Determine whether the following two planes x + 4y − z = 7 and 5x − 3y −7z = 11 are parallel, orthogonal, coincident (that is, the same) or none of these.

please show full working for learning purposes

Given two planes 2x - y + z = 7 and x + 3y - 4z = 1.

(a) Give an orthogonal vector to each plane.

(b) Do the planes intersect? Why or why not?

(c) If they intersect, find the parametric equation of the intersection line, if not, find the distance of both planes.

7. Two children in the same class took the same achievement test at the beginning and the end of the school year. The scores of this standard achievement test form a normal distribution. Both children improved on their scores. The score of Child A increased from the 47th to the 57th percentile while the score of Child B increased form the 87th to the 97th percentile.

a. Did both children make improvement of equal magnitude in terms of z scores? Circle one. (2 points)

YES NO
b. If “Yes”, why? If “No”, who made a greater improvement in z scores? (1 point)

Select two salts that dissolve in water to give a solution with pH <7.

A. CaF2

B. CH3 NH3 Cl

C. CrCl3

D. Sr(ClO4 ) 2

E. NaNO2

F. KNO3

Problem Set 2 is due in class on Thursday, February 7.

1. There are two workers in an economy, Maeve and Dolores. They can make either cowboy hats or lassos. In one day, Maeve can make 40 cowboy hats, or she can make 20 lassos. In the same day, Dolores can make 30 cowboy hats, or she can make 10 lassos.
   1. What is the opportunity cost of a cowboy hat for Maeve?
   2. What is the opportunity cost of a lasso for Maeve?
   3. What is the opportunity cost of a cowboy hat for Dolores?
   4. What is the opportunity cost of a lasso for Dolores?
   5. Who has the absolute advantage in making cowboy hats?
   6. Who has the absolute advantage in making lassos?
   7. Who has the comparative advantage in making cowboy hats?
   8. Who has the comparative advantage in making lassos?
   1. Can Dolores and Maeve benefit by trading with each other? If so, at what range of prices might they be able to trade and still benefit?
2. There are two workers in an economy, Calvin and Hobbes. They can each make either water balloons or sleds. In one day, Calvin can make 15 water balloons, or he can make 30 sleds. In one day, Hobbes can make 20 water balloons, or he can make 20 sleds.
   1. What is the opportunity cost of a water balloon for Hobbes?
   2. What is the opportunity cost of a sled for Hobbes?
   3. What is the opportunity cost of a water balloon for Calvin?
   4. What is the opportunity cost of a sled for Calvin?
   5. Who has the absolute advantage in making sleds?
   6. Who has the absolute advantage in making water balloons?

1

7. Who has the comparative advantage in making sleds?
8. Who has the comparative advantage in making water balloons?
1. Can Calvin and Hobbes benefit by trading with each other? If so, at what range of prices might they be able to trade and still benefit?

Question 1 (4 + 4 + 7 = 15 marks)
a. Audits and Reviews are two types of attestation services provided by public
accounting firms. Discuss the similarities and differences between these two
types of attestation services. Which type provides the most assurance? (4
marks)
Suggested Answer for part a:
Click or tap here to enter text.

b. What is auditor independence and why is it so important?
Suggested Answer for part b:
Click or tap here to enter text.

c. The following are 7 examples of audit procedures:
1.Trace selected quantities from the inventory list to the physical inventory to make
sure that it exists and the quantities are the same.
2. Stand by the payroll time clock to determine whether any employee &#39;punches in&#39;
more than one time.
3. Calculate the ratio of cost of goods sold to sales as a test of overall
reasonableness of gross margin relative to the preceding year.
4. Question operating personnel about the possibility of obsolete or slow-moving
inventory.
5. Review the total of repairs and maintenance for each month to determine whether
any month&#39;s total was unusually large.
6. Re-foot entries in the sales journal to determine whether they were correctly
totalled by the client.
7. Obtain a written statement from the client&#39;s bank stating the client&#39;s year-end
balance on deposit.
Required:
For each of the audit procedure, classify audit procedure according to the following
eight types of audit evidence: (1) physical examination, (2) confirmation, (3)
documentation, (4) observation, (5) inquiry of the client, (6) recalculation, (7)
reperformance, and (8) analytical procedures.

answer please

Q-7      A company sells its two products A and B. The prices of products A and B are $5 and $8 per unit respectively. The material costs for A and B are $0.5 and $1.5 per unit respectively. The labour charges of $0.5 per unit is same for both of the products A and B. The fixed cost of the business is estimated as $3000.

1. Formulate the total revenue function if x1 and x2 units are sold of product A and B respectively.
2. Formulate the total cost function if x1 and x2 units are produced of product A and B respectively.
3. Formulate the total profit function if x1 and x2 units are produced and sold of product A and B respectively.
4. Calculate the total profit if 50,000 units of product A and 80,000 units of product B are produced and sold.

7- CAPITAL BUDGETING CRITERIA

A firm with a 14% WACC is evaluating two projects for this year's capital budget. After-tax cash flows, including depreciation, are as follows:

1. Calculate NPV for each project. Round your answers to the nearest cent. Do not round your intermediate calculations.
   Project M    $
   Project N    $

   Calculate IRR for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M      %
   Project N      %

   Calculate MIRR for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M      %
   Project N      %

   Calculate payback for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M      years
   Project N      years

   Calculate discounted payback for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M      years
   Project N      years

2. Assuming the projects are independent, which one(s) would you recommend?
   -Select-Only Project M would be accepted because NPV(M) > NPV(N).Only Project N would be accepted because NPV(N) > NPV(M).Both projects would be accepted since both of their NPV's are positive.Only Project M would be accepted because IRR(M) > IRR(N).Both projects would be rejected since both of their NPV's are negative.Item 11
3. If the projects are mutually exclusive, which would you recommend?
   -Select-If the projects are mutually exclusive, the project with the highest positive NPV is chosen. Accept Project N.If the projects are mutually exclusive, the project with the highest positive IRR is chosen. Accept Project M.If the projects are mutually exclusive, the project with the highest positive MIRR is chosen. Accept Project M.If the projects are mutually exclusive, the project with the shortest Payback Period is chosen. Accept Project M.If the projects are mutually exclusive, the project with the highest positive IRR is chosen. Accept Project N.Item 12
4. Notice that the projects have the same cash flow timing pattern. Why is there a conflict between NPV and IRR?
   -Select-The conflict between NPV and IRR is due to the fact that the cash flows are in the form of an annuity.The conflict between NPV and IRR is due to the difference in the timing of the cash flows.There is no conflict between NPV and IRR.The conflict between NPV and IRR occurs due to the difference in the size of the projects.The conflict between NPV and IRR is due to the relatively high discount rate.Item 13

(a) Two teams, A and B, are playing in the best-of-7 World Series; whoever gets to 4 wins first wins the series. Suppose the home team always has a small advantage, winning each game with probability 0.6 and losing with probability 0.4. Also assume that every game is independent. What is the probability that team A will win the series in exactly 6 games if the series is played in the following format: A–A–B–B–B–A–A, meaning that the first two games are played on team A’s field, followed by three games on team B’s field, and the final two games back on team A’s field?

[Note: Do not use the negative binomial straight up. You will run into trouble, because in this case, the winning probability shifts from one team to the other depending on who has the home field advantage.]

(b) You’re a huge Boston Red Sox fan, and in the current1 best-of-7 World Series they have a probability of p = 0.4 of winning each game. After the Sox lose Game 1, you get so inebriated that you sleep for two days, and miss the next two games. Upon awakening, you rush out to the street and ask the first person you see, “What happened in Games 2 and 3?” “They split them,” comes the reply. Should you be happy? In other words, how do the Sox’s chances of winning look now compared to after Game 1?

This information is for problems 7 – 14:
Two economics professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:
                                                Mean Grade                      Standard Deviation
Professor Welker            83.6                                                        21.6
Professor Ackerman       79.7                                                        12.0
At the 0.01 level of significance, what is your conclusion?

This information is for problems 7 – 14:
Two economics professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:
                                                Mean Grade                      Standard Deviation
Professor Welker            83.6                                                        21.6
Professor Ackerman       79.7                                                        12.0
At the 0.05 level of significance, what is your conclusion?