argon is to be compressed steadily from 120 kpa and 310 k to 700 kpa and 430 k. a heat loss of 20 kj/kg occurs during the compression process. neglecting kinetic energy changes, determine the power input required for a mass flow rate of 90 kg/min. >> pwrin b3

Answers

Answer 1

The power input required for a mass flow rate of 90 kg/min for the compression process of argon from 120 kPa and 310 K to 700 kPa and 430 K is 37.4 MW.


Given data mass flow rate, m = 90 kg/min, heat loss, Q = 20 kJ/kgInitial pressure, p₁ = 120 kPa. Final pressure, p₂ = 700 kPa, and initial temperature, T₁ = 310 K, final temperature, T₂ = 430 K.

We know that the power input is given by:

P in = m * (h₂ - h₁)

where h₁ and h₂ are the specific enthalpies at states 1 and 2 respectively. Since argon is compressed steadily, it can be assumed that the process is reversible. Thus, we can use the isentropic relation to determine the specific enthalpies:

For state 1:

s₁ = s₂ => entropy is constant h₁ = h(T₁, p₁)

For state 2:

s₂ = s₁ => entropy is constant h₂ = h(T₂, p₂)

The specific enthalpies can be determined using tables for argon. Substituting the values:

P in = m * (h₂ - h₁)

P in = 90 kg/min * ((1528.1 - 924.4) kJ/kg)

P in = 37.4 MW

Therefore, the power input required is 37.4 MW.

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Related Questions

a 25.0 ml sample of a saturated caoh2 solution is tritrated with and the equiavence what is the concentration of the hydroxide ion

Answers

The concentration of the hydroxide ion in the saturated Ca(OH)₂ solution is 0.080 M.

To calculate the concentration of hydroxide ion in the saturated Ca(OH)₂ solution, we need to use the results of the titration.

Assuming that the titrant is a strong acid, the balanced chemical equation for the reaction is; H⁺ + OH⁻ → H₂O

The equivalence point of the titration is reached when all of the hydroxide ions in the saturated Ca(OH)₂ solution have reacted with the acid. At this point, the moles of H⁺ added equals the moles of OH⁻ in the original solution. Therefore, we can use the volume and concentration of the titrant, along with the volume of the saturated Ca(OH)₂ solution, to calculate the concentration of OH⁻.

Let's assume that the titrant used is 0.1 M HCl, and that it took 20.0 ml of HCl to reach the equivalence point. This means that 20.0 ml of HCl contains 0.002 moles of H⁺ ions. Since the reaction is 1:1, there are also 0.002 moles of OH⁻ ions in the original 25.0 ml of saturated Ca(OH)₂ solution.

To calculate the concentration of OH⁻ in the saturated Ca(OH)₂ solution, we can use the following equation.

OH⁻ concentration = moles of OH⁻ /volume of solution

OH⁻ concentration = 0.002 moles / 0.025 L

OH⁻ concentration = 0.080 M

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48g of methane was burned in an excess of air. What mass of carbon dioxide would be produced in the reaction assuming complete combustion? Use the information below to answer the question.

48g of methane was burned in an excess of air. What mass of carbon dioxide would be produced in the reaction

Answers

Answer:

132g

Explanation:

CH4= 12+4=16  

moles= m/Mr    moles=48/16=3 mol

CO2= Mr=44

there are the same number of moles as methane:

Mass= Mrxmoles

44x3=132g

The mass of the carbon dioxide produced by the combustion of the 48 g of methane is equal to 132 g.

What is the combustion reaction?

Combustion reaction involves the complete oxidation of the hydrocarbon such reactions generally release only carbon dioxide and water as products.

A hydrocarbon undergoes combustion to produce carbon dioxide and water as the product. No other side products are formed in the combustion reaction.

The given combustion reaction of the methane can be written as follows:

CH₄   + 2 O₂ →  CO₂  +  2H₂O

Given the amount of methane for combustion = 48 g

The molar mass of methane = 16g/mol

The molar mass of the carbon dioxide, CO₂ = 44g/mol

16 grams of methane produce carbon dioxide = 44g

The  48 grams of methane will produce CO₂ = (44/16) ×48 = 132 g

Therefore, the mass of 132 g of carbon dioxide is produced by the combustion of 48g of methane.

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How many electrons are in the outermost energy level of a neutral
Fluorine atom?

Answers

Answer:

The answer is 7 (seven)

Explanation:

Fluorine has seven of eight possible electrons in its outermost energy level, which is energy level II.

A total of 8 L of He is stored at sea level (1013 mb). If the gas is carried to the top of a mountain where the pressure is 500 mb, what volume will it occupy if the temperature and mass are held constant?

Answers

Here, the final volume can be determined using Boyle's law. The volume at 1013 mb pressure  is 8 L. Then the volume at  500 mb will be 16 L.

What is Boyle's law ?

Boyle's law states that, at constant temperature, the volume of a gas is inversely  proportional to the pressure of the gas.

Hence, PV = a constant.

Let P1 and V1 be the initial pressure  and volume and P2 and V2  be the final pressure and volume then we can write it as,

P1 V1 = P2 V2.

Given that, P1 = 1013 mb

P2 = 500 mb

V1 = 8 l

V2 = P1 V1 / P2

V2  = 1013 mb  × 8 L /500 mb

     = 16 L.

Therefore, the volume of the gas at a pressure of 500 mb is 16 l.

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How many grams of Sodium will have the same number of atoms as 6 grams of Magnesium?
Atomic mass of Sodium is 23 u and atomic mass of Magnesium is 24 u.

Answers

Answer:

92gm

Explanation:

Atomic mass of Mg=24g=1 mole of Mg

∴  24g =1 mole of Mg contain 6.022×10^23 atom 

∴  6gm contains 246.022×1023×6

                            =4×6.022×10^23 atoms

Now according to question, there are 6.022×1023 atoms of Na 

23gm of Na contains 6.022×10^23 atoms

∴6.022×4×10^23 atoms of Na weighs 23×6.022×10^23×4/6.022×10^23⇒92gm

3.0 mol Na reacts with 1.4 mol
F2 according to the equation below:
2Na+ F₂ → 2NaF

How many moles of NaF form
from 3.0 mol Na?

Answers

The number of moles of NaF that will be produced from 3moles of Na is 3 moles.

How to calculate number of moles?

Stoichiometry is the study and calculation of quantitative (measurable) relationships of the reactants and products in chemical reactions (chemical equations).

According to this question, sodium reacts with fluorine as follows:

2Na+ F₂ → 2NaF

Based on the above equation, 2 moles of Na will produce 2 moles of NaF

This means that 3 moles of Na will produce 3 moles of NaF.

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Formation of heat and/or light when two substances are combined indicate a _______ change.

Answers

Chemical change because a new substance is being formed if it’s not chemical then probably physical :)

Answer:

It's a chemical change

The following unbalanced reaction describes the salicylic acid synthesis: C8H8O3 + NaOH + H2SO4 → C7H6O3 + Na2SO4 + CH3OH + H2O a. Given that the density of methyl salicylate is 1.18 g/mL, calculate the moles of methyl salicylate used during the synthesis. b. Use the volume and concentration of sodium hydroxide to calculate the mom sodium hydroxide added to the reaction mixture. c. Use the volume and concentration of sulfuric acid to calculate the moles of sulfuric acid added to the reaction mixture. d. Determine the limiting reactant.

Answers

A. To calculate the moles of methyl salicylate used during the synthesis, we first need to determine the mass of methyl salicylate produced. From the balanced equation, we can see that one mole of salicylic acid produces one mole of methyl salicylate.

B. To calculate the moles of sodium hydroxide added to the reaction mixture, we need to use its volume and concentration. The balanced equation shows that one mole of salicylic acid reacts with one mole of sodium hydroxide. Therefore, the moles of sodium hydroxide added will be equal to the moles of salicylic acid used.

We can calculate the moles of salicylic acid used as described in part (a), and then use the volume and concentration of sodium hydroxide to calculate the moles of sodium hydroxide added:

moles of sodium hydroxide = volume of sodium hydroxide x concentration of sodium hydroxide

C. To calculate the moles of sulfuric acid added to the reaction mixture, we can use its volume and concentration. The balanced equation shows that one mole of salicylic acid reacts with one mole of sulfuric acid.

Therefore, the moles of sulfuric acid added will be equal to the moles of salicylic acid used.

We can calculate the moles of salicylic acid used as described in part (a), and then use the volume and concentration of sulfuric acid to calculate the moles of sulfuric acid added:

moles of sulfuric acid = volume of sulfuric acid x concentration of sulfuric acid

D. To determine the limiting reactant, we need to compare the number of moles of each reactant used to the stoichiometric coefficients in the balanced equation. The reactant that is used up completely (i.e. has the smallest number of moles relative to its stoichiometric coefficient) is the limiting reactant.

For example, if we find that we used 0.05 moles of salicylic acid and 0.08 moles of methanol, we can see from the balanced equation that salicylic acid is the limiting reactant because it has a stoichiometric coefficient of 1, while methanol has a coefficient of 0.5.

The moles of methyl salicylate produced will be equal to the moles of salicylic acid used.

Assuming that we know the mass of salicylic acid used, we can convert it to moles using its molar mass:

moles of salicylic acid = mass of salicylic acid / molar mass of salicylic acid

Once we know the moles of salicylic acid used, we can calculate the moles of methyl salicylate produced.

moles of methyl salicylate = moles of salicylic acid

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In each equation, how is the mass number on the left side of the arrow related to the sum of mass numbers on the right side of the arrow? Is this true for atomic numbers?

Answers

Answer:

yes true

Explanation:

MASS OF REACTANT SIDE = MASS OF PRODUCT SIDE

In the chemical equation the number of atoms of each of the elements are equal on both the sides of arrow as it follows the law of conservation.

What is a chemical equation?

The chemical equation is given as the reaction with the reactants reacting, resulting in the formation of the products. The stoichiometric coefficient in the balanced chemical reaction determines the moles of reactant and products involved in the reaction.

The left side of the arrow consisted of the number of reactants, and the right side of the arrow consisted of the number of products.

The balanced chemical equation follows the law of conservation, and thereby the number of products and the reactants atoms at both the side of the arrow are equal.

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a liquid that occupies a volume of 0.820 L and has a mass of 2.56 kg
what is the density of this liquid in kg/L

Answers

Answer:

3121.95 kilogram/cubic meter

Explanation:

I used an online calculator

Hope I helped!

how do these ion things work?

how do these ion things work?

Answers

Answer:

ion know figure it out its you who learning ab it

Explanation:

Answer:

..This sounds like a "you" problem..

Nah I'm k i d d i n g I actually don't know .

Explanation

PLEASE HELP ME WITH THIS CHEMISTRY HOMEWORK!!! WILL GIVE BRAINLIEST!!! :)

PLEASE HELP ME WITH THIS CHEMISTRY HOMEWORK!!! WILL GIVE BRAINLIEST!!! :)

Answers

Explanation:

Plugging into the following equations will give you the answer (the answer is the attached image):

\(pH+pOH=14\)

\(pH=-log_{10}([H^+])\)

\(pOH=-log_{10}([OH^-])\)

\([H^+][OH^-]=10^{-14}\)

\([H^+]=10^{-pH}\)

\([OH^-]=10^{-pOH}\)

PLEASE HELP ME WITH THIS CHEMISTRY HOMEWORK!!! WILL GIVE BRAINLIEST!!! :)

Drought is a weather condition. true or false

Answers

Answer:

true

Explanation:

drought is a period of unusually persistent dry weather that persists long enough to cause serious problems such as crop damage and/or water supply shortages. The severity of the drought depends upon the degree of moisture deficiency, the duration, and the size of the affected area.

A radioactive sample has activity 4.20kBq and half-life 32 minutes. Measurements are taken every 5 minutes for one hour. Plot a graph of the activity against time for this sample.

Answers

Plotting the graph of activity against time for a radioactive sample with an initial activity of 4.20 kBq and a half-life of 32 minutes, with measurements taken every 5 minutes for one hour, shows a decreasing exponential curve.

The activity of a radioactive sample decreases exponentially over time according to the formula A(t) = A0 * (1/2)^(t / T), where A(t) is the activity at time t, A0 is the initial activity, t is the time elapsed, and T is the half-life.

In this case, the initial activity A0 is 4.20 kBq and the half-life T is 32 minutes. Measurements are taken every 5 minutes for one hour, which corresponds to 12 measurements in total.

To plot the graph, we calculate the activity at each time point using the given formula and plot the points on a graph. The x-axis represents the time in minutes, and the y-axis represents the activity in kBq.

Starting with t = 0 minutes, the activity is 4.20 kBq. For each subsequent measurement at intervals of 5 minutes, we calculate the activity using the formula. The resulting data points can be plotted on a graph, connecting them with a decreasing exponential curve.

Note: Since the prompt doesn't specify the unit for time, we assume minutes for consistency with the half-life given in minutes.

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What is molar mass?
A. The number of moles in one gram of substance
B. The mass of one molecule of a substance
C. The mass of one mole of a substance
D. The number of molecules In one mole of a substance

Answers

C
The periodic table has a mass of one mole of a element, which is also the molar mass of that single atom.
A molar mass•relative atomic mass

What Group is this element in?

What Group is this element in?

Answers

Answer:

sodium

Explanation:

A student has 3.86 g of iron metal. a How many moles of iron does the student have? Show your work. 0.86g Fe 0.0 motfe b Given your answer to (a) and the fact that rust has the formula Fe203, how many moles of oxygen would be required to convert all of the iron to rust? Show your work. c Given your answer to (b), how many grams of oxygen would be required? Show your work. d What would be the mass of rust produced if all of the iron was converted to rust? Show your work.

Answers

a. To find the number of moles of iron, divide the mass of iron by its molar mass. The molar mass of iron is 55.845 g/mol.

3.86 g Fe / 55.845 g/mol = 0.069 mol Fe

b. To convert all of the iron to rust, we need enough oxygen to combine with all of the iron to form Fe2O3. The formula for rust is Fe2O3, which means that for every two moles of iron, we need three moles of oxygen. Given the number of moles of iron that we have, we need 3/2 * 0.069 mol = 0.104 mol of oxygen.

c. To find the mass of oxygen required, multiply the number of moles of oxygen by its molar mass. The molar mass of oxygen is 15.999 g/mol.

0.104 mol O2 * 15.999 g/mol = 1.68 g O2

d. To find the mass of rust produced, multiply the number of moles of iron by the molar mass of rust. The molar mass of rust is 159.68 g/mol.

answer: 0.069 mol Fe * 159.68 g/mol = 11.4 g Fe2O3

How would the calculated concentration of the hci be affected if the sodium hydroxide were poured from ma beaker that contained some water before the naoh were added to it

Answers

Answer:

This question is incomplete

Explanation:

This question is incomplete. However, the beaker that contained some water before NaOH were added means that the resulting solution in that beaker will be more dilute. When this diluted sodium hydroxide solution is added to HCl (not hci), the reaction below occurs

HCl + NaOH ⇒ NaCl + H₂O

The reaction above is a neutralization reaction. The concentration of the acid (HCl) will reduce when a base (sodium hydroxide) is added and will also reduce more because of the presence of more water (in the base) which normally reduces the concentration of ions present in an acid or a base to become more dilute.

A 2.06 g solid sample of an unknown monoprotic acid was dissolved in distilled
water to produce a 35.0 mL solution at 25°C. This solution was then titrated with
0.300 M NaOH. The equivalence point was reached when 48.73 mL of 0.300 M
NaOH were delivered.
a. Find the number of moles of acid in the solid sample.
b. Find the molar mass of the unknown acid.

Answers

the molar mass of the unknown acid is approximately 141.1 g/mol.

a. To find the number of moles of acid in the solid sample, we first need to calculate the number of moles of NaOH used in the titration. We can do this using the equation:

moles NaOH = M NaOH x V NaO

where M NaOH is the molarity of the NaOH solution, and V NaOH is the volume of NaOH solution used at the equivalence point.

Substituting the given values, we get

moles NaOH = 0.300 mol/L x 0.04873 L = 0.014619 mol

Since NaOH and the unknown acid react in a 1:1 mole ratio, the number of moles of acid in the sample is also 0.014619 mol.

b. To find the molar mass of the unknown acid, we can use the equation

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

Substituting the given values, we get:

molar mass = 2.06 g / 0.014619 mol = 141.1 g/mol

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The number of moles in the acid is 0.014619 moles and the molar mass of the unknown monoprotic acid is 140.92 g/mol.

How to calculate the number the moles in acid?



To find the number of moles of acid in the solid sample, first determine the moles of NaOH used in the titration. You can do this using the formula:

moles = volume (L) × concentration (M)
moles of NaOH = 48.73 mL × (1 L / 1000 mL) × 0.300 M = 0.014619 moles

Since it's a monoprotic acid, the moles of the acid are equal to the moles of NaOH at the equivalence point:
moles of acid = 0.014619 moles

b. To find the molar mass of the unknown acid, use the formula:

molar mass = mass of the sample (g) / moles of the acid
molar mass = 2.06 g / 0.014619 moles = 140.92 g/mol

So, the molar mass of the unknown monoprotic acid is approximately 140.92 g/mol.

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Is the ghost in Hamlet a metaphor?.

Answers

Ghosts are frequently used as metaphors for the need for justice since they are seen as supernatural echoes of a moral injustice.

What does the Ghost in Hamlet stand for? Hamlet's father's ghost makes an unsettling revelation and seeks retribution in Shakespeare's tragedy Hamlet.It is customary to interpret ghosts as metaphors for the desire for justice because they are seen as supernatural reminders of a moral injustice.Inspiring Hamlet to exact his father's retribution is the ghost, a symbol.The ghost makes his first entrance, which starts the entire plot's action.Hamlet learns the truth from the ghost's warnings and becomes enraged enough to exact revenge on his father after they turn out to be true.Act 1, Scene 2 of Hamlet's first soliloquy features an insightful metaphor that reads as follows: "This unweeded garden is going to seed.Things foul and repulsive in nature / Just possess it."Hamlet muses over the recent happenings in Elsinore in this despondent monologue.

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How many orbitals does the elements in period 5 have

Answers

Answer:

18

Explanation:

the basic subunit of the ancient egyptians' royal cubit stone is the span. (True or False)

Answers

True. The ancient Egyptians used the royal cubit as a unit of measurement for their architectural and engineering projects. The basic subunit of the royal cubit stone was the span, which measured about 22.5 centimeters.

The royal cubit was divided into seven palms, with each palm divided into four fingers. This standardized system allowed the ancient Egyptians to build massive structures like the pyramids and temples with remarkable accuracy. The span was a crucial component of this system, as it allowed the builders to measure and cut stones to precise lengths. Overall, the royal cubit and its subunits were essential tools for the ancient Egyptians in their architectural and engineering endeavors.
True. The basic subunit of the ancient Egyptians' royal cubit stone is the span. The royal cubit was a unit of measurement used by the Egyptians and was approximately 52.3 cm (20.6 inches) long. It was subdivided into smaller units called spans, each consisting of approximately 26.2 cm (10.3 inches). The span served as a convenient and consistent method for measuring distances and lengths in construction, agriculture, and other aspects of ancient Egyptian life.

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A sample of gas has a volume of 2.00L at 25.0 degrees Celcius and 1.08atm. What volume ( in liters) will it have at 100 degrees Celcius and 1.5atm?

Answers

Answer:

Explanation:

The question requires us to calculate the volume (in L) of a gas under the conditions given.

The following information was provided by the question:

Initial volume of gas = V1 = 2.00 L

Initial temperature of gas = T1 = 25.0 °C

Initial pressure of gas = P1 = 1.08 atm

Final temperature of gas = T2 = 100 °C

Final pressure of gas = P2 = 1.50 atm

To solve this problem, we'll need to apply the equation of ideal gases (shown below) twice: first, to determine the number of moles of gas, and again to calculate the volume of gas under the final conditions. Note that we'll determine the number of moles of gas under the initial conditions because this amount won't change (as we're talking about the same sample of gas).

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Consider the equation for acetic acid plus water HC2H2O2 + H2O --> C2HcO2- + H3O+ a)compare the strengths of the two acids in the equation. Do the same for the two bases. b) Determine which direction -- forward or reverse -- is favored in the reaction.

Answers

Considering the two acids and bases involved, the reverse reaction is favored.

Reversible reaction

The term reversible reaction refers to a reaction that can go either forward or backwards depending on the conditions of the reaction.

We must recall that acetic acid is a weak acid hence the equilibrium position would always lie towards the left hand side of the equation. Hence considering the two acids and bases involved, the reverse reaction is favored.

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Savvas Realize. Investigation 8 Experiment 1

Savvas Realize. Investigation 8 Experiment 1

Answers

Answer:

–1065.25 KJ of energy.

Explanation:

From the question given above, the following data were obtained:

4FeO + O₂ —> 2Fe₂O₃  ΔH = –560.66 kJ

From the balanced equation above,

The formation of 2 moles of Fe₂O₃ released –560.66 kJ of energy.

Finally, we shall determine the amount of heat energy released when 3.8 moles of Fe₂O₃ are produced. This can be obtained as follow:

From the balanced equation above,

The formation of 2 moles of Fe₂O₃ released –560.66 kJ of energy.

Therefore, the formation of 3.8 moles of Fe₂O₃ will release

= (3.8 × –560.66)/2 = –1065.25 KJ of energy.

Thus, –1065.25 KJ of energy is released from the reaction.

What are the conditions that are required for electrical energy to be present in an electrical circuit?

Answers

Answer:

 a supply of electric charges which are free to flow, some form of push to move the charges through the circuit and a pathway to carry the charges.

Explanation:

There's your answer have a good day

I NEED OXIDATION AND REDUCED FOR BOTH ASAP PLS HELP (make sure its correct)

I NEED OXIDATION AND REDUCED FOR BOTH ASAP PLS HELP (make sure its correct)

Answers

Have you tried the app chem balancer I found it a great help when working on chemistry

Which of the following aré changing when a change of state occurring

Answers

When there is change of state solid to liquid to gas or in any order then there will be change in intermolecular bonds. amount of intermolecular bonds.

Express the number 0.00342 in scientific notation.

Answers

0.00342 can be expressed in scientific notation as \(3.42 * 10^{-3}\).

Scientific notation is a system used to express large as well as small numbers in a compact manner.  In general, a number can be expressed in scientific notation as  \(a*10^{b} \\\).

Where, a is a decimal number greater than 1 but less than 10 and b indicates the decimal power. "b" is positive for numbers greater than 1 and negative for numbers less than 1.

Scientific notation is helpful to make calculations involving very large or small numbers less complicated.

We can express 0.00342 in scientific notation as \(3.42 * 10^{-3}\).

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If you get a root canal or any other potentially painful procedure done at the dentist's office, he or she will probably inject your gums with a local anesthetic to "numb the pain." Neurons that trigger pain are called nociceptors. They trigger pain in order to alert the body to potentially dangerous stimuli. Most local anesthetics hinder the activity of all local neurons, not just nociceptors, so pain is not the only sensation that goes away temporarily. Because all feeling is gone, you can end up drooling on yourself without knowing it.

Considering this information about local anesthestics, which of the following statements best demonstrates that science is an ongoing process that changes in response to new information and discoveries?
A. There are a variety of local anesthetics being used today, including lidocaine, prilocaine, and mepivacaine.
B. Sir Charles Sherrington, who discovered nociceptors, wrote a book about the nervous system that helped show its role in allowing organisms to adapt to their environments.
C. Unlike a local anesthetic, a general anesthetic causes a person to lose consciousness rather than sensation in one area.
D. Scientists have discovered a way to use a compound found in hot peppers, capsaicin, along with an anesthetic in order to block nociceptors only.

Answers

It’s d I took the test a few day ago
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(Round your answer to four decimal places.) (c) What is the probability that fewer than 3 parts will be defective? (Round your answer to four decimal places.) (d) What is the expected number of defective parts? (e) What is the variance for the number of defective parts? Why government needs to support K-12 education? Think from market imperfection, redistribution and political reasons. Which equations arise when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers? (123, 2347) (Check all that apply.) Check All That Apply 1 = 10 - 3.3 1 = 37.10 - 3. 123 1 = 37.2347-706 - 123 1 = 37.10 -9.41 d d 1 = 36.2347-583 123 Classes that serve one another or serve a purpose can be in a I Choose from the list: stored directory project folder packaged embedded A triangle has vertices at (-4, 0), (2, 8), and (8, 0). Complete the table. Write answers as decimalsrounded to the nearest hundredth, when necessary. Different factors in hosts and of pathogens themselves can influence the epidemiology of a disease. Which of the following are HOST factors that would influence epidemiology?- religious and cultural practices- previous exposure or immunization of a population to a disease agent- gender- age of population- general health of a population- genetic background of infected individuals phoebe has a hunch that older students at her very large high school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. she takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. a simple random sample of 104 seniors reveals that 78 of them bring a bag lunch.Do these data give convincing evidence to support Phoebes hunch? In Worcester v. Georgia (1832), the Marshall Court defined the Indian tribes as ______ in much the same way that Georgia was. sovereign entities. 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. Predict the product(s) obtained when benzoquinone is treated with excess butadiene: Which of the following terms refers to digital and networked information and communication technologies that began emerging in the later half of the twentieth century?A. Digital MediaB. Mediated CommunicationC. Social MediaD. New Media a. Write a program that reads a file "data.in" that can be of any type (exe, pdf, doc, etc), and then copy its content to another file "data.out". For example, if it's a pdf file, "data.out" should be opened successfully by a PDF reader. If it's a video file, the output file can be replayed.b. Please use binary file read/write for your program.c. The file size ranges between 1MB-50MB.d. Comment at the top of the program for how to execute your program Suppose households spend 75 cents of each additional dollar of after-tax income. If the government spends $100 million on goods and services, GDP will _____ by $_____ million Financial information is presented below:Operating Expenses: $45,000Sales: 150,000Cost of Goods Sold: 77,000The Gross Profit rate would be:.487.300.700.187 On your way home, you have come across a small birdie on the roadside. Write a diary entry describing your experience with it secrete the hormones, estrogen and progesterone, whereas _____ secrete the hormone, testosterone. A 1.00 liter solution contains 0.32 M ammonia and 0.42 M ammonium iodide.If 0.110 moles of calcium hydroxide are added to this system, indicate whether the following statements are true or false.(Assume that the volume does not change upon the addition of calcium hydroxide.)_______TrueFalse A. The number of moles of NH3 will increase._______TrueFalse B. The number of moles of NH4+ will increase._______TrueFalse C. The equilibrium concentration of H3O+ will decrease._______TrueFalse D. The pH will remain the same._______TrueFalse E. The ratio of [NH3] / [NH4+] will remain the same.