5. Let S be a nonempty subset of R that is bounded above, with upper bound b. Prove that b = sup(S) if the following condition holds : for every e > 0 there is IE S such that b - e

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: 2/18 – 12/32 + 3V50

A: The solution is given below in the next step:

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: b. N(0)

A: Given,  r→t=sint, t, cost                   ...1

Q: 2/5+4/8

A: We have to find the sum

Q: a3-16a

A: a³−16a ⇒a(a²−16) ⇒a(a² −4²) ⇒a(a+4)(a−4)

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: 1. O O O O lim (In(x))* ? 5.

A: Consider the given expression. y=limx→0+lnxxx Take ln on both sides of the equation.…

Q: 4 3/4 - 2 5/6

A: Given that the expression is

Q: expand (a-b)7

A: The solution is given in the next step.

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: 2

A: The Laplace inverse can be found by splitting the expression into three parts as it have power of 3…

Q: 20/5+5+2*8

A: Consider the given expression

Q: Randomly drawing and immediately three red M&Ms in a row from a bag that contains 10 red M&Ms out of…

A: Given: 30 total M&Ms in that 10 red M&Ms.

Q: coefficient of variaton for given populaion   5,8,9,11,15,16,17,19

A:

Q: 1/4 +5/4

A: Solution: The objective is to find the value of the given expression

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: 1) (8s° - 9s) - (3s° + 4)

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

Q: 10. 15gr, 20s

A: Given

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: | (16 – 2*) dz =

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

Q: (1– 3csc(

A:

Q: 1 3 8.

A:

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

A:

Q: Find A.

A: Given

Q: 4) Using Rational Root Theorem and Descartes' Rule of signs. Find all roots of f(x)= x° + 8. What…

A:

Q: 2/5 +7/12

A: Please see the answer below.

Q: 3 3/4 + 2 7/28

A:

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

A:

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.

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.