24. The Law of Cosines (a) Two boats leave the same port at teh same time. One travels at a speed of 40 mi/h in the direction N 48° E and the other travels at a speed of 20 mi/h in the direction S 12°E. How far apart are the boats after 3/2 hours? (b) Two boats leave the same port at the same time. One travels at a speed of 10 mi/h in the direction S 12° W and the other travels at a speed of 20 mi/h in the direction S 72° W. How far apart are the boats after one hour? (c) A pilot flies in a straight path for 2 hours. She then makes a course correction, heading 45° to the right of her original course and flies 1 hour in the new direction. If she maintains a constant speed of 200 miles per hour, how far is she from her starting position? (d) Two straight roadsd diverge at an angle of 45°. Two cars leave the intersection at 4 pm, one traveling at 40 mi/h and the other at 60 mi/h. How far apart are the cars at 4:30pm? (e) Use either Law of Sines or Law of Cosines to determine possibilities for ZA, ZB, and ZC in the triangle AABC if b = (f) Triangle AABC has a = 7, 6 = 8 and c= 10. Solve for cos A. = 10/13, a = 10 and c= 30. 24.(a) 90mi (b) 10/3mi (c) 10/6 – 2/2mi (d) 10/13 – 6v2mi 7/13 (e) cos(A) 26 13 (f) cos(A) 32
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.
Part C
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