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Question: 1. Prove or give a counterexample: Every multiple of 6 that is greater than or equal to 12 is the sum of two consecutive primes. (For example, 30 = 13+17)
2. (Adapted from [10]) Figure shows a network of canals around artificial islands in a pond, created as a duck playground. White Duck (pictured in Figure A.10) swims aimlessly around the playground and then goes to see Grey Duck. White Duck says, "I swam through each of the 16 canal intersections at the playground exactly twice. In fact, here's the order in which I swam: a-o-n-h-k-g-b-m-i-e-p-f-c-l-d-j-c-g-n-h-j-k-d-l-p- i-e-f-b-o-a-m." "The canal intersections aren't usually labeled," replies Grey Duck, "so I don't exactly know the path you took. But you know what? I think you can't be quite right about where you swam." White Duck pauses to think, then responds, "Ah, yes, you're right. I switched two of the letters in my order." Can you figure out what White Duck's error was?
Develop the transfer function for the effect of (u) on (y) for the following differential equations, assumong u(0)=0 and y(0)=0.
Let f be Lebesgue integrable on [0,1]. Prove that the limit, as k goes to infinity, of the integral from 0 to 1 of (x^k)f(x)dx is equal to 0.
Write the first 15 terms of the sequence - Find the first five terms of the sequence an = (xn - 1) / (n+1)
Find the composition of the simple harmonic motion of the same period in the perpendicular directions
linda stevens was recently promoted from accounts payable clerk to accounting specialist. previously she earned 10.50
Each letter stands for a different digit, 0 to 9. No two letters stand for the same digit. TOM + NAG = GOAT. Determine which digit each letter represents.
One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on his bus. Compute the expectations of X and Y.
Eliminate the parameter to find a Cartesian equation of the curve. Sketch the curve and indicate with an arrow the direction in which the cuve is traced as the parameter increases
Refer to the Buena School District bus data. Select the variable referring to the number of miles traveled last month, and then organize these data.
In a mass production of bolts it is found that 5% are defective. Bolts are selected at random and put into packet of 10.
Do you think that green consumerism is an oxymoron? Do you think that your own consumer behaviors are environmentally sustainable? Why or why not?
Demostrate that your result gives the obviously correct answer for the limiting case.
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