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let X and Y be the random variables that count the number of heads and the...
Let H={I,r} in D4. Determine all of the distinct left cosets of H in D4. Then...
let X be the random variable that equals the number of tails minus the number of...
how many strings of 8 lower case letters from the English alphabet contain the letter a?...
when a test for steroids is given 95% of the players taking steroids test positive and...
Consider the function f : R → R defined by f(x) = ( 5 + sin...
On Ellipse x2/4+y2=1 , ( 21/2 , - 21/2 /2 ) equation of tangent
A body at an unknown temperature is placed in a room which is held at a...
what is the conditional probability that a random generated bit string of length 5 contains at...
how many ordered pairs of integers (a,b) are needed to guarantee that there are two ordered...
Consider the mapping R^3 to R^3 T[x,y,z] = [x-2z, x+y-z, 2y] a) Show that T is...
Written Exercises for Section 1. Prove (or disprove) the following. Exercise 1.1. An ordered field has...
Suppose we want to prove statement "Every even number squared is divisible by 4" using induction....
Solve step by step power series solution for: y'' - 2 y' + y = 0....
find all real zeros of the function y= 2x⁴ - 6x³ + 12x² - 8x
Let S be the set of all functions from Z to Z, and consider the relation...
Let a, b ∈Z and n ∈N. (a) True/False: If a2 ≡ b2 (mod n), then...
Discuss the validity of the statement. If the statement is always true, explain why. If not,...
∫_C 5/(z-2-2i)(z+1-i) = ??? C:z=2√2cosθ+i√2sinθ i=√(-1)
In the study of logarithns and exponentials we first learn about one-to-one functions and inverse functions...
Consider the Mapping T: R2 -->P1 where T(a,b) = (a-b)x + 2a Find Ker(T) Show that...
The temperature at a point (x,y,z) is given by T(x,y,z)=200e−x2−y2/4−z2/9, where Tis measured in degrees celcius...
(a) Determine the feasible region graphically for the following inequalities. x1 + x2 ≤ 4 4x1...
Calculate the Fourier Series S(x) of f(x) = sin(x/2), -pi < x < pi. What is...
Why we can let sequence an=1/2n(pi) to be a sequence of function 2xsin(1/x)-cos(1/x)??? Please explain it.
Problem 2. Let F : R → R be any function (not necessarily measurable!). Prove that...
PQ#2. Brand Z (in PQ#1) is planning a Buy Two Get One Free (B2GO) promotion in...
anhydrous Dextrose (MW=180) is a 2-ion electrolyte, dissociating 80% in a given concentration (therefore, use a...
Let P(u) be the linear function mapping vector x ∈ Rn to the difference between x...
Question 2 Impact of price reduction on revenue A hardware store in a regional city is...
1. If the interval is bounded, then it is finite. Yes/No? Example Please 2. Conversely, If...
Prove that 5n2 +15n is divisible by 10 for every n ≥ 2, by mathematical induction.
Prove by induction on n that 13 | 2^4n+2 + 3^n+2 for all natural numbers n.
Given the function, , state whether the graph of the function has been reflected across the...
Consider the following linear program: MIN Z = 50A + 60B s.t. 6A + 8B ≤...
Axis of Rotation (3d) The following matrix is the matrix of rotation. Find the axis of...
Sturm-Liouville problem: y′′+λy= 0, y′(0) = 0, y(1) +y′(1) = 0. Determine the four smallest eigenvalues...
Consider a cardboard box without a lid with dimensions x,yx,y and zz having volume 500cm3500cm3. Find...
Let S be the boundary of the solid bounded by the paraboloid z=x^2+y^2 and the plane...
Sturm-Liouville problem: y′′+λy= 0, y′(0) = 0, y(1) +y′(1) = 0. Determine the four smallest eigenvalues...
Suppose that 44,000 people in New Zealand (population 4,400,000) carry a particular rare gene X that...
Consider the following expression: 7^n-6*n-1 Using induction, prove the expression is divisible by 36. I understand...
Solve y''+4xy'-y=0 using the power series method (frobenius)
use residues to evaluate the definite integral integral (0 to 2 pi) ( d theta/ (...
Air Shangrila sells to both tourist and business travelers on its single route. Tourists always stay...
Let D be the solid in the first octant bounded by the planes z=0,y=0, and y=x...
Using the Singular Value Decomposition, show that for any square matrix A, it follows that A*A...
The game of monopoly is played on a square board with 10 spaces per side (so...
y = x^3 on (-1,1) What is the least squares parabola? use numerical methods
Decide whether each of the following arguments are valid by first converting to a question of...
Do each of the following: a) How many integer solutions to x 1 + x 2...
1.4.3. Let T(x) =Ax+b be an invertible affine transformation of R3. Show that T ^-1 is...
Quantum Problem. Please need step-by-step. Show your work. The bad news don't stop at the prestigious...
Investment A yields a gain that is normally distributed with mean 7 and standard deviation 3.2....
Suppose that, in each period of a two-period stock price model, the cost of a security...
i) Given that 5x3-2x+y=2, find the value of at x=1. ii) Determine the slope of...
Topic: Math - Linear Algebra Focus: Matrices, Linear Independence and Linear Dependence Consider four vectors v1...
Find a particular solution consider x(0) = 1, x′(0) = −1, and x′′(0) = 0. x′′′...
Given PI at 9 + 71.83, Δ = 7°10′, and D = 8 degrees, compute the...
Problem 3. Let S be a subspace of a Hilbert space H. Prove that (S⊥)⊥ is...
You purchase a car worth $28196 and make a down payment of $3935. You intend to...
Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at (−4,2),...
explain cantors theorem in detail
Prove that either 172017+ 1983 or 172017+ 1984 is not a perfect square.
A fair coin is tossed for n times independently. (i) Suppose that n = 3. Given...
Consider the second order linear partial differential equation a(x, y)uxx + 2b(x, y)uxy + c(x, y)uyy...
Suppose we have a RLC circuit with an inductor of L = 1, a resistor of...
Create a loan repayment schedule for a loan of $30015 and payments of $8088 made annually....
Use the Big M method to solve the following LP: min z=x1+x2 x1+x2=2 2(x1)+2(x2)=4 x1, x2...
You start with 3 leaves in a tree. Each day, you cut off one leaf off...
If for integers a, b we define a ∗ b = ab + 1, then: (a)...
Find the real and imaginary roots for x^3+x^2+1. Do not use decimal approximations. Leave in RADICAL...
1. Solve the following initial value problem using Laplace transforms. d^2y/dt^2+ y = g(t) with y(0)=0...
Abstract Algebra (Modern Algebra) Prove that every subgroup of an abelian group is abelian.
The math department at the Mathland Institute of Science consists of twenty-five professors and eighteen lecturers....
Suppose you decide to obtain a four-year lease for a car and negotiate a selling price...
what are the left cosets of dihedral group D2n and their double cosets (H-H) ? let...
NON-ZERO matrix of 14 * 8 what is the minimum possible rank? what is the maximum...
Do each of the following. a) How many ternary strings of length 20 contain at least...
If for integers a, b we define a ∗ b = ab + 1, then: (a)...
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