(1 point) A tank is filled with 1000 liters of pure water. Brine containing 0.05 kg of salt per liter enters the tank at 6 liters per minute. Another brine solution containing 0.07 kg of salt per liter enters the tank at 9 liters per minute. The contents of the tank are kept thoroughly mixed and the drains from the tank at 15 liters per minute. A. Determine the differential equation which describes this system. Let S(t) denote the number of kg of salt in the tank after t minutes.

A) dS/dt = ?

B) Solve the differential equation for S(t).

A marketing research firm provides you with the following information. Historically, they have correctly predicted a positive market 82% of the time and correctly predicted a negative market 76% of the time. Without any market survey information, the estimate for a favorable market is 50% and an unfavorable market is 50%.

a)  What is the probability (in percentage) of a favorable market, given that the market survey predicts a favorable market? Answer in integer value.

b)  What is the probability (in percentage) of an unfavorable market, given that the market survey predicts an unfavorable market?  Answer in integer value.

Determine if the following sets are real vector spaces with the indicated operations.

(a) The set V of all ordered pairs (x, y) of real numbers with the addition defined by (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2 + 1) and scalar multiplication defined by α(x, y) = (αx, αy + α − 1), α ∈ R

(b) The set V of all 2 × 2 real matrices X with the addition of M22 but scalar multiplication ∗ defined by α ∗ X = αXT , α ∈ R

Solve the following system :

z” + y ′ = cos x,

y” − z = sin x,

z(0) = −1, z′ (0) = −1, y(0) = 1, y′ (0) = 0.

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