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In a school, 100 students have access to three software packages A, B and C.
28 did not use any software
8 used only packages A
26 used only packages B
7 used only packages C
10 used all three packages
13 used both A and B
If twice as many students used package B as package A, Using Venn Diagram:
1. Calculate the no. of students using packages A & C only but not B.
2. Calculate the no. of students using packages C & B only but not A.
Are there values of r and s for which [1,0,0,0,r-2,2,0,s-1,r+2,0,0,3] has rank 1 or 2? If so, find those values
A researcher claims that at least 10% of all football helmets have manufacturing flaws
that could potentially cause injury to the wearer. A sample of 200 helmets revealed that
16 helmets contained such defects. Does this finding support the researcher’s claim?
Given the moment-generating function Mx(t) = e^(3t+8t^2) , find the moment
generating function of the random variable Z = (X-3)/4, and use it to
determine the mean and the variance of Z.
(a) Evaluate∫[
x
√x
2+1
]dx.
(b) Use MATLAB to generate some typical integral curves of f(x) =
x
√x
2+1
over the
interval (−5,5).
2% of the trees in a plantation are known to have a certain disease.what is the probability that,in a sample of 250 trees.
(I) less than 1% are diseased
A sample of 200 people of age 21 with a population standard deviation of 5. Test the hypothesis that the population mean is 18.9 at à,=0.05.
Let.
1 0 0
0 3 6
0 -1 -2
Verify that C 2 = C holds. Find the eigenvalues and eigenvectors of C.
Let. (Matrix)
2 0 1
2 -2 2
0 4 1
(a) Find A2 and A3 , and verify that: A 3 − A 2 − 12A = −12i
holds, where I stands for the identity matrix.
(b) Find A−1 by multiplying the equation above on both sides by A−1
Compute the determinant, and use Gauss-Jordan elimination to find the inverse of the following matrix (if it exists).
218 0 0
0 218 2
0 1 1
