Problem 5. Give the definition of an abstract simplicial complex.

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 Evaluate -1 0 5 by: 3 - 2 expanding along the first row expanding along the second column A A 1.…

A:

Q: 1/3+2/9

A: Given 1/3 + 2/9

Q: b. N(0)

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

Q: Prove that X Pn dx %3D

A: Recurrence relation.  Partial fraction.

Q: a3-16a

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

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: (5) Find the greatest common divisor of a. 72 and 120 b. 224 and 430

A: GCD of two numbers.

Q: 5/14+1/6

A: 514+16=15+742

Q: 4 3/4 - 2 5/6

A: Given that the expression is

Q: n?_4

A:

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: 16 2/5- 8 4/9

A:

Q: 20/5+5+2*8

A: Consider the given expression

Q: Reduce the following to the lowest terms. Show how to calculate the greatest common divisor by the…

A: The given fraction number is,Here we can write,As we can see the number 4 can be canceled out.This…

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: factors of 20 that add up to 9

A:

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

A:

Q: Expand (a −b)4

A:

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

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

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: expansion of (1-2m)“

A:

Q: (2) 4 2. 2. 2/3

A:

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

A:

Q: 29 Using the combination formula expand (5+x)

A:

Q: 22 7/8 - 7=

A: Given,

Q: 3 3/4 + 2 7/28

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.