Evaluate
To evaluate the integral \[ \int_{-5}^{5}(x^3 + x) \, dx \] we can take advantage of the properties of definite integrals and the symmetry of the integrand. First, let's split the integral into _________ ____ ______ _____ _________ ____ ________.
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State whether the following statement are TRUE or FALSE. Give reason in support of your answer.
a) Derivative of 1/x with respect to x is 1.
b) If A is a matrix of order 2 by 3 and B is a matrix of order 3 by 2, then order of the matrix A + B is 2 by 3.
c) If and
they are perpendicular to each other.
d) If probability of an event E is 1/2 and probability of the event is 1/6, then probability of the event F is 1/3, where events E and F are independent.
e) If the first term of an AP is 5 and 101 term of the AP is 1005 then common difference of the AP will be 105
Solve the following system of equations using Cramer’s rule. x + 3y + 2z = 6, – x + 4y + 5z = 8, 2x + 5y + 3z = 10
In a factory there are three machines A, B, C which produce 10%, 40% and 50% items respectively. Past experience shows that percentage of defective items produced by machines A, B, C are 5%, 4%, 2% respectively. An item from the production of these machines is selected at random and it is found defective. What is the probability (6) that it is produced by machine A?
Prove that is an orthogonal matrix.
Assume that in a population each person is equally likely to have a particular disease and disease status of each individual is independent of each other, then find the probability that out of the 5 randomly selected individuals who are tested for this particular disease exactly 3 have this disease.
Solve the differential equation
In an iron determination (taking 1 g sample every time) the following four replicate results were obtained: 24.8, 25.2, 23.6 and 24.7 mg iron. Calculate the coefficient of variation and relative standard deviation in ppm of the given data.