From a point on the circumference of a circle of radius a, achord is drawn in a random direction (all directions are equally likely).25.4aand that theShow that the expected value of the length of the chord isvariance of the length is 2a (1 – 8/n). Also show that the chance is thatthe length of the chord will exceed the length of the side of an equilateraltriangle inscribed in the circle. /

Answered: Image /qna-images/answer/c9cdfe63-825b-4836-bd18-2013cda5d3bb.jpg

Answered: 25. From a point on the circumference…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.CT: Test

Problem 14CT

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Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.
5.11. A point is chosen at random on a line segment of length Interpret thisstatement, and find the probability that the ratio of the shorter to the longersegment is less than 1/4.
A surface has infinite parallel lines at distance d from adjacent lines. We have a needle of length I which we throw randomly on the surface. What is the probability that the needle intersects a line? Assume l < d.
A gravity retaining wall may fail either by sliding (A) or overturning (B) or both (Figure 1). Assume:i. Probability of failure by sliding is twice as likely as that by overturning; that is, P(A) = 2P(B)ii. Probability that thee wall also fails by sliding, given that it has failed by overturning P(A|B) = 0.8.iii. Probability of failure of wall = 10-3a. Determine the probability that sliding will occur.b. If the wall fails, what is the probability that only sliding has occurred?
Suppose PEL(V) and P2 = P. Prove that V = null(P) ☺ range(P)
A point is chosen from an equilateral triangle whose edge length is ? = 6 ??. What is the probability that the distance of the chosen point from the centroid of the triangle is less than ? = √6?(In geometry, an equilateral triangle is a triangle in which all three sides are equal. The centroid, of a triangle happens to be the mean of the three vertices, but the definition is the center of mass of the whole triangle.)
Background: A dog named Zip is often tied to a zipline. Fig 1A: Top view of yard. When tied, Zip travels in such a way that the hook on the line slides back and forth as he moves. A coordinate system is defined as described in the picture to the right. Figure 1A shows a top view and Figure 1B shows a Fig 1B: Sideview of zipline. sideview. A measurement system is connected to the hook. It periodically records the position on the line during the time Zip is connected to it. After 50,000 x=0 location of hook observations (electronically recorded) a continuous model for where the hook is located was developed by - 10m < x < 10m a team of engineers. They came up with the model that p(x) = {A + 10) otherwise 1) Sketch a graph for p(x). Do you need to fill in this form? You can use Fill & Sign to complete form yourself or get others to sign. 2) What is the average position of the hook on the zipline?
Since the length of a downhill ski is related to the height of the individuals renting them, it is fair to assume X: the length (cm) of women's skis at rental outlets in Colorado is normally distributed. X ~ Normal (u 150, o = 10) = Use Rguroo to answer: a) The probability of women's ski lengths to be between 132 and 140 cm is P(132 154) = . Round answer to three decimal places. c) The ski length of is identified to be at the 75th percentile of all women's skis lengths at rental outlets. Round the answer to two decimal places.
Questions a-c are already completed just need d-f completed! thanks :)
kon, : 25.9. Mr. Y quite often flies from town A to town B. He can use the airport bus which costs he takes it, there is a 0·08 chance that he will miss the flight. A hotel limousine costs Rs. 27 with a 0-96 chance of being on time for the flight. For Rs. 50 he can use a taxi which will make 99 of 100 flights. If Mr. Y catches the plane on time, he will conclude a business transaction which will produce a profit of Rs. 1,000, otherwise he will lose it. Which mode of transportation should Mr. Y use ? Answer on Rs. 13 but the basis of EMV criterion.
Please solve asap. Easy problem. 1st exercise.
3:38 www-awu.aleks.com/alekscgi/x/Isl.exe/1. O REA. Evalu... Evaluate the expression when m = - 3. 2. m² + 6m +8

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