For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. 40. Find the length of the arc of a circle of radius 12 inches subtended by a central angle of " radians. 41. Find the length of the arc of a circle of radius 5.02 miles subtended by the central angle of ". 42. Find the length of the arc of a circle of diameter 14 meters subtended by the central angle of 5 43. Find the length of the arc of a circle of radius 10 centimeters subtended by the central angle of 50°. 44. Find the length of the arc of a circle of radius 5 inches subtended by the central angle of 220°. 45. Find the length of the arc of a cirdle of diameter 12 meters subtended by the central angle is 63°. 456 CHAPTER 5 TRIGONOMETRIC FUNCTIONS For the following exercises, use the given information to find the area of the sector. Round to four decimal places. 46. A sector of a circle has a central angle of 45° and a radius 6 cm. 47. A sector of a circle has a central angle of 30° and a radius of 20 cm. 48. A sector of a circle with diameter 10 feet and an angle of , radians. 49. A sector of a circle with radius of 0.7 inches and an angle of a radians. For the following exercises, find the angle between 0° and 360° that is coterminal to the given angle. 50. -40° 51. –110° 52. 700° 53. 1400° For the following exercises, find the angle between 0 and 27 in radians that is coterminal to the given angle. 10л 55. 13л 56. 6. 44л 57. 54.
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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