Peterson Packaging Inc. does not currently pay dividends. The company will start with a ​$0.70 dividend at the end of year three and grow it by 10​% for each of the next six years. After six years of​ growth, it will fix its dividend at ​$1.36 forever. If you want a 15​% return on this​ stock, what should you pay today given this future dividend​ stream?

Answer:

(a)

[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]

(b) Rate = 5

(c) Rate = 5

Step-by-step explanation:

Given

The attached graph

Solving (a): The piece-wise function

For the first line

Calculate the slope of the first line

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex](x_1,y_1) = (0,0)[/tex]

[tex](x_2,y_2) = (5,25)[/tex]

So, the slope is:

[tex]m = \frac{25 - 0}{5 - 0}[/tex]

[tex]m = \frac{25}{5}[/tex]

[tex]m = 5[/tex]

The equation is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (0,0)[/tex]

[tex]y = 5(x - 0) + 0[/tex]

[tex]y = 5(x) + 0[/tex]

[tex]y = 5x[/tex]

So, the function of the first line is:

[tex]f(x) = 5x;\ 0 < x \le 5[/tex]

For the second line

Calculate the slope of the second line

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex](x_1,y_1) = (5,20)[/tex]

[tex](x_2,y_2) = (9,40)[/tex]

So, the slope is:

[tex]m = \frac{40 - 20}{9 - 5}[/tex]

[tex]m = \frac{20}{4}[/tex]

[tex]m = 5[/tex]

The equation is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (5,20)[/tex]

[tex]y = 5(x - 5) + 20[/tex]

[tex]y = 5x - 25 + 20[/tex]

[tex]y = 5x -5[/tex]

So, the function of the second line is:

[tex]f(x) = 5x -5;\ x>5[/tex]

Hence, the piece-wise function is:

[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]

Solving (b): The rate at which customers that buy up to 5lb buy.

[tex]x = 5[/tex]

This question implies that, we determine the rate at which this customer buys.

For [tex]x = 5[/tex]

[tex]f(x) = 5x;\ 0 < x \le 5[/tex]

The slope of the above function is 5.

So, this customer buys at the rate of $5 per lb

Solving (b): The rate at which customers that buy more than 5lb buy the extra pounds above 5lb.

For [tex]x > 5[/tex]

[tex]f(x) = 5x -5;\ x>5[/tex]

Assume x = 6

[tex]f(6) = 5 * 6 - 5[/tex]

[tex]f(6) = 30 - 5[/tex]

[tex]f(6) = 25[/tex]

Express as 20 + 5

[tex]f(6) = 20 + 5 * 1[/tex]

Assume x = 7

[tex]f(7) = 5 * 7 - 5[/tex]

[tex]f(7) = 35 - 5[/tex]

[tex]f(7) = 30[/tex]

[tex]f(7) = 20 + 10[/tex]

Express 10 as 5 * 2

[tex]f(7) = 20 + 5 * 2[/tex]

So, we have:

[tex]f(6) = 20 + 5 * 1[/tex]

[tex]f(7) = 20 + 5 * 2[/tex]

This can be generalized as:

[tex]f(x) = 20 + 5(x - 5)[/tex]

For the above functions;

20 represents the amount they buy the first 5

5 represents the rate at which they buy extra pounds above 5

Hence, they buy the extra pounds at the rate of $5 per pound

Answer:

130 square feet

Step-by-step explanation:

Answer:

2.5 cm

Step-by-step explanation:

Since the triangles are similar, we can use ratios to solve

AC          BC

-------- = ---------

FH             GH

12            15

-------- = ---------

18             x

Using cross products

12x = 15*18

Divide each side by 12

12x/12 = 15*18/12

x = 2.5

Answer:

Kindly check explanation

Step-by-step explanation:

H0 : μ = 5500

H1 : μ > 5500

The test statistic assume normal distribution :

Test statistic :

(Xbar - μ) ÷ s/sqrt(n)

(5625.1 - 5500) ÷ 226.1/sqrt(15) = 2.1429 = 2.143

Pvalue from test statistic :

The Pvalue obtained using the calculator at df = 15 - 1 = 14 is 0.025083

α = 0.05

Since ;

Pvalue < α

0.025083 < 0.05 ; Reject H0

The confidence interval :

Xbar ± Tcritical * s/sqrt(n)

Tcritical at 95% = 1.761 ;

margin of error = 1.761 * 226.1/sqrt(15) = 102.805

Lower boundary : (5625.1 - 102.805) = 5522.295

(5522.295 ; ∞)

The hypothesized mean does not occur within the constructed confidence boundary. HENCE, there is significant eveidbce to support the claim that the true mean life of a biomedical device is greater than 5500

Answer:

Step-by-step explanation:

14/19/24

Answer:

$6.50

Step-by-step explanation:

39 / 6 = 6.5

Answer:

$6.50

Step-by-step explanation:

Hi,

To get the cost per ticket, all you have to do is divide 39 by 6. When you do that you get, 6.5 which means each ticket costs $6.50.

I hope that helps :)

Answer:

x=30.6

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

a= -4

b = -2

5(a-b)

5( -4 - (-2))

5( -4 + 2)

5(-2)

-10

Step-by-step explanation:

[tex]\tt{}4 \frac{2}{5} + k = - 3 \frac{2}{11} [/tex]

[tex]\tt{} \frac{22}{5} + k = - \frac{35}{11} [/tex]

[tex]\tt{}k = \frac{35}{11} - \frac{22}{5} [/tex]

[tex]\tt{}k = - \frac{417}{55} [/tex]

[tex]\tt{}k = - 7 \frac{32}{55} [/tex]

Answer:

120.2 or in other words, the answer is the last option, D

Answer:

16.1

Step-by-step explanation:

Answer:

I believe the answer is x = 16.1

Step-by-step explanation:

Answer:

4/7, 1/4,1/2, 2/3

Step-by-step explanation:

Answer:

21.4476105895

Step-by-step explanation:

Using a calculator [tex]\sqrt{460\\}[/tex]

Answer:

approximately 21.448 or 2 times the square root of 115

Step-by-step explanation:

The two numbers have 1 as a common factor and nothing else. Hence 1 is the HCF. This proves that the HCF of any two consecutive numbers is always a one.

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.

Answer:

It's so sad no one answered saying that they do.

Step-by-step explanation:

Answer:

96 ft

Step-by-step explanation:

Well add the given numbers up and calculate unkown sides using given measurments

Answer:

JONATHAN WILL NEED 14 PAGES.

Explanation:

33 + 67 = 100

100 - 12 = 88

88 ÷ 6 = 14.6666667

14.6666667 ⇒ 14

(Round 14.6666667 down to 14 because Johnathan does not have .6666667 of a page.)

Answer:

m<B, m<C, m<A

Step-by-step explanation:

The length of sides and angle measures correspond. This means the angle opposite to the longest side is the largest, etc. The shortest side is AC, which is the opposite of <B, making it the smallest. Then, the same logic can be applied to <C which is the middle, and <A which is the largest. Therefore, from least to greatest the angles are m<B, m<C, m<A.

Answer:

A

Step-by-step explanation:

Answer:

A) less than -5

Step-by-step explanation:

If it is lesser than -5, that means the line will be going to the left. This also means that the circle will be an open circle, not shaded.

Answer:

64 inches

Step-by-step explanation:

There are 12 inches in a foot

12 x 5 is 60

64 is greater then 60

Answer:

Percy’s strengths is his loyalty to his friend. When he was in danger, he could have escaped and saved his own life. But he showed loyalty by choosing to stay and fight to help his friend. He says, “… there was Grover, needing my help.” Percy’s only weakness in this section is becoming frozen by his fear. When his mother tells him to run, he can’t. The text says, “But I just stood there, frozen in fear, as the monster charged her.”

Step-by-step explanation:

Answer:

Step-by-step explanation:

4y - 2(5 - y + 4) = 4y - 2(9 - y)

                         = 4y + 9*(-2) - y *(-2)

                         = 4y  - 18 + 2y      {Combine like terms 4y and 2y}

                         = 6y - 18

6y - 18 = 6*y - 6*3

           = 6(y - 3)

6y- 18 =  2 *3y - 2*9

          = 2(3y -9)

2(3y - 9) and 6(y- 3 ) are equivalent to 4y - 2(5- y +4)

Others are not equivalent

Answer:

4.21875

Step-by-step explanation:

2.25*1.875 =4.21875

The area of the rectangle is 135/32 or 4 whole number 7/32 whose side measures are 2 whole 1/4 and 1 whole 7/8.

It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.

The formula for finding the area of a rectangle is given by:

Area of rectangle = length × width

We have side measures of the rectangle:

[tex]\rm a = 2\frac{1}{4} \\\\\rm b = 1\frac{7}{8}[/tex]

The area of the rectangle A is given by:

[tex]\rm A = (2\frac{1}{4} )\times(1\frac{7}{8} )[/tex]

[tex]\rm A = (\frac{9}{4} )\times(\frac{15}{8} )[/tex]

[tex]\rm A = \frac{135}{32}[/tex]  or

[tex]\rm A =4 \frac{7}{32}[/tex]

Thus, the area of the rectangle is 135/32 or 4 whole number 7/32 whose side measures are 2 whole 1/4 and 1 whole 7/8.

Learn more about the area here:

brainly.com/question/14383947

Answer:

10

Step-by-step explanation:

take 6-5=1

6+5=11

These are the parameters of a triangle. If the third side length is equal to 11 then that is impossible.

1<x<11

So the largest value for x would be 10

Hope that helps :)