Use the summation properties and rules to evaluate each series. n(n+1) Summation Rules: Σ=1 1 = n; Σ ²₁ i = 2 20 Find the sum: Σ²0₁ (4i² − 7i + 9) n ; Σi=1 i² = n(n+1)(2n+1) 6

Q: Simplify $536 оооо 4

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A: Given that Pizza parlor offers mushrooms, onions, and sausage as toppings for the plain cheese base.

Q: A certain hospital has 415 patients; 76 have high blood pressure only, 123 have heart problems only,…

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Q: From a list of 49 captains, 4 are to be promoted to major. In how many ways can this be done?

A: GivenNo.of captains=49No.of captains promoted as major =4

Q: Evaluate: 40!/4!38!.

A: To evaluate 40!4! 38!. By the definition of factorial,  n!=n ×(n-1)×(n-2)×...×3×2×1 That is  40! =…

Q: There are 10 students in a class. In how many ways can an instructor give at most three students a…

A: n = 10 Let x represent the number of students given grade A.   The number of ways a student can be…

Q: n a survey of 42 people, 16 liked country music, five people liked country and rap, 17 people liked…

A: Given that there are total 42 people, in which people who liked country music is 16, total number of…

Q: A license plate consists of 2 letters followed by 4 numbers, and to avoid confusion, the numbers 1…

A: GivenNo.of letters from A-Z =26No.of numbers from 1-0 excluding 1 and 0 = 8

Q: Prove: The sum of an odd number of odd numbers must be odd.

A: Let us prove this by induction, that if n is odd and a1,a2,. . .. .an are odd, then ∑i=1nai is odd.…

Q: In how many ways can six books be lined up along a shelf?

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Q: In how many ways the letters of the word “ROLLER” can be arranged?

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Q: In a survey of 426 people, a pet food manufacturer found that 92 owned a dog but not a cat, 103…

A: Determine how many owned both a cat and dog. From the information, given that   Number of people…

Q: In you own words, describe the difference between a permutation and a combination.

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Q: From a list of 39 captains, 8 are to be promoted to major. In how many ways can this be done?

A: We need to find the value by combination rule

Q: If 4 coins are tossed, in how many ways can they fall?

A: Each coin has two possible outcomes - heads or tails.    H = Heads, T = Tails Each of the 4 tosses…

Q: There are two copies each of 4 different books. In how many ways can they be arranged on a shelf?

A: GivenTwo copies each of 4 different booksTotal no.of books=2×4=8

Q: 14! divided by (14-6)!

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Q: How many ways are there to deal a hand of 4 cards if you dont care about the order of cards in your…

A: In a standard deck of cards, there are total 52 cards.

Q: The Reverend minister of a church always insist that every member shake hands with every other…

A: Given: Number of person is, n=90. Number of times required handshake is 1 time. The objective is…

Q: Determine 0!, 1!, 3!, and 4!.

A: Here, the values of 0!, 1!, 3! and 4! are required to be computed.

Q: What is the largest sum of money-all in coins, with no silver dollars-that I could have in my pocket…

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Q: There are 10 students in a class. In how many ways can an instructor give at least one student a…

A: There are 10 students So sample size, n= 10 And we've to find ways for at least 1 student. So r= 1

Q: What is the sum of number 10 to 40?

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Q: Determine 0!, 1!, 3!, and 4!.

A: Factorial Rule:The total number of ways n different objects can be arranged where order of the…

Q: state

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Q: Evaluate: 12!/8!

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Q: In a survey of 426 people, a pet food manufacturer found that 143 owned a dog but not a cat, 59…

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Q: If 10 people come from different places and shake hands in how many different way could this be done

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Q: umand

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Q: What’s the indicated value of 20!?

A: 20! =?

Q: If the U.S. Economy grew by 4% for three consecutive years, the economy would have grown by 12% over…

A: Given the U.S. Economy grew by 4% for three consecutive years the economy would have grown by 12%…