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Use polar coordinates to find the volume of the given solid.
Inside both the cylinder x^2 + y^2 = 8 and the ellipsoid 4x^2 + 4y^2 + z^2 = 64
One of the students is randomly selected. Let X denote the number of students that were on the bus carrying this randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on his bus. Compute..
Kiran drove from Tortula to Cactus, a distance of 288 mi. She increased her speed by 8 mi/h for the 392 mi trip from Cactus to Dry Junction. If the total trip took 13 h, what was her speed from Tortula to Cactus?
A surfboard manufacturing company has determined that the cost function c(x), in hundreds of dollars, for producing x hundreds of boards is c(x) = .2x^2 -.84x + 3.625.
Assume that f(z) is analytic at the origin and f(0) = first derivative of f at 0 = 0. Prove that f(z) can be written in the form f(z) = [z^2]g(z), where g(z) is analytic at z = 0.
Could you explain to me the difference between functions and linear equations? I need to know if all linear equations are functions and if there are any instances in which a linear equation is not a function.
A sample of 100 provided a sample mean of 75.7. The population standard deviation is known to be 12. At 0.01 level of significance, what is your conclusion? Use either the p-value approach on the critical value of approach.
Suppose that a pair of 20-sided dice are rolled (the sides are numbered 1-20). What is the probability that the sum of the dice is 13?
Let N be a positive integer. Let d be an integer relatively prime to phi(N) (phi denotes the euler totient function). Prove that there exists a d' in Z (=integers) with dd'=1 mod phi(N).
A rope is wrapped around a pole so that a force of 75 lbs acts on one end and a force of 53 lbs acts on the other end. If the angle between the two forces is 114 degrees what is the resultant force?
Find the distance of the ship from the lighthouse.
Rewrite the following system of equations as an augmented matrix. Put the matrix in reduced row echelon form to find the solution to the system of equations.
Assume the readings on a thermometers are normally distrubuted with a mean of 0 degree C and a standard deviation of 1.00 degree Celsius. Find the proabilitys that a randomly selected thermometer read leass than 1.43.
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