the electron in a ground-state h atom absorbs a photon of wavelength 94.98 nm. to what energy level does the electron move?

Answers

Answer 1

The electron moves to the energy level [tex]n_{final}[/tex] = 1.093. Please note that energy levels in hydrogen are typically represented by integers, so we can round the value to the nearest whole number. Therefore, the electron moves to the energy level n = 1

To determine the energy level to which the electron moves, we can use the equation:

ΔE = hc/λ

Where ΔE is the change in energy, h is Planck's constant (approximately 6.626 x 10⁻³⁴ J·s), c is the speed of light (approximately 3.00 x 10⁸ m/s), and λ is the wavelength of the absorbed photon.

Let's convert the wavelength from nanometers to meters:

λ = 94.98 nm = 94.98 x 10⁻⁹ m

Now we can calculate the change in energy:

ΔE = (6.626 x 10⁻³⁴ J·s)(3.00 x 10⁸ m/s)/(94.98 x 10⁻⁹ m)

ΔE ≈ 2.206 x 10⁻¹⁸ J

The change in energy corresponds to the transition between energy levels in the hydrogen atom. The energy levels in the hydrogen atom are described by the formula:

ΔE = -13.6 eV ₓ (1/n_final²- 1/n_initial²)

Solving for [tex]n_{final}[/tex], we can find the energy level to which the electron moves:

[tex]n_{final}[/tex]= √(1/(1 - ΔE/(13.6 eV)))

Using the calculated value of ΔE, we find:

[tex]n_{final}[/tex] =√(1/(1 - 2.206 x 10^-18 J/(13.6 x 1.602 x 10^-19 J/eV)))

[tex]n_{final}[/tex] = √(1/(1 - 0.1625))

[tex]n_{final}[/tex] =√(1/0.8375)

[tex]n_{final}[/tex] =√(1.192)

[tex]n_{final}[/tex] = 1.093

The electron moves to the energy level [tex]n_{final}[/tex] = 1.093.

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Related Questions

A mass of 80 grams of Bromine would be

Answers

I’m pretty sure it’s a

Which of the following statements IS true regarding nucleophilic acyl substitution? Aldehydes and ketones go through acyl elimination, not substitution. The alcohol is reformed in the second step. The mechanism proceeds through a carbocation intermediate. The leaving group ability of the heteroatom group determines the reactivity towards nucleophilic acyl substitution.

Answers

The  true statement is, the leaving group ability of the heteroatom group determines the reactivity towards nucleophilic acyl substitution.

What is Nucleophilic acyl substitution?

Nucleophilic acyl substitution describes a class of substitution reactions involving nucleophiles and acyl compounds.

Also, nucleophilic acyl substitution is a type of substitution reaction involving an acyl group and a nucleophile.

Thus, the statement that is true regarding nucleophilic acyl substitution is, the leaving group ability of the heteroatom group determines the reactivity towards nucleophilic acyl substitution.

Thus, in nucleophilic acyl substitution, a nucleophile displaces the leaving group, resulting in a carbonyl compound.

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Using data in Appendix E in the textbook,
calculate the standard emf for each of the following reactions:
1.H2(g)+F2(g)→2H+(aq)+2F−(aq).
2.Cu2+(aq)+Ca(s)→Cu(s)+Ca2+(aq).
3.2ClO−3(aq)+10Br−(aq)+12H+(aq)→Cl2(g)+5Br2(l)+6H2O(l).

Answers

Answer: The standard emf for each of the following reactions are:

1. 2.87V    2. 3.21V   3. -3.91V.

Explanation: The standard emf of the given reaction is given by the formula:EMF= E°(reduced) - E°(oxidized)

1. H2(g) + F2(g) → 2H+(aq) + 2F-(aq).The balanced equation is:H2(g) + F2(g) → 2H+(aq) + 2F-(aq)The standard reduction potentials are given by:E°(H+(aq)/H2(g)) = 0V and E°(F-(aq)/F2(g)) = +2.87V.The standard emf can be calculated using the given formula:EMF = E°(reduced) - E°(oxidized)= 2.87 - 0= 2.87V

2. Cu2+(aq) + Ca(s) → Cu(s) + Ca2+(aq).The balanced equation is:Cu2+(aq) + Ca(s) → Cu(s) + Ca2+(aq)The standard reduction potentials are given by:E°(Cu2+(aq)/Cu(s)) = 0.34V and E°(Ca2+(aq)/Ca(s)) = -2.87V.The standard emf can be calculated using the given formula:EMF = E°(reduced) - E°(oxidized)= 0.34 - (-2.87)= 3.21V

3. 2ClO-3(aq) + 10Br-(aq) + 12H+(aq) → Cl2(g) + 5Br2(l) + 6H2O(l)The balanced equation is:2ClO-3(aq) + 10Br-(aq) + 12H+(aq) → Cl2(g) + 5Br2(l) + 6H2O(l)The standard reduction potentials are given by:E°(Cl2(g)/2Cl-(aq)) = +1.36V and E°(Br2(l)/2Br-(aq)) = +1.09V.The standard emf can be calculated using the given formula:EMF = E°(reduced) - E°(oxidized)= 1.36 - (5*1.09)= -3.91V.

Hence,The standard emf for each of the following reactions are:1. 2.87V2. 3.21V3. -3.91V.

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What form of electromagnetic radiation does gamma radiation use?

Answers

Answer:

Gamma-rays are a form of electromagnetic radiation, as are radio waves, infrared radiation, ultraviolet radiation, X-rays and microwaves. Gamma-rays can be used to treat cancer, and gamma-ray bursts are studied by astronomers.

Explanation:

Hope this helped Mark BRAINLIEST!!!

Gamma Rays are ionizing Electromagnetic radiation, obtained by the decay of an atomic nucleus. Gamma rays are more penetrating, in matter, and can damage living cells to a great extent. Gamma rays are used in medicine (radiotherapy), industry ( Sterilization and disinfection) and the nuclear industry.

If 4.1 g of 3H2 (g) + N2 (g) → 2NH3 (g) is actually produced, what is the percent yield?
So like, here's the equation:
3H2 (g) + N2 (g) → 2NH3 (g)
And the question is, "If 4.1 g of ammonia is actually produced, what is the percent yield?"
Could you please help? I've been stuck for two days and I have no one to ask. Thanks!!

Answers

Answer:

Explanation:

The first thing that you need to do here is to calculate the theoretical yield of the reaction, i.e. what you get if the reaction has a

100

%

yield.

The balanced chemical equation

N

2

(

g

)

+

3

H

2

(

g

)

2

NH

3

(

g

)

tells you that every

1

mole of nitrogen gas that takes part in the reaction will consume

3

moles of hydrogen gas and produce

1

mole of ammonia.

In your case, you know that

1

mole of nitrogen gas reacts with

1

mole of hydrogen gas. Since you don't have enough hydrogen gas to ensure that all the moles of nitrogen gas can react

what you need



3 moles H

2

>

what you have



1 mole H

2

you can say that hydrogen gas will act as a limiting reagent, i.e. it will be completely consumed before all the moles of nitrogen gas will get the chance to take part in the reaction.

So, the reaction will consume

1

mole of hydrogen gas and produce

1

mole H

2

2 moles NH

3

3

moles H

2

=

0.667 moles NH

3

at

100

%

yield. This represents the reaction's theoretical yield.

Now, you know that the reaction produced

0.50

moles of ammonia. This represents the reaction's actual yield.

In order to find the percent yield, you need to figure out how many moles of ammonia are actually produced for every

100

moles of ammonia that could theoretically be produced.

You know that

0.667

moles will produce

0.50

moles, so you can say that

100

moles NH

3

.

in theory

0.50 moles NH

3

.

actual

0.667

moles NH

3

.

in theory

=

75 moles NH

3

.

actual

Therefore, you can say that the reaction has a percent yield equal to

% yield = 75%

−−−−−−−−−−−−−

Consider if the reaction is conducted with 3 moles of hydrogen and 2 moles of nitrogen as it in the balanced reaction, and if only 4.1 g of ammonia is produced, then the percent yield will be 12%.

What is percent yield?

The ratio of  the actual yield to the theoretical yield multiplied by 100 is the percent yield. No simple reactions can achieve a 100 % yield.

As per the given reaction, 3 moles of hydrogen reacts with 2 moles of nitrogen and produce 2 moles of ammonia. Molar mass of ammonia is 17 g/mol. Thus, 2 moles are 34 g/mol.

Assume that if the theoretical yield is 34 g, then the percent yield for actual yield of  4.1 g is,

4.1 /34 ×100 = 12.1 %.

Now lets assume that only one mole of hydrogen is reacted here, number of moles of ammonia produced by one mole of hydrogen is :

=  1 mole × 2 mol / 3 moles

= 0.66 moles.

0.66 moles = 0.66 × 17 g/mol = 11.22 g.

For a theoretical yield of 11.22 g, the percent yield will be

= 4.1 /11.22

= 36.6 %.

Therefore, by assuming if 3 moles of hydrogen are reacted then percent yield will be 12% for 4.1 g of actual yield and 36 % if only one mole of hydrogen is reacted.

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Which of the following is the strongest acid? Select one: a. CH3CH2OH b. CH3OCH3 c. CH3COOH d. CH3NHCH3 e. CH3CH=CH2

Answers

Out of the given options, CH3COOH is the strongest acid.

The strength of an acid is determined by its ability to donate protons. The more the acid donates protons, the stronger it is.Acid strength increases with decreasing pKa value. The pKa value of CH3COOH is 4.76. The lower the pKa value, the stronger the acid. CH3OCH3 is a weakly acidic compound with a pKa value of 15.5, whereas CH3CH2OH is a slightly acidic compound with a pKa value of 16. CH3NHCH3 is a non-acidic compound because it lacks an acidic hydrogen atom. CH3CH=CH2 is an alkene and is not an acidic compound.To summarize, CH3COOH is the strongest acid among the given options with a pKa value of 4.76.

So, option c is the correct answer.

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How does the way in which the solar system formed explain the orbits, sizes, and compositions of the planets?

Answers

Answer:

DUE TO GRAVITATIONAL COLLAPSE SOLAR SYSTEM IS FORMED , ORBITS ARE CURVED TRAJECTORIES AND SIZE AND COMPOSTION OF PLANET ARE VERY UNIQUE AND COMPOSED OF ROCKS AND METALS and evolution of solar system has began 4.5 billion years ago,due to gravitational collapse of a small particle from a giant cloud.

A shell container is useful for

Answers

A shell container is useful for:It is used to carry many things.Also, Containers give developers the ability to create predictable environments that are isolated from other applications. And;Containers can also include software dependencies needed by the application, such as specific versions of programming language runtimes and other software libraries.

You have to make 500 mL of a 1.50 M BaCl2. You have 2.0 M barium chloride solution available. Determine how to make the needed dilution

Answers

Answer:

There are needed 375mL of the 2.0M BaCl₂ solution completing to 500mL with water.

Explanation:

We can find with the volume and concentration of the barium chloride the moles of BaCl₂ required. With the moles and the concentration of our stock solution we can know the volume of the 2.0M BaCl₂ solution required as follows:

Moles required:

0.500L * (1.50mol / L) = 0.750 moles BaCl₂

Volume stock solution:

0.750 moles BaCl₂ * (1L / 2.0mol) = 0.375L

There are needed 375mL of the 2.0M BaCl₂ solution completing to 500mL with water.

If you see a large “H” on the weather map, what type of weather can you expect there?

Answers

Answer:

High pressure.

Explanation:

The weather should have clear skies, if it is a Large "L" it would be could be stormy.

Hope this helps! have a great day!

Please help I'm not sure what the answers are​

Answers

Answer:

An element's mass number (A) is the sum of the number of protons and the number of neutrons. The small contribution of mass from electrons is disregarded in calculating the mass number.

Reactants of a combustion reaction include

select all that apply
Fuel
Oxygen
Water
Carbon Dioxide

Answers

Answer:  fuel and oxygen are reactants.

Explanation:

Answer:

fuel and oxygen

Explanation:

I take test


Balance C12H22011 → C + H2

Answers

Answer:

What is this?

Explanation:

Which ion is the counter ion in the coordination compound[Co(NH3)4Cl2]NO3? O NOs O NH3 O cI

Answers

The counter ion in the coordination compound [Co(NH3)4Cl2]NO3 is NO3-.

In a coordination compound, there is a central metal ion or atom that is surrounded by ligands. The ligands coordinate to the metal ion through donation of electron pairs. In this compound, the central metal ion is cobalt (Co), which is coordinated to four ammonia (NH3) ligands and two chloride (Cl) ligands.

The counter ion is the ion that balances the charge of the entire coordination compound. In this case, the coordination compound carries a net charge of 0 because the total charges of the ligands (4NH3 with no charge and 2Cl- with a -1 charge each) sum up to 0. Therefore, to balance the charge, a counter ion is required.

The counter ion in this compound is NO3-, which is a nitrate ion. The nitrate ion carries a -1 charge, which balances the overall charge of the coordination compound.

The counter ion in the coordination compound [Co(NH3)4Cl2]NO3 is NO3-. It serves to balance the charge of the coordination compound, which has a net charge of 0 due to the coordination of the ligands.

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Molecular crystals are held together by the intermolecular forces of dispersion and dipole-dipole forces and by hydrogen bonding. True or False

Answers

Molecular crystals are held together by the intermolecular forces of dispersion and dipole-dipole forces and by hydrogen bonding. The statement is True.

Molecular crystals are held together by the intermolecular forces of dispersion, dipole-dipole forces, and hydrogen bonding.

Dispersion forces are the weakest intermolecular forces and are present in all molecules. They are caused by the temporary uneven distribution of electrons in a molecule, which creates a temporary dipole.

The temporary dipole in one molecule can induce a dipole in another molecule, resulting in a weak attractive force.

Dipole-dipole forces are stronger than dispersion forces and are present in molecules that have a permanent dipole. The positive end of one dipole is attracted to the negative end of another dipole, resulting in a stronger attractive force.

Hydrogen bonding is the strongest intermolecular force and is present in molecules that contain a hydrogen atom bonded to a highly electronegative atom, such as oxygen, nitrogen, or fluorine.

The hydrogen atom is partially positive, while the electronegative atom is partially negative. This creates a strong attractive force between the hydrogen atom of one molecule and the electronegative atom of another molecule.

The type of intermolecular force that is most important in holding a molecular crystal together depends on the structure of the molecules in the crystal.

For example, a crystal of water is held together by hydrogen bonding, while a crystal of methane is held together by dispersion forces.

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(0904) How many atoms are there in 56.2 grams of Krypton, Kr?

Answers

Answer:

56.2÷6.02×10^23

=9.34×10^23

Explanation:

Divide the given mass of the atom by the mass of an Atom (the avogadro's constant) to find the number of atoms in the given mass.

Is Chlorine and Sodium an Ionic or Covalent bond?

Answers

Answer:

It is an Ionic bond

Is combining ammonium chloride and water a physical or chemical change

Answers

No, ammonium chloride in water is not a physical reaction. It is a chemical reaction. Hope this helps!

if this atom has one additional neutron but the other subatomic particles remained the same as shwon, this slightly different atoms would be called

Answers

If this atom has one additional neutron but the other subatomic particles remained the same as shown, this slightly different atom would be called an isotope.

What is an isotope?

An isotope is a variant of an atom that has a different number of neutrons. Because isotopes of the same element have the same number of protons in the nucleus, they all have the same atomic number. However, they can differ in mass number, and therefore in atomic mass. In a neutral atom, the number of protons in the nucleus equals the number of electrons that orbit the nucleus, giving the atom a net electrical charge of zero.

However, the number of neutrons in the nucleus can differ, implying that isotopes of the same element may have different atomic masses.

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Match the different methods used for calculating revenue and profit to the formulas used for calculating them. total revenue average revenue marginal revenue gross profit net profit

Answers

Answer:

See explanation below

Explanation:

1) Total Revenue:

Total revenue refers to the total amount of income that is generated when a company sells or offers their service.

It is usually calculated as the product of the product or services sold by the quantity.

It is calculated by ;

TR = Q * P

Where TR = Total Revenue

Q = Quantity

P = Price

2.) Average Revenue:

Average revenue is the revenue gotten by a company per unit of output sold. It is calculated by:

AR = TR / Q

Where AR = Average Revenue

TR = Total Revenue

Q. = Quantity

3.) Marginal Revenue:

This is the net revenue that is generated by selling an additional unit of commodity; which is the change in total revealer unit. It is calculated by:

MR = change in Total Revenue / change in Quantity

Where MR = Marginal Revenue

4.) Gross Profit:

Gross profit is the amount of revenue left after factoring out the cost of production and sales and servicing.

It is calculated by subtracting revenue from the cost of goods sold -

Gross Profit = Revenue - Cost of goods sold

Net Profit:

Net profit is the amount of money a company has left after subtracting all interests, tax expenses and cost.

It is calculated by;

Net Profit = Gross Profit - Expenses

What two properties of sound remain the same when sound quality differs? Check all that apply.

Answers

Answer: I don’t know sorry

Explanation:

PLEASE HELP!?Consumers must eat other organisms for energy. Which organisms are consumers in this food chain?

Answers

Answer:

Consumers must consume other organisms to get the food that they need and are known as Heterotrophs as they cannot make their own glucose. These consumers eat producers (plants). Herbivores are considered as first order consumers. These consumers eat consumers and producers (animals and plants).

How many moles of sulfur
dioxide are in 2.26 x 10^33 sulfur dioxide molecules?

Answers

Answer:

moles = no. of molecules / Avogadro's number

         = 2.26 x 10^33 / 6.022 x 10^23

         = 3752906011

Round to significant figures which is 3 = 3.75 x 10^9 mol

Explanation: The formula for finding how many moles of a substance when given the amount of molecules is: moles = number of molecules / Avogadro's number

When copper sulphate is dissolved in water in a beaker, a bright blue liquid or solution is formed. If copper sulphate is added until no more will dissolve, a saturated solution is formed. Some blue crystals will remain at the bottom of the beaker?

Please answers quick

Answers

Answer:

ok i dont get your question fully but i'll answer

When copper sulfate is dissolved in water in a beaker, a bright blue liquid or solution is formed. If copper sulfate is added until no more will dissolve, a saturated solution is formed. And some blue crystals will remain at the bottom of the beaker due to crystallization reaction. It is the process by which a solid form, where the atoms or molecules are highly organized into a structure known as a crystal.

In a 0.879 M potassium permanganate (KMnO4) aqueous solution, what is the SOLUTE?

Answers

Answer:

Potassium Permanganate

Explanation:

A solution is defined as the mixture of two or more substances. The substance that is in big proportion is called as Solvent, the substance that is in low amount is called as Solute.

In an aqueous solution, the solvent is the water. As the aqueous solution is 0.879M KMnO4, the solute is:

Potassium Permanganate

add single electron dots and/or pairs of dots as appropriate to show the lewis symbols of the following neutral atoms.

Answers

Hydrogen is the only exception, as it has only one valence electron.

The Lewis symbol for an atom includes its symbol and valence electrons represented as dots. The following are the Lewis symbols for neutral atoms with their electron dots and pairs of dots:- Hydrogen (H): 1 electron; Lewis symbol: H •- Helium (He): 2 electrons; Lewis symbol: He ••- Carbon (C): 4 electrons; Lewis symbol: C •• ••- Nitrogen (N): 5 electrons; Lewis symbol: N •• •• •••- Oxygen (O): 6 electrons; Lewis symbol: O •• •• ••••- Fluorine (F): 7 electrons; Lewis symbol: F •• •• ••• •••The number of valence electrons for each atom is determined by the group number on the periodic table. Hydrogen is the only exception, as it has only one valence electron.

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NEED HELP ASAP
You need to prepare a 100. mL of a 0.050M solution of CaCl2. How many grams of CaCl2 are needed?

Answers

Answer:

9.

Explanation:

.

Question 1 (1 point) How many stars are in our solar system? A. About 20.000 B. About 300,000 C. One D. About 5,000 ​

Answers

Answer:

C. one star

Explanation:

Of course our solar system has one unique star which is the sun while others have atleast two which are called binary solar

For the following aqueous equilibria, designate the Brønsted-Lowry conjugate acid-base pairs and establish the weaker side: a. NH3(aq) + H₂O(1) NH4+ (aq) + OH-(aq) b. HCN(aq) + H₂O(1) ⇒ H3O+(aq) + CN- (aq) 1-4 C. NH4+ (aq) + CO3²-(aq) NH3(aq) + HCO3(aq)

Answers

For the following aqueous equilibria;

a. The weaker side is the left side of the equation: NH₃(aq) + H₂O(l).b. The weaker side is the left side of the equation: HCN(aq) + H₂O(l).c. The weaker side is the right side of the equation: NH₃(aq) + HCO₃⁻(aq).

How to determine weaker side?

a. NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq)

The Brønsted-Lowry conjugate acid-base pairs in this equilibrium are:

NH₃ (conjugate base) and NH₄⁺ (conjugate acid)

H₂O (conjugate acid) and OH⁻ (conjugate base)

To determine the weaker side, compare the strengths of the conjugate acid-base pairs. In this case, NH₃ is a weaker base than H₂O, and NH4+ is a stronger acid than OH-. Therefore, the weaker side is the left side of the equation: NH₃(aq) + H₂O(l).

b. HCN(aq) + H₂O(l) ⇌ H₃O⁺(aq) + CN⁻(aq)

The Brønsted-Lowry conjugate acid-base pairs in this equilibrium are:

HCN (conjugate base) and H₃O⁺ (conjugate acid)

H₂O (conjugate acid) and CN⁻ (conjugate base)

To determine the weaker side, compare the strengths of the conjugate acid-base pairs. In this case, HCN is a weaker base than H₂O, and H₃O⁺ is a stronger acid than CN-. Therefore, the weaker side is the left side of the equation: HCN(aq) + H₂O(l).

c. NH₄⁺(aq) + CO₃²⁻(aq) ⇌ NH₃(aq) + HCO₃⁻(aq)

The Brønsted-Lowry conjugate acid-base pairs in this equilibrium are:

NH₄⁺ (conjugate acid) and NH₃ (conjugate base)

CO₃²⁻ (conjugate base) and HCO₃⁻ (conjugate acid)

To determine the weaker side, compare the strengths of the conjugate acid-base pairs. In this case, NH₃ is a weaker base than NH₄⁺, and HCO₃⁻ is a stronger acid than CO₃²⁻. Therefore, the weaker side is the right side of the equation: NH₃(aq) + HCO₃⁻(aq).

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Which type of radioactive decay results in no change in mass number and atomic number for the starling nucleus? A) beta B) alpha C) electron capture D) gamma E) positron emission

Answers

The type of radioactive decay that results in no change in mass number and atomic number for the starting nucleus is gamma decay. The correct answer is option D.

Gamma decay is a type of radioactive decay that involves the emission of gamma rays from an atomic nucleus. Gamma rays are high-energy photons that are emitted when the nucleus undergoes a transition from a higher energy state to a lower energy state. Gamma decay does not result in a change in the atomic number or mass number of the nucleus, as no particles are emitted from the nucleus. Instead, the nucleus simply releases energy in the form of a gamma ray. Therefore, option D) Gamma is the correct answer.

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Define a relation on R by rs if r = |s and check as to whether is an equivalence relation on R or not. which french philosopher supported freedom of religion despite criticizing the roman catholic church? rousseau voltaire john calvin ren descartes .Where does Databricks Machine Learning fit into the Databricks Lakehouse Platform?It is one of the core services of the Lakehouse Platform, tailored towards data practitioners who need to manage users and workspace governanceIt is one of the core services of the Lakehouse Platform, tailored towards data practitioners building data pipelines to make data available to everyone in an organizationIt is one of the core services of the Lakehouse Platform, tailored towards data practitioners building and managing machine learning modelsIt is one of the core services of the Lakehouse Platform, tailored towards data practitioners who need to query data and publish visual insights A data set lists the grade point averages of 11th grade students. Which of the following methods could be used to display the data, and why? A.Bar chart, because the data is categorical B.Bar chart, because the data is numerical C.Histogram, because the data is categorical D.Histogram, because the data is numerical Answers for each question should be at least 100 words. If possible do not copy directly from any source because it will be turned in through turn it in.What is inbound marketing and how does it differ from traditional marketing methods? How can online media help a firm with inbound marketing efforts?What are the benefits and risks associated with social networks? Select a company you are familiar with and discuss how social networking can benefit of harm this company. in a healthy cell (no ras mutations) when the growth factor is present and no drugs are present, which statement accurately describes the state of the erk protein? Direct labor variancesBellingham Company produces a product that requires 3 standard direct labor hours per unit at a standard hourly rate of $20.00 per hour. 15,800 units used 65,400 hours at an hourly rate of $19.25 per hour.What is the direct labor (a) rate variance, (b) time variance, and (c) cost variance? Round your answers to the nearest dollar. Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number..a. Direct labor rate variance $ b. Direct labor time variance $ c. Direct labor cost variance $ The trace of a (square) matrix A is defined as the sum of its diagonal entries, and is denoted by tr(A). Now suppose A is any 2 x 2 matrix (ca) = = and let p(1) = 12 +al+B be the characteristic polynomial of A. Show that a = -tr(A) and B = det(A). Hence for any 2 x 2 matrix A, its characteristic polynomial should always be p(1) = 12 tr(A)X + det(A). pedro, age 57, is the soile owner of his principal residence, which he has owned and occupied for 10 years. maria, his spouse, has lived with pedro for the full 10 years. he sells his house for a realized gain of $340,000 in 2022. how much of the gain must pedro and maria recognize on their 2022 tax return if they file as married filing jointly?$340,000$90,000$250,000$0 If the government initiates an expansionary monetary policy at the same time that its budget deficit increases, then the interest rate will __________________.A. remain unchangedB. either increase or decreaseC. increaseD. decrease