Suppose A = {2, 5, 7, 9, 13, 25, 26}. (a) Find n(A). n(A) =  (b) True or false: 7  A True False     (c) True or false: 2  A True False     (d) True or false: 12  A True False

Q: Q1) a) How many 3 digits passcodes are there if first digit must be a 1 or 2 ?   b) How many 3…

A: a). There are 10 digits (0,1,2,3,...,9)  in total. If the first digit is filled with 1 or 2, then…

Q: A carnival game is played by rolling a ball into a hole. Eight players are needed to play the game…

A: Combination only includes number of ways of selection whereas, permutation includes number of ways…

Q: Show that 8(-n--8()

A: By properties we know that,

Q: What is the probability that an 8-digit driver's license number chosen at random will not have 4 as…

A: Given Data: The number of digits in the license number is: n=8 The possible number of ways is,…

Q: -1<9+n<7

A: Given,           -1 &lt; 9 + n &lt; 7

Q: +6n +3 is Θ (n)

A: 1st expression is TRUE

Q: . Show that n! > 3ª for n> 7.

A:

Q: A.) During which month is Herb incur the most expenses? B.) During which month did Lis incur the…

A: Most expenses is the point on the graph, when it takes the peak value, whereas least expensive is…

Q: Show that 1/n - 1/(n+2)= 2/(n(n+2))

A:

Q: Show that (n + 1)!)" < 2! · 4! - (2n)!.

A: The objective is to prove the given statement using induction

Q: Evaluate O a. 3/4ln4 O b. 3/2ln2 O c. 2/3ln3 O d. 5/6ln6

A:

Q: A theater hall has n rows of seats. The first row has 25 seats, the second row has 33 seats, and the…

A:

Q: if 6(2n-8)=-84,then4n=

A: Given  62n−8=−84

Q: 6.) Derike the binomial idendity nent) (un-) C Hint: For mzz, c^)+2(^) +m?]

A: To derive the binomial identity22+42+62+.........+2n2=nn+14n-16

Q: n² < 2" for n = 4, 5, 6, ... (Hint: 2n + 1 < 2" for n= 3,4,5, ...)

A:

Q: 2. A cinema can accommodate 200 customers. Let Z denote the number of customers in the cinema. What…

A: If there are maximum 200 customers that can be accommodated in the cinema, then the possibilities of…

Q: n= 8 Using Simpsons Rule

A: Simpsons Rule: ∫abf(x) dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4f(xn-1)+f(xn).............(1) where,…

Q: 6. C, C, C,

A: GIVEN EVALUATE EACH 8C2.6C2.4C2

Q: Isit true that n? + 1 € N(n)?

A:

Q: ken two at a ken three at a

A: 1 2 3 4 5 6 j o y f u l The different arrangements formed from the 6 letters word = 6!

Q: Find the order of 2 2; in C

A: Order is 8

Q: se a university announced that it admitted 2500 students for the following sity has dorm room spots…

A: It is an important part of statistics. It is widely used.

Q: A baseball pitcher threw 3678  pitches during part of a recent season. Of these, 1681 were thrown…

A: From the given information,In a baseball,Total number of pitches (N) =3678Number of no strikes(X) =…

Q: Droof that n! %3D1 オ=O K!(n=k)!

A:

Q: n² < 2" for n = 4,5, 6, ... (Hint: 2n + 1 < 2" for n = 3,4, 5, ...)

A:

Q: q+12-2(q-22)>0

A:

Q: 8. Use the Boolean rules to simplify ¬((pVq) → (¬pVq)).

A: Formula: p → q≡ ¬p ∨ q The given Boolean expression is: ¬(p∨q)→(¬p∨q) Rewrite the expression using…

Q: 3. What is the quotient and what is

A:

Q: Show that (n + 1)! > 2"+3, for n > 5.

A:

Q: What is the coefficient of p5q5 in the expansion of (p+q)10?

A:

Q: (b) Give two different interpretations of the bino- mial coefficient (") for non-negative integers n…

A: First we will give two different interpretations of the binomial coefficient nk for non-negative…

Q: n=9, p=0.2x<3

A: Here we need to find P(X&lt;3).

Q: Show that √3 € Q [√6].

A: Let 3∈Q6 Then there exists rationals a,b such that 3=a+b6 Consider:…

Q: Use a combinatorial argument to show that n 1(n 3 |

A: The LHS of the expression is nn-2. This is the number of ways selecting n-2 objects from n objects.…

Q: Show that n! > 3ª for n > 7.

A: The given inequality is, n!&gt;3n We need to prove that, the inequality is true for n≥7 Firstly,…

Q: An employee of a car parts store was mistaken and saved the defective flashlights, along with the…

A: Probability quantifies the chances of happening an event. The probability values always lie in the…

Q: A recent study shows that 18% of adults in the US do not use the Internet. Suppose that 12 adults…

A: It is given that n =12 and p =0.18.

Q: 6. Ajeepney can accommodate 16 passengers. If X denotes the number of male passengers in the jeepney…

A: Given: The total number of passengers a jeepney can accommodate is n=16. Let X be a random variable…

Q: Show that 13 + 23 + · · · + n3 = (n(n + 1)/2)2.

A:

Q: 22 Evaluate. (n - 1)!, where n = 3 2 5 6

A: This can be solved as follows:

Q: R5) If nC5 = nC12 then n =_

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: Szdx is 2(1 – x²)7 +c is it: +c_ is it : V1-x a)True b)false

A: Use sin²x+cos²x=1  And integrating the function  We get the required result

Q: (c) Show that for 2" > 4n for n ≥ 5.

A:

Q: Q2:- A) How Many ways you can write 12 digits number from the digits 1,2,3,4,5,6,7,8,9,10,11,12 if…

A:

Q: 26. In how many ways can: a. five people be seated in a row? b. eight people line up for…

A: Given that  In how many ways can:   a. five people be seated in a row?   b. eight people line up for…

Q: Show that 2^n &gt;=1/8 for n&gt;= -3.

A:

Q: -3- -7= Using chips A. Using zeros B. Changing to addition

A: our objective is to evaluate.

Q: In a game of Texas Hold’em 2 cards are dealt to each player face down. 5 more cards are then played…

A: From a pack of 52 cards total 12 is chosen in C1252 ways to be distributed to the players and then 5…

Q: se mathematical induction to show    n ≥ 0, 7n - 1 is divisible by 6

A: Given: n≥0, 7n-1 To prove: 7n - 1 is divisible by 6

Q: Use a combinatorial argument to show that n 1 2 - 2 3 2 2

A: To use combinatorial argument to prove whether the given statement is correct or incorrect. The…