answer:The determinant of the given matrix is calculated as follows: [ begin{align*} text{det} &= -frac{1}{5} left| begin{array}{cc} -frac{24}{5} & frac{7}{5} frac{21}{10} & frac{27}{10} end{array} right| - left(-frac{21}{5}right) left| begin{array}{cc} -5 & frac{7}{5} frac{8}{5} & frac{27}{10} end{array} right| - left(-frac{41}{10}right) left| begin{array}{cc} -5 & -frac{24}{5} frac{8}{5} & frac{21}{10} end{array} right| &= -frac{1}{5} left( -frac{24}{5} cdot frac{27}{10} - frac{7}{5} cdot frac{21}{10} right) + frac{21}{5} left( -5 cdot frac{27}{10} - frac{7}{5} cdot frac{8}{5} right) + frac{41}{10} left( -5 cdot frac{21}{10} - (-frac{24}{5}) cdot frac{8}{5} right) &= -frac{1}{5} left( -frac{648}{50} - frac{147}{50} right) + frac{21}{5} left( -frac{135}{10} - frac{56}{25} right) + frac{41}{10} left( -frac{105}{10} + frac{192}{25} right) &= frac{795}{250} - frac{2835}{50} - frac{41}{10} left( -frac{105}{10} + frac{768}{250} right) &= frac{159}{50} - frac{567}{10} - frac{41}{10} left( -frac{105}{10} + frac{768}{250} right) &= -frac{2508}{50} - frac{41}{10} left( -frac{105}{10} + frac{768}{250} right) &= -frac{25683}{500} end{align*} ] Therefore, the determinant is -frac{25683}{500}.

answer:The government imposes taxes on goods with highly inelastic demand, such as necessary goods and fuels. Because the demand for these goods does not decrease significantly in response to price increases, the government can generate revenue through taxation without causing a substantial decline in consumption. This minimizes deadweight loss, which is the economic loss that occurs when taxes distort market incentives and reduce overall economic efficiency. By taxing goods with inelastic demand, the government can generate revenue while minimizing the negative impact on the economy.

answer:The complete ionic equation for this reaction is: [ Pb(NO_3)_2(aq) (lead(II) nitrate) + K_2SO_4(aq) (potassium sulfate) rightarrow PbSO_4(s) (lead(II) sulfate) + 2KNO_3(aq) (potassium nitrate) ] Breaking apart the aqueous compounds into their respective ions, we get: [ Pb^{2+}(aq) + 2NO_3^-(aq) + 2K^+(aq) + SO_4^{2-}(aq) rightarrow PbSO_4(s) + 2K^+(aq) + 2NO_3^-(aq) ] In this equation, the spectator ions are the nitrate ions (NO_3^-) and potassium ions (K^+), which remain unchanged on both sides of the equation. The final complete ionic equation, showing only the non-spectator ions, is: [ Pb^{2+}(aq) + SO_4^{2-}(aq) rightarrow PbSO_4(s) ] The solid lead(II) sulfate (PbSO_4) is the only compound that precipitates, while potassium nitrate (KNO_3) remains in the aqueous phase.

answer:To find the pH of the solution, we'll use the Henderson-Hasselbalch equation: [ pH = pK_a + log left( frac{[base]}{[acid]} right) ] First, we need to determine the acid dissociation constant (K_a) for ethylammonium ion, since K_aK_b = 1.0 × 10^-14: [ K_a = frac{1.0 times 10^{-14} rm M^2}{5.6 times 10^{-4} rm M} approx 1.79 times 10^{-11} rm M ] Now, we calculate the pK_a: [ pK_a = -log(1.79 times 10^{-11} rm M) approx 10.75 ] Next, we plug the values into the Henderson-Hasselbalch equation: [ pH = 10.75 + log left( frac{0.05 rm M}{0.75 rm M} right) ] [ pH = 10.75 - 1.17 approx 9.58 ] Thus, the approximate pH of the solution is 9.58.