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If P(E1)=P(E2)=0.15, P(E3)=0.4, and P(E4)=2P(E5), calculate the P (E4) and P(E5).
1.Consider the equation xe^x = cos x
(a) Apply the intermediate value theorem to show that the function has a root in the interval
[0, 1].
(b) Find the real root using the secant method. Start with the two points, x1 = 0 and x2 = 1
and carry out the first four iterations.
(c) Find the real root using the Newton-Raphson method. Start with an initial approximation,
x0 = 0.5 correct to two decimal places.
2.Consider the initial value problem
dy = t(y + t) − 2, y(0) = 2. It is derivative of y respect to t
dt
(a) Use Eulers method with step sizes h = 0.3, h = 0.2 and h = 0.15, compute the approximations to y(0.6).
(b) Use the fourth order Runge-Kutta method Compute y(0.4) with h = 0.2.
Consider the equation xe^x = cos x
(a) Apply the intermediate value theorem to show that the function has a root in the interval
[0, 1].
Draw a graph having the given properties:
1. Simple graph : 6 vertices with degrees 2,3,3,3,4,5
2. Simple graph: 9 vertices with degrees 1,1,3,3,4,4,5,5,6
3. Simple graph: 7 vertices with degrees 3,3,3,3,3,3,6
4. Simple graph: 5 vertices with degrees 4,4,4,4,4
5. Simple graph: 6 vertices with degrees 1,2,3,4,5,5
6. Simple graph: 5 vertices having degrees 2,2,4,4,4
7. Simple graph : 8 vertices with degrees 2,2,3,3,3,4,4,7
8. Simple graph: 8 vertices with degrees 2,3,3,4,4,4,5,5
A firm produces three products A, B, and C, each of which passes through three departments: Fabrication, Finishing and Packaging. Each unit of product A requires 3, 4 and 2 hours; a unit of B requires 5, 4 and 4 hours while each unit of product C requires 2, 4, 5 hours respectively in the three departments. Every day, 60 hours are available in fabrication department, 72 hours in the finishing department and 100 hours in the packaging department. If the unit contribution of product A is ETB 5, of product B is ETB 10, and of product C is ETB 8, determine the number of units of each of the products, which should be made each day to maximize the total contribution. Also determine if any capacity would remain unutilised.
a. Write the formulation for this linear program.
b. Solve the Linear programming problem using simplex method.
Explain the concept of regression and point out its usefulness in dealing with business
problems.
In a survey of 200 students, 78 of the 120 females in the sample passed math 17 on their first take while this figure is 60 among the males. Will you agree that the proportion of males who passed math 17 on their first take is higher than the proportion of females who passed math 17 on their first take?test at a 0.05
A population consists of five numbers 1, 2, 3, 4, 5 and 6. Suppose samples of size 2 are drawn from this
population.
(a) Find the mean and variance of the population
(b) Describe the sampling distribution of the sample means.
(c) Find the mean and variance of the sampling distribution of the sample means.
What is the answer of "express the null hypothesis and alternative hypothesis in notation form of the scenario " it is believe that we that the mean yearly salary of professors in the philippines is 480,000.00 p pesos. a random sample of 65 professors revealed a mean salary of 500,000.00 pesos. can it be concluded the the mean salary is greater than 480,000.00 pesos? "
Let R1 and R2 be the relations on { 1, 2, 3, 4 } given by
R1 = { (1,1), (1,2), (3,4), (4,2) }
R2 = { (1,1), (2,1), (3,1), (4,4), (2,2) }
List the elements of R2 Ο R1
#340153 on Dec 2023