1.8(a) Convert the decimal number 7510 to binary by using the sum-of-power-of-2 method. Ans:

Q: Expand (7 – 3x)“ in ascending powers of x, up to and including the 4" term. Hence, approximate…

A: We know (n+1)! = (n+1) n! Crn = n!(n-r)! r!

Q: 6. The decimal expansion of 135/ 225432 will terminate after how many decimals?

A:

Q: Consider the sequence {ax}1 defined by a1 = 2, and ak = 3ax-1 for k 2 2. Compute a4.

A:

Q: Give a formula for the number of permutations of [n] with no cycles of length exactly 2. Your…

A: Formula for the number of permutations of [n] with no cycles of length exactly 2 is derived.

Q: Find 96307 7 (mod 739) using the techniques described in Example 8.4.4 and Example 8.4.5. First…

A: To find 96307mod739. It can be computed by evaluating the following,…

Q: The upper limit of the number of primes less than 23456 is O 2612 O 2331 O 5367 O 7136

A: Given number is 23456. We have to find number of primes less than 23456. formula for the number of…

Q: Consider the sequence {ax}, defined by а, 3D 1, ад — 1, and ak 3 а-1+ ak-2 for k > 3. Compute as.

A: We have given two terms of sequence {a_k}, a_1=1 and a_2=1 and then sequence {a_k} is defined by…

Q: 2. (- 5 i 3-2i,

A:

Q: The fraction can be represented by the repeating decimal 0. 142857. What is the 41st digit after the…

A:

Q: How

A: Here use combination

Q: b) How many bit (or binary) sequences are there of length six with a 1 as the first digit?

A: A bit string is list if 0s and 1s For each of our 6 bits we have 2 choices 0 and 1

Q: Every even integer greater than 2 is sum of two primes? Give your views on this?

A: We know that 2 is even prime. And all other primes are odd.

Q: You brush your teeth very, very carefully in the morning at 6am leaving only 1000 bacteria on your…

A: We will find a sequence for number of bacteria .

Q: Find the sum of the positive even integers up to and including 50.

A:

Q: Find the last 3 decimal digits of 712345 via a simplification which is aided by Fermat's Little…

A:

Q: Show the solution. 111101001 + 11100101 + 111111101 + 10111011 01011001110 + 01010111000 (Binary to…

A: we only solve one problem at time so please submit that here one by one.

Q: 10b) Determine the binary expansion of the decimal number 666. You must show your work step by step…

A: A binary number is a number expressed in the base-2 numeral system or binary numeral system, a…

Q: 11:45 Question 3 Find all three-digit numbers with different digits with the property that those…

A: There are no numbers on which such property works.

Q: 96, a0ose -bsine =0 a'simo +baose asimo-baose Then,

A:

Q: Apply Taylov's expansion and find The seyies for tenn at 4

A: Taylor's expansion of tan2x at π4 Now fx=∑n=0∞fnan!x-an fx≈Px=∑n=0∞fnan!x-an Now derivation of given…

Q: Compute the following. 5! 4!

A:

Q: 5 (9 9 () 2. Find a reduced residue system modulo 2", where m is a positive integer. in a reduced…

A: To find a reduced residue system modulo 2m, where m is a positive integer.

Q: Express the repeating decimal 1.2345345345 . . . as a  fraction.

A: we have to express the repeating decimal 1.2345345345 . . . as a  fraction.

Q: Prove that the nth Fibonacci number fn≤αn−1, where α is the golden ratio.

A:

Q: 5. A certain bacteria triples every 2 hours. If at 9:00 am there are initially 1000 bacteria, how…

A:

Q: Use the formula to compute In(1.11) correct to five decimal places. In(1 – x) = - x" n = 1 In(1.11)…

A:

Q: Solve for d, 19d ≡ 1 mod (37422000) using the "Extended Euclid's Algorithm"

A: The solution is given by using Extended Euclid's Algorithm as follows

Q: Estimate the absolute error in storing a quantity V = 804.03 on a computer using double precision…

A: Solution:- Relative error: Relative error = absolute error/ Real value for example: In a measurement…

Q: Find the first five terms of the séquence an= 1 as as express in Standard form

A: Given  an = 1+ 1/n  To find the first five terms

Q: Compute the following: N!(N-4)!

A: Note that n!=n×n-1×n-2×…×3×2×1. Consider the given expression N!N-4!. This can be written as…

Q: Consider all numbers between 20000 and 70000. Efficiently determine: A) How many of these numbers…

A: Part A - Let’s represent the number as ABCDE. You have to considere the special cases first, since…

Q: In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order…

A: Introduction: It is understood that a player wins the jackpot if they choose the 5 distinct number…

Q: 1. Find the binary expansion of (233)10-

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

Q: Find the sum of the first five natural even numbers using sigma notation.

A: We have to find sun of first 5 even natural numbers.

Q: to binary. II. Show that any weight not exceeding 2 - 1 may be measured using weights of 1, 2,…

A:

Q: Exercise 9: Prove by contradiction that 3 doesn't have a finite number of decimal places.

A:

Q: A.)Many printed airline tickets contain a 10-digit document number followed by a check digit. The…

A:

Q: 8. 17

A: Find UT

Q: Let φdenote the Euler phi-function. Answer a and b (a) If n = 2a3b, for natural numbers a, b, show…

A:

Q: A second-stage smog alert has been called in a certain area of Los Angeles County in which there are…

A: Introduction: Denote the random variable X as the number of firms violating at least one of the…

Q: Is there a formula or way to determine how many transpositions there are for a cycle of a given…

A: All cycles can be decomposed into a composition of two transpositions. In permutation, the number of…

Q: Find the number of words of 5 letters such that each can be formed with the letters of the word…

A: We need to find number of 5 letters that can be formed by given word without repetition.

Q: How many bit strings (sequences of 0's & 1's) have length 12 and contain: (a) exactly three 1's? (b)…

A: a) We have to pick 3 positions for three 1's. Then the positions of 0's will be fixed.  From 12…

Q: Use generating functions to determine the number of 9-digit sequences of the digits 1,2,3,4,5,and 6…

A: We need to find ,  number of 9-digit sequences of the digits 1,2,3,4,5,and 6 in which each even…

Q: 3- Convert binary number (28MA)10 to corresponding decimal number... 4- The number 0.0155625 is…

A: 3)Given:       2810   Decimal to binary conversion:       Divide 2810 successively by 2 until the…

Q: Find the first 4 terms of Toaylor Polyuocuial generated by fCx)= xlnx at a=2.

A: We find first four terms of Taylor polynomial generated by f(x)=xln(x) at a=2.

Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 8 in.…

A: Let x be the length of a side of the cardboard. Since we are making a square box, the dimensions of…