b.) varies only in name from a one way analysis of varianceSolut.pdf

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1) (-3xy^-3)^-4/(xy^-1)^-2 = (xy^-1)^2/(-3xy^-3)^4 ( revesring the num and denom.) Now , (x^2*y^-2)/(81x^4*y^-12) = x^2-4*y^(-2+12)/81 = x^-2*y^10/81 2) x^2 +4x+3 by (x+3) x^2 +4x +3 = x^2 +3x+x +3 ( Factorising) x(x+3) +1(x+3) = (x+1)(x+3) So, we have (x+1)(x+3)/(x+3) = (x+1) 3) 4b^2 -4b -3 by 2b-1 4b^ -6b+2b -3 = 2b(2b-3) +1(2b-3) ( factorising) = (2b+1)(2b-3) (2b+1)(2b-3)/(2b-1) = 2b-3 (cancelling out common term ) 4) (7x^2 +x^3)/(x^2 +5x -14) We have to look for points where denominator is zero and function is undefined x^2 +5x -14 = x^2 +7x -2x -14 = x(x+7)-2(x+7) = (x-2)(x+7) Denominator is zero at x =2 , -7 Domain : All real except x = 2 and x =-7 Solution 1) (-3xy^-3)^-4/(xy^-1)^-2 = (xy^-1)^2/(-3xy^-3)^4 ( revesring the num and denom.) Now , (x^2*y^-2)/(81x^4*y^-12) = x^2-4*y^(-2+12)/81 = x^-2*y^10/81 2) x^2 +4x+3 by (x+3) x^2 +4x +3 = x^2 +3x+x +3 ( Factorising) x(x+3) +1(x+3) = (x+1)(x+3) So, we have (x+1)(x+3)/(x+3) = (x+1) 3) 4b^2 -4b -3 by 2b-1 4b^ -6b+2b -3 = 2b(2b-3) +1(2b-3) ( factorising) = (2b+1)(2b-3) (2b+1)(2b-3)/(2b-1) = 2b-3 (cancelling out common term ) 4) (7x^2 +x^3)/(x^2 +5x -14) We have to look for points where denominator is zero and function is undefined x^2 +5x -14 = x^2 +7x -2x -14 = x(x+7)-2(x+7) = (x-2)(x+7) Denominator is zero at x =2 , -7 Domain : All real except x = 2 and x =-7.

b.) varies only in name from a one way analysis of variance
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b.) varies only in name from a one way analysis of variance

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Ac- + H2O ~~> OH + AcH Kb = [OH-][AcH]/[Ac-] Kb=10^-14/Ka = 5.556x10^-10 [OH-]______[AcH]________[Ac-] initial_____0_______0_________1M change___+x______+x_________-x final______x_______x__________0.052-x Kb = x2/(0.052-x) = 5.556x10-10 Solve for x: x=5-log(0.535) = [OH-] pOH = -log[OH] = 5.27 pH=14-pOH=8.73 Solution Ac- + H2O ~~> OH + AcH Kb = [OH-][AcH]/[Ac-] Kb=10^-14/Ka = 5.556x10^-10 [OH-]______[AcH]________[Ac-] initial_____0_______0_________1M change___+x______+x_________-x final______x_______x__________0.052-x Kb = x2/(0.052-x) = 5.556x10-10 Solve for x: x=5-log(0.535) = [OH-] pOH = -log[OH] = 5.27 pH=14-pOH=8.73.

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100 DIM C(50) (50 is max number of servers) 110 INPUT S,NSTOP (S,NSTOP = number of servers, customers to be simulated) 120 FOR D=1 TO NSTOP 130 IA= (IA = interarrival time) 140 A=A+IA (A = arrival time) 150 J=0 160 J=J+1 (J = index of server being probed) 170 IF J=S+1 THEN K=K+1 (K = number of customers that are blocked) 180 IF J=S+1 THEN 270 190 IF AA THEN AB=AB+M- A (AB = cumulative time during which all servers busy) 270 NEXT D 280 PRINT K/NSTOP,AB/A (fraction of customers blocked, fraction of time all servers are simultaneously busy) Solution 100 DIM C(50) (50 is max number of servers) 110 INPUT S,NSTOP (S,NSTOP = number of servers, customers to be simulated) 120 FOR D=1 TO NSTOP 130 IA= (IA = interarrival time) 140 A=A+IA (A = arrival time) 150 J=0 160 J=J+1 (J = index of server being probed) 170 IF J=S+1 THEN K=K+1 (K = number of customers that are blocked) 180 IF J=S+1 THEN 270 190 IF AA THEN AB=AB+M- A (AB = cumulative time during which all servers busy) 270 NEXT D 280 PRINT K/NSTOP,AB/A (fraction of customers blocked, fraction of time all servers are simultaneously busy).

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1 Suppose, annualized growth in inflation rate is I 4.5 = 1.2*(1+I) ^3 (1+I)^3 = 4.5/1.2 = 3.75= 1.553^ (1/3) I = 55.3% In an economy, when GDP is growing consistently and unemployment rate is also falling. Though, growth rate in inflation rate is very high and it is approx. 55.3%. It means that demand is increasing and it is more than the supply. It is also causing overheating of the economy. Here, more money is chasing few goods. It leads to further increase in price. And it drives inflation on the higher side. Data given the problem confirms the economic scenario mentioned. It propels the inflation further and it is very high as a proof. 2 Inflation is growing with annualized rate of 55.3%. In this case, Federal Reserve should use contraction policy. As a part of it, Federal Reserve should deploy right money policy. It will discourage people to borrow and demand will come down. Thus, inflation will be controlled. 3. Federal Reserve can increase reserve requirements. Further, Federal Reserve can also sell government securities in open market. It will suck cash out of the system and contractionary policy will be implemented. Reduced government expending will also help. It will help curbing the inflation. 4 If recession happens and due to this reason, layoff takes place as well as demand decreases then contractionary economic policy will be ineffective. In those circumstances, Federal Reserve has to reverse the strategy. Technological change can also make a reduction in demand of products. In that industry, contractionary policy will be discouraging. Also, for those product categories where demand is inelastic in nature. Contractionary policy will not work. Note: Already answered similar question on Chegg Q&A board. Thus, above answer is the modified version as per the requirements mentioned in the question. Solution 1 Suppose, annualized growth in inflation rate is I 4.5 = 1.2*(1+I) ^3 (1+I)^3 = 4.5/1.2 = 3.75= 1.553^ (1/3) I = 55.3% In an economy, when GDP is growing consistently and unemployment rate is also falling. Though, growth rate in inflation rate is very high and it is approx. 55.3%. It means that demand is increasing and it is more than the supply. It is also causing overheating of the economy. Here, more money is chasing few goods. It leads to further increase in price. And it drives inflation on the higher side. Data given the problem confirms the economic scenario mentioned. It propels the inflation further and it is very high as a proof. 2 Inflation is growing with annualized rate of 55.3%. In this case, Federal Reserve should use contraction policy. As a part of it, Federal Reserve should deploy right money policy. It will discourage people to borrow and demand will come down. Thus, inflation will be controlled. 3. Federal Reserve can increase reserve requirements. Further, Federal Reserve can also sell government securities in open market. It will suck cash out of the system and contractionary policy will be implemented. Red.

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1. Corporations, limited liability companies (LLCs), general and limited partnerships, and sole proprietorships are the more common legal entities used for operating a business. 2.Corporations and LLCs offer owners limited liability. General partners and sole proprietors may be held personally responsible for the debts of the general partnership and sole proprietorship. However,limited partners are not responsible for the partnership’s liabilities. 3.A business entity may be legally classified as a corporation, limited liability company (LLC), a general partnership (GP), a limited partnership (LP), or a sole proprietorship under state law. However, for tax purposes a business entity can be classified as either a separate taxpaying entity or as a flow-through entity. Separate taxpaying entities pay tax on their own income. In contrast, flow-through entities generally don’t pay taxes because income from these entities flows through to their business owners who are responsible for paying tax on the income. C corporations are separate taxpaying entities and if elected some flow-through entities may be treated as separate taxpaying entities. Flow-through entities are usually taxed as either partnerships, sole proprietorships, or disregarded entities. 4.A taxation principle referring to income taxes that are paid twice on the same source of earned income. Double taxation occurs because corporations are considered separate legal entities from their shareholders. As such, corporations pay taxes on their annual earnings, just as individuals do. When corporations pay out dividends to shareholders, those dividend payments incur income-tax liabilities for the shareholders who receive them, even though the earnings that provided the cash to pay the dividends were already taxed at the corporate level. 5. Double tax is actually more favorable if you, 1. Pay reasonable salaries to shareholders. 2. Lease property from shareholders. 3. Defer or eliminate dividend payments. 4. Defer capital gains taxes on shares by making lifetime gifts of appreciated stock Solution 1. Corporations, limited liability companies (LLCs), general and limited partnerships, and sole proprietorships are the more common legal entities used for operating a business. 2.Corporations and LLCs offer owners limited liability. General partners and sole proprietors may be held personally responsible for the debts of the general partnership and sole proprietorship. However,limited partners are not responsible for the partnership’s liabilities. 3.A business entity may be legally classified as a corporation, limited liability company (LLC), a general partnership (GP), a limited partnership (LP), or a sole proprietorship under state law. However, for tax purposes a business entity can be classified as either a separate taxpaying entity or as a flow-through entity. Separate taxpaying entities pay tax on their own income. In contrast, flow-through entities generally don’t pay taxes because income fr.

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(a) Ka for C6H5NH3+ = Kw/Kb for C6H5NH2 = 10-14/4.27 x 10-10 = 2.342 x 10-5 Henderson-Hasselbalch equation: pH = pKa + log([C6H5NH2]/[C6H5NH3+]) = -log Ka + log([C6H5NH2]/[C6H5NH3+]) 4.20 = -log(2.342 x 10-5) + log(0.50/[C6H5NH3+]) log(0.50/[C6H5NH3+]) = -0.4304 0.50/[C6H5NH3+] = 10-0.4304 = 0.3712 [C6H5NH3+] = 1.347 1.35 M (b) Initial moles of C6H5NH2 = volume x concentration = 1.00 x 0.50 = 0.50 mol Initial moles of C6H5NH3+ = volume x concentration = 1.00 x 1.35 = 1.35 mol C6H5NH3+ + NaOH => C6H5NH2 + H2O + Na+ Moles of NaOH added = mass/molar mass = 4.00/40.00 = 0.100 mol Moles of C6H5NH2 = initial moles of C6H5NH2 + moles of NaOH added = 0.50 + 0.100 = 0.600 mol Moles of C6H5NH3+ = initial moles of C6H5NH3+ - moles of NaOH added = 1.35 - 0.100 = 1.25 mol Henderson-Hasselbalch equation: pH = pKa + log([C6H5NH2]/[C6H5NH3+]) = -log Ka + log(moles of C6H5NH2/moles of C6H5NH3+) since volume = 1.00 L for both = -log(2.342 x 10-5) + log(0.600/1.25) = 4.31 Solution (a) Ka for C6H5NH3+ = Kw/Kb for C6H5NH2 = 10-14/4.27 x 10-10 = 2.342 x 10-5 Henderson-Hasselbalch equation: pH = pKa + log([C6H5NH2]/[C6H5NH3+]) = -log Ka + log([C6H5NH2]/[C6H5NH3+]) 4.20 = -log(2.342 x 10-5) + log(0.50/[C6H5NH3+]) log(0.50/[C6H5NH3+]) = -0.4304 0.50/[C6H5NH3+] = 10-0.4304 = 0.3712 [C6H5NH3+] = 1.347 1.35 M (b) Initial moles of C6H5NH2 = volume x concentration = 1.00 x 0.50 = 0.50 mol Initial moles of C6H5NH3+ = volume x concentration = 1.00 x 1.35 = 1.35 mol C6H5NH3+ + NaOH => C6H5NH2 + H2O + Na+ Moles of NaOH added = mass/molar mass = 4.00/40.00 = 0.100 mol Moles of C6H5NH2 = initial moles of C6H5NH2 + moles of NaOH added = 0.50 + 0.100 = 0.600 mol Moles of C6H5NH3+ = initial moles of C6H5NH3+ - moles of NaOH added = 1.35 - 0.100 = 1.25 mol Henderson-Hasselbalch equation: pH = pKa + log([C6H5NH2]/[C6H5NH3+]) = -log Ka + log(moles of C6H5NH2/moles of C6H5NH3+) since volume = 1.00 L for both = -log(2.342 x 10-5) + log(0.600/1.25) = 4.31.

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(1) Q = 50 - 6.25P When demand increases by 20%, the new demand Q2 = 1.2 x Q So: 1.2 x Q = 1.2 x (50 - 6.25P) or, Q1 = 60 - 7.5P (2) Original Qd = 50 - 6.25P Qs = - 10 + 12.5P In equilibrium, Qd = Qs 50 - 6.25P = - 10 + 12.5P 18.75P = 60 P = 3.20 Q = - 10 + (12.5 x 3.2) = 30 (3) New Qd = 60 - 7.5P Equating with Qs: 60 - 7.5P = - 10 + 12.5P 20P = 70 P = 3.50, Q = - 10 + (12.5 x 3.5) = 33.75 (4) (a) elasticity of demand = Change in quantity demanded / change in price = 0.20 / [(3.5 - 3.2) / 3.2] ** = 2.13 ** change in quantity demanded = 20% (0.20) given (b) Elasticity of supply = change in quantity supplied / change in price = [(33.75 - 30) / 30] / [(3.5 - 3.2) / 3.2] = 0.125 / 0.0938 = 1.33 Solution (1) Q = 50 - 6.25P When demand increases by 20%, the new demand Q2 = 1.2 x Q So: 1.2 x Q = 1.2 x (50 - 6.25P) or, Q1 = 60 - 7.5P (2) Original Qd = 50 - 6.25P Qs = - 10 + 12.5P In equilibrium, Qd = Qs 50 - 6.25P = - 10 + 12.5P 18.75P = 60 P = 3.20 Q = - 10 + (12.5 x 3.2) = 30 (3) New Qd = 60 - 7.5P Equating with Qs: 60 - 7.5P = - 10 + 12.5P 20P = 70 P = 3.50, Q = - 10 + (12.5 x 3.5) = 33.75 (4) (a) elasticity of demand = Change in quantity demanded / change in price = 0.20 / [(3.5 - 3.2) / 3.2] ** = 2.13 ** change in quantity demanded = 20% (0.20) given (b) Elasticity of supply = change in quantity supplied / change in price = [(33.75 - 30) / 30] / [(3.5 - 3.2) / 3.2] = 0.125 / 0.0938 = 1.33.

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#include using namespace std; int main() { int n; cout<<\"enter n between 1 and 10 : \"; cin>>n; cout<<\"\ Roman numeral is : \"; switch(n) { case 1: cout<<\"I\"; break; case 2: cout<<\"II\"; break; case 3: cout<<\"III\"; break; case 4: cout<<\"IV\"; break; case 5: cout<<\"V\"; break; case 6: cout<<\"VI\"; break; case 7: cout<<\"VII\"; break; case 8: cout<<\"VIII\"; break; case 9: cout<<\"IX\"; break; case 10: cout<<\"X\"; break; } return 0; } Solution #include using namespace std; int main() { int n; cout<<\"enter n between 1 and 10 : \"; cin>>n; cout<<\"\ Roman numeral is : \"; switch(n) { case 1: cout<<\"I\"; break; case 2: cout<<\"II\"; break; case 3: cout<<\"III\"; break; case 4: cout<<\"IV\"; break; case 5: cout<<\"V\"; break; case 6: cout<<\"VI\"; break; case 7: cout<<\"VII\"; break; case 8: cout<<\"VIII\"; break; case 9: cout<<\"IX\"; break; case 10: cout<<\"X\"; break; } return 0; }.

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a. The results are inconclusive because the king size cigarettes are different sizes than the filtered cigarettes. b. No, the filters do not appear to make a difference because there is insufficient evidence to warrant the rejection of the claim. c. No, the filters do not appear to make difference because there is sufficient evidence to warrant the rejection of the claim. d. Given the king size cigarettes have the largest mean, it appears that the filters do make a difference(although this conclusion is not justified by the results from analysis of variance) Solution a. The results are inconclusive because the king size cigarettes are different sizes than the filtered cigarettes. b. No, the filters do not appear to make a difference because there is insufficient evidence to warrant the rejection of the claim. c. No, the filters do not appear to make difference because there is sufficient evidence to warrant the rejection of the claim. d. Given the king size cigarettes have the largest mean, it appears that the filters do make a difference(although this conclusion is not justified by the results from analysis of variance).

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let be A=x1i+y1j B=x2i+y2j A+B=(x1+x2)i+(y1+y2)j lA+Bl^2=(x1+x2)^2+(y1+y2)^2 now lAl^2=x1^2+y1^2 lBl^2=x2^2+y2^2 and AB=x1x2+y1y2 now lAl^2+2AB+lBl^2=x1^2+x2^2+2x1x2+2y1y2+y1^2+y2^2=(x1+x2)^2+(y1+y2)^2=lA+Bl^2 there fore lA+Bl^2=lAl^2+2AB+lBl^2 or lA+Bl^2=lAl^2+lBl^2+2lAllBl=lAl^2+2AB+lBl^2 Solution let be A=x1i+y1j B=x2i+y2j A+B=(x1+x2)i+(y1+y2)j lA+Bl^2=(x1+x2)^2+(y1+y2)^2 now lAl^2=x1^2+y1^2 lBl^2=x2^2+y2^2 and AB=x1x2+y1y2 now lAl^2+2AB+lBl^2=x1^2+x2^2+2x1x2+2y1y2+y1^2+y2^2=(x1+x2)^2+(y1+y2)^2=lA+Bl^2 there fore lA+Bl^2=lAl^2+2AB+lBl^2 or lA+Bl^2=lAl^2+lBl^2+2lAllBl=lAl^2+2AB+lBl^2.

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