MN | QP and MQ || NP MQ 32.Given: TH Prove: = NP

Q: How would you do proof by cases for the following?   3|x^3 - x

A: We have to prove

Q: How might you tell if a number is even or odd in bases two, three, four, five, six, seven, eight,…

A: Given data:- The given numbers are 2, 3, 4, 5, 6, 7, 8, 9, 10 Explain the generalize to bases of n.

Q: In the expression (x+y)', the exponent represents repeated multiplication, so the expression may be…

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Q: We need to find all the whole numbers that have remainder 1 upon division by 4 and write our answer…

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Q: While this problem can easily be done with a calculator, illustrate how a person could solve this…

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Q: specfically though, tell me what i'd put in EACH specfiic box.

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Q: Pascal's Triangle 1 1 2 [ 3 ] 1 6 I4I1 15 I 10 I 10 I 5[1 I 6 I 15 I 20 I 15I 6I 1 [7 [21 [35[ 35 I…

A: Answer

Q: If you know that a term in Pascal’s Triangle can be represented by 20C15, what row # and position is…

A: To find- If you know that a term in Pascal’s Triangle can be represented by C1520, what row number…

Q: 5. Add. 644 seven + 326seven 1303 The sum is 1303 seven (Simplify your answer.)

A:

Q: Find the eighth row in Pascal's triangle. List the entries of the eighth row in Pascal's triangle in…

A: Solution-: We find the 8th row of pascal's triangle=?

Q: The nth row of Pascal's triangle lists the coefficients of (x +y)^.

A: Here draw pascal triangle for some 1 to 4 rows and conclude for nth row

Q: you’re thinking of a number 1-50 and i have to guess what it is. i asked these questions in this…

A: Given: A numbers between 1-50. To find: Find a number greater than 25, divisible by 2, 3 and 5 and…

Q: In how many ways can a person walk 5 blocks north and 4 blocks west, if the streets are arranged in…

A: A person can walk 5 blocks north and 4 blocks west, if the streets are arranged in a standard…

Q: Find the value of the following: 9!9!/10!6! If your answer is not an integer,  write it as an…

A: Factorial is obtained by multiplying that number to every other number below it. For example,…

Q: This problem involves Pascal's Triangle. a. List the entries C(7, 0), C(7, 1), ..., C(7, 7) of the…

A: a) C(7,0)= 1 ; C(7,1)=7;C(7,2)=21 ;C(7,3)=35; C(7,4)=35; C(7,5)=21C(7,6)=7; C(7,7)=1 B) (a+b)7=…

Q: 13. Evaluate each of the following. (a) (4 + 12i) + (32 – 3i) (b) (4 + 12i) — (32 -3і) (c) (4 + 121)…

A: since you have posted multiple questions , so I'll solve first three for you , for rest question's…

Q: Each of the computations below was performed using a hand-held calculator. The answer that was…

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Q: What is the 4th term in the n = 8 row of Pascal's Triangle?

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Q: Click and drag the steps to show that at least three of any 25 days chosen must fall in the same…

A: In discrete mathematics, there are two basic methods for proving a statement is true: proof by…

Q: Need help with all, please and thank you.

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Q: How many three-letter "words" (some may be nonsense words) can be made from 4 letters "FGHI" if…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: Back Chapter 6 -Practice Problems Solution: B Problem 17: Find the number n of distinct permutations…

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Q: Problem 3. How many 7-digit numbers have no two adjacent digits equal.

A: To count the number of 7-digit numbers with no two adjacent digits equal, we can use the following…

Q: and COMI jc janod adject STROSEd HD mol Kane jo sangen and jeung and danig

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Q: Find all base 5 digits X such that (124X213)5 is divisible by (2)5 3. а. b. (4)5

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Q: 1. Svetlana has several homework problems that have strange answers for the P-value when she copied…

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Q: Solve this maths problem : A natural number less than 100 has remainder 2 when divided by 3,…

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Q: Write down the 7th row of Pascal's Triangle.

A: We have to find the 7th row of Pascal's Triangle

Q: Zxt3 12 the length of the If X=9 what is base?

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Q: use your own words to describe the steps of the method of mathematical induction

A: We have to write the steps for method of mathematical induction

Q: 1 1 49. x² + x 1 51. + 3 x2 + 7x + 12 1 1 53. x+3 x² - 9 2.

A: We are solving the first three questions and for the next questions post the question again and also…

Q: 1) Compute the following arithmetic opera explained engineering problem: a. (6j-7) / (3j-12) b.…

A: Note-Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Solve the following problems: (b) A states license plate has 7 characters. Each character can be a…

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Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.