Prepare journal entries to record the following transactions related to long-term bonds of Quirk Co.

On April 1, 2016, Quirk issued $2,000,000, 9% bonds for $2,151,472 including accrued interest. Interest is payable annually on January 1, and the bonds mature on January 1, 2026. (Credit account titles are automatically indented when the amount is entered. Do not indent manually. If no entry is required, select "No Entry" for the account titles and enter 0 for the amounts.)

Date Account Titles and Explanation Debit Credit

April 1

On July 1, 2018 Quirk retired $600,000 of the bonds at 102 plus accrued interest. Quirk uses straight-line amortization. (Credit account titles are automatically indented when the amount is entered. Do not indent manually. If no entry is required, select "No Entry" for the account titles and enter 0 for the amounts. Round answers to 0 decimal places, e.g. 5,275.)

Account Titles and Explanation Debit Credit

(To record interest and premium on bonds)

(To record entry for retirement of bonds)

Given a 2x2 matrix, A =

1 4

2 -1

Find its eigen values, eigen vectors. Can matrix be diagnolized?

1) Evaluate the integral from 0 to 1 (e^(2x) (x^2 + 4) dx)
(a) What is the first step of your ‘new’ integral?
(b) What is the final antiderivative step before evaluating?
(c) What is the answer in simplified exact form?

2) indefinite integral (cos^2 2theta) / (cos^2 theta) dtheta
(a) What is the first step of your ‘new’ integral?
(b) What is the simplified integral before taking the antiderivative?
(c) What is the answer in simplified form?

Evaluate (please answer all of them)

1) ∫ 1.67 ?^(1/3) ?? =

2) ∫ [(?^3+ sin(4?)) / (?^4−cos(4?)+4)] ?? =

3) ∫ ???^8(4?)cot(4?) ?? =

4) ∫ sec^2(4?) ???^5(4?) ?? =

5) ∫ (4x^3) / ((x^4)+3) dx=

X and Y are independent Exponential random variables with mean=4, λ = 1/2.

1) Find the joint CDF of the random variables X, Y and  Find the probability that 4X > Y .

2) Find the expected value of X^3 + X*Y .

lim x approaches to 0 ( - cos (x^2) - 1) / e^x^4 - 1

Answer using l'hopital

Please dont skip steps and be detailed with explanation

(a) Show that the lines
r 1 (t) = (2,1,−4) + t(−1,1,−1) and r 2 (s) = (1,0,0) + s(0,1,−2)
are skew.
(b) The two lines in (a) lie in parallel planes. Find equations for these two planes. Express your
answer in the form ax+by+cz +d = 0. [Hint: The two planes will share a normal vector n. How would one find n?]
would one find n?]

2. Use the Laplace transform to solve the initial value problem.
?"+4?=?(?), ?(0)=1, ?′(0)=−1

  = { 1, ? < 1
where ?(?) =   {0, ? > 1.

What is Best fit distribution for this data/

1) Consider the following requirements for a certain product.

Beginning inventory = 300 units

Setup cost = $300 per setup

Lead time = 1 week

Holding cost = $5 per unit per week

(a) Develop the lot-for-lot MRP table - (complete table below).

(b) Calculate the total relevant costs.

Answer (Show all mathematical work):

a)

b) Total relevant costs = $?,???.