lat123

Based on extensive testing, it is determined by the manufacturer of a washing machine that the time Y (in years) before a major repair is required is characterized by the probability density function 

𝑓(𝑦) = { 0.25 𝑒 ^−𝑦/4,     𝑦 ≥ 0 

            0,                     𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒

(A) Find the mean and standard deviation of Y. 

An important factor in solid missile fuel is the particle size distribution. Significant

problems occur if the particle sizes are too large. From production data in the past, it has been determined that the particle size (in micrometers) distribution is characterized by:

𝑓(𝑥) = { 3𝑥 ^−4      𝑥 > 1 

            0              𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒

Find the mean particle size. Find the variance of X. 

From a box containing 5 dimes and 2 nickels, three coins are selected at random without replacement. Find the probability distribution for the total T of the 3 coins. Express the probability distribution graphically as a probability histogram. 

A school club consists of 20 male and 5 female students. In how many ways can two male and two female students be chosen?

Two 10-cm-diameter charged disks face each other, 25 cm apart. The left disk is charged to - 50 nC and the right disk is charged to + 50 nC .

What is the electric field E, both magnitude and direction, at the midpoint between the two disks?

What is the force F on a -2.3 nC charge placed at the midpoint?

An electret is similar to a magnet, but rather than being permanently magnetized, it has a permanent electric dipole moment. Suppose a small electret with electric dipole moment 1.0 × 10−7 Cm is 25 cm from a small ball charged to + 70 nC, with the ball on the axis of the electric dipole.

What is the magnitude of the electric force on the ball?

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = 2 + sec(x), −π/3 ≤ x ≤ π/3, y = 4; about y = 2

What would the area be between these two curves, out to 5 decimal places?

(16/(1+x^4)) and 8x^2

A worker pushes a 32 kg box on a rough floor by a force of 160N at an angle of 25 degrees below the horizontal line. The coefficient of the kinetic friction between the floor and the box is 0.150.

A.) Find the net work done on the box when the box has moved 4.55m.

B.) Assuming that the box starts from rest, what is the speed of the box after it has moved 4.5m. (Answer strictly based on work and energy theorem.)

Also, do you mind showing all steps as to how you get your answer?

A 2.0-m-long, 1.0-mm-diameter wire has a variable resistivity given by

ρ(x)=(2.5×10−6)[1+(x1.0m)2]Ωm

where x is measured from one end of the wire.

What is the current if this wire is connected to the terminals of a 18.0 V battery?

A heavy ball with a weight of 110 N is hung from the ceiling of a lecture hall on a 4.8-m-long rope. The ball is pulled to one side and released to swing as a pendulum, reaching a speed of 5.2 m/s as it passes through the lowest point.

What is the tension in the rope at that point?

A snowboarder glides down a 60-m-long, 15∘ hill. She then glides horizontally for 10 m before reaching a 20 ∘ upward slope. Assume the snow is frictionless.

A.) What is her velocity at the bottom of the hill?

B.) How far can she travel up the 20 ∘ slope?

How would I solve this?

A 8.0 ×107 kg train applies its brakes with the intent of slowing down at a 1.1 m/s2 rate.

A.) What magnitude force must its brakes provide?

How do I solve this?

A truck with a heavy load has a total mass of 7500 kg. It is climbing a 15∘ incline at a steady 15 m/s when, unfortunately, the poorly secured load falls off! Immediately after losing the load, the truck begins to accelerate at 1.5 m/s2.

A.) What was the mass of the load? Ignore rolling friction.

How would I solve this problem?

A circular track has several concentric rings where people can run at their leisure. Phil runs on the outermost track with radius rP while Annie runs on an inner track with radius rA = 0.76 rP. The runners start side by side, along a radial line, and run at the same speed in a counterclockwise direction.

A.) How many revolutions has Annie made when Annie's and Phil's velocity vectors point in opposite directions for the first time?

How would I solve: 2 ln (x) - ln (x^3) = 4