The first five Hermite polynomials are 1, 2t, −2 + 4t 2 , −12t + 8t 3 , and 12 − 48t 2 + 16t 4 . These polynomials arise naturally in the study of certain important differential equations in mathematical physics. Show that the first five Hermite polynomials form a basis of P4.

Josh has a rewards card for a movie theater he receives 15 points for becoming a rewards card holder he earns 3.5 points for each visit to the movie theater he needs at least 55 points to earn a free movie ticket which inequality can josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket.

Jane moves from a house with 71 square feet of closet space to an apartment with 45.44 square feet of closet space. what is the percentage decrease of jane’s closet space?

Harry and jay are both flying on the same plane with an airline that randomly assigns seats to passengers. of the 182 total seats on the plane, 62 are window seats, 58 are middle seats, and the rest are aisle seats. what is the approximate probability that both harry and jay will be assigned aisle seats on the same plane? a. 11.48% b. 3.3% c. 2.08% d. 26.26%