Do 5 steps, starting from x₀=[1 1 1]^T and using 6S in the computation. Hint. Make sure that you solve each equation for the variable that has the largest coefficient (why?). Show the details

10x₁ + x₂ + x₃ = 6
x₁ + 10x₂ + x₃ = 6
x₁ + x₂ + 10x³ = 6

Introduction to logic:

Translate each argument using the letters provided and prove the argument valid using all eight rules of implication.

1. Sam will finish his taxes and Donna pay her property taxes or Sam will finish his taxes and Henry will go to the DMV. If Sam finishes his taxes, then his errands will be done and he will be stress-free for a time. Therefore, Sam will finish his taxes and he will be stress-free for a time. (S, D, H, E, F)
   
2. If Roxy flies to North Dakota, then her dog Charles will be alone for the weekend or Mary will watch Charles for the weekend. It is not the case that Roxy's flight will be delayed or her dog Charles will be alone. Furthermore, it is not the case that North Dakota will face a blizzard or Mary will watch Charles for the weekend. Therefore, Roxy will not fly to North Dakota. (R, C, M, D, B)

iii Show that any finite Lattice L has a b0 and b1, where t ≥ b0, t ≤ b1, for all t ∈ L.

Show that the Canter set C has measure equal to zero. Please write a clear detailed proof.

What happens to the x and y values under several kinds of transformations?

I know that:

y = f(-x) reflection over the y axis therefore (x,y) = (-x,y)

y = -f(x) reflection over the x axis therefore (x,y) = (x,-y)

y = f(x - or + 3) shift opposite direction in x direction therefore (x + or - 3, y)

y = f(x) + or - 3 shift in the direction of the sign therefore (x, y + or - 3)

y = f(2x) I know that this is a horizontal transformation, specifically a compression but what is happening to the coordinates and how would I represent this as a horizontal stretch? Also, what are the rules for this type of transformation? Is it when a > 0 then it is a compression?

y = 2f(x) I know that this is a vertical stretch but what is happening to the coordinates and how would I represent this as a vertical compression? Also, what are the rules for this type of transformation?

Applying and Analyzing Inventory Costing Methods
At the beginning of the current period, Chen carried 1,000 units of its product with a unit cost of $32. A summary of purchases during the current period follows.

UnitsUnit CostCostBeginning Inventory1,000$32$32,000Purchase #11,8003461,200Purchase #28003830,400Purchase #31,2004149,200

During the current period, Chen sold 2,800 units.

(a) Assume that Chen uses the first-in, first-out method. Compute both cost of good sold for the current period and the ending inventory balance. Use the financial statement effects template to record cost of goods sold for the period.
Ending inventory balance $Answer

Cost of goods sold              $Answer

Use negative signs with answers, when appropriate.

(b) Assume that Chen uses the last-in, first-out method. Compute both cost of good sold for the current period and the ending inventory balance.
Ending inventory balance  $Answer

Cost of goods sold              $Answer

(c) Assume that Chen uses the average cost method. Compute both cost of good sold for the current period and the ending inventory balance.
Ending inventory balance $Answer

Cost of goods sold              $Answer

The ledger accounts of AXX Internet Company appear as follows on March 31, 2019:

All accounts have normal balances.

Required:

1. Prepare the closing entries.
2. Post the transactions in to the appropriate ledger accounts. Hint: Be sure to enter beginning balances.

   Journal entry worksheet

3. Record the closing entry for revenue.

4. Note: Enter debits before credits.

   	Date General Journal Debit Credit Mar 31, 2019

Post the transactions in to the appropriate ledger accounts. Hint: Be sure to enter beginning balances.

Imagine that someone has just devised a new muscular endurance test. What would you do to prove that it is a valid test? (Show all steps, including evaluative ones.)

Speeding on the I-5. Suppose the distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 73.8 miles/hour and a standard deviation of 4.96 miles/hour. Round all answers to four decimal places.

What proportion of passenger vehicles travel slower than 64 miles/hour?

What proportion of passenger vehicles travel between 63 and 70 miles/hour?

How fast do the fastest 10% of passenger vehicles travel?

Suppose the speed limit on this stretch of the I-5 is 75 miles/hour. Approximately what proportion of the passenger vehicles travel above the speed limit on this stretch of the I-5?

Linear Algebra Conceptual Questions
• What are the possible sizes of solution sets for linear systems?

• List as many things that are equivalent to a square matrix being nonsingular as you can.

• List as many things that are equivalent to a square matrix being singular as you can. (Should be basically the same as your list above except all opposites) • Give an example of a singular matrix that is NOT just the zero matrix.

• If a system has m equations and n unknowns where m < n, what are the possibilities for number of solutions to the system?

• Rephrase the question above, and your answer to it, in terms of the rank of the coefficient matrix for the system.

Does there exist a non-cyclic group of order 99? If the answer is yes, then find two non-isomorphic groups of order 99.

5.

(a) Let σ = (1 2 3 4 5 6) in S6. Show that G = {ε, σ, σ^2, σ^3, σ^4, σ^5} is a group using the operation of S6. Is G abelian? How many elements τ of G satisfy τ^2 = ε? τ^3 = ε? ε is the identity permutation.

(b) Show that (1 2) is not a product of 3-cycles. Must be written as a proof!

(c) If a^4 = 1 and ab = b(a^2) in a group, show that a = 1. Must be written as a proof!

(d) Show that a group G is abelian if and only if (gh)^2 = (g^2)(h^2) for all g and h in G. Must be written as a proof!

Show that
(a)Sn=<(1 2),(1 3),……(1 n)>.
(b)Sn=<(1 2),(2 3),……(n-1 n)>
(c)Sn=<(1 2),(1 2 …… n-1 n)>

Supply proofs for the following miscellaneous propositions from the course in a metric space context:

(a) A convergent sequence is bounded.

(b) The limit of a sequence is unique.

(c) A n -neighborhood is an open set.

(d) A finite union of open sets is open.

(e) A set is open if and only if its complement is closed.

(f) A compact set (you may use either definition) is closed and bounded.