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Concept explainers
Losses After Deductible A manufacturer’s annual losses follow a distribution with density function
To cover its losses, the manufacturer purchases an insurance policy with an annual deductible of 2. What is the mean of the manufacturer’s annual losses not paid by the insurance policy? Choose one of the following. (Hint: The loss not paid by the insurance policy will equal the actual loss if the actual loss is less than the deductible. Otherwise it will equal the deductible.) Source: Society of Actuaries.
(a) 0.84 (b) 0.88 (c) 0.93 (d) 0.95 (e) 1.00
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Chapter 18 Solutions
Finite Mathematics and Calculus with Applications
- aThe average rate of change of a function f between x=a and x=b is the slope of the ___________ line between (a,f(a)) and (b,f(b)).arrow_forwardFind the average rate of change for each function over the given interval. y=1x1 between x=2 and x=0arrow_forwardUse the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.arrow_forward
- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forwardVelocity A car is moving along a straight test track. The position in feet of the car, s(t), at various times t is measured, with the following results. Find and interpret the average velocities for the following changes in t. a. 0to2seconds b. 2to4seconds c. 4to6seconds d. 6to8seconds e. Estimate the instatneous velocity at 4 seconds. i. by finding the average velocity between 2 and 6 seconds, and ii. by averageing the answers for the average velocity in the two seconds before and the two seconds after that is, the answers to parts b and c. f. Estimate the instantaneous velocity at 6 seconds using the two methods in part e. g. Notice in parts e and f that your two answers are the same. Discuss whether this will always be the case, and why or why not.arrow_forward
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