Question Consider the following random experiment: we toss a two-sided coin (H on one side and T on the other side) n = 3599 times. In any given toss, the probability the coin comes up H is p = P(H) = 0.78. Each time the coin comes up H we give Tom 2 dollars and take from Tom 1 dollar if it comes up T (so Tom either gets 2 or gets -1, i.e., loses 1 dollar). How many dollars do we expect Tom will get on "average", i.e., per experiment?

5.90 Genetics of peas. According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white in a 3:1 ratio. That is, each plant has probability 3/4 of having red blossoms, and the blossom colors of separate plants are independent. (a) What is the probability that exactly 8 out of 10 of these plants have red blossoms? (6) What is the mean number of red-blossomed plants when 130 plants of this type are grown from seeds? (c) What is the probability of obtaining at least 90 red-blossomed plants when 130 plants are grown from seeds?

A projectile is launched with an initial speed of 43.0 m/s at an angle of 35.0° above the horizontal. The projectile lands on a hillside 3.90 s later. Neglect air friction. (Assume that the +x-axis is to the right and the +y-axis is up along the page. (30 points) a) What is the projectile's velocity at the highest point of its trajectory? (You must find the magnitude and direction of the velocity). Magnitude: (10 points) Direction: (10 points)

An airplane propeller is 2.88 m in length (from tip to tip) and has a mass of 117 kg. When the airplane's engine is first started, it applies a constant net torque of 1850 N⋅m to the propeller, which starts from rest. What is the angular acceleration of the propeller? Model the propeller as a slender rod. What is the propeller's angular speed after making 5.00 revolutions? How much work is done by the engine during the first 5.00 revolutions? What is the average power output of the engine during the first 5.00 revolutions? What is the instantaneous power output of the motor at the instant that the propeller has turned through 5.00 revolutions?

See attached aaВW2DaaW1Given that w1 - 15 kN/m, w2 = 14.5 kN/m and a = 1.5 m,determine the internal normal force, shear force and bending|moment at points D and E of the two-member frame. Round allanswers to the nearest integer.Normal force at Din kN (round to the nearest integer):kNShear force at D in kN (round to the nearest integer):kNBending moment at Din kNm (round to the nearest integer):kNmNormal force at E in kN (round to the nearest integer):kNShear force at Ein kN (round to the nearest integer):|kNMagnitude of bending moment at E in kNm (round to the nearestinteger):kNm

a a W2 D a --- E a W1 Given that w1 = 2 kN/m, W2 = 1.5 kN/m and a = 1.5 m, determine the internal normal force, shear force and bending moment at points D and E of the two-member frame. Round all answers to the nearest integer. Normal force at D in kN (round to the nearest integer): Normal force at Din kN (round to the nearest integer): KN Shear force at D in kN (round to the nearest integer): KN Bending moment at D in kNm (round to the nearest integer): kNm Normal force at Ein kN (round to the nearest integer): kN Shear force at Ein kN (round to the nearest integer): KN Magnitude of bending moment at Ein kNm (round to the nearest integer): kNm

A projectile is launched with an initial speed of 50.0 m/s at an angle of 35.0" above the horizontal. The projectile lands on a hillside 3.5 s later. Neglect ar fretion. (Assume that the treats is to the right and the +y-axis is up along the page.) (a) What is the projectile's velocity at the highest point of its trajectory? magnitude m/s direction counterclockwise from the x- (b) What is the straight-line distance from where the projectile was launched to where it hits its target?