Guff plc, an all-equity firm, has the following earnings per share and dividend history (paid annually).
Year Earnings per share Dividend per share
This year 21p 8p
Last year 18p 7.5p
2 years ago 16p 7p
3 years ago 13p 6.5p
4 years ago 14p 6p

This year’s dividend has just been paid and the next is due in one year. Guff has an opportunity to invest in a new product, Stuff, during the next two years.

The directors are considering cutting the dividend to 4p for each of the next two years to fund the project. However, the dividend in three years can be raised to 10p and will grow by 9 per cent per annum thereafter due to the benefits from the investment. The company is focused on shareholder wealth maximization and requires a rate of return of 13 per cent for its owners.
Required
a. If the directors chose to ignore the investment opportunity and dividends continued to grow at the historical rate what would be the value of one share using the dividend valuation model?
b. If the investment is accepted, and therefore dividends are cut for the next two years, what will be the value of one share?
c. What are the dangers associated with dividend cuts and how might the firm alleviate them?

The y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).

The y-intercept is the point where a function or a curve intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

The y-intercept of a function is the point where the graph of the function intersects the y-axis. To find the y-intercept of the function F(x) = 2(x - 7)(x - 3), we need to substitute 0 for x in the equation:

F(x) = 2(x - 7)(x - 3)

So, we have:

F(0) = 2(0 - 7)(0 - 3)

Simplifying this expression, we get:

F(0) = 2(-7)(-3)

F(0) = 42

Therefore, the y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).

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Answer:

Step-by-step explanation:

Start by finding the slope of the line that passes through both the 12 roses bouquet and the 18 roses bouquet.

point 1: (12,61)

point 2: (18,79)

m=y^2-y^1/x^2-x^1

m=79-61/18-12

m=18/6

m=3

then, using one of the points find the fixed costs

P=m*r+b

using 12,61

61=3*12+b

61-36=b

b=25

Answer:

The general equation that represents the linear relationship is:

P=25+3r

The break even sales for the current year using the contribution per unit  is 5.27.

The formula to find the break even sales is,

Break even sales = Fixed costs / Contribution per unit

Now,

Contribution per unit = Sales price per unit - Variable cost per unit.

Sales price = $6,512

Variable cost = (75% × cost of goods sold) + (50% × marketing, general and administration expenses)

                      = (75% × $1,628) + (50% × $592)

                      = $1517

Contribution margin = $6,512 - $1517 = $4995

Contribution per unit = $4995 / 37 = $135 per million

Fixed costs = (25% × cost of goods sold) + (50% × marketing, general and administration expenses)

                   = $703

Break even sales = 703 / 135 = 5.21

Hence the break even sales is 5.27.

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Answer:

average rate of change = 12

Step-by-step explanation:

the average rate of change of f(x) in the interval a ≤ x ≤ b is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here the interval is 2 ≤ x ≤ 4 , then

f(b) = f(4) = 2(4)² - 2 = 2(16) - 2 = 32 - 2 = 30

f(a) = 2(2)² - 2 = 2(4) - 2 = 8 - 2 = 6

then

average rate of change = [tex]\frac{30-6}{4-2}[/tex] = [tex]\frac{24}{2}[/tex] = 12

Answer:

254.34

Step-by-step explanation:

πr^2

3.14*81

254.34

Answer:the upper right one( the dash line that hit -2

Step-by-step explanation:

Okay, let's solve this step-by-step:

3.25x×400=2.50x+600

1300x = 1500

x = 500

So when x = 500, the costs are equal.

That's correct. An observation is considered an outlier if it is more than 1.5 times the interquartile range (IQR) above the third quartile (Q3) or below the first quartile (Q1).

The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

In this case, the first quartile Q1 is 5 and the third quartile Q3 is 16. So the IQR is:

IQR = Q3 - Q1 = 16 - 5 = 11

An observation is considered an outlier if it is more than 1.5 times the IQR above Q3 or below Q1.

To find the upper outlier bound, we add 1.5 times the IQR to Q3:

Upper outlier bound = Q3 + 1.5(IQR) = 16 + 1.5(11) = 32.5

So any observation above 32.5 is considered an outlier.

To find the lower outlier bound, we subtract 1.5 times the IQR from Q1:

Lower outlier bound = Q1 - 1.5(IQR) = 5 - 1.5(11) = -11.5

So any observation below -11.5 is considered an outlier.

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Answer:

Step-by-step explanation:

Let's use variables to represent the amount of money each person had at first.

Let x be the amount of money that Theriault Luigi had.

Then, according to the problem, Faber Kozlowski had 6 times as much money as Theriault Luigi, which means Faber Kozlowski had 6x dollars.

After Faber Kozlowski spent 1/3 of his money, he had 2/3 of his money left, which is (2/3)(6x) = 4x dollars.

After Theriault Luigi spent 4/5 of his money, he had 1/5 of his money left, which is (1/5)x dollars.

Together, they had a total of $1155 left, which means:

4x + (1/5)x = 1155

Multiplying both sides by 5 to eliminate the fraction gives:

20x + x = 5775

Combining like terms gives:

21x = 5775

Dividing both sides by 21 gives:

x = 275

Therefore, Theriault Luigi had $275 at first, and Faber Kozlowski had 6 times as much, which is $1650 at first.

So, the answer to (a) is $275 + $1650 = $1925.

For (b), Theriault Luigi spent 3/4 of his remaining money on a hoodie, which means he spent (3/4)(1/5)x = 3/20 of his original amount of money on the hoodie.

Therefore, Theriault Luigi spent 3/20 of his original amount of money on the hoodie.

Answer:

(a) $1925

(b) 15%

Step-by-step explanation:

(a)

Let f = original amount of money Faber had.

Let t = original amount of money Theriault had.

"Faber Kozlowski had 6 times as much money as Theriault Luigi. "

f = 6t

"After Faber Kozlowski spent 1/3 of his money"

He has now: 2/3 f

"and Theriault Luigi spent 4/5 of his money"

He has now: 1/5 t

"they had a total of $1155 left"

2/3 f + 1/5 t = 1155

f = 6t

2/3 f + 1/5 t = 1155

2/3 (6t) + 1/5 t = 1155

4.2t = 115

t = 1155/4.2

t = 275

f = 6t = 6(275) = 1650

f + t = 275 + 1650 = 1925

Part (a) answer: $1925

(b)

Original amount: t = 275

He first spent 4/5 of the original amount, so he had 1/5 left.

275/5 = 55

He spent 3/4 of $55 on the hoodie.

3/4 × $55 = $41.25

$41.25/$275 × 100% = 15%

Part (b) answer: 15%

Answer:

1.75 inches (pls give brainliest lol!)

Step-by-step explanation:

Let's use a proportion to solve the problem:

On the first map, 2.8 inches represents 25 miles:

2.8 / 1 = 25 / x

Simplifying the equation, we get:

x = 25(2.8)/1 = 70

Therefore, the distance between the two cities in the first map is 70 miles.

Now, let's find the distance between the same two cities on the second map, which has a scale of 1 inch to 40 miles:

We want to find how many inches on the second map represent 70 miles. Let's call this value y.

1 / 40 = y / 70

Solving for y, we get:

y = 70/40 = 1.75

Therefore, the two cities would be 1.75 inches apart on the second map with the 1 inch to 40 miles scale.

The answer is , (a) Empirical probability of sunfish rental = 0.5417 or 54.17% , (b) Empirical probability of kayak rental = 0.125 or 12.5% , (c) Empirical probability of rowboat rental = 0.3333 or 33.33% .

Empirical probability is an estimate of the probability of an event based on the frequency of its occurrence in a sample of data. It is calculated by dividing the number of times the event occurred by the total number of observations in the sample. Empirical probability is often used when there is no theoretical probability available, or when the theoretical probability is difficult to calculate or unknown. It is a useful tool in fields such as statistics, finance, and machine learning.

a) The empirical probability that the next boat rental is a sunfish is the number of sunfish rentals divided by the total number of rentals:

Empirical probability of sunfish rental = number of sunfish rentals / total number of rentals

Empirical probability of sunfish rental = 26 / 48

Empirical probability of sunfish rental = 0.5417 or 54.17%

b) The empirical probability that the next boat rental is a kayak is the number of kayak rentals divided by the total number of rentals:

Empirical probability of kayak rental = number of kayak rentals / total number of rentals

Empirical probability of kayak rental = 6 / 48

Empirical probability of kayak rental = 0.125 or 12.5%

c) The empirical probability that the next boat rental is a rowboat is the number of rowboat rentals divided by the total number of rentals:

Empirical probability of rowboat rental = number of rowboat rentals / total number of rentals

Empirical probability of rowboat rental = 16 / 48

Empirical probability of rowboat rental = 0.3333 or 33.33%

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Answer:

3) The graph that has three x-intercepts

9) Plot the points on the graphing calculator, and then generate a linear regression equation. That equation is:

y = 2.857x - 1.4286

The closest equation is y = 3x - 2. That equation best represents the regression line for this data.

Answer:

Step-by-step explanation:arcsin(1) = pi/2

Answer:

-|x|+1

Step-by-step explanation:

Answer:

[tex]\boxed{17}[/tex]

Step-by-step explanation:

Pythagorean theorem:

[tex]c^2=a^2+b^2[/tex]

where:

[tex]c=[/tex] hypothenuse

[tex]a=[/tex] the small size of the triangle

[tex]b=[/tex] the large size of the triangle

In this problem, we have the values of a and b, so:

[tex]c^2=(8)^2+(15)^2\\c^2=64+225\\c^2=289\\\sqrt{c^2}=\sqrt{289}\\ c=17[/tex]

Therefore the value of the unknown side of the triangle is 17.

Hope it helps.

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

The zeros of f according to their multiplicity are:

Zero of multiplicity 1: x = -8, x = -3, x = 0, x = 9

Zero of multiplicity 2: None

Zero of multiplicity 3: None

Here,

We have,

The zeros of a polynomial function are the values of x that make the function equal to zero. The multiplicity of a zero is the number of times it appears as a factor in the polynomial.

In the given function f(x), the zeros are the values of x that make the function equal to zero.

We can find these values by setting the function equal to zero and solving for x.

f(x) = 7x(x-9)(x+8)^2(x+3) = 0

Therefore, the zeros of f(x) are x = -8, x = -3, x = 0, and x = 9.

To determine the multiplicity of each zero, we can look at the degree to which the corresponding factor appears in the polynomial.

For example, x = -8 is a zero of multiplicity 2 because it appears as a factor twice in the function, as (x+8)^2.

Similarly, x = -3, x = 0, and x = 9 are zeros of multiplicity 1 because they each appear as a factor once in the function.

There are no zeros of multiplicity 3 or higher in this function, so we can list "None" for those categories.

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The length of the shorter leg is 6 centimeters, and the length of the longer leg is x + 14 = 20 centimeters.

Explanation:

Let x be the length of the shorter leg of the right triangle.

According to the problem, the longer leg is 14 centimeters longer than the shorter leg, so its length is x + 14.

We also know that the length of the hypotenuse of the right triangle is 26 centimeters.By the Pythagorean theorem, we have:

x^2 + (x + 14)^2 = 26^2

Simplifying the left side:

x^2 + x^2 + 28x + 196 = 676

Combining like terms:

2x^2 + 28x - 480 = 0

Dividing by 2:

x^2 + 14x - 240 = 0

Factoring:

(x + 20)(x - 6) = 0

Therefore, x = -20 or x = 6.

Since the length of a side cannot be negative, we reject x = -20 and conclude that x = 6.

So the length of the shorter leg is 6 centimeters, and the length of the longer leg is x + 14 = 20 centimeters.

The solution of the graph is approximately

The solution of a graph depends on the type of graph and the problem being represented. In general, a solution of a graph refers to a point or set of points that satisfy the conditions or constraints of the problem.

For the problem, the solution of the graph is the point where the two graphs intersects.

Deducing from the graph this is at point x approximately 4.455 the closest value to this point in the option is x = 71/16

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To find the missing angle measure, we need to use the fact that the sum of angles in a triangle is 180 degrees. Let's denote the missing angle as x. We know that one angle is 38 degrees and another angle is 12.5 degrees.Therefore, the missing angle measure is 129.5 degrees.

By subtracting these two angles from 180 degrees, we get:

180 - 38 - 12.5 = 129.5

Without additional information, it is not possible to determine the remaining parts of the triangle. We would need the lengths of at least one side or the measures of other angles to solve for the missing parts.

The given information states that AC is equal to AB minus mzB. Without knowing the values of AB and mzB, we cannot determine the exact length of AC. We would need additional information to solve for the length of AC.Therefore, the missing angle measure is 129.5 degrees.

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The measurement of angle Y which is a twin angle will be equal to 116 degrees which is option A.

What is an Isosceles Triangle?

The triangle which has any two sides equal in length is called as Isosceles Triangles. Also the two angles which is opposite to the equal sides are equal and third angle is unequal. The unequal side which is present is called the base of the triangle. Measurement of the altitude can be done from base to the vertex (which is topmost) of the triangle.

Here, the value of angle X is given 32 degree.

Therefore the value of angle Z will also be 32 degree (due to the property of isosceles triangle)

By angle sum property:

X+Y+Z=180

32+Y+32=180

Therefore, Y = 116 degree

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The slope of the line which passes through points (-2, 1) and (0, -3) is calculated as: m = -2.

In order to find the slope of the line given in the graph, pick two points on the line, then plug in their coordinates into the slope formula given as:

Slope (m) = change in y / change in x = y2 - y1 / x2 - x1

We have:

(-2, 1) = (x1, y1)

(0, -3) = (x2, y2)

Plug in the values:

Slope (m) = (-3 - 1) / (0 - (-2))

m = -4 / 2

Slope of the line (m) = -2

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The slope of the line represented by the graph is equal to -2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (-3 - 3)/(0 + 3)

Slope (m) = (-6)/(3)

Slope (m) = -2.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to -2.

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The slope of the line which passes through points (-2, 1) and (0, -3) is calculated as: m = -2.

In order to find the slope of the line given in the graph, pick two points on the line, then plug in their coordinates into the slope formula given as:

Slope (m) = change in y / change in x = y2 - y1 / x2 - x1

We have:

(-2, 1) = (x1, y1)

(0, -3) = (x2, y2)

Plug in the values:

Slope (m) = (-3 - 1) / (0 - (-2))

m = -4 / 2

Slope of the line (m) = -2

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The slope of the line represented by the graph is equal to -2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (-3 - 3)/(0 + 3)

Slope (m) = (-6)/(3)

Slope (m) = -2.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to -2.

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The p-value method yields P (T > 2.119) = 0.0359. It may be said that, at a 1% level of significance, there has been no decline in crime since the program's inception.

The observations for the paired t-test are drawn from a single random pair sample. There are the same number of observations in both samples. Each respondent has two observations for the experimental variable recorded.

The alternative is:

[tex]H_{0} =[/tex]: Since the program's launch, there has been no drop in the number of crimes.

The alternate theory is that:

[tex]H_{a} =[/tex] Since the start of the programme, fewer crimes have been committed.

Mathematically,

[tex]H_{0} =[/tex] μo = 0

[tex]H_{a} =[/tex] μd > 0

Given table:

Number of Crimes   Before   After   d = (before - after)    d²

A                                  14           2          14-2 =  12              14² = 144                                

B                                  7            7           17 - 7 =  0              0² = 0

C                                  4            3           4 - 3 =  1                 1² = 1

D                                  5            6           5 - 6 = -1              -1² = 1

E                                  17            8          17-8 =  9                 9² = 81
F                                  12           13          12 - 13 = -1             -1² = 1
G                                 8              3          8 - 3=  5              5² = 25
H                                 9              5          9 -5 =  4              4² = 16

Total                           8                             29                        269

The formula for the t statistic is:

t = ∑d / √[n(∑d²) - (∑d)²] / (n - 1)

t = 29 / √[8*269 - 29²] / (8 - 1)

t = 2.119

As a result, the test statistic's value is 2.119.

The p-value is inconsequential since it exceeds the specified significance level of 0.01 in this case.

This indicates that at a 1% level of significance, the null hypothesis cannot be ruled out.

As a result, it may be said that, at a 1% level of significance, there has been no crime decline in since the program's inception.

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Sample Response: I subtracted the highest and lowest numbers. The range for new cars was 31. The range for old cars was 75. The range for used cars was much bigger.

Answer:

Without access to specific data on monthly car sales, it is impossible to determine which type of car had the largest range in monthly sales. However, one possible method for finding this information would be to gather sales data for various car models across multiple months and compare the ranges of their sales figures. Alternatively, one could use industry reports or market analysis to determine which car types tend to have the largest fluctuations in sales from month to month.

Step-by-step explanation:

Without access to specific data on monthly car sales, it is impossible to determine which type of car had the largest range in monthly sales. However, one possible method for finding this information would be to gather sales data for various car models across multiple months and compare the ranges of their sales figures. Alternatively, one could use industry reports or market analysis to determine which car types tend to have the largest fluctuations in sales from month to month.

The number that could represent point Q is to be considered as the option c.  2 1/2.

Calculation of the number:

Since

p = -4

q could be 6.5 units to the right or to the left of point p.

So, to the right, it should be like

=p + q

= -4 +  6.5

= 2.5

Hence, The number that could represent point Q is to be considered as option c.  2 1/2.

In mathematics, a tool known as a number line offers a graphical representation of numerical values arranged in sequential order from left to right with zero located in the center. This instrument is frequently applied throughout mathematical fields when interpreting negative and positive numbers along with fractions and decimals.

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The values of y and z that make the triangles to be congruent are 13 each

From the question, we have the following parameters that can be used in our computation:

The triangles

For the two triangles to be congruent, the following equations must be true

2y = y + 13

y + 5z - 20 =  2y + z + 19

When the above equations are evaluated, we have

y = 13

Next, we have

4z = y + 39

So, we have

4z = 13 + 39

Add and divide by 4

z = 13

Hence, the values of y and z are 13

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The equation sin(4x) = 1/2 has two solutions on the interval (0, 2π]: x = π/24 and x = 5π/24.

The equation sin(4x) = 1/2 has two solutions on the interval (0, 2π].

The first solution occurs when 4x = π/6, or x = π/24. This corresponds to an angle of π/24 radians, or 7.5°.

The second solution occurs when 4x = 5π/6, or x = 5π/24. This corresponds to an angle of 5π/24 radians, or 112.5°.

Therefore, the equation sin(4x) = 1/2 has two solutions on the interval (0, 2π]: x = π/24 and x = 5π/24.

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The probability that a designer does not prefer red is 0.77. The Option 2 is correct.

Probability is a measure of how likely an event is to happen. Probability is represented as a fraction and always lies between 0 and 1.

The total number of opinions is:

= 92 + 86 + 46 + 91 + 37 + 46 + 2

= 400

The number of designers who do not prefer red is the sum of the opinions for all colors except red:

= 86 + 46 + 91 + 37 + 46 + 2

= 308

Therefore, the probability that a designer does not prefer red is:

= 308/400

= 0.77.

Full question "A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that:

Primary Color Number of Opinions

Red 92

Orange 86

Yellow 46

Green 91

Blue 37

Indigo  46

Violet 2

What is the probability that a designer does not prefer red? 1.00 0.77 0.73 0.23".

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Based on the given frequency distribution, the estimated mean carrying load of the beams tested is approximately 904.2 pounds per square foot.

To estimate the mean carrying load of the beams tested, we need to find the weighted average of the midpoints of each data class.

First, we need to find the midpoint of each class interval. We can do this by taking the average of the lower and upper limits of each interval:

Midpoint of 860 to 879 = (860 + 879) / 2 = 869.5

Midpoint of 880 to 899 = (880 + 899) / 2 = 889.5

Midpoint of 900 to 919 = (900 + 919) / 2 = 909.5

Midpoint of 920 to 939 = (920 + 939) / 2 = 929.5

Midpoint of 940 to 959 = (940 + 959) / 2 = 949.5

Next, we can find the weighted average of these midpoints, using the frequencies as weights. We can set up a table to organize our calculations:

Data class Midpoint Frequency Midpoint x Frequency

860-879           869.5                5                  4,347.5

880-899           889.5         9                         8,005.5

900-919           909.5         12                        10,914

920-939           929.5          6                         5,577

940-959            949.5          2                          1,899

Total                          34                       30,743.5

To find the weighted average, we divide the sum of the products in the last column by the total frequency:

Weighted average = Sum of (Midpoint x Frequency) / Total frequency

Weighted average = 30,743.5 / 34

Weighted average ≈ 904.2

Therefore, based on the given frequency distribution, the estimated mean carrying load of the beams tested is approximately 904.2 pounds per square foot.

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Answer:160/30000 simplified would be 2/375

Step-by-step explanation:

Exact Form:

[tex]\frac{2}{375}[/tex]

Decimal Form:

0.0053

The standard form equation of the ellipse as described in the task content is;

It follows from the task content that the standard form equation of the ellipse is to be determined.

Recall, the equation of an ellipse takes the form;

(x - h)²/a² + (y - k)²/b² = 1

where (h, k) is the center and a represents the distance of the center to each vertex on the major axis and b represents the distance from the center to each vertex on the minor axis.

Therefore, for the given scenario where center is at the origin; the equation of the ellipse is;

x²/4² + y²/(5/2)² = 1

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