answer:To find the rank of the matrix A, we can reduce it to row echelon form: A = begin{pmatrix} frac{65}{7} & frac{52}{7} & frac{37}{7} & -5 frac{67}{7} & -frac{60}{7} & frac{50}{7} & frac{26}{7} end{pmatrix} sim begin{pmatrix} frac{67}{7} & -frac{60}{7} & frac{50}{7} & frac{26}{7} 0 & frac{7384}{469} & -frac{771}{469} & -frac{4035}{469} end{pmatrix}. Since there are two nonzero rows in the row echelon form, the rank of A is 2. Therefore, the rank of the matrix A is 2.

answer:Price elasticity of supply is an economic concept that measures the responsiveness of suppliers to changes in the price of a good or service. It is calculated as the percentage change in quantity supplied divided by the percentage change in price. A high price elasticity of supply indicates that suppliers are very responsive to changes in price, while a low price elasticity of supply indicates that suppliers are not very responsive to changes in price. Factors that affect price elasticity of supply include: * The availability of substitutes: If there are many close substitutes for a good or service, suppliers will be more responsive to changes in price. * The cost of production: If the cost of producing a good or service is high, suppliers will be less responsive to changes in price. * The time it takes to adjust production: If it takes a long time to adjust production, suppliers will be less responsive to changes in price. Price elasticity of supply is an important concept for businesses and policymakers to understand. Businesses can use price elasticity of supply to make decisions about pricing and production. Policymakers can use price elasticity of supply to design policies that affect the supply of goods and services. Price elasticity of supply measures the responsiveness of quantity supplied to a change in price. It is calculated as the percentage change in quantity supplied divided by the percentage change in price.

answer:Let's denote the number of slices Ashley ate as x. Then Jessica ate x + 2 slices. Together, they ate x + (x + 2) = 2x + 2 slices. Since they ate dfrac{8}{12} of the pie, we have: 2x + 2 = dfrac{8}{12} * 12 Solving for x, we get: x = 2 Therefore, Ashley ate 2 slices.

answer:The square of the given matrix is calculated as follows: left( begin{array}{cc} 0 & 1 -3 & -frac{3}{2} end{array} right)^2 = left( begin{array}{cc} 0 cdot 0 + 1 cdot (-3) & 0 cdot 1 + 1 cdot (-frac{3}{2}) -3 cdot 0 + (-frac{3}{2}) cdot (-3) & -3 cdot 1 + (-frac{3}{2}) cdot (-frac{3}{2}) end{array} right) = left( begin{array}{cc} -3 & -frac{3}{2} frac{9}{2} & -frac{9}{4} end{array} right) Upon reviewing the answer, there seems to be an error in the calculation of the entry in the second row, second column. Let's correct that: left( begin{array}{cc} 0 & 1 -3 & -frac{3}{2} end{array} right)^2 = left( begin{array}{cc} 0 cdot 0 + 1 cdot (-3) & 0 cdot 1 + 1 cdot (-frac{3}{2}) -3 cdot 0 + (-frac{3}{2}) cdot (-3) & -3 cdot 1 + (-frac{3}{2}) cdot (-frac{3}{2}) end{array} right) = left( begin{array}{cc} -3 & -frac{3}{2} frac{9}{2} & frac{9}{4} end{array} right) The corrected answer is now accurate.