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- F(A,B,C, D,E) =E ml0,1;3,6,8,9,14,ky1319,25,2931) DE 61 10 60 00 61 10/sites/Sem1 20202021 TK1114 Lab IT1IT2/Shared%20Documents/General/LabFinal(Taksir). E D Page view A Read aloud I Input Standard Input Output Standard Output Topic Medium Problem Marks 6 Problem Description The dot product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. The dot product of two vectors a = [a , a2, ..., an ] and b = [bi , b2, ..., bn ] is defined as: a.b = aibı + azb2 +...+ anbn where E denotes summation and n is the dimension of the vector space. For instance, in three- dimensional space, the dot product of vectors [1, 3, -5] and [4, -2,-1] is: [1,3, -5] [4,-2,-1] = (1 x 4) + (3 x -2) + (-5 x -1) = 4 – 6+ 5 = 3 Write a program to find the dot product of the given vectors. Input First line of input is an integer N (1Python question Application: Big-O Notation (Q8-11) For each of the time complexities in this segment give the tightest bound in terms of a simple polylogarithmic function using big-O notation. Note: use the ‘^’ symbol to indicate exponents, i.e., write O(n^2) for O(n2). Question 8 (Big-O Notation 1) T(n) = n2+ log n + n Question 9 (Big-O Notation 2) T(n) = n/3 + 4 log n + 2n log(n) Question 10 (Big-O Notation 3) T(n) = 7n5 + 2n Question 11 (Big-O Notation 4) T(n) = (n%5) + 12,00012 - fx =sort(StudentList!A2:F38,2, true) A C 1 Student ID Surname Forename 10009lAkins Lewis 10026 Allen Mary Explain the formula highlighted above and each of the parts in the formular. In other words, briefly describe in your own words what it does and what the result is. For this question, describe the following parameters in the formula above: - StudentList!A2:F38 is the range of cells (A2:F38) pulled from the sheet labeled Studentlist! - ,2 is - ,true isJupyter Notebook Fixed Income - Certicificate of Deposit (CD) - Compound Interest Schedule An interest-at-maturity CD earns interest at a compounding frequency, and pays principal plus all earned interest at maturity. Write a function, called CompoundInterestSchedule, that creates and returns a pandas DataFrame, where each row has: time (in years, an integer starting at 1), starting balance, interest earned, and ending balance, for an investment earning compoundedinterest. Use a for(or while) loop to create this table. The equation for theith year's ending balance is given by: Ei =Bi (1+r/f)f where: Ei is year i's ending balance Bi is year i's beginning balance (note: B1 is the amount of the initial investment (principal) r is the annual rate of interest (in decimal, e.g., 5% is .05) f is the number of times the interest rate compounds (times per year) The interest earned for a given year is Ei - Bi Note the term of the investment (in years) is not in the above equation; it is used…4. Langauge concatentation (a) Let L = {\, a}. Characterize L20. (b) Let L = D* · {aa, bb} · E*. Characterize L. (c) Compute L1 L3 and L2L3 where L1 = {}, L2 = {X}, and L3 = {b}.31. Let f(x) = [x2/3]. Find f(S) if a) S = {-2, –1, 0, 1, 2, 3}.Q2) Simplify the following function for F using a K-map. F(A,B,C,D) = E m(0, 2, 8, 10, 12, 14)c++ Calculate the number of sequences with K elements that meet the following criteria: Each element is a positive integer ranging from L to R inclusive. All elements' bitwise XOR is ranging from A to B inclusive. Since the number of sequences matching the preceding constraints can be fairly big, compute it with modulo 998,244,353. Input Format Each test case's first and only line contains the five space-separated integers L, R, A, B, and K. Constraints 0≤LR 2^60 0≤AB ≤ 2^60 1K50 Output Format For each test case, output a single integer value denoting the number of sequences K modulo 998,244,353. Sample Input: 26 54 18 34 1 Sample Output: 9 Explanation: The number of sequences is given by 9.SEE MORE QUESTIONS