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Find a polar equation of the conic with focus at the pole and the given eccentricity and directrix
e=3/2, rsin(theta)=1
Suppose that f and g are continuous functions and (integral sign) from 2 - 0 of f(x) dx = 5 and (integral sign) from 2-0 of g(x) dx = 13. Compute the following.
The length of a rectangular room is 4 feet longer than twice the width. If the room's perimeter is 212 feet, find the length of the room.
An equilateral triangle with sides 10 m is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it.
23% of the seniors at a high school failed pre-calculus. If 1138 students failed pre-calculus, how many seniors are at this high school?
Find the probability that a male resident who was newly diagnosed with AIDS in 1998 contracted it via homosexual contact. Find the probability that a female resident who was newly diagnosed with AIDS in 1998 contracted it via intravenous drug use.
Identify the critical points and find the maximum value and minimum value on the given interval g(x)=1/1+x^2 ; I=[-3,1]
The monthly incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a standard deviation of $150. find the probability that a randomly selected employee earns less than $900 a month.
For the function: f(x)=(x^2/4)+e^(-x^2), sketch a graph of the function. Calculate the first and second derivatives, and use these answers to approximate the locations of the local maximum, minima, and the inflection points.
Suppose G is an abelian group of order m. Let m, n be relatively prime. Show that for every element g in G, there exists an element x in G such that x^m=g. Abelian Groups and Relatively Prime Order
What percent of the cruises will have 1,970 passengers or more? What percent of the cruises will have 1,600 or fewer passengers? How many passengers are on the cruises with the fewest 25 percent of passengers?
How far should its base set away from the building wall? Explain your answers and show your calculation. NOTE: You may need to apply the Pythagorean Theorem when solving this question.
In a certain manufacturing process the probability of a type I defect is 0.14, the probability of a type II defect is 0.34, and the probability of having both types of defects is 0.04. Find the probability of having neither type of defect.
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