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1. What is a polygon? What is the difference between an equiangular polygon, an equilateral polygon, and a regular polygon? Provide an example of each.
2. We can use the Pythagorean Theorem to solve problems that involve right triangles. Provide an example of a day-to-day situation that involves right triangles and the use of the theorem.
3. A drug manufacturing company wants to manufacture a capsule that contains a spherical pill inside. The diameter of the pill is 4mm and the capsule is cylindrical, with hemispheres on either end. The length of the capsule between the two hemispheres is 10mm. Describe how we could find the exact volume the capsule will hold, excluding the volume of the pill. What is the value that you get from your calculation? Why is it important for us to be able to determine the exact volume of that capsule?
Find the probability
Suppose that N and M are two normal subgroups of G and that N intersection M = (e). Show that for any n belongs to N, m belongs to M, nm = mn.
A fast food outlet has an average of 8 cars at the drivethrough during "lunch rush" 11am-1pm. On average, 2 cars per min. arrive at the resaurant parking lot, and consider the drivethrough
Use a triple integral to find the volume of the given solids. The tetrahedron bounded by the coordinate planes and the plane
Let F be a finite field. Prove that F[x] contains infinitely many primes. (note that over an infinite field the polynomials of degree 1 are an infinite set of primes in the ring of polynomials).
Show that the real part of the function z^(1/2) is always positive. Suppose f: G --> C ( C complex plane) is analytic and that G is connected. Show that if f(z) is real for all z in G, then f is a constant.
Prove that there is a bijection from the open interval (0, 1) to the half-open interval (0, 1].
A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 46.5ft^3. What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.
Applications of the law of Cosines - Evaluate the side of a regular dodecagon that is inscribed in a circle with radius 4 cm.
Solve the following linear, first-order differential equations and ensure that the initial conditions are satisfied. Show whether or not the steady-state solutions are stable.
Tom and Jim decided to play the following game for points. A single die is rolled. If it shows a non-prime number, Tom receives points equal to two times the number of dots showing
Binomial Probability: Survey of Drivers, The graph below shows the results of a survey of drivers who were asked to name the most annoying habit of other drivers. You randomly select six people who participate in the survey and ask each one of the..
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