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I need to know if these are true, and if so why.
a) In a rooted binary tree with 16 vertices, there must be a path of length 4.
b) No tree has a Hamilton path.
One month ago the ratio of nurses to doctors on a hospital staff was 3:5. Since that time two additional nurses joined the staff, no nurses left & the number of doctors remained the same. Find the ratio of nurses to doctors.
integral over gamma of e^(iz) / z^2 dz, where gamma(t) = e^(it), 0=
Rate related problems and Determine the general expression for the car's acceleration at any time t, and show that car is decelerating 2(2/3) seconds after starting from rest.
Find number of ways using permutation
If the speed ( in m/sec ) of a particle moving on the x-axis at time t seconds (t>0) is given by: V(t)=t^3-8t^2+15t+10 estimate during what time period the speed of the particle is less than 10m/sec.
How is the solution affected if the constraints are changed to y(0) = 0 and y'(0) = 1 ? What is the special about this case?
The diameters of grapefruits in a certain orchard are normally distributed with a mean of 7.10 inches and a standard deviation of 0.50 inches.
How do I determine the short-run profit maximizing price and quantity? How do I determine the maximum profit accruable to the firm?
What does the final row of the augmented matrix in echelon form (the above description) tell you about the solution to the system of 5 linear equations?
Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive?
Provide an example of a matrix that can be solved using Gaussian elimination. Show specifically how row operations can be used to solve the matrix.
A mini license plate for a toy car must consist of three numbers followed by a letter. Each number must be a 3,6, or 9. Repetition of digits is NOT permitted. Each letter must be an A, B, or C.
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