answer:Crossing over allows for the exchange of genetic material between homologous chromosomes, creating new combinations of alleles. This process shuffles the genetic material, resulting in gametes with unique combinations of genes. Independent assortment ensures that the chromosomes are randomly distributed to the gametes. This means that each gamete has an equal chance of receiving any combination of chromosomes from each parent. As a result, the offspring inherit a diverse mix of genes from both parents, further increasing genetic diversity.

answer:To calculate the current share price, we need to discount the expected future dividends back to the present using the required return. The price at Year 3 can be calculated as follows: Price at Year 3 = D4 / (Return - Growth) = (4 x 1.05) / (0.10 - 0.05) = 84.00 Next, we need to discount the dividends from Years 1, 2, and 3 back to the present using the required return. Present Value of Dividends = D1 / (1 + r)^1 + D2 / (1 + r)^2 + D3 / (1 + r)^3 = 6 / (1 + 0.10)^1 + 9 / (1 + 0.10)^2 + 4 / (1 + 0.10)^3 = 17.27 Finally, we can calculate the current share price by adding the present value of the dividends to the price at Year 3. Current Share Price = Present Value of Dividends + Price at Year 3 = 17.27 + 84.00 = 101.27 Therefore, the current share price of North Side Corporation is 101.27.

answer:a) Straight-line method depreciation for 2010: Depreciable Amount = Cost - Salvage Value Depreciable Amount = 80,000 - 8,000 Depreciable Amount = 72,000 Depreciation Expense per Year = Depreciable Amount / Estimated Useful Life Depreciation Expense per Year = 72,000 / 8 years Depreciation Expense for 2010 = 9,000 b) Straight-line method depreciation for 2010, assuming purchase on September 1, 2010: Time in Service for 2010 = (12 months in the year - purchase month) + 1 Time in Service for 2010 = (12 - 9) + 1 Time in Service for 2010 = 4 months Depreciation Expense for 2010 = (Depreciation Expense per Year / 12) * Time in Service for 2010 Depreciation Expense for 2010 = (9,000 / 12) * 4 Depreciation Expense for 2010 = 3,000 So, the depreciation expense for 2010 under the straight-line method is 9,000 and 3,000 for scenarios a) and b) respectively.

answer:To prove the equivalence, we must establish the implications in both directions. 1 implies 2: Let S = {x_1, ldots, x_n} be a linearly independent subset of V. Assume c_1T(x_1) + ldots + c_nT(x_n) = 0. By linearity of T, we have T(c_1x_1 + ldots + c_nx_n) = 0. Since T is injective, c_1x_1 + ldots + c_nx_n = 0. As S is linearly independent, it follows that c_1 = ldots = c_n = 0, thus T(S) is linearly independent. 2 implies 1 (Contraposition): Assume T is not injective, then ker(T) neq {0}. There exists a non-zero vector x in ker(T), which implies T(x) = 0. Consider the subset S = {x}; since S is linearly independent, by statement 2, T(S) should also be linearly independent. However, T(S) = {0}, which is a linearly dependent set (as 0 is the only element and 0 = lambda cdot 0 for any scalar lambda). This contradiction shows that if T is not injective, statement 2 cannot hold, completing the proof.