133 1.5 Applications and Modeling with Quadratic Equations 47.Height of a Projected Ball An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall, and the initial velocity of the ball is 30 ft per sec. The height s of the ball in feet is given by the equation sI2.7t2 +30t + 6.5, where t is the number of seconds after the ball was thrown. (a) After how many seconds is the ball 12 ft above the moon's surface? Round to the nearest hundredth. (b) How many seconds will it take for the ball to hit the moon's surface? Round to the nearest hundredth. 48. Concept Check The ball in Exercise 47 will never reach a height of 100 ft. How can this be determined algebraically? (Modeling) Solve each problem. See Example 4. 49. NFL Salary Cap In 1994, the National Football League introduced a salary cap that limits the amount of money spent on quadratic model players' salaries. The y 0.2313x2 + 2.600x +35.17 approximates this cap in millions of dollars for the years 1994-2009, where x = 0 represents 1994, x 1 represents 1995, and so on. (Source: www.businessinsider.com) (a) Approximate the NFL salary crp in 2007 to the nearest tenth of a million dcilars (b) According to the model, in what year did the salary cap reach 90 million dollars? 50. NFL Rookie Wage Scale Salaries, in millions of dollars, for rookies selected in the first round of the NFL 2014 draft can be approximated by the quadratic model y 0.0258.x2- 1.30x+23.3, where x represents draft pick order.Players selected earlier in the round have highe salariae th Ssanrie ar0dwensasn Sureds Surens alpsnu SOEI S tightly or app broken
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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