Concept explainers
Propulsion In Exercises 71 and 72, use the weight of the rocket to answer each question. (Use 4000 miles as the radius of Earth and do not consider the effect of air resistance.)
How much work is required to propel the rocket an unlimited distance away from Earth’s surface?
How far has the rocket traveled when half of the total work has occurred?
5-mctric-ton rocket
Probability A nonnegative function f is called a probability density function if
The probability that x lies between a and b is given by
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Calculus (MindTap Course List)
- Average Traffic Spacing The headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per flour, the probability P that the headway is at least t seconds is given by P=0.87t. a. What is the limiting value of P? Explain what this means in practical terms. b. The headway h can be calculated as the quotient of the spacing f, in feet, which is the average distance between vehicles, and the average speed v, in feet per second, of traffic. Thus, the probability that spacing is at least f feet is the same as the probability that the headway is at least f/v seconds. Use function composition to find a formula for the probability Q that the spacing is at least f feet. Note: Your formula will involve both f and v. c. If the average speed is 88 feet per second 60 miles per hour, what is the probability that the spacing between two vehicles is at least 40 feet?arrow_forwardUsing the uniform probability density function shown in Figure, find the probability that the random variable X is between 1.0 and 1.9.arrow_forwardUsing the uniform probability density function:U f(x)=1-(b-a) for a<=x<=b 0 elsewhere The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:f(x) = 8 for 11.975 ≤ x ≤ 12.100andf(x) = 0 elsewhere a. What is the probability that a bottle will be filled with 12.02 or more ounces?b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?c. Quality control accepts production that is within .02 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard?arrow_forward
- The probability density of a random variable X is given in the figure below. From this density, the probability that X is at least 1.42 is:arrow_forwardThe probability density of a random variable X is given in the figure below. From this density, the probability that X is between 0.62 and 1.68 is:arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning