Engineering Data Analysis & Differential Equations – Exam

Two die are rolled. Find the probability that the sum of the two die is at most 8

A semiconductor company will hire 7 men and 4 women. In how many ways can the company choose from 10 men and 8 women?

What is the probability of getting at least 2 heads when a coin is tossed six times?

The geometric mean and arithmetic mean of the two numbers are 12 and 13 respectively. Find the larger number

Determine the variance of the series 1, 5, 9, 13… if n = 10

There are 15 basketball teams in a tournament. If each team plays every other team once, what is the minimum number of days can they all play without any team playing more than one game in any day?

In how many ways can a selection of 6 books from 15 books be made when 1 specified book is always excluded and 1 specified book is always included?

A four-digit number is selected at random. What is the probability that it is a perfect square?

What is the probability that of 5 cards dealt from a well-shuffled deck, 2 will be face cards and 3 will be non-face cards?

Four cards are to be dealt successively, at random from an ordinary deck of playing cards. Find the probability of receiving a spade, a heart, a diamond and a club in any order

Three teachers in Economics reported mean examination grades of 79, 74 & 82 in their classes, which consisted of 32, 25 and 17 students, respectively. Determine the mean grade for all their classes

Three teachers in Economics reported mean examination grades of 79, 74 & 82 in their classes, which consisted of 32, 25 and 17 students, respectively. Determine the standard deviation for all their classes.

The mean weight of 500 male students at a certain college is 150 lb and standard deviation of 10 lb. Assuming that the weights are normally distributed, find how many students weigh between 119.5 and 155.5 lb.

A fair coin is tossed 400 times. Find the probability that the probability that the number of heads will not differ from 200 ± 10.

If the probability that an individual suffers a bad reaction from an injection is 0.001. Determine the probability that out of 2000 individuals exactly 3 individuals will suffer a bad reaction.

From the following points (2, 1), (3, 3), (5, 7), (7, 11), (9, 15), and (10, 17). Find the equation for the least-squares line.

From the following points (2, 1), (3, 2), (5, 7), and (10, 17). Find the equation for the least-squares parabola.

The random sample of 50 mathematics grades out of a total of 200 shows a mean of 75 and standard deviation of 10. With a confidence level of 95%, determine upper limit of the confidence interval.

The standard deviation of the lifetimes of a sample of 200 light bulbs was 100 h. Find the 99% confidence limits for the standard deviation of all such electric bulbs.

The lifetime of a Television Set will last an average for 8 years. Using an exponential density function, what is the probability that it will between 8 to12 years?

Determine the order and degree of the differential equation x (y” ) + y’ + y³ = 0.

Solve the differential equation  y’ – y = 4.

Solve the differential equation  +  = 2.

Find the differential equation of the family of parabolas having their vertices at (-1,  2) and opening to the right or left.

Find the equation of the curve passing thru (-2, 3) and whose normal line at (x, y) has a slope of -1/(4x).

Evaluate : dy/dx = 2y / x at  x = 1 ; y = 2

A certain radioactive substance has a half-life of 30 hours. How long does it takes for 60 % of the radioactivity to be dissipated?

15 mg of a radioactive substance with a half-life of 18 hours is injected into a patient’s bloodstream. The patient’s returns to the medical facility after 24 hours and a technician determine that there are 3 mg of the substance in the patient’s pancreas. How much of the substance is in the remainder of the patient’s body?

Solve for (D³ + 4D) y = 0

A 6 H coil whose resistance is 24 Ω is connected in series with a 12 Ω resistor and to a 270 V battery and a switch. The switch is closed at t = 0 second, the initial current is 0. Determine the steady state current.

The acceleration of the particle is given by a = 2 + 12 t in m/s² . If the velocity of this particle is 11 m/s after 1 minute, find the velocity after 2 minutes.

Find the differential equation whose general solution is   y = c₁e^-x + c₂ e^x

If a population is increasing exponentially at the rate of 1.75% per year. What will be the percentage increase over a period of 20 years?

During the worst 4-hr period of the hurricane, the wind velocity in mph is given by v(t) = 6t – t² +120, 0 What is the average wind velocity during this period?

A cup of coffee at temperature 190^oF is placed on a table in a room 60^o After 3 minutes, the temperature of the coffee is 155 ^oF. What is the temperature (in ^oF) of the coffee after 10 minutes?

A tank contains 300 liters of pure water. A brine solution with 2 kg/ liter of salt enters at 3 liters/minute, and the well-stirred mixture leaves at the 3 liters/minute. How many kg of salt remains in the tank after 30 minutes?

An ecological study shows that a lake can support a maximum population of 5000 fish. The logistic function that governs the fish population is P(t) = where t is measured in months. What is the population growth rate after 5 months?

Environmentalists predict that in t years, the deer population in a forest will be P(t) =   thousand. What is the initial population of the deer in this forest?

Determine the inverse Laplace transform of the function F(s) = (100)/(s² +50s +10625)

Determine the initial value and final value respectively, of the function F(s) = (100)/(s² +50s +10625)