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1. The circular flow diagram is a model used to demonstrate how a given economic system functions through the interactions of 1st agent of economics and 2nd agent of economics. Identify the roles of each of these actors through a set of example.

Using a suitable diagram, draw and elaborate  the Circular Flow Diagram (Physical and non-Physical flow) in economies.        

What is Social Psychology?

A chemist reacts 10.5 g of ag with 7.5 g of s in the reaction from the previous question what’s the percent yield if a chemist actually obtains 9.8 g of ag2s in the lab

What is one topic or section that stood out to you in chapter 9?  Text book: Berns, Roberta. Child, Family and Community: Socialization and Support Wadsworth Publishing, 11th edition, 2023.
What is your opinion on children and media and why? 

On 01 July 2022, Persian Ltd acquired 551,250 ordinary shares of Sumo Ltd, that is, Persian Ltd holds 70% shares in Sumo Ltd. The purchase consideration was as follows:

• Cash paid $ 950,000
• A deferred cash settlement to be paid in three years’ time of $ 475,000
• By an exchange of one share in Persian Ltd for every four shares in Sumo Ltd. The market price of Persian Ltd share at the date of acquisition was $ 2.95 and the market price of each Sumo Ltd share at the date of acquisition was $ 3.15

Legal fees associated with the acquisition were $ 10,500.

The discount rate of Persian Ltd is 10 %.

(a) Calculate the fair value consideration (Costs of investment) transferred to acquire control of Sumo Ltd at the date of acquisition. Your answer should include a brief explanation if any of the above issue(s) is/are not required to be accounted in your working(s).                    

Give an example of when you might utilise Microsoft Excel's Fill tool and describe its function.

A certain linear system is known to satisfy the following differential equation: 

𝑥'' + 10𝑥' + 100𝑥 = 𝑓(𝑡)
𝑥(0) = 𝑥'(0) = 0

Compute the transition matrix 𝜙 and the covariance matrix 𝑄?

At the state fair, Erin and her cousin ride the Ultra Drop roller coaster. When the ride plummets down the first hill it dips below the loading platform. At the bottom, a camera snaps the rider’s picture before hurtling them back toward the sky.

The equation the roller coaster's path 3x^2-9x+38=2x^2+18 models over time. The variable y represents height (in feet) above or below the platform. At y=0 the roller coaster is even with the platform. The variable x represents the amount of time (in seconds) elapsed since the ride began.

1 Write the equation in standard form. (

2 Write the factored form of the equation you found in Part I.

3 Use the zero product rule to solve the factored form of the equation you found in Part II. Show your work and check your solution(s).

4 What does your answer to Part III tell you about the roller coaster's height at certain points in time?

5 The equation for the roller coaster's path can also be written as y=(x-4.5)^2-0.25

What is the name for this form of the equation? What is the height and time at which Erin's picture is taken during the roller coaster ride?

a) Start by writing the equation of the circle. (Recall that the general form of a circle with the center at the origin is x2 + y2 = r2. 

b) Now solve this equation for y. Remember the roller coaster is above ground, so you are only interested in the positive root.

2. Graph the model of the roller coaster using the graphing calculator. Take a screenshot of your graph and paste the image below, or sketch a graph by hand

Model 1: One plan to secure the roller coaster is to use a chain fastened to two beams equidistant from the axis of symmetry of the roller coaster. You need to determine where to place the beams so that the chains are fastened to the rollercoaster at a height of 25 feet.

3. Write the equation you would need to solve to find the horizontal distance each beam is from the origin.

4. Algebraically solve the equation you found in step 3.Round your answer to the nearest hundredth.

5. Explain where to place the two beams. 

Model 2: Another plan to secure the roller coaster involves using a cable and strut. Using the center of the half-circle as the origin, the concrete strut can be modeled by the equation and the mathematical model for the cable is. The cable and the strut will intersect.

6. Graph the cable and the strut on the model of the roller coaster using the graphing calculator. Take a screenshot of your graph and paste the image below, or sketch a graph by hand. 

7. Algebraically find the point where the cable and the strut intersect. Interpret your answer. 

Model 3: Another plan to secure the roller coaster involves placing two concrete struts on either side of the center of the leg of the roller coaster to add reinforcement against southerly winds in the region. Again, using the center of the half-circle as the origin, the struts are modeled by the equations and. A vertical reinforcement beam will extend from one strut to the other when the two cables are 2 feet apart.

*Recall that a reinforcement beam will extend from one strut to the other when the two struts are 2 feet apart.

10. Explain where to place the beam.

What method(s) would you choose to solve the equation:

x2 + 2x - 6 = 0

A. Square roots; there is no x-term.

B. Quadratic formula, graphing; the equation cannot be factored easily since the numbers are large.

C. Factoring; the equation is easily factored.

D. Quadratic formula, completing the square or graphing; the coefficient of x2-term is 1, but the equation cannot be factored.

In a quadratic equation, why is the least value always equal to?

Pittman Company is a small but growing manufacturer of telecommunications equipment. The company has no sales force of its own; rather, it relies completely on independent sales agents to market its products. These agents are paid a sales commission of 15% for all items sold.

Barbara Cheney, Pittman’s controller, has just prepared the company’s budgeted income statement for next year as follows:
 

*Primarily depreciation on storage facilities.

As Barbara handed the statement to Karl Vecci, Pittman’s president, she commented, “I went ahead and used the agents’ 15% commission rate in completing these statements, but we’ve just learned that they refuse to handle our products next year unless we increase the commission rate to 20%.”

“That’s the last straw,” Karl replied angrily. “Those agents have been demanding more and more, and this time they’ve gone too far. How can they possibly defend a 20% commission rate?”

“They claim that after paying for advertising, travel, and the other costs of promotion, there’s nothing left over for profit,” replied Barbara.

“I say it’s just plain robbery,” retorted Karl. “And I also say it’s time we dumped those guys and got our own sales force. Can you get your people to work up some cost figures for us to look at?”

“We’ve already worked them up,” said Barbara. “Several companies we know about pay a 7.5% commission to their own salespeople, along with a small salary. Of course, we would have to handle all promotion costs, too. We figure our fixed expenses would increase by $3,900,000 per year, but that would be more than offset by the $5,200,000 (20% × $26,000,000) that we would avoid on agents’ commissions.”

The breakdown of the $3,900,000 cost follows:

“Super,” replied Karl. “And I noticed that the $3,900,000 equals what we’re paying the agents under the old 15% commission rate.”

“It’s even better than that,” explained Barbara. “We can actually save $119,600 a year because that’s what we’re paying our auditors to check out the agents’ reports. So our overall administrative expenses would be less.”

“Pull all of these numbers together and we’ll show them to the executive committee tomorrow,” said Karl. “With the approval of the committee, we can move on the matter immediately.”

Required:

1. Compute Pittman Company’s break-even point in dollar sales for next year assuming:

a. The agents’ commission rate remains unchanged at 15%.

b. The agents’ commission rate is increased to 20%.

c. The company employs its own sales force.

2. Assume that Pittman Company decides to continue selling through agents and pays the 20% commission rate. Determine the dollar sales that would be required to generate the same net income as contained in the budgeted income statement for next year.

3. Determine the dollar sales at which net income would be equal regardless of whether Pittman Company sells through agents (at a 20% commission rate) or employs its own sales force.

4. Compute the degree of operating leverage that the company would expect to have at the end of next year assuming:

a. The agents’ commission rate remains unchanged at 15%.

b. The agents’ commission rate is increased to 20%.

c. The company employs its own sales force.

Use income before income taxes in your operating leverage computation.