Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.)

x2 − 2.25y2 + 22.5y − 92.25 = 0

Cost of common stock equity Ross Textiles wishes to measure its cost of common stock equity. The​ firm's stock is currently selling for ​$64.19. The firm just recently paid a dividend of ​$4.04. The firm has been increasing dividends regularly. Five years​ ago, the dividend was just ​$2.99.

After underpricing and flotation​ costs, the firm expects to net $58.41 per share on a new issue.

A. Determine average annual dividend growth rate over the past 5 years. Using that growth​ rate, what dividend would you expect the company to pay next​ year?

B. Determine the net​ proceeds, Nn​, that the firm will actually receive.

C. Using the​ constant-growth valuation​ model, determine the required return on the​ company's stock, rs​, which should equal the cost of retained​ earnings, rr.

D. Using the​ constant-growth valuation​ model, determine the cost of new common​ stock, rn.

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A. The average annual dividend growth rate over the past 5 years is ___ % ​(Round to two decimal​ places.)

Using that growth​ rate, the dividend you expect the company to pay next year is ​$__. ​(Round to two decimal​ places.)

B. The net​ proceeds, Nn​, the firm will actually receive are __ (Round to two decimal​ places.)

C. Using the​ constant-growth valuation​ model, the cost of retained​ earnings, rs​, is __%. ​(Round to two decimal​ places.)

D. Using the​ constant-growth valuation​ model, the cost of new common​ stock, rn​, is __%.​(Round to two decimal​ places)

In order to get into the Ferris wheel, you first must climb onto a platform several feet above ground level. That platform accommodates the cars (also called gondolas) to pass by without touching the ground. From that platform, the cars then travel a total of 224 feet in the air. The Ferris wheel has a radius of 106 feet. Using this information, answer the following questions. You can type the answers to questions 1-5, but 6 and 7 should have hand-written work to accompany any answer you provide. Answers without handwritten submissions will not be awarded any points for questions six and seven.

1) What is the diameter of the Ferris wheel? 212ft

2) How close to the bottom of the cars come to the ground? 12 ft

3) Given the information from question 2, about how high is the platform if you walk from the platform into the floor of the gondolas with no gap in height? 12ft

4) How high is the center of the Ferris wheel from the ground?

In order to answer questions 5 and 6, you’ll need to imagine the image of a Ferris wheel superimposed onto a coordinate grid.

5) Assuming the center of the Ferris wheel lies on the y-axis, what would the coordinates of the center of the Ferris wheel be?

6) Use the information from the problem, and your answer to part 5, to write an equation of the wheel.

7) In one rotation, how far does a patron travel while riding the Ferris wheel at the State Fair of Texas?

The initial size of a culture of bacteria is 1500. After one hour the bacteria count is 6000.

A.) Find a function n(t) = n₀e^rt that models the population after t hours (round your r value to five decimal places.) n(t)=

B.) Find the population after 1.5 hours. (round answer to nearest whole number.) n(1.5)=

C.) After how many hours will the number of bacteria reach 10,000? (round your answer to one decimal place.)

An investment firm recommends that a client invest in bonds rated​ AAA, A, and B. The average yield on AAA bonds is 4​%, on A bonds 5​%, and on B bonds 8​%. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond under the following​ conditions? A.  The total investment is ​$18 comma 000​, and the investor wants an annual return of ​$940 on the three investments. B.  The values in part A are changed to ​$33 comma 000 and ​$1 comma 720​, respectively. A.  The client should invest ​$ nothing in AAA​ bonds, ​$ nothing in A​ bonds, and ​$ nothing in B bonds.

Solve the following linear programming problem using generalised simplex method

Maximise z= 2x1+3x2

subject to -2x1+x2>=3

3x1+x2<=5

x1,x2>=0

Find the solution set of the linear system: {█(■(

x_1+x_4=260

-x_3+x_4+x_5=-200

x_2+x_3=300

x_1-x_2-x_5=150

A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the 500 students surveyed, 129 like Snickers, 118 like Twix, 145 like Reese's Peanut Butter Cups, 22 like Snickers and Twix, 54 like Twix and Reese's Peanut Butter Cups, 55 like Snickers and Reese's Peanut Butter Cups, and 8 like all three kinds of chocolate candy. How many students like Snickers, but not Twix or Reese's Peanut Butter Cups?

a) 129

b) 69

c) 61

d) 60

e) 121

f) None of the above.

2. A coroner uses a formula, derived from Newton's Law of Cooling, to calculate the elapsed time since a person died. The formula is t = -10 ln ((T-R)/ (37-R))

where t is the time in hours since the death, T is the body's temperature measured in C and R is the constant room temperature in C.

An accountant stayed late at work one evening and was found dead in his office the next morning. The officece temperature was constant at 21C

(a) At 10 am the coroner measured the body temperature. The temperature of the body was found to be 29.7C. Determine the accountant's estimated time of death, leave your answer

correct to the nearest minute.

(b) What would the temperature of the body be at 10am, if the accountant had died at 2am?

(c) Sketch graphs of t versus T for R = 18; 21; 24 on the same axes, clearly showing the vertical asymptote for each graph.

(d) If the constant oce temperature had been less than 21C, would the time of death found in (a) be earlier or later. Give reasons for your answer.

3×3 Systems Elimination by Addition

1) -5x-2y+20z=-28
2)   2x-5y+15z=-27
3) -2x-2y-5z= -12

Please write out all of the steps so I'll be able to figure out the formulas myself.

In this project we are going to model the Ball Toss with a quadratic function. So at 30 cm intervals, we draw 4 vertical lines extending from the eraser tray to the top of the marker board. We number the lines with their distances from the left most vertical line (which serves as the y-axis).Each of our volunteers selects a line and stand facing it at close proximity to the board. Between the board and the volunteers, I toss the ball to the catcher. Each of the volunteers will mark the height above the eraser tray at which the ball crosses his/her line. We will measure and label the height from the eraser tray to the marks.

We have the following data: M(0,23.5); N(30,37.2); P(60,35.8); Q(90,19.3)

These data represent a set of ordered pairs or a function. Since this function has an infinite number of ordered pairs, we are going to find an equation that defines this function. So we should use an equation in x and y where x represents the first coordinate and y represents the second coordinate. We should create a coordinate plane by drawing a horizontal number line called the x-axis, and a vertical line called the y-axis.

1. In this specific model of ball toss

    a) What does the x-axis represent?

    b) What do the x-coordinates represent?

    C) What do the y-coordinates represent?

2. Display your data in the coordinate plane or plot the points using a graph paper (Consider each    square 10cm).Make sure you label the axis and the points.

3. Draw a smooth curve containing these points.

4. What shape does the graph have?

5. How does this shape open?

6. What kind of function this graph represents?

7. Write the standard form of the equation that represents this function.

8. Use the 3 points M (0, 23.5); N (30, 37.2) and P (60, 35.8) that verify the equation you wrote in question #7

    a) Find the quadratic polynomial that predicts y from x. (Hint: you should resolve a system of linear equation to find the coefficients of the equation). (Round your answers to the nearest ten thousandths). (Remember to show all your work)

b) Is the leading coefficient positive or negative?

    c) Does your answer for question (8b) contradict with your answer for question (5)? (If yes, check your work over before you continue).

9. a) What does the function say the height of the ball was when it was 120cm from the y-axis? (Round your answer to the nearest tenth).

   b) What is the sign of this height?

   c) What is the position of the ball to the eraser tray?

   d) Write this ordered pairs and plot its point T on the graph.

10. a) At what values of x does the function say the ball should have hit the eraser tray? (Round the values of x to the nearest cm)

      b) Display these points I and J on the graph and write their coordinates.

      c) What are these points called?

11. a) At what distances from the y-axis was the ball 28 cm above the eraser tray?(Round your answers to the nearest cm)

     b) Write these ordered pairs and plot their points R and S on the graph.

12. a) At what distance from the y-axis was the ball at its highest point?(Round your answer to the nearest cm).

     b) What was the maximum height of the ball measured, of course, from the eraser tray? (Round your answer to the nearest cm).

     c) What is the name of this highest point of the graph?

     d) Write the coordinate of the highest point V and plot it on the graph.

please answer q2, q3,24,q5,q6 and q11,q12

Radon-222 decays at a continuous rate of 17.3% per day. How much will 170 mg of Radon-222 decay to in 7 days?



NOTE: Round your answer to 4 decimal places.

show your work. Find the sin t and cos t for t =150^o.

You may need to draw the reference angle first, but you only have to enter the sine and cosine values.