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Given an example of a tree of order 6 containing four vertices of degree 1 and two vertices of degree 3.


  • Determine whether each of the following statements is a proposition or not. If it is, give its truth value.p: Mindanao is an island in the Philippines. 
  • q: Find a number which divides your age. 
  • r: My seatmate will get a perfect score in the Logic exam.
  • s: Welcome to the Philippines!

Find the complete solution of xdy + (x ^ 3 - xy ^ 2 - y) dy = 0

Find the complete solution of:



1.) (x ^ 2 y + y ^ 3 - y) d x + (x ^ 3 + xy ^ 2 + x) dy = 0

Given that P(X=2)=8P(X=4)+80P(X=46) for a Poisson distribution variate X. Find

1) P(X<2)

2) P(X>4)

3) P(X>=1)


In a normal distribution 41% of items are under 55 and 11% are over 66. Find the mean and variance of the distribution.


Two balls are drawn in succession without replacement from an urn containing 5 orange balls and 6 violet balls. Let V be the random variable representing the number of violet balls 0 orange balls. Find the values of the random variable V.

Non-Exact Differential Equations. Find the complete solution of ydx + (x + y ^ 2) dy = 0

Determine the mean, variance and standard deviation of the probability mass fucntion:

X: 0,1,2,3,4

P(x): 0.1, 0.2, 0.3, 0.3, 0.1


thanks!!!


Last year the employees of the city health department donated an average of $ 8 to the rescue squad. Test the hypothesis at the 0.01 level of significance that the average contribution this year is still $ 8 if a random sample of 35 employees showed an average donation of $ 8.90 with a standard deviation of $ 1.75.

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