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Advanced-Math Questions
Let C(x) be the statement student x has a cat, let D(x) be the statement, x...
Find the volume of the solid whose base is rotating around the region in the first...
Problem 3: (a) How many elements in S8 commute with the permutation (123)(45678)? (b) How many...
Show that the set of all functions from the positive integers to the set {1, 2,...
A function f : A → B is called constant if there exists b ∈ B...
Find n for which the nth iteration by the fixed point method is guaranteed to approximate...
Date Cash Flow July 13,2008 -1100 Jan 26, 2009 200 March 9, 2010 200 June 25,...
Two drivers, Alison and Kevin, are participating in a race. Beginning from a standing start, they...
Let pp be a polynomial, and let θ∈(−1,1)θ∈(−1,1). Show that the series ∑∞k=1p(k)θk∑k=1∞p(k)θk converges absolutely.
2. We consider the symmetric group S5. Let s= (12)(345). Find the order of s
suppose p is a prime number and p2 divides ab and gcd(a,b)=1. Show p2 divides a...
Let O ∈ (AB) and C /∈ AB. Prove that there is a point D on...
Let A, O, B be collinear with O ∈ (AB), C, O, D also collinear with...
Consider the statement, "If you will give me magic beans, then I will give you a...
Prove that a positive integer n, n > 1, is a perfect square if and only...
If ABCD is a convex quadrilateral prove that the diagonals (AC) and (BD) intersect
In 1980 the population of alligators in a particular region was estimated to be 1300. In...
How many 4-regular graphs of order 7 are there? Justify your answer.
] Consider the autonomous differential equation y 0 = 10 + 3y − y 2 ....
In a lottery, a player selects 7 numbers out of the first 100 positive integers. We...
A tank contains 100 gallons of pure water. A salt solution with concentration 2.5 lb/gal enters...
What is the contrapositive of the following: "If I am on time for work then I...
At a price of $16 per ticket to a stadium football game, 40,000 people attend the...
Problem 1 Let {an} be a decreasing and bounded sequence. Prove that limn→∞ an exists and...
How many different ways to distribute 12 strawberries, 7 oranges, and 6 bananas among five people...
1. Give a direct proof that the product of two odd integers is odd. 2. Give...
Consider the following numbers 3, 6, 9, 12, . . . , 75. Show that if...
For the given quadric surface, describe the effect that changing the valie of a, b,c has...
1. Prove that an integer a is divisible by 5 if and only if a2 is...
determine conditions on integers a and b for which ab is even. then prove that the...
Determine specificity of fuzzy set A whose membership function is expressed in the form A(x) =...
Find the Shapley-Shubik power distribution of each of the following weighted voting systems. [10:10,5,3,1] [11:10,5,3,1] [15:10,5,3,1]
List the first five terms of the sequence. Start with 1 as the index of the...
Determine the entropy of a source with probabilities 2/3,2/9,2/27,2/81,2/243,1/243
Prove that if a > b then gcd(a, b) = gcd(b, a mod b).
The smallest positive solution of the congruence ax ≡ 0( mod n) is called the additive...
5- What three aspects of the visual arts relate directly to mathematics?
(For this part, view Z as a subset of R.) Let A be a non-empty subset...
Find a particular solution to the differential equation using the Method of Undetermined Coefficients. 4.4.22 x''(t)...
Find all integers n (positive, negative, or zero) so that (n^2)+1 is divisible by n+1. ANS:...
Cook Security Systems has a $37,500 line of credit, which charges an annual percentage rate of...
Find necessary and sufficient conditions for A to be the complement of a compact set.
Find necessary and sufficient conditions for A to be the complement of a compact set.
Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle...
Let ? be an ?×? matrix, and consider the equation ??⃗ = 0⃗. Show that for...
2. Determine whether the following pairs of vector spaces are isomorphic. If so, give an explicit...
Given the components of the vectors, A, B, and C Ax = 5 Bx=4 Cx =10...
Consider the following sequence: 0, 6, 9, 9, 15, 24, . . .. Let the first...
Gravely Gears (GG) makes gears using an automated machine costs $12,000 and has a 25% probability...
Find the greatest common divisor of the given polynomials over the given field. Then write the...
Answer each of the questions below. (a) Find an equation for the tangent line to the...
Let A and B be sets. Prove that (A∪B)\(A∩B) = (A\B)∪(B\A)
Problem B: Consider a graph G with 20 vertices, that has an Euler cycle. Prove that...
The distribution function ? of a random variable ? is given by ?(?) = { 0,...
Define a sequence (xn)n≥1 recursively by x1 = 1, x2 = 2, and xn = ((xn−1)+(xn−2))/...
Prove that for every natural number m, it holds 2*m + 1 ≤ 3^m. .
there are three brands you can choose; H&M, Banana, and Zara. H&M and Banana clothes cost...
find the maclaurin series: g(x) = x/(3-x)^3
A company supplies fertilizers to its customers on a make-to-order basis by blending appropriate amounts of...
G is a complete bipartite graph on 7 vertices. G is planar, and it has an...
True or false and explain why? A system of 2 equations in 3 unknown has infinitely...
1. Rabbits are sawing a log. They made 10 cuts. How many blocks of wood did...
Prove that limz->∞ f(z) = ∞ if and only if limz->0 1/ (f(1/z)) = 0.
Find all solutions to the following equations: (a) z^6 = 1 (b) z^4 = −16 (c)...
Suppose you need to $5,000 as the down payment on a car. If you have an...
S = {<3, -2, 1, -4>, <2, 1, -2, -2>, <0, -7, 8, -2>} Determine whether...
Are the following statement True or False? Justify your answers (a) Euclid's development of geometry is...
In every problem but the last one, you must use the successor function (s) and/or the...
State whether the statement is true or false. Also,please give a simple and clear explanation. A....
In every problem but the last one, you must use the successor function (s) and/or the...
when cylinder x^2+y^2=1, y^2+z^1=1 and x^2+z^1=1 intercept with each other, set up a triple integral to...
find the appropriate series solution about the point x0=1 for y''-xy'-y=0
n digit string of length n over alphabet {0,1, . . . ,9} a. How many...
n digit string of length n over alphabet {0,1, . . . ,9} How many n...
Can you explain how proof by induction works and give an example?
1-solve for x and y 3x+(y-2)i=(5-2x)+(3y-8)i 2-solve for z and write the answer with standard form...
The Fibonacci sequence is defined as follows F0 = 0 and F1 = 1 with Fn...
Consider the problem of summing n numbers by adding together various pairs of numbers and/or partial...
Suppose that you have an alphabet of 26 letters: (a) How many possible simple substitution ciphers...
Bob has invented a game with paper cups. He lines up 121 cups face down in...
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