The position of an object at time t is given by s(t) = -9 – 3t. Find the instantaneous velocity at t = 8 by finding the derivative. (9 points)

Find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ± x. (5 points)

Given that P = (-4, 11) and Q = (-5, 8), find the component form and magnitude of . (5 points)

Based on scientific research the recommended amount of water to drink in a day is: 

Express the complex number in trigonometric form. -4i (5 points)

A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 25 feet and the height from the ground to the front doors is 7 feet, how long is the ramp? (Round to the nearest tenth.) (5 points)

Calculate [H3O+] and [OH-] in the following aqueous solution. Classify the following solution as acidic, neutral, or basic.             pH =   4.2500                        

Find the derivative of f(x) = at x = -2. (6 points)

(06.03 MC)  Aaliyah wants to determine how age and gender are related to movie genre preference in her town. She selects a simple random sample of 35 males from the 20- to 30-year age group and records their age, gender, and movie genre preference (comedy, romance, or horror). She also selects an independent simple random sample of 45 females from the 45- to 55-year age group and records the same information. Which is the most important observation about Aaliyah’s plan? (3 points)

(04.02 MC)  An individual can win a prize by drawing the highest numbered card out of five cards. After each draw, the card is replaced and the cards are shuffled for another chance. If the prize is not won, the card is again replaced and mixed in with the other cards. If a prize is won, the highest card is replaced and the five cards are shuffled for a new game. If an individual makes seven draws, what is the probability the individual will win a prize exactly two times? (3 points)