Construct a linear equation for this model

What is the value of the y-intercept? What does it mean?

What is the value of the slope? What does it mean?

If you use 10 megabytes of data how much would you expect to pay for your bill?

Where else might you use this type of model? Be specific.

What are all the values of k for which the series [(k^3+2)*(e^-k)]^n converges from n=0 to n=infinity?

Suppose that the coefficient matrix of a homogeneous system of equations has a column of zeros. Prove that the system has infinitely many solutions. What are the possibilities for the number of solutions to a linear system of equations? Can you definitively rule out any of these?

( X, τ ) is normal if and only if for each closed subset C of X and each open
set U such that C ⊆ U, there exists an open set V satisfies C ⊆ V ⊆clu( V) ⊆ U

Q1- Out of Trapezoidal rule and Simpson’s 1/3rd rule which one is better explain in detail. Also solve one application based problem using that rule. Compare the exact and approximate result to compute the relative errore.

Find the eigenfunctions for the following boundary value problem.

x²y?? ? 15xy? + (64 + ?)?y ?=? 0,    y(e^?1) ?=? 0, ?y(1) ?=? 0.

In the eigenfunction take the arbitrary constant (either c₁ or c₂) from the general solution to be 1

A circle is divided in 6 sectors by 3 diameters.
Each sector contains a pawn. We are allowed to chose two pawns and
move each of them to a sector bordering the one it stands on at the
moment.
Is it possible to gather all 6 pawns in one sector using such
operations? Prove your answer

1.Find the present value at time 0 of $15086 due at the end of 4.88 years if the force of interest δ=0.023δ=0.023.

2.If an investment will double in 8.15 years at a constant force of interest δ, then

3.An investment of $1300 at t = 0 accumulates at a constant force of interest δδ= 4% for the first 4 years and at a nominal annual rate of interest of 5% compounded semiannually thereafter. Find the accumulated value of this investment at time t = 11.

4.An investment pays $1150 at time 0 and $2250 at the end of 3 years. Find the accumulated value of this investment at time 8 if the force of interest δt=0.02(1+t)2δt=0.02(1+t)2.

5.An investment of $1700 at t = 4 accumulates at a force of interest δt=0.003+0.009t2δt=0.003+0.009t2. Find the accumulated value of this investment at time t = 9.

6.How long does it take an amount to triple if the force of interest δ=0.062δ=0.062.

if a in G (group ) such as o(a)=mn

prove the existence of g and h in G such as a=gh=hg and o(g)=m o(h)=n

Historically speaking, several attempts have been made to create ‘metric time’ using factors of 10, but our current system won out. If 1 day was 10 metric hours, 1 metric hour was 10 metric minutes, and 1 metric minute was 10 metric seconds, what time would it really be if a metric clock reads 2:9:1? Similarly, convert 11:13:31 P.M. to metric time. You may assume that each new day starts at midnight.

The definition of a (well-defined) function f : X → Y . Meaning of domain, range, and co-domain

Let S be the two dimensional subspace of R^4 spanned by
x = (1,0,2,1) and y = (0,1,- 2,0)
Find a basis for S^⊥

Customers arrive in a certain shop according to an approximate Poisson process on the average of two every 6 minutes.

(a) Using the Poisson distribution calculate the probability of two or more customers arrive in a 2-minute period.

(b) Consider X denote number of customers and X follows binomial distribution with parameters n= 100. Using the binomial distribution calculate the probability oftwo or more customers arrive in a 2-minute period.

(c) Let Y denote the waiting time in minutes until the first customer arrives. (i) What is the pdf ofY? (ii) Find q1=π0.75

(d) Let Y denote the waiting time in minutes until the first customer arrives. What is the probability that the shopkeeper will have to wait more than 3 minutes for the arrival of the first customer ?

(e) What is the probability that shopkeeper will wait more than 3 minutes before both of the first two customers arrive?