Advance Math question and answers for July 17, 2023
- Q If p,p+2 are twin primes, prove 4((p−1)!+1)+p≡0 modp(p+2)
- Q Convert the base-10 number to Two’s Complement. Show yourwork.(a) −12 (b) −32 (c) −57 (d) −112 (e) −24 (f) −85
- Q Use the Intermediate value theorem to find an interval of lengthone that contains a root of the equation. a) x^3=9 b) 3x^3+x^2=x+52. Still consider equations 1a and 1b A)How many...
- Q We will write Δ(m,n) for the set of order preserving functionswith source m and target n.Let f ∈ ∆(k, n), g ∈ ∆(m, n), and h ∈ ∆(n, p). Suppose...
- Q Consider all positive integers less than 100. Find the number ofintegers divisible by 3 or 5?Consider strings formed from the 26 English letters. How manystrings are there of length 5?How...
- Q 3. Let a and b be positive integers. Is gcd(5a + b,11a + 2b) = gcd(2a + b, 3a + 2b)?If yes provide a proof. If not, provide a counterexample.
- Q How to solve it by wolfram mathematica:The fraction 49/98 is a curious fraction, as an inexperiencedmathematician in attempting to simplify it may incorrectly believethat 49/98 = 4/8, which is correct,...
- Q A firm offers terms of 1.4/10, net 60.  a.What effective annual interest rate does the firm earn when acustomer does not take the discount? (Use 365 days a year.Do not round...
- Q Let v1 be an eigenvector of an n×n matrix A corresponding to λ1,and let v2, v3 be two linearly independent eigenvectors of Acorresponding to λ2, where λ1 is not equal...
- Q Fake news reporter Chocolate Medaughter has had anotherinteresting scoop to tell to the world. Suppose that the rate ofexposure of this new story to new people is proportional to thenumber...
- Q As the new owner of a supermarket, you have inherited a largeinventory of unsold imported Limburger cheese, and you would liketo set the price so that your revenue from selling...
- Q For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find thefollowing, and use it to graph the function.Find: a)(2pts) Domainb)(2pts) Interceptsc)(2pts) Symmetryd) (2pts) Asymptotese)(4pts) Intervals of Increase...
- Q 7. (10 pts.) Amelia visits several islands. The individuals oneach these islands are either truth-tellers or liars. Amelia isinterested in finding out whether everyone on a given island is atruth-teller,...
- Q Consider the following Markov chain with P{X0 = 2} = 0.6 andP{X0 = 4} = 0.4:1 2 3 4 5 61 0 0 0 0 1 02 .2 .05 0...
- Q Question 2: Pocket Politics (any resemblance to recent events ispurely coincidental) Long time ago, in a country far far away, aTotally Racist Unqualified Malicious President ruled the land withan iron...
- Q A fishing boat leaves a dock at 2:00pm and travels due east at aspeed of 20km/h. Another boat has been heading due north at 15 km/hand reaches the same dock...
- Q A bottle ofmilkmilkinitially has a temperature of7575degrees°F.It is left to cool in a refrigerator that has a temperatureof4545degrees°F.After 10 minutes the temperature of themilkmilkis5757degrees°F.a. Use​ Newton's Law of​ Cooling,Upper T...
- Q Let G be a group of order 42 = 2 * 3 * 7(a) Let P7 be a Sylow 7-subgroup of G and let P3 be a Sylow3-subgroup of G...
- Q 12. (a) Is the subset { (e,0), (e,6), (e,12), (h,0), (h,6),(h,12) }, a subgroup of the direct product group ( V x Z18 )? (V isthe Klein four group.) Carefully...
- Q Determine the equation of a sine or cosine function for thevertical position, in metres, of a rider on a Ferris Wheel, after acertain amount of time, in seconds. The maximum...
- Q You are a company and just issued a $20m 3-year fixed rate bond.Your investment bank suggests that you enter into an interest rateswap to turn this into a floating rate...
- Q We want to design a rectangular box without a lid with a volumeof 64000 cm^3. Find the dimensions that maximize the surface area.Using Lagrange MultipliersCan you explain your reasoning pls
- Q 1.(a) Show that the length of the broken line satisfiesLength(L) ≥ |AB|.(b) Show that L achieves the lower boundLength(L) = |AB|if and only if the vertices V1,...,Vk−1 all lie on...
- Q 1. Find the :(a) Inverse using explicit Gauss-Jordan elimination(b) The eigenvalues(c) Respective eigenvectors(2 0 -20 4 0-2 0 5)
- Q 1. A six-sided die is weighted so that all even numbers have anequal chance of coming up when the die is rolled, all odd numbershave an equal chance of coming...
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