 6% of the top-fifth earner and the bottom-fifth worker's income was 14,600. Find the top-fifth worker's income in 2020. which statement concerning solutions is false? multiple choice solutions are homogeneous mixtures. solutes can be ionic or covalent. colloidal suspensions are solutions. solutions can have the solid, liquid, or gas state. solutions consist of solutes and solvents. What is the value of x + y when x= 3 and y=4? A soda company had sales of $35,107 million in 2010 and $45,984 million in 2014. Use the Midpoint Formula to estimate the sales in 2012. Assume that the sales followed a linearpattern.$ __ million CORRECT ANSWER ONLY THANK YOU f has a range of (-4, infinity), and a graph that is symmetric about the line x = -1 , and has a y- intercept of -3