Sketch the graph of a function f(x) that satisfies all the given conditions. Clearly label any asymptotes, extreme values and points of inflection.

f(x) is only discontinuous at x = −4.

f(x) has a global minimum but no global maximum.

f'(x) > 0 only on the intervals (−∞, −4) and (1, 3).

f(x) only changes concavity at x = −1 and x = 4.

limx→∞ f(x) = 4.

Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, five green ones, two white ones, and two purple ones. She grabs seven of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]

She has all the red ones.

Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, three green ones, four white ones, and three purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]

She has at least one green one

Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, three green ones, four white ones, and two purple ones. She grabs five of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]

She has two red ones and one of each of the other colors.

Question 2: A bipartite graph with 2n vertices (namely |V1| = |V2| = n) is d-regular if and only if the degree of every vertex in V1 ∪ V2 is exactly d. Show that a d-regular bipartite graph always has a perfect matching (a matching of size n that includes all vertices).

***Remarks: All the graphs here are without self loops and parallel or anti-parallel edges. A network is a directed graph with source s and sink t and capacity ce > 0 on every edge e. In all the algorithms, always explain their correctness and analyze their complexity. The complexity should be as small as possible. A correct algorithm with large complexity, may not get full credit. The number of vertices is denoted by n, and the number of edges by m. ***

How would I prove this ?

R > A / R > ( A v W )

I was thinking that this would work but I am not sure.

2. R > (A v W) 1, MP

Solve the following initial value problem ut + 2ux − 2u = e t+2x , u(x, 0) = 0

Prove that for every n ∈ N:

a) (10^n + 3 * 4^(n+2)) ≡ 4 mod 19, [note that 4^3 ≡ 1 mod 9]

b) 24 | (2*7^(n) + 3*5^(n) - 5),

c) 14 | (3^(4n+2) + 5^(2n+1) [Note that 3^(4n+2) + 5^(2n+1) = 9^(2n)*9 + 5^(2n)*5 ≡ (-5)^(2n) * 9 + 5^(2n) *5 ≡ 0 mod 14]

A) Using the scenario described by “Each store employs one or more employees; each employee is employed by one store”, work the following problems: 1. Identify each entity. 2. Identify each relationship type. Justify your answer. 3. Create the basic Crow's Foot ERD using Visio.

B) Using the scenario described by “A job assignment can be assigned to more than one employee at a time; each employee can have only one job assignment”, work the following problems: 1. Identify each entity. 2. Identify each relationship type. Justify your answer. 3. Create the basic Crow's Foot ERD using Visio

Prove that R(4; 4) = 18.

I am required to make at least three (3) substantive posts in this discussion. Your initial response of at least 150 words. I need to describe two (2) uses for quadratic equations. Provide your own original examples.

11. Solve numerically the following Boundary Value Problem.

X²Y” – X(X+2)Y’ + (X+2)Y = 0

Y(1) = e and Y(2) = 2e²

The value of e = 2.71828

Let⇀F and⇀G be vector fields defined on R3 whose component functions have continuous partial derivatives. Furthermore, assume that ⇀∇×⇀F=⇀∇×⇀G.Show that there is a scalar function f such that ⇀G=⇀F+⇀∇f.

Calculate each of the following (or indicate why it is not defined) (a) (1,2,3,4) x (4,3,2,1) (b) (1,1,1) x [(1,2,3) x (3,3,0)] (C) (1,1,1). [(1,2,3) x (3,3,0) (d) (1,1,1) x [(1,2,3). (3,3,0)] (e) (1,1,1) x [(1,2,3) - (3,3,0)] (f) (1,1,1) + [(1,2,3) X (3,3,0)]

This is a Combinatorics Problem

Consider the problem of finding the number of ways to distribute 7 identical pieces of candy to 3 children so that no
child gets more than 4 pieces. Except Stanley (one of the 3 children) has had too much candy already, so he’s only
allowed up to 2 pieces. Write a generating function & use your generating function to solve this problem.

You invest your $2500 COVID-19 stimulus check into 3 separate accounts. The Certificate of Deposit (CD) pays 4% interest annually. The stock market pays 5% annually. The toilet paper hoarding business pays 10% annually. If the amount spent on the toilet paper hoarding business is $400 more than you spent on the CD, and the total interest gained is $169, how much money did you invest in each venture. Please show all your equations, and the matrix you used to solve this.