math 10 2023.pptx in statistics and probability information
- 1. math
- 2. Search-for-a-pattern 1. 25, 24, 22, 19, 15, ____ 2. 3, 5, 8, 13, 21, ____ 3. 1, 3, 6, 10, 15, ____ 4. 4, 5, 8, 17, 44, ____ 5. 9, 16, 25, 36, ____ 6. 21, 22, 43, 67, ____ 7. 16, 8, 4, 2, 1, ____ 8. 13, 25, 47, 69, ____ 9. 2, 3, 5, 7, 11, ____ 10. 1/2, 3/5, 5/8, 7/11, ____
- 3. SEQUENCE A succession of numbers in a specific order.
- 4. FINITE SEQUENCE A sequence with a definite number of terms.
- 5. INFINITE SEQUENCE A sequence with no definite number of terms.
- 7. INFINITE SEQUENCE A sequence with no definite number of terms.
- 8. Arithmetic Sequences • Is a sequence in which the difference between any two consecutive terms is the same. • The constant difference is called the common difference.
- 10. Example • What is the next three terms of the sequence 7, 5, 3, 1, -1, …
- 11. Example • Find the 12th term of the arithmetic sequence 3, 5, 7, 9, …
- 12. Example • Find the 7th term of an arithmetic sequence if the third term is 5 and the fifth term 11.
- 13. Arithmetic Means • The terms of an arithmetic sequence that are between two given term.
- 14. Example • Insert three arithmetic means between 17 and 1.
- 15. Example • An object is falling from the rest travels 16 ft. during the first second, 48 ft. during the 2nd second, 80 ft. during the third second, and so on. How far does the object fall a. during the 7th second, b. after 7 seconds
- 16. Example • If form an arithmetic sequence, find x and the 16th term.
- 17. Solve each problem 1. Find the 23rd term of the sequence 5.7, 3.6, 1.5, … 2. If the 3rd term of an arithmetic sequence is 13 and the 9th term is 37, what is the common difference? 3. If form an arithmetic sequence, find x and 5th term.
- 18. Solve each problem 4. Find the 10th term of the sequence -37, - 34, -31,… 5. Find the value of x, if
- 19. Sample (5, 3), (3, 3)
- 20. Midpoint Formula • The and are any of the two points in a coordinate plane, then the midpoint M of has coordinates
- 21. example Find the coordinates of the midpoint M of the segments whose endpoints are: 1. (-7, 6), (-5, -1) 2. (1, 0), (5, 2) 3. (-5, -4), (1, -1)
- 22. example 1. The vertices of MLQ are M(5, 1), L(-3, 2), and Q(-4, -7). Find the length of the median to .
- 23. Exercise A. Give the midpoint of the given segment joining the given pairs of the points. 1. (4, 0), (8, 0) 2. (2, -1), (6, 3) 3. (4, 5), (2, 8)
- 24. Exercise B. Give the midpoint of the given segment joining the given pairs of the points. 1. Find the length of the median to
- 26. What is probability? Probability is the underlying concepts and skills on which important methods of inferential statistics are founded.
- 27. Do you know how to count? • Table of values • Tree Diagram • Systematic listing
- 28. Table of values One technique in counting is to tabulate values.
- 29. Example Find the number of outcomes in tossing a coin twice. Solution. Head (H) Tail (T) Head (H) HH HT Tail (T) TH TT
- 30. Tree Diagram One technique in counting is drawing a tree that show all possible outcomes.
- 31. Systematic listing another technique in counting that involves coming up with an actual list of all possible outcomes.
- 32. Example How many three digits even number can be formed using 0, 1, 2, 3? Solution. 100, 102, 110, 112, 120, 122, 130, 132, 200, 202, 210, 212, 220, 222, 230, 232, 300, 302, 310, 312, 320, 322, 330, 332.
- 33. Fundamental Principle of counting if one event can occur in m ways, and another event can occur in n ways, then these events can occur in mn ways, provided that the two events are independent events.
- 34. Example Two independent events are formed from the digits 0,1,2,3,4,5,6,7,8,9. a. How many two digits numbers can be formed ? b. How many of these are even? c. How many of these are odd? d. How many of these are divisible by 3?
- 35. Example A cell phone service provider offers two free smart phone app. If there are 24 different apps to choose from, how many different combination of the two apps a client have?
- 36. Exercise Give the number of possible outcomes. 1. Tossing a coin three times 2. Rolling a yellow die and a red die 3. Choosing a book to read from 7 fiction and 9 non-fiction 4. The number of ways a student can wear his 6 shirts, 4 pants, and 2 shoes.
- 37. Exercise
- 38. Exercise 1. How many 2-digit numbers can be formed from the four integers 1,2,3, and 4 if repetition is allowed? 2. If a coin is flipped 4 times, how many different sequences of heads and tails are possible?
- 39. Exercise 3. How many ways can a postman posts 3 letters in 5 letter boxes? 4. A mall has five gates. How many ways can one enter and exit the mall?
- 40. Quiz Time! 1. If two dice are rolled, how many outcomes are there? How many of these have a dot sum greater than 8? Less than 10? 2. How many three digit numbers less than 150 can be formed from the digits 0,3,4,6 and 9?
- 41. Permutation Permutation refers to an arrangement of objects in a definitive order. Changing the order of the objects being arranged creates a new permutation.
- 42. Permutation The number of permutation of n object taken r at a time is
- 43. Example Evaluate
- 44. Task Create a presentation showing the computation of probability of winning in gambling games such as lotto, roulette, etc.
- 45. Example Eight students are lined up to be seated. a. how many ways can 4 of them be seated in a row of 4 chairs? b. How many ways can all of them be seated in a row of 8 chairs?
- 46. Permutation with repetition The number of permutation of n object of which p are alike, q are alike, r are alike, and so on is
- 47. Example How many different ways can a letter of the following words be arranged? a. QUEZON b. PANGASINAN c. MANILA d. TAGAYTAY
- 48. Circular Permutation The number of permutation of n objects are arranged in a circle is
- 49. Example How many ways can the letter A, B, C be arranged around a circle?
- 50. Part 2 show your solution G. Solve the following:
- 51. Part 2 show your solution H. A contains 5 green, 7 yellow and 10 orange ping pong balls. How many ways can 5 be selected, if
- 52. Part 2 show your solution I. List all the possible outcome of tossing a coin 5 times.
- 53. The slope of a line A slope m of a nonvertical line that passes through and is
- 54. The slope of a line In using the definition, it is important to note that if the points are interchanged, the slope is not changed since
- 55. Find the slope of the line that passes through each of the following pairs. a. and b. and c. and d. and
- 56. Line and its slope The standard form of a linear equation is
- 57. Example Transform the given equation to standard form.
- 58. Line and its slope The slope intercept form of a linear equation is
- 59. Example Transform the given equation to slope form
- 60. Events and their operation • Sample space • Outcome • Event • Mutually exclusive • Union of sets • Intersection of sets
- 61. Sample space A sample space is the set of all possible outcomes of an experiment.
- 62. Outcome Possible result of an experiment or trial.
- 63. Event An event is an outcome or defined collection of outcome.
- 64. Mutually exclusive Two events A and B are mutually exclusive or disjoint, if they have no common outcome.
- 65. Mutually exclusive Two events A and B are mutually exclusive or disjoint, if they have no common outcome.
- 66. Union of sets The union of sets A and B is the set of all elements belonging to A to B or to both.
- 67. Cardinality of sets The union of sets A and B is the set of all elements belonging to A to B or to both.