Two functions g and fare defined in the figure below.

Problem 4 Let V = P(R) and let L(V) be the vector space of all linear transformation on V. For j ≥ 1 define T;(ƒ(x)) = f(i)(x), where ƒ(¹)(x) is the j-th derivative of f(x). Prove that the set {T₁, T2,...,‚Tn} is a linearly independent subset of L(V) for any positive integer n.

Based on the frequency distribution below, what would the cut-off score be if only the top 10% of students received a prize? SCORE 60-64 55-59 50-54 45-49 40-44 35-39 30-34 FREQ. 5 9 12 17 18 11 6

Determine the values of the following quantities: a. X1,15 b. X1,25 c. X01,25 d. x005,25 e. X99,25 f. X995,25

What would be the least amount of money needed to purchase exactly 19 muffins?                    Number of Muffins:                  Total Price:                                1                      ⇒              $0.60                           Box of 6              ⇒              $3.25                           Box of 12             ⇒              $5.75     A. $9.00B. $9.25C. $9.35D. $9.95