A cube is constructed from 4 white unit cubes and 4 blue unit cubes. How many different ways are there to construct the 2 x 2 x 2 cube using these smaller cubes? (Two constructions are considered the same if one can be rotated to match the other.) (A) 7 (B) 8 (C) 9 (D) 10 (E) 11

Q: value of ∑n=1∞(6an+9bn) if ∑n=1∞an=8 and ∑n=1∞bn=2.

A:

Q: 4. Determine the binomial coefficients in the 4th row of Pascal's triangle and use them to expand 3x…

A:

Q: 12 Find the term of (a – 3b)" that has b in it.

A:

Q: What is the 4th term of the expansion of (1 - 2x)" if the binomial coefficients are taken from the…

A: (1-2x)n binomial coefficients1 6 15 20 15 6 1

Q: 2. Find the missing numbers in the magic square below. 2 13 10 11 6. 12 15 1 4-

A: Consider the provided table,

Q: 5 21 197 Determine if w = -3 is in Nul A, where A =| 13 23 2 8 14

A: If the value of A . w=0 then w is in Nul A. Otherwise it is not.

Q: A grain of rice weighs 0.03 grams. Assume 1 grain of rice is placed on the first square, 2 grains…

A: given that

Q: 24. A cube is constructed from 4 white unit cubes and 4 blue unit cubes. How many different ways are…

A: We need to find the number of ways we constructed the 2 x 2 x 2  from 4 white and  4 blue unit cube.

Q: John wanted to take his nephew fishing on this man-made pond. If there are 16 whole squares that…

A: Option D is correct answer. 11 Detailed explanation given below.

Q: 2n+1 In Section 8, Example 2, if you follow the same procedure for the result is Зп-5 N = + ??? 9e 3…

A: Introduction: The theory of functions' limits is the foundation of calculus because these are the…

Q: how do you find "In (5/2) " on a calcualtor

A: To find ln(5/2)

Q: how many different bases can R^2 and R^3 have?

A: Explain about the count of number of bases of ℝ2 and ℝ3.

Q: How many four-digit combinations can be formed using digits 0 to 9?

A: Total number of digits n=10 Number of digits for combination r=4

Q: of the n robabilit

A:

Q: What is the conjugate of the partition n = (n – k)+k, where n 2 2 and 1<k< [n/2]?

A:

Q: For a set of three objects, find the number of different subsets of size 2. (Use row 3 of Pascal's…

A:

Q: What is the 4th term in the n = 8 row of Pascal's Triangle?

A:

Q: an аn аррох ne •mation Composite Simpson-

A: Given, we have to integrate fx=2xe1/2x on 0,2. So, f'x=212xe1/2x+e1/2xf'x=x+2e1/2x…

Q: Vn E N, nº – n is divisible by 6.

A:

Q: Suppose that in a popular restaurant, 4 people can sit around a lazy susan table (a round table with…

A: Given" Total persons=6  Number of seats on round table=4

Q: 2. Janyce conjectured that in the visual pattern below, there would be 3n - 1 small squares in the…

A:

Q: ( 4 25 77 ) ind the cholesky factorization A=GG¹

A: Matrix is positive definite. So cholesky factorisation is possible.

Q: Amani is trying to find the value of the 4th coefficient in the 10th row of Pascal's Triangle. Which…

A: Amani is trying to find the value of the 4th coefficient in the 10th row of pascal's Triangle. The…

Q: The sum of the nth row of Pascal's triangle equals 2". O True O False

A: Given that the nth row of Pascal's triangle equal to 2n

Q: 5. Given a real number x and a positive integer k, how many multiplications are used to find kx by…

A: Given,A real number x and positive integer kTo find: Total number of multiplications used with the…

Q: Find a formula for the general term a, {5, 8, 11, 14, 17, .} 5n + 3 On+3 O 3n + 2 O 2n + 3

A: We can answer the question as below

Q: What is the row of Pascal's triangle containing the binomial coefficients (), 0 < k < 9?

A: The first row of pascal triangle contains only one element i.e. 1. In second row, there are two…

Q: A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in.…

A: Solution Given That, A box with a square base and no top is to be made from a square piece of…

Q: How many ways can you reflect the following figures onto itself? a. Regular heptagon (7 sides) b.…

A: Regular Heptagon (7 sides): 7   Regular Octagon (8 sides): 8

Q: A box with a square base and no top is to be made from a square piece of cardboard by cutting 2 in.…

A: Let consider that x be the length of one side of the cardboard When 2 inches are removed from each…

Q: Write down the 7th row of Pascal's Triangle.

A: We have to find the 7th row of Pascal's Triangle

Q: Given an n x n grid, where n is always a power of two. Prove that for such a grid you can always…

A:

Q: Three cubes of metal whose edges are 3, 4 and 5 cm respectively, are melted without any loss of…

A: i) The volume of the cube of edge 3 cm is 33 cm3. i.e. 27 cm3. The volume of the cube of edge 4 cm…

Q: 22= 6898 65 %3D 1+/0013 Is +zd

A:

Q: 121. If B1, B2, and B3 are bases for R2, and if 4 2 6. | PB1-B2 = 3 and PB-B3 = 2 2 3 what is PB3-B?

A: Let us consider basis: B1={e1,e2}B2={v1,v2} Transition matrix from B1 to B2 v1=ae1+be2v2=ce1+de2…

Q: 1. Show that b, = (n!)'/n > 20.

A: Consider n!1n=an1n.

Q: (a) A team of 5 debaters of IUB is to be chosen from a section where we have 6 male and 4 female…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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

A:

Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 7 in.…

A: Given: A box with a square base and no top is to be made from a square piece of cardboard by cutting…

Q: 2. Nhat is the value of n for the row of Pascal's Triangle that is: 4 1 6 4 1? correct value of n)…

A: Follow the procedure given below.

Q: If A is 2 x 8, B is 5 x 2 and C is 8 x 5 then: a) BA has dimension b) CB has dimension c) AC has…

A:

Q: nd [Po90].

A: answer is in next step

Q: 10. If you spin the spinner 70 times, how many times would you expect the spinner to land on a…

A: Here total section of spines are 5 in which we want to find spinner to which land on section with 2.

Q: Is it true that for any odd n the number 2" +1 is divisible by 3? Prove your answer.

A: We prove this by using PMI(Principle of Mathematical induction)

Q: Prime divisors of two numbers a and b are 2,3 and 5 and product of these numbers a and b is 5400.…

A: The prime factors of the two numbers are 2, 3, and 5 and the product of these two numbers is 5400.

Q: A person is holding two drillbits one is7/16 and the other is 25/64, and wants to first drill a hole…

A: We have to make 7/16 to 64ths    To get 64 from 16 we will multiply 16 by 4.