Using Hess's Law

Find the heat of reaction for 3H2(g) + O2(g) → 3H2O(g) given that:

2H2(g) + O3(g) → 2H2O(g) ΔH = -483.6kJ

2O3(g) → 3O2(g) ΔH = -248.6 kJ

Answers

Answer 1

Based on Hess's law, the heat of reaction for the given equation is -1201.8 kJ.

What is the heat of the given reaction?

The heat of reaction of the given equation is calculated using Hess's law as follows:

Equation of reaction: 3 H₂ (g) + O₂ (g) → 3 H₂O (g)

The intermediate equations are:

2 H₂ (g) + O₃ (g) → 2 H₂O (g) ΔH = -483.6kJ

2 O₃ (g) → 3 O₂ (g) ΔH = -248.6 kJ

Reversing the second equation and multiplying the first equation by 3 will give the initial equation:

3 O₂ (g) → 2 O₃ (g) ΔH = 248.6 kJ

3 {2 H₂ (g) + O₃ (g) → 2 H₂O (g) ΔH = -483.6kJ}

ΔH = 1450.8 kJ + 248.6 kJ

ΔH =  -1201.8 kJ

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Related Questions

ZSM-5, a catalyst material, has a surface area of 581 m²/g. What is the surface
area of this material in cm²/mg?

ZSM-5, a catalyst material, has a surface area of 581 m/g. What is the surfacearea of this material in

Answers

ZSM-5 is a catalyst material, which has a surface area of 581 m²/g. This is equivalent to a surface area of 5810 cm²/mg.

What is a catalyst?

A catalyst is a substance that increases the rate of a chemical reaction without itself undergoing any permanent chemical change. Catalysts have large surface areas to increase the reaction rate.

Biological catalysts are known as enzymes.

ZSM-5 is a catalyst material, which has a surface area of 581 m²/g. We want to convert this value to cm²/mg.

Step 1: Convert 581 m²/g to cm²/g.

We will use the conversion factor 1 m = 100 cm.

581 m²/g × (100 cm/1 m)² = 5.81 × 10⁶ cm²/g

Step 2: Convert 5.81 × 10⁶ cm²/g to cm²/mg.

We will use the conversion factor 1 g = 1000 mg.

5.81 × 10⁶ cm²/g × (1 g/1000 mg) = 5810 cm²/mg

ZSM-5 is a catalyst material, which has a surface area of 581 m²/g. This is equivalent to a surface area of 5810 cm²/mg.

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Methane (CH4, 16.05 g/mol) reacts with oxygen to form carbon dioxide (CO2, 44.01 g/mol) and water (H2O, 18.02 g/mol). Assume that you design a system for converting methane to carbon dioxide and water. To test the efficiency of the system in the laboratory, you burn 5.00 g methane. The actual yield is 6.10 g water. What is your percent yield?

Answers

Taking into account definition of percent yield, the percent yield for the reaction is 54.22%.

Reaction stoichiometry

In first place, the balanced reaction is:

CH₄+ 2 O₂ → CO₂ + 2 H₂O

By reaction stoichiometry (that is, the relationship between the amount of reagents and products in a chemical reaction), the following amounts of moles of each compound participate in the reaction:

CH₄: 1 moleO₂: 2 molesCO₂: 1 moleH₂O: 2 moles

The molar mass of the compounds is:

CH₄: 16 g/moleO₂: 32 g/moleCO₂: 44 g/moleH₂O: 18 g/mole

Then, by reaction stoichiometry, the following mass quantities of each compound participate in the reaction:

CH₄: 1 mole ×16 g/mole= 16 gramsO₂: 2 moles ×32 g/mole= 64 gramsCO₂: 1 mole ×44 g/mole= 44 gramsH₂O: 2 moles×18 g/mole= 36 grams

Mass of water formed

The following rule of three can be applied: if by reaction stoichiometry 16 grams of CH₄ form 36 grams of H₂O, 5 grams of CH₄ form how much mass of H₂O?

mass of H₂O= (5 grams of CH₄×36 grams of H₂O) ÷16 grams of CH₄

mass of H₂O= 11.25 grams

Then, 11.25 grams of H₂O can be produced when you burn 5.00 g of methane

Percent yield

The percent yield is the ratio of the actual return to the theoretical return expressed as a percentage.

The percent yield is calculated as the experimental yield divided by the theoretical yield multiplied by 100%:

percent yield= (actual yield÷ theoretical yield)× 100

where the theoretical yield is the amount of product acquired through the complete conversion of all reagents in the final product, that is, it is the maximum amount of product that could be formed from the given amounts of reagents.

Percent yield for the reaction in this case

In this case, you know:

actual yield= 6.10 gramstheorical yield= 11.25 grams

Replacing in the definition of percent yields:

percent yield= (6.10 grams÷ 11.25 grams)× 100

Solving:

percent yield= 54.22%

Finally, the percent yield when methane reacts with oxygen to form carbon dioxide and water is 54.22%.

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What two processes can harm soil fertility

Answers

Over-tilling and Over farming are the two processes that can harm the fertility of the soil.

Over-tilling refers to the exceeding levels of tilling and levelling the soil which adversely affects the quality of the soil. This is because tillage fractures the soil, it disrupts soil structure, accelerating surface runoff and soil erosion. Tilling of soil also reduces crop residue, which help cushion the force of pounding raindrops.

Without crop residue, soil particles become more easily dislodged, being moved or 'splashed' away. The splashed particles clog soil pores, effectively sealing off the soil's surface, resulting in poor water infiltration and hence subsequently affects the soil fertility.

Similarly, the main effect of over-farming is soil depletion. When crops are grown in the same place year after year, the soil becomes depleted of the nutrients that the plants need to grow. This can lead to lower yields and poorer quality crops. In extreme cases, it can lead to desertification.

So, these two are the processes that can harm soil fertility.

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2 C2H6 + 7O2 --> 4CO2 + 6H2O

What is the UNSIMPLIFIED molar ratio used to convert H2O into CO2?

Answers

Based on the equation of the reaction, the unsimplified molar ratio used to convert H₂O into CO₂ is:

moles of CO₂ = moles of  H₂O * 4/6

What is the molar ratio of a reaction?

The molar ratio of a reaction is the ratio in which the mole of the reactants combines to form products.

The molar ratio of a reaction can be expressed as the molar ratio of reactants and reactants, reactants and products, or products and products.

The molar ratio of a reaction is obtained from the balanced equation of the reaction.

Considering the given reaction;

equation of reaction: 2 C₂H₆ + 7 O₂ ----> 4 CO₂ + 6 H₂O

The molar ratio of the products carbon dioxide, CO₂ and water, H₂O is 4 : 6.

This means that in the given reaction of the combustion of ethane, for every 4 moles of carbon dioxide formed, 6 moles of water will be formed.

Hence the conversion factor to convert moles of  H₂O to moles of CO₂ is:

moles of CO₂ = moles of  H₂O * 4/6

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Calculate the energy of light having a wavelength of 395 nm.
show work

Answers

Answer: \(5.032\times 10^{-19}\ J\)

Explanation:

Given

The wavelength of the light is \(\lambda =395\ nm\)

Energy associated with a photon(light) is given by \(E=\frac{hc}{\lambda}\)

where, \(h=\text{Planck constant}\)

\(c=\text{speed of light}\)

\(\Rightarrow E=\dfrac{6.626\times 10^{-34}\times 3\times 10^8}{395\times 10^{-9}}\\\\\Rightarrow E=5.032\times 10^{-19}\ J\)

Therefore, the energy associated with the light is \(5.032\times 10^{-19}\ J\)

If a 60-newton force pushes a cart to the right, and a 20-newton force pushes the cart to the left, what is the net force on the cart? What direction is it in? ​

Answers

Answer:

I think it's 40 and to the right?

Explanation:

60-20 equals 40, and the force to the right is greater so it's to the right.

what’s the amino acid for this?

whats the amino acid for this?

Answers

The amino acid for this should be Arginine. I am not entirely sure.

How many cars are in 2.5 moles of cars?

Answers

The number of tires contained by 2.5 moles of cars is 10 tires.

What is number of moles?

The number of moles of a substance equals the ratio of its given mass in a chemical reaction to the mass of one mole of that substance.

The number of tires contained by 2.5 moles of cars is calculated as follows;

1 moles of a car contains 4 tires

2.5 moles of cars will contain -------?

Substitute the given parameters and solve for the number of tires contained in 2.5 moles of cars.

= 2.5 moles x 4 tires/1 mole

= 10 tires

Thus, the number of tires contained by 2.5 moles of cars is 10 tires.

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how do you fight off ADHD medication

Answers

Answer:A medication break can ease side effects. A lack of appetite, weight loss, sleep troubles, headaches, and stomach pain are common side effects of ADHD medication.

Explanation: It may boost your child’s growth. Some ADHD medications can slow a child’s growth in height, especially during the first 2 years of taking it. While height delays are temporary and kids typically catch up later, going off medication may lead to fewer growth delays.

It won’t hurt your child. Taking a child off ADHD medication may cause their ADHD symptoms to reappear. But it won’t make them sick or cause other side effects.

If the heat released during condensation goes only to warming the iron block, what is the final temperature (in ∘C
) of the iron block? (Assume a constant enthalpy of vaporization for water of 44.0 kJ/mol
and a heat capacity for iron of 0.449 J/(g⋅∘C)
.)

Answers

Answer: sweet home

Explanation:

How many moles of KI are present in 0.85L of a 0.55 M KI solution?

Answers

Answer: Amount of moles is 0.47 mol

Explanation: Amount of moles n = cV = 0.55 M · 0.85 l = 0.4675 mol

There are 0.4675 moles of KI in 0.85L of a 0.55 M KI solution

WHAT IS MOLARITY?

Molarity is a measure of the concentration of a solution. It is calculated by dividing the number of moles (n) of a solute by the volume of a solution (V)

Molarity = number of moles (n) ÷ volume (V)

According to this question, the molarity of a KI solution with a volume of 0.85L is 0.55 M. Hence, the number of moles of KI in the solution can be calculated as follows:

Molarity = n/V

0.55 = n/0.85

n = 0.55 × 0.85

n = 0.4675 moles

Therefore, there are 0.4675 moles of KI in 0.85L of a 0.55 M KI solution.

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which gas is fossil fuel

Answers

Answer:

methane

Explanation: methane is obtained from the decaying of flora and fauna mostlyunder damp

A gas occupies a volume of 5L at 300torr.What will be the volume of gas if the pressure increases to 400torr at constant temperature?​

Answers

The pressure increases from 300 torr to 400 torr, the volume of the gas decreases from 3.75L.

What is pressure?

Pressure is the force per unit area applied on a surface by a fluid, such as a gas or liquid. It is measured in terms of pascals (Pa), or the equivalent unit of kilograms per square meter (kg/m2). Pressure is a measure of the amount of force that is exerted on an object by another object in the same or opposite direction. It is a critical concept in many areas of science, including physics, chemistry, engineering, and medicine. Pressure is created when a fluid is in motion and its movement is resisted by the resistance of the object or medium it comes into contact with.

The volume of a gas is inversely proportional to its pressure, meaning that as pressure increases, volume decreases. Therefore, when the pressure increases from 300 torr to 400 torr,
the volume of the gas decreases from 5L to 5L x (300/400)
= 3.75L.

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A student isolated an unknown organic compound through extraction. The student measures the melting point and fins it to be 115-122 C. The student looks through the list of possible strucures and decides the comound is most likely 2-napthol. Do you believe this choice is correct?

Answers

Hope this helps!

https://www.chegg.com/homework-help/questions-and-answers/student-isolated-unknown-organic-compound-extraction-student-measures-melting-point-finds--q77093697

How many chlorine atoms are found in 8.3 moles of chlorine?

Answers

Answer:

5*10²⁴ chlorine atoms are found in 8.3 moles of chlorine.

Explanation:

Avogadro's Number or Avogadro's Constant is called the number of particles that make up a substance (usually atoms or molecules) and that can be found in the amount of one mole of said substance. Its value is 6.023*10²³ particles per mole. Avogadro's number represents a quantity without an associated physical dimension, so it is considered a pure number that allows describing a physical characteristic without an explicit dimension or unit of expression. Avogadro's number applies to any substance.

Then you can apply the following rule of three: if 1 mole of the compound contains 6.023 * 10²³ atoms, 8.3 moles of the compound how many atoms does it have?

\(amount of atoms=\frac{8.3 moles*6.023*10^{23}atoms }{1 mole}\)

amount of atoms≅ 5*10²⁴ atoms

5*10²⁴ chlorine atoms are found in 8.3 moles of chlorine.

4. Study the flow diagram below the answer the questions that follow C Mg (a) Write the chemical formulae of products () A B (b) Write the equations for the reactions that form products (1) (11) C...... D and E​

Answers

Answer:

where is flow diagram.....

.........

The nurse discovers that one of her assigned clients is bleeding excessively from an abdominal incision. The nurse gives specific prescriptions to an unlicensed assistive personnel (UAP) to attend to the other clients and tells another nurse to call the primary health care provider immediately. In this situation, the nurse is implementing which leadership style?

Answers

A Good Samaritan law will protect the nurse.

balance and identify the type of rxn
_H2O+ _SO3 _H2SO4

Answers

To balance the equation and identify the type of reaction, let's start by assigning coefficients to each compound: 2H2O + 1SO3 -> 1H2SO4

To balance the equation, we need to ensure that the number of atoms on both sides is the same. Here, we have two hydrogen (H) atoms on the left side and two on the right side, so hydrogen is already balanced.

We have two oxygen (O) atoms on the left side and four on the right side, so we need to balance oxygen by adding a coefficient of 2 in front of the water molecule:

2H2O + 1SO3 -> 1H2SO4

Now the equation is balanced with two hydrogen, four oxygen, and one sulfur (S) atom on both sides.

The type of reaction represented by this equation is a combination or synthesis reaction. In a combination reaction, two or more substances combine to form a new compound. In this case, water (H2O) and sulfur trioxide (SO3) combine to form sulfuric acid (H2SO4).

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Suggest how any unreacted iron can be separated from the mixture. ​

Answers

Answer: By use of magnet

Explanation: This is because pure iron is magnetic hence can be attracted

by a magnet

explain how the particles of a substance change as a substance changes from a solid to a liquid to a gas.

Answers

Answer:

Some substances can change from the solid state to the gas state without ever becoming a liquid. During this process, known as sublimation, the sur- face particles of the solid gain enough energy to become a gas.When dry ice becomes a gas, it absorbs thermal energy from water vapor in the air.

Explanation:

Do you think there is a limit to the size of Atoms scientist can make? prove with evidence.

Answers

Answer:

Yes, there is a limit to the size of atoms that scientists can make.

Explanation:

In the nucleus, atoms contain protons and neutrons. It is known that as the number of protons in the nucleus increases, the atom becomes unstable due to the repulsion of positively charged protons clumped together in the small space of the nucleus.

However, an attractive force exists between neutrons and protons which binds the nucleus together and minimizes repulsion between protons. Even neutrons have recently been found to slightly repel each other.

Several attempts made at synthesizing many very heavy elements lately have proved abortive because the elements only exist for a few fractions of a second owing to large repulsion between the particles in the nucleus.

This goes a long way to show that there is a limit to the number of protons and neutrons that can be assembled together to form a new nucleus. We cannot bring an unlimited number of nucleons together to form new atoms due to inter particle repulsive forces.

17. HAZWOPER training and certification recognizes:
a. A large number (as much as 80%) will self-present or be self-referred victims
b. Awareness level training will promote proper initial triage actions
c.
Victims will use any entrance they can enter at the hospital, in addition to the
emergency department entrance
d. Both A and C

Answers

HAZWOPER training and certification recognize:

a large number (as much as 80%) will self-present or be self-referred victimsVictims will use any entrance they can enter at the hospital, in addition to the emergency department entrance

The correct option is both A and C

What is the HAZWOPER training and certification?

HAZWOPER (Hazardous Waste Operations and Emergency Response) training and certification recognize that a large number of victims (as much as 80%) in hazardous waste incidents or emergencies will self-present or be self-referred for medical treatment.

Additionally, HAZWOPER training acknowledges that victims may use any entrance they can access at a hospital, not just the emergency department entrance.

This is because individuals affected by hazardous materials may arrive at different areas of the hospital seeking medical assistance.

Therefore, option d. Both A and C are correct statements regarding the recognition of HAZWOPER training and certification.

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Which of the following would be considered a strong base?

a H₂SO4
b. CO₂
c. Ca(OH)₂
d. C₁₂H₂O..​

Answers

Ca(OH)2 is a strong base.

It’s name is calcium hydroxide and often it is easy to tell if something is a strong base if it has (OH) in the name.

Match each reaction to its correct type by dragging it to the appropriate box on the left. Click Done to
check your answers. Drag the items on the left to the correct location on the right.

Answers

From the image attached;

Reaction 1 - Oxidation reduction

Reaction 2 - Precipitation reaction

Reaction 3 - Acid base reaction

Reaction 4 - Reaction with oxygen

What is reaction?

A reaction is a procedure or an occurrence in which a change takes place, frequently leading to the conversion of one or more compounds into other substances. A chemical reaction, which entails the rupturing and creation of chemical bonds between atoms or molecules, is what is meant when the word "reaction" is used in reference to chemistry.

When reactant molecules collide with enough force and in the right orientation, the current chemical bonds are broken, and new bonds are formed, converting the reactants into products.

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Match each reaction to its correct type by dragging it to the appropriate box on the left. Click Done

Task:
For each "station", click on the link. You should describe the initial appearances and observations of the
reaction during and after. Using your observations, determine if the change is a physical or chemical change.
Station #1: Lead Nitrate and Potassium lodide solutions. Shower of yellow
QUESTION/OBSERVATION
INITIAL APPEARANCE (what does the
substance look like in the beginning)

Answers

The expected observations for the chemical reaction involving lead nitrate and potassium iodide are as follows as per theory.

INITIAL APPEARANCE:

Before the reaction, you'd have two separate solutions:

Lead Nitrate solution: This is typically a clear, colorless solution.

Potassium Iodide solution: This is also usually a clear, colorless solution.

REACTION OBSERVATIONS:

As soon as you combine these two solutions, a chemical response takes place, resulting in the almost instantaneous development of a yellow precipitate. Lead iodide is a substance that cannot be dissolved in water.

FINAL APPEARANCE:

The final mixture would have a yellow precipitate (lead iodide) suspended in the solution.

The reaction leads to the formation of lead iodide, a substance with distinctive properties, suggesting a chemical change. The presence of this novel compound is indicated by the yellow hue of the precipitate.

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How many mg of water are present in a 500. mg sample of 2.9 m/m% solution?

Report your answer to 3 significant figures and without units.

Answers


The answer is 14.5 mg.

To solve the problem, we need to first understand what a 2.9 m/m% solution means. "m/m%" stands for mass per mass percentage, which indicates the mass of the solute (in this case, water) divided by the total mass of the solution (water + solvent, which is not specified). Therefore, a 2.9 m/m% solution means that for every 100 grams of the solution, 2.9 grams are water.

To find the amount of water present in a 500 mg sample of this solution, we can set up a proportion:

2.9 g water/100 g solution = x g water/500 mg solution

Simplifying this proportion by converting units to milligrams, we get:

2.9 mg water/100 mg solution = x mg water/500 mg solution

Cross-multiplying and solving for x, we get:

x = 14.5 mg

Therefore, there are 14.5 mg of water present in a 500 mg sample of 2.9 m/m% solution.

CuI2 (light brown solid) name copper compounds

Answers

CuI2 is not a known compound. Copper compounds typically have different oxidation states for copper, resulting in various compound names.

Copper(II) oxide (CuO): It is a black solid compound where copper is in the +2 oxidation state. It is commonly used as a pigment and in catalytic reactions.

Copper(II) sulfate (CuSO4): It is a blue crystalline compound in which copper is in the +2 oxidation state. It is used in various applications such as agriculture, electroplating, and as a laboratory reagent.

Copper(I) oxide (Cu2O): It is a red crystalline compound in which copper is in the +1 oxidation state. It is used as a pigment, in solar cells, and as a catalyst.

Copper(II) chloride (CuCl2): It is a greenish-brown solid compound in which copper is in the +2 oxidation state. It is utilized in various chemical processes, including etching and catalyst synthesis.

Copper(II) nitrate (Cu(NO3)2): It is a blue crystalline compound where copper is in the +2 oxidation state. It is commonly used in the production of catalysts, as a coloring agent, and in electroplating.

These are just a few examples of copper compounds with different oxidation states and properties. It's important to note that the compound CuI2 mentioned in the question, if it exists, would be an exception to the typical nomenclature for copper compounds.

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What is the concentration (M) of CH3OH in a solution prepared by dissolving 11.7 g of CH3OH in sufficient water to give exactly 100. mL of solution

Answers

Answer:

\(3.65~M\)

Explanation:

We have to remember the molarity equation:

\(M=\frac{mol}{L}\)

So, we have to calculate "mol" and "L". The total volume is 100 mL. So, we can do the conversion:

\(100~mL\frac{1~L}{1000~mL}=~0.1~L\)

Now we can calculate the moles. For this we have to calculate the molar mass:

O: 16 g/mol

H: 1 g/mol

C: 12 g/mol

\((16*1)+(1*4)+(12*1)=32~g/mol\)

With the molar mass value we can calculate the number of moles:

\(1.7~g~of~CH_3OH\frac{1~mol~CH_3OH}{32~g~of~CH_3OH}=0.365~mol~CH_3OH\)

Finally, we can calculate the molarity:

\(M=\frac{0.365~mol~CH_3OH}{0.1~L}=3.65~M\)

I hope it helps!

HELPPPP PLZ



A student pushes a 40-N block across the floor for a distance of 10 m.

How much work was done to move the block?


400 Pascals

400 Newtons

400 Joules

400 Watts

Answers

400 Joules

Work done is measured in Joules (J) remember that

Answer:400 joules

wut do u need

Explanation:

Calculate the amount of heat needed to boil 120.g of acetic acid (HCH3CO2), beginning from a temperature of 16.7°C.

Answers

Answer:

The total amount of heat needed = 72.2116  kJ

Explanation:

Given that ;

the mass of acetic acid = 120.0 g

The initial temperature \(T_1\) = 16.7 °C  = (16.7 + 273.15 ) K = 298.85 K

The standard molar mass of acetic acid = 60.052  g/mol

Thus ; we can determine the number of moles of acetic acid;

number of moles of acetic acid = mass of acetic acid/ molar mass of acetic acid

number of moles of acetic acid = 120.0 g/ 60.052 g/mol

number of moles of acetic acid =  1.998 moles

For acetic acid:

The standard boiling point  \(T_2\) = 118.1 °C = ( 118.1 + 273.15 ) K = 391.25 K

The enthalpy of vaporization of acetic acid \(\Delta H_{vap}\) = 23.7 kJ/mol

The heat capacity of acetic acid   c = 2.043  J/g.K

The change in temperature Δ T = \(T_2 - T_1\)

Δ T = (391.25 - 289.85)K

Δ T = 101.4 K

The amount of heat needed to bring the liquid acetic acid at 16.7°C to its boiling point is ;

q = mcΔT

From our values above;

q = 120 g ×  2.043  J/g.K × 101.4 K

q = 24859.2  J

q = 24859 /1000 kJ

q = 24.859 kJ

we have earlier calculated our number of moles o f acetic acid to be 1.998 moles;

Thus;

The needed amount of heat = \(\Delta_{vap} *numbers \ of \ moles\)

The needed amount of heat = \(23.7 \ kJ/mol * 1.998 \ moles\)

The needed amount of heat = 47.3526 kJ

Hence;

The total amount of heat needed = 24.859 kJ + 47.3526 kJ

The total amount of heat needed = 72.2116  kJ

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(Be sure toinclude the steps and unit in the answer.) * How much money will it take to buy the items in 15 years what$97 would have purchased today? The prices grow at average annualrate of 6.1 percent, compounded annually. Can someone please help me? Which of the following represents a rational number that is NOT an integer?A 27 5B -50 5C -100 50D 10 2 a 5-year-old child who had a repair for transposition of the great arteries shortly after birth is growing normally and has been asymptomatic since the surgery. the np notes mild shortness of breath with exertion and, upon questioning, learns that the child has recently reported dizziness. what will the nurse practitioner do Is copper and silver nitrate a physical change or Chemical change The numberof typing mistakes made by a secretary has a Poisson distribution. Themistakes are made independently at an average rate of 1.65 per page.3.54.3.5.2Find the probability that a one-page letter contains at least 3 mistakes. [5]Find the probability that a three-page letter contains exactly 2 mistakes. If futures are over-priced, the expectation is that the changein mispricing over the next period will be negative.Group of answer choicesTrue, orFalse Amy is writing the program for a video game. For one part of the game she uses the rule (x, y) - (x+2, y-3) to move points on the screen.(a) What output does the rule give when the input is (-5, 2)? Show your work.(b) What output does the rule give when the input is (3, -4)? Show your work. 1) Consider the real vector space V=R n, and let V . The point of this problem is to get another interpretation of the dual space in this case. We mentioned in class that we can "think" of as a "row" vector by considering its matrix representation under the standard basis (it will be a 1n matrix, ie a row vector.) Let us now prove that every row vector gives rise to a linear functional. Let (x 1,,x n) be a "row" vector (ie, a 1n matrix) with each x iR and define the functional :VR by a 1a 2a n:=(x 1,,x n) a 1a 2a n=x 1a 1+x 2a 2+x na nFirst off, convince yourself that this is actually a linear functional (a) (2 points) Recall that there is a bijection V =L(V,R)M 1n(R) that sends a linear map to its matrix representation. Show that this construction above (that sends a 1n matrix to the linear functional ) is just the inverse of this isomorphism. (In other words, if you start with a linear functional, take its matrix, and then define this new linear functional as above, you get the original linear functional you started with) (b) (1 point) Under this identification above, and letting V=R 3what is the row vector that corresponds to the dual basis vector e 1? How about e 3?Previous question Read the excerpt from Tools of the Spymaster."The numbers that Major Tallmadge assigned to members of the Culper Ring were from a secret writing system he invented. He substituted digits for words that would be used in messages. "Long Island," for example, was 728, "arms" was 7, and "city" was 88. There was a number for each month, such as 341 for "January." He made four copies of his codes. He kept one and gave the others to Woodhull, Townsend, and General Washington. For words that did not have a number code, Tallmadge gave his agents a cipher. In a cipher, each letter in a message is replaced by another letter or a number.The authors purpose in this excerpt is toA)teach readers about a code system used during the American Revolution.B)persuade readers that ciphers are the greatest American invention.C)argue that Major Tallmadge made a mistake in sharing copies of his codes.D)compare the American codes for secret letters to the British codes. Nationwide, public elementary and secondary education account for roughly what percentage of local government expenditures? A. less than 5 percent B. about 40 percent C. more than 75 percent D. about 20 percent Oracin con la palabra bolo You hire two research assistants to recruit study participants, ages 20-50, into your cross-sectional study. You obtain full permission to obtain participants' home phone numbers for recruitment purposes. Study recruitment occurs from 9am-5pm, Monday-Friday, as your research assistants call the home phone numbers of potential participants to determine study eligibility and willingness to participate. What would be your primary concern Who benefited the mostfrom the creation ofParliament? TRUE / FALSE. wolley inc. uses part a68 in one of its products. the company's accounting department reports the following annual costs of producing the 10,000 units of the part.