For a fraction nonconforming of p = 0.05, which type of plan would give you the lowest ASN?

Let B = {u₁,u₂} where

u₁ = 1 and u₂ = 0   

0 1

and

B^' ={ v₁ v₂] where v₁= 2 v₂= -3

1 4

be bases for R2

find

1.the transition matrix from B′ to B
2. the transition matrix from B to B′
3.[z]B if z = (3, −5)
4.[z]B′ by using a transition matrix
5. [z]B′ directly, that is, do not use a transition matrix

1. 17 years ago, I purchased 124 shares of a stock worth $12.67 per share. There was a 3:1 split, a 3:1 split, and a 5:1 split during that time period. Today the stock is worth $3.5 per share. If the dividend yield was on average 12% during the last 17 years, what was the total rate of return?

Round your answer to the nearest whole number.

2. Suppose a corporation sells stock at $15 per share. Compute the dividend yield if the total dividend for the quarter is $133,226 distributed among 1,890,085 shares.

Round your answer to the nearest tenth of a percent.

A university proposed a parking fee increase. The university administration recommended gradually increasing the daily parking fee on this campus from $6.00 in the year 2004, by an increase of 8% every year after that. Call this plan A. Several other plans were also proposed; one of them, plan B, recommended that every year after 2004 the rate be increased by 60 cents.

a. Let t=0 for year 2004 and fill in the chart for parking fees under plans A and B.

Round your answers for the values under Plan A to two decimal places, and enter the exact answers for the values under Plan B.

b. Write an equation for parking fees FA as a function of t (years since 2004) for plan A and an equation FB for plan B.

Enter the exact answers.

FA=

Edit

FB=

Edit

c. What will the daily parking fee be by the year 2025 under each plan?

Round your answer for the value under Plan A to two decimal places, and enter the exact answer for the value under Plan B.

Under plan A, the daily parking fee in the year 2025 with be $.

Under plan B, the daily parking fee in the year 2025 with be $.

d. Imagine that you are the student representative to the Board of Trustees. Which plan would you recommend for adoption?

For students,

Plan APlan B

is less expensive over the next  years, so it should be recommended.

ANTM Lease and BHP Ltd. sign a lease agreement dated 1 January 2019, that calls for ANTM
to lease a backhoe to BHP beginning January 1, 2019. The agreement asks ANTM Lease give
the right use of a backhoe to BHP for the periods of 1 January 2019 to 1 January 2024.
The terms and provisions of the lease agreement and other pertinent data are as follows:
1. The term of the lease is five years. The lease agreement is non-cancelable, requiring
equal rental payments of $17,500 at the end of each year/31 December (annuity-due
basis).
2. The backhoe has a fair value at the commencement of the lease of ????, an estimated
economic life of five years, and a guaranteed residual value of $4,000. (BHP expects
that it is probable that the expected value of the residual value at the end of the
lease will be greater than the guaranteed amount of $4,000.)
3. The lease contains no renewal options. The backhoe reverts to ANTM Lease at the
termination of the lease.
4. BHP incremental borrowing rate is 4 percent per year.
5. BHP depreciates its equipment on a straight-line basis.
6. ANTM sets the annual rental rate to earn a rate of return of 5 percent per year; BHP is
aware of this rate.
Instructions:
a. Determine who is the lessee and lessor.
b. Determining the value of right-of-use asset and lease liability for lessee.
c. Journals on the date of beginning of the agreement for lessee.
d. Prepare the table of payments and interest expense for lessee.
e. Prepare the journal to recognize interest expense, depreciation expense at the end of
years, and payments made during the lease agreement.
f. Compute the fair value of the backhoe for the lessor at the beginning of the contract;
and prepare the table and journal needed by the lessor during the lease agreement.
g. If the fair value of the backhoe is $1,000 at the end of the lease agreement, prepare the
journal entry on 1 January 2024 for lessee and lessor.

6a. Let V be a finite dimensional space, and let Land T be two linear maps on V. Show that LT and TL have the same eigenvalues.

6b. Show that the result from part A is not necessarily true if V is infinite dimensional.

Two dentists, Lydia Russell and Jerry Carlton, are planning to establish practices in a newly developed community. Both have allocated approximately the same total budget for advertising in the local newspaper and for the distribution of fliers announcing their practices. Because of the location of their offices, Russell is expected to get 49% of the business if both dentist advertise only in the local newspaper; if both dentist advertise through fliers, then Russell is expected to get 45% of the business; if Russell advertises exclusively in the local newspaper and Carlton advertises exclusively through fliers, then Russell is expected to get 57% of the business. Finally, if Russell advertises through fliers exclusively and Carlton advertises exclusively in the local newspaper, then Russell is expected to get 55% of the business.

(a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.)

Is the game strictly determined?

YesNo     

(b) Find the optimal strategy for both Russell (row) and Carlton (column). (Round your answers to three decimal places.)

Solve the differential equation by variation of parameters.

y''+ y = sin^2(x)

Let Un×n be an upper triangular matrix of rank n. If any arithmetic operation takes 1µ second on a computing resource,

compute the time taken to solve the system Ux = b, assuming it has a unique solution. What would be the time taken if Un×n is lower triangular

Q5a) A leading company in Delhi is planning to rent houses and open spaces.
The houses are in three categories namely, having three bedrooms, two bed-
rooms and single bedroom homes. A market survey conducted by a team indi-
cates that a maximum of 650 three bedroom homes, 500 two bedroom homes
and 300 single bedroom homes can be rented. Also, the number of three bed-
room homes should be at least 60% of the number of two bedroom and single
bedroom homes. Open space is proportionate to the number of home units
at the rates of at least 10 sq.ft, 15 sq.ft and 18 sq.ft for three bedroom, two
bedroom and single bedroom homes respectively. However, land availability
limits open space to no more than 10000 sq.ft. The monthly rental income is
estimated at Rs. 45000, Rs. 56250 and Rs. 90000 for single bedroom, two
bedroom and three bedroom homes respectively. The open space rents for Rs.
7500/sq.ft. Formulate the above as an LPP so as to get maximal revenue.
b) Convert the following problem to standard form explaining the various
steps.
Minimize: Z = −3x1 + x2 + x3
Subject to: x1 − 2x2 + x3 ≤ 11
− 4x1 + x2 + 2x3 ≥ 3
2x1 − x3 = −1
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0

Construct the Dual and solve the Dual by the graphical and simplex method.

Minimize Z = 1x1 + 1x2 + 2x3

Subject to:

2x1 + 2x2 + 1x3 >= J

5x1 + 6x2 + 7x3 >= K

x1, x2, and x3 >= 0

constant resources:

J = 15

K = 17

Please do on paper..

Prof. X has two brilliant students Y and Z in his class. He introduces the
concept of vector spaces, bases and dimension in his 5th session. As an exercise,
he gives a vector space V of dimension n and asks Y and Z to find a basis. Y
produces a set S with n elements. But Z being lazy, takes the set S, removes
a vector and adds a new vector to it creating a new set T. Prof. X looks at set
T and confirms to class that it is a basis. He then asks the class if the set S
produced by Y could be a basis without telling them what it is. While student
U says yes, student W says need not and Prof. X says that both U and W
could be correct. Justify the statement of Prof. X with suitable examples of V
over F, n, S and T.

Q2a) Consider a transformation T : R
2×2 → R
2×2
such that T(M) = MT
.
This is infact a linear transformation. Based on this, justify if the following
statements are true or not. (2)
a) T ◦ T is the identity transformation.
b) The kernel of T is the zero matrix.
c) Range T = R
2×2
d) T(M) =-M is impossible.
b) Assume that you are given a matrix A = [aij ] ∈ R
n×n with (1 ≤ i, j ≤ n)
and having the following interesting property:
ai1 + ai2 + ..... + ain = 0 for each i = 1, 2, ...., n
Based on this information, prove that rank(A) < n. (2)
c) Let A ∈ R
m×n be a matrix of rank r. Suppose there are right hand sides
b for which Ax = b has no solution, which of following expression(s) is/are
correct: r < m, r = m, r > m.
Now, consider the linear system AT y = 0. Do you think this linear system can
have non-zero solutions, that is y 6= 0 such that AT y = 0. Give justification for
all your answers.

-When first observed, an oil spill covers 8 square miles. Measurements show that the area is tripling every 6 hrs. Find an exponential model for the area A (in mi²) of the oil spill as a function of time t (in hr) from the beginning of the spill. (Enter a mathematical expression.)

A(t)=

-An internet analytics company measured the number of people watching a video posted on a social media platform. The company found 129 people had watched the video and that the number of people who had watched it was increasing by 30% every 3 hours.

A=

-A restaurant owner deposits $6,000 into an account that earns an annual interest rate of 6% compounded monthly. Find an exponential growth model for A, the value of the account (in dollars) after t years. (Enter a mathematical expression)

A=

**please show work

Let T = (V,E) be a tree, and letr, r′ ∈ V be any two nodes. Prove that the height of the rooted tree (T, r) is at most twice the height of the rooted tree (T, r′).