Concept explainers
Areas of Curved Regions the Monte Carlo method can be used to estimate the area under the graph of a function. The figure below shows the region under the graph of
Modify the program from Problem 5 to carry out this Monte Carlo simulation and
mate the required area.
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Chapter 9 Solutions
College Algebra
- Advertising The effectiveness of a television commercial depends on many times a viewer watches it. After some experiments an advertising agency found that if the effectiveness E is measured on a scale of 0 to 10, then E(n)=23n190n2 where n is the number of tines a viewer watches a given commercial. Fer a commercial to have maximum effectiveness, how many times should a viewer watch it?arrow_forwardCounting when Order Does Not Matter This is a continuation of Exercise 15. In many situations, the number of possibilities is not affected by order. For example, if a group of 4 people is selected from a group of 20 to go on a trip, then the order of selection does not matter. In general, the number C of ways to select a group of K things from a group of n things is given by C=n!k!(nk) if k is not greater than n. How many different groups of 4 people could be selected from a group of 20 to go on a trip? How many groups of 16 could be selected from a group of 20? Your answers in parts a and b should have been the same. Explain why this is true. What group size chosen from among 20 people will result in the largest number of possibilities? How many possibilities are there for this group size?arrow_forwardHarvard Step Test The Harvard Step Test was developed4 in 1943 as physical fitness test, and modifications of it remain in use today. The candidate steps up and down on a bench 20 inches high 30 times per minute for 5 minutes. The pulse is counted three separate times for 30 seconds each: at 1 minute, 2 minutes, and 3 minutes after the exercise is completed. If P is the sum of the three pulse counts, then the physical efficiency index E is calculated using E=15,000P. The following table shows how to interpret the results of the test. Efficiency Index Interpretation Below 55 Poor condition 55 to 64 Low average 65 to 79 High average 80 to 89 Good 90 & above Excellent a. Does the physical efficiency index increase or decrease with increasing values of P? Explain in practical terms what this means. b. Express using functional notation the physical efficiency index of someone whose total pulse count is 200, and then calculate that value. c. What is the physical condition of someone whose total pulse cont is 200? d. What pulse counts will result in an excellent rating?arrow_forward
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