Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow.

An individual retirement account, or IRA, earns tax-deferred interest and allows the owner to invest up to $5000 each year. Joe and Jill both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.1%. Joe deposits $5000 once each year, while Jill has $96.15 (which is 5000/52) withheld from her weekly paycheck and deposited automatically. How much will each have at age 65? (Round your answer to the nearest cent.) Joe $ Jill $

In each case, determine a 3 × 3 matrix ? that fits the description. Justify that the conditions are met in each case.

(a) Matrix ? has rank 1 and ? + ? is not invertible.

(b) Matrix A is symmetric and the null space of ? is a point.

What is the remainder of 23451638 divided by 5? What is the remainder of 23451638 divided by 4? [Hint: This is easy, use 4 and 5 divide 100.]

4. Use a proof by contradiction to show that the square root of 3 is irrational. You may use the following fact: For any integer k, if k2 is a multiple of 3, then k is a multiple of 3. Hint: The proof is very similar to the proof that √2 is irrational.

5. Use a direct proof to show that the product of a rational number and an integer must be a rational number.

6. Use a proof by contradiction to show that the sum of an integer and an irrational number must be irrational.

Read Proposition 1.23, the paragraph between the proposition and its proof, and the proof.
a. In your own words, explain the meaning of the two different mathematical ideas of "existence" and "uniqueness".
b. How do the ideas of "existence" and "uniqueness" relate to the phrase "one and only one"?
c. In your own words, explain why the proof of a "one and only one" statement will have two distinct parts.

Prove Proposition 1.26. Proposition 1.26. Let m,n ∈ Z. If mn = 0, then m = 0 or n = 0.

Prove Proposition 2.3. Proposition 2.3. 1 ∈ N.

Let G be a Group. The center of, denoted by Z(G), is defined to be the set of all elements of G that with every element of G. Symbolically, we have

Z(G) = {x in G | ax=xa for all a in G}.

(a) Prove that Z(G) is a subgroup of G.

(b) Prove that Z(G) is an Abelian group.

The cutting ratio in an orthogonal cutting model is given by To/Tc = sinϕ/Cos(ϕ-α)

What is:

ϕ = ?

α = ?

Several years ago Brant, Inc., sold $960,000 in bonds to the public. Annual cash interest of 9 percent ($86,400) was to be paid on this debt. The bonds were issued at a discount to yield 12 percent. At the beginning of 2016, Zack Corporation (a wholly owned subsidiary of Brant) purchased $160,000 of these bonds on the open market for $181,000, a price based on an effective interest rate of 7 percent. The bond liability had a carrying amount on that date of $930,000. Assume Brant uses the equity method to account internally for its investment in Zack.

1. a. & b. What consolidation entry would be required for these bonds on December 31, 2016 and December 31, 2018?

PLEASE SOLVE IN EXCEL.

Consider a cash flow profile in which $3000 is received at t=1, spent at t=2, and received at t=5, and $3000 is received at t=3. Suppose the interest rate is 3% the first 2 periods, 5% the next two periods and is 7% the 5th period. ( Note: t denotes end of period t.) Create a cashflow and present value table. Find the equivalents for the cash flow profile for the following items. a) Present worth b) Uniform series equivalent c) Geometric Series Equivalent (j = 1% for the entire period) • Show your calculation in detail and explain how the results are obtained.

Find the (a) amplitude, (b) period, (c) phase shift (if any), (d) vertical translation(if any), and (e) range of each function. then graph the function over at least one period.

1) y=-1/4 sin(3/4x+180degrees/8)

2)y=-3+3sin1/2x

3)y=2/3cos(x=180degrees/2)

x^2=ln(cy^2) Find the perpendicular orbits of the family of curves

Linear Optimization (Math 423) Problem, prove an analog of the follow theorem:

Thm 2.4: Consider the constraints Ax = b and x ≥ 0 and assume
that the m X n matrix A has linearly independent rows. A vector
x ∈ Rⁿ is a basic solution if and only if we have Ax = b, and there
exist indices B(1), ... , B(m) such that:
(a} The columns A_B(1),...,A_B(m) are linearly independent;
(b} If i ≠ B(1),...,B(m), then x_i = 0.