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Suppose that a school has 20 classes: 16 with 25 students in each, three with 100 students in each, and one with 300 students for a total of 1000 students
a) What is the average class size?
b) Select a student randomly out of the 1000 students. Let the random variable X equal the size of the class to which this student belongs and define the p.m.f. of X
c) Find the mean of X.
The average molecular velocity v (m/s) of a gas in a certain container is given by the formula below, where T is the temperature in kelvins. The temperature is related to the pressure (in atmospheres) by T = 400P. Find the indicated derivative. v=..
Hits on a personal web site occur quite infrequently. They occur randomly and independently with an average of five per week.
The group of even permutations of n symbols is denoted by A_n and is called the alternating group of degree n. Show that A_8 contains an element of order 15.
Assume that the average annual salary for a worker in the United States is $28,500 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,250. Find the following
A metal storage tank with a mximum volume of 1200 m^3 is to be constructed in the shape of a right circular sylinder surmounted by a hemisphere. What radial and height dimensions will require the least amount of material?
A wooden artifact from an ancient tomb contains 55% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number.)
A motorboat travels 469km in 7 hours going upstream. It travels 493km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Does every graph have a spanning tree? If not, then can you tell from the number of nodes and the number of edges a graph has whether it has a spanning tree, or do you need more information?
The triangle (15,34, 35; 252) is the smallest acute Heron triangle indecomposable into two Pythagorean triangles. Realize it as a lattice triangle, with one vertex at the origin.
Each tire on an automobile has a radius of 1.25 feet. How many revolutions per minute does a tire make when the automobile is traveling at a speed of 88 feet per second?
Find the area of the shaded region. The hexagon is regular. Round to the nearest hundredth.
A cylinder is to be constructed so that it will have a minimum surface area while holding 128 pi cubic feet of gasoline. Determine the necessary dimmensions. Be sure to verify your answers indeed guarantee that a minimization has been accomplished..
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