Determine the points in the interval (1, 6) at which the function has discontinuities. For each f(x) is discontinuous at x = point state the conditions in the continuity checklist that are violated. In order for f to be continuous at a, the following three conditions must hold. 1. f(a) is defined (a is in the domain of f). 2. lim f(x) exists. (Use a comma to separate answers as needed.) 3. lim f(x) = f(a) (the value of f equals the limit of f at a). 4- 2-

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: factors of 24 that add up to 10

A: factors of 24 that add up to 10

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: 4. Determine (16-912) dt c4

A: We will solve the problem.

Q: Simplify.2 Express 0(3n° – 2n² + n) n) as:

A: Given that O(3n^3 - 2n^2 + n)

Q: 7 items chosen 5 at a time

A:

Q: a = 4

A:

Q: 4 3/4 - 2 5/6

A: Given that the expression is

Q: 1 7. 27 2.

A:

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: 20/5+5+2*8

A: Consider the given expression

Q: factors of 20 that add up to 9

A:

Q: 6 2/5 ÷ 4

A: Given query is to solve the expression.

Q: 42. The term that does not contain x in the expansion of 8x +

A:

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

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

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: 1/5 + 1/10 + 1/15

A: Sum of numbers

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

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

Q: -3n in

A:

Q: 6 3/20 - 6 3/8

A:

Q: | (16 – 2*) dz =

A: To find : the value of ∫0216-x4dx   Using the formula ∫abxndx=1n+1bn+1-an+1

Q: 5. Find the coefficient of a¹¹b4 in the expansion of (a + b)¹5.

A:

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

A: We have

Q: 土4 7

A:

Q: 22 7/8 - 7=

A: Given,

Q: randomly drawing three green skittles in a row from a bag that contains eight green skittles out of…

A: Given that a bag contains 25 skittles in which eight are green. Three green skittles are drawn from…

Q: How many different ways could you choose any 4 gumballs from the 25 gumballs in the…

A: We can choose 4 gumballs from the 25 gumballs in 25C4 ways.

Q: Expand 2(c+ 3).

A: Distributive property states that if x,y and z are three real numbers then x(y+z)=xy+xz.

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.