Suppose you have a coin which is rigged so that the probability of tossing a head is 1/8. You toss the coin 3 times. Consider each of the following events. E1E1: T on first flipE2E2: H on first flipE3E3: T on second flipE4E4: Exactly two HE5E5: Not all flips identical(a) P(E1)P(E1) = (b) P(E2)P(E2) = (c) P(E3)P(E3) = (d) P(E4)P(E4) = (e) P(E5)P(E5) = (f) P(E2|E1)P(E2|E1) = (g) P(E3|E1)P(E3|E1) = (h) P(E4|E1)P(E4|E1) = (i) P(E5|E1)P(E5|E1) = Note: for best results, enter exact values or decimal approximations accurate to at least 5 decimal places.

The blue whale is the largest animal living on the earth. the average blue whale measures 100 feet long (30 meters) and weighs 300,000 pounds (136,000 kilograms). a whale’s head is 1⁄3 of the length of its body. a new baby whale is 1⁄4 the length of a grown whale. the average man is 1⁄17 the length of a blue whale, and 1⁄1,818 its weight. a human baby measures 1⁄4 of the length of an adult. calculate the following information: how long is a whale’s head? how long is a new baby whale? how tall is the average man? how much does the average man weigh? how tall is the average human baby?

Astudent drew a circle and two secant segment. he concluded that if pq ~= ps, then qr ~= st. do you agree with the student’s conclusion? why or why not?

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).