Suppose that {an} converges to a and lal < 1. Prove that {(an)"} converges to 0. (NOTE: You may not simply apply the Power Property for Limits. Why not? Also, the theorem proved in class that, if |c < 1, then lim c" 0, does not apply directly (though it may prove useful). Why not?) %3|

Q: How many even 3-digit numbers can be formed from the digits 1, 3, 4, 8, and 9 with no repetitions…

A: Out of the total 5 digits 1, 3, 4, 8 and 9 given, the even digits are 4 and 8. For the 3- digit…

Q: 4 2 G F -8 -4 -2 2 10 -2 -4 E 10 K 00

A: Formula for area is length multiply by breadth. Similarly for square its a^2 if side of square is…

Q: How many ordered triples of letters are there taken from the letters A, T, C, and G?

A: given letters: A,T,C and Gtotal number of letters = 4

Q: A = 6 -2 -2 10 -3 5 1 ---3-0 C=0-2 a = 1, b = [3 08]. -10 1 . B 5 2 11 9 4 4 7 0 0 11

A: We have to solve given Questions.

Q: Find L{1}ℒ{1}.

A:

Q: 4. Determine (16-912) dt c4

A: We will solve the problem.

Q: 6/4 - 2/4

A: Explanation and solutions is given below.....

Q: 7 items chosen 5 at a time

A:

Q: a = 4

A:

Q: 6. Determine the equation of the circle whose center is at (4, 5) and tangent to the circle whose…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4 3/4 - 2 5/6

A: Given that the expression is

Q: n?_4

A:

Q: expand (a-b)7

A: The solution is given in the next step.

Q: Prove that the number of partitions of n into at most k parts is equal to that of partitions of n +…

A: given , number of partitions of n into k parts  we have to prove that , partitions of number n + k…

Q: find  3/4 + 1/8

A:

Q: 16 2/5- 8 4/9

A:

Q: 3/8+5/24

A: The given expression is 3/8 + 5/24.Simplify the given expression as follows.

Q: ne binomial:

A:

Q: 6 2/5 ÷ 4

A: Given query is to solve the expression.

Q: -3 -10

A: The given equation is:  -3   2÷-10    7

Q: 5 7/12 + 1 3/4 + 4 1/2

A: Given that 5712+134+412Solution  :5712+134+412=57+39+24612

Q: 1) (8s° - 9s) - (3s° + 4)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: There are 1/8 blue balls, 1/4 green balls, 1/12 red balls and there are 26 white balls. How many…

A:

Q: 9 5/12 - 3 2/3 =

A: Case 1: Let the given number be in mixed fraction notation.

Q: 6 3/20 - 6 3/8

A:

Q: W 4. What is the value of the 4th term of the expansion (a + b)"? O a5 O 5a*b O 10a²63 10a b?

A:

Q: 7. Solve the auxiliary equation of repeated roots (4D - 4D3 - 23D2 + 12D + 36)y 0.

A:

Q: Compute the indicated product.   -1 3   9 2 0   3 9 3

A:

Q: 5 2/5+ n= 75/6

A: Given query is to find the value of n.

Q: Find A.

A: Given

Q: 4 1/2 +6 1/5=

A: We have

Q: 2/5 +7/12

A: Please see the answer below.

Q: (5/6)3

A: Cube means multiplying three times:   563=56×56×56=5×5×56×6×6=5363=125216

Q: 土4 7

A:

Q: 22 7/8 - 7=

A: Given,

Q: 1. Use expansion along the 3rd row -4 3 1 2 -1 1 7 5

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.