The board of directors of Midwest Foods has declared a dividend of $3,500,000. The company has 300,000 shares of preferred stock that pay $2.85 per share and 2,500,000 shares of common stock. After finding the amount of dividends due the preferred shareholders, calculate the dividend per share of common stock.

Answer:

14π or 43.96

Step-by-step explanation:

C = 2πr and we know that r = 7 so C = 14π or 43.96.

Answer: x = 6.32 or -0.32

Step-by-step explanation:

2x² - 6x + 10  = 0

No we divide the expression by 2 to make the coefficient of x² equals 1

We now have

x² - 3x + 5     = 0

Now we remove 5 to the other side of the equation

x² - 3x          = -5

we add to both side square of  half the coefficient of x which is 3

x² - 3x + ( ⁻³/₂)²  = -5 + (⁻³/₂)²

(x  -  ³/₂)²           = -5 + ⁹/₄

Resolve into fraction

(x  - ³/₂)²             = ⁻¹¹/4

Take the roots of the equation

 x - ³/₂               = √¹¹/₄

 x - ³/₂               = √11/₂

x                       = ³/₂ ± 3.32/₂

                         = 3+ 3.32 or 3 - 3.32

                         =  6.32 or - 0.32

Answer:

Step-by-step explanation:

[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]

Convert the mixed number to an improper fraction

[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]

To divide by a fraction, multiply the reciprocal of that fraction

[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]

Reduce the number with the G.C.F 7

[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]

Reduce the numbers with the G.C.F 17

[tex] \frac{5}{6} \times \frac{3}{2} [/tex]

Reduce the numbers with the G.C.F 3

[tex] \frac{5}{2} \times \frac{1}{2} [/tex]

Multiply the fraction

[tex] \frac{5}{4} [/tex]

In mixed fraction:

[tex]1 \frac{1}{4} [/tex]

Hope this helps..

Good luck on your assignment...

Answer:

Inventory turnover ratio is 3.74

explanation:

Inventory turnover is a ratio of the number of times a company's inventory is sold and replaced in a given period.

Inventory turn over ratio is calculated as ; Cost of goods sold ÷ Average stock of goods sold

= $35,500 / $9500

= 3.74

Answer:

  $0.50

Step-by-step explanation:

Let's remove common factors from the equations.

Subtracting the first equation from the second, we find the cost of an apple:

  (2x +y) -(x +y) = 1.75 -1.25

  x = 0.50

The cost of one apple is $0.50.

Answer:

[tex]\large \boxed{\text{Eight days}}[/tex]

Step-by-step explanation:

1. Calculate the hours

[tex]\text{Hours} = \text{1800 flags} \times \dfrac{\text{1 h}}{\text{45 flags}} = \textbf{40 h}[/tex]

2. Calculate the days

[tex]\text{Days} = \text{40 h} \times \dfrac{\text{1 da}}{\text{5 h}} = \text{8 da}\\\\\text{It will take $\large \boxed{\textbf{eight days}}$ to make 4500 flags.}[/tex]

Answer:

Number : 41

Step-by-step explanation:

Say that this number is x. The sum of this number ( x ) and 9 subtracted from 60 will be 10. Therefore we can create the following equation to solve for x,

60 - (x + 9) = 10,

60 - x - 9 = 10,

51 - x = 10,

- x = 10 - 51 = - 41,

x = 41

This number will be 41

Answer:

[tex]\boxed{m = -2}[/tex]

Step-by-step explanation:

[tex]0 = 4+4(m+1)[/tex]

Resolving Parenthesis

[tex]0 = 4+4m + 4[/tex]

[tex]0 = 4m+8[/tex]

Subtracting 8 to both sides

[tex]-8 = 4m[/tex]

[tex]4m = -8[/tex]

Dividing both sides by 4

m = -8/4

m = -2

Step-by-step explanation:

4+4m+4= 0

4m+8=0

4m=-8

m= -8/4=-2

Answer:

z(max) = 650 $

x₁ = 10 units

x₂ = 15 units

Step-by-step explanation:

That is a linear programming problem, we will use a simplex method to solve it

Formulation:

Let´s call  x₁  number of chairs   and x₂ number of tables then :

Item              (in hours)     cutting       assembly      finishing        Profit ($)

Chairs (x₁)                              1                   2                     1                      20

Tables (x₂)                              2                   1                      1                      30

Availability                           40                 42                   25

Objective Function

z  =  20*x₁   +  30x₂   ( to maximize) subject to:

x₁  +  2x₂   ≤  40

2x₁  + x₂    ≤  42

x₁ + x₂     ≤    25

x₁  ,   x₂  >= 0

Using excel or any other software we find:

z(max) = 650

x₁ = 10

x₂ = 15

The chairs and tables manufactured by the factory is an illustration of linear programming, where the maximum revenue is 674

Let x represent chairs, and y represent tables

So, the given parameters are:

Cutting:

So, the constraint is:

[tex]\mathbf{x + 2y \le 40}[/tex]

Assembly:

So, the constraint is:

[tex]\mathbf{2x + y \le 42}[/tex]

Finishing:

So, the constraint is:

[tex]\mathbf{x + y \le 25}[/tex]

The unit profit on the items are:

So, the objective function to maximize is:

[tex]\mathbf{Max\ z = 20x + 30y}[/tex]

And the constraints are:

[tex]\mathbf{x + 2y \le 40}[/tex]

[tex]\mathbf{2x + y \le 42}[/tex]

[tex]\mathbf{x + y \le 25}[/tex]

[tex]\mathbf{x,y \ge 0}[/tex]

Using graphical method (see attachment for graph), we have the following feasible points:

[tex]\mathbf{(x,y) = \{(10,15),\ (17,8),\ (14.67, 12.67)\}}[/tex]

Calculate the objective function using the feasible points.

[tex]\mathbf{z = 20 \times 10 + 30 \times 15}[/tex]

[tex]\mathbf{z = 650}[/tex]

[tex]\mathbf{z = 20 \times 17 + 30 \times 8}[/tex]

[tex]\mathbf{z = 580}[/tex]

[tex]\mathbf{z = 20 \times 14.67+ 30 \times 12.67}[/tex]

[tex]\mathbf{z = 673.5}[/tex]

Approximate

[tex]\mathbf{z = 674}[/tex]

Hence, the maximum revenue is 674

Read more about linear programming at:

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Answer:  ($143.69, $156.31)

Step-by-step explanation:

Confidence interval to estimate  population mean :

[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]

, where [tex]\sigma[/tex] = population standard deviation

n= sample size

[tex]\overline{x}=[/tex] Sample mean

z= critical value.

As per given,

n= 40

[tex]\sigma[/tex] = $15.50

[tex]\overline{x}=[/tex] $150

Critical value for 99% confidence level = 2.576

Then, 99% confidence interval for the population mean:

[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]

Hence, the required confidence interval : ($143.69, $156.31)

Answer:

C.

Step-by-step explanation:

So, here's what you need to remember:

If we have a function f(x) and a factor k:

k(f(x)) will be a vertical stretch if k is greater than 1, and a vertical compression if k is greater than zero but less than 1.

f(kx) will be a horizontal compression if k is greater than 1, and a horizontal stretch if k is greater than zero but less than 1.

We are multiplying 0.5 to the function. In other words: 0.5f(x).

This is outside the function, so it's vertical.

0.5 is less than 1, so this would be a vertical compression

Answer:

63

Step-by-step explanation:

Given that;

The bag has two red marbles,  n(red) =2

three green ones marbles,  n(green) = 3

one lavender one marbles,  n(lavender) = 1

two yellows marbles,            n(yellow ) = 2

two orange marbles.              n(orange) = 2

number of non green marbles = 2+1+2+2 = 7

The objective is to find out how many sets of four marbles include exactly two green marbles

Since sets of four marbles contain exactly two green marbles, then N(select 2 from 3 marbles and 2 from 7 marbles)

= [tex]^3C_2 \times ^{7}C _2[/tex]

= [tex]\dfrac{3!}{2!(3-2)!} \times \dfrac{7!}{2!(7-2)!}[/tex]

= [tex]\dfrac{3*2!}{2!} \times \dfrac{7*6*5!}{2!(5)!}[/tex]

=  [tex]3 \times 7\times 3[/tex]

= 63

Answer:

x=-11

Step-by-step explanation:

x+8=-3

x=-3-8 :- collect like term

since we are adding two negative numbers, we will let the number be negative but add them.

x=-11

Hope it helps :)

Answer:

x=-11

Step-by-step explanation:

x+8=-3

collect like terms;

x=-3-8

x=-11

Answer:

Option One:

type : linear growth

a : 120

b : 130

Option 2:

type: linear growth

d : 121

e : 133

Step-by-step explanation:

its right on EDG 2020

Option One:

type: linear growth

a: 120

b: 130

Option 2:

type: linear growth

d: 121

e: 133

Linear growth occurs with the aid of including an equal amount in each unit of time. An exponential increase happens while a preliminary population will increase by the same percent or issue over the same time increments or generations.

Linear and exponential relationships vary within the way the y-values change whilst the x-values increase with the aid of a steady quantity: In linear dating, the y-values have identical variations. In an exponential relationship, the y-values have identical ratios.

Learn more about Linear growth here: brainly.com/question/4025726

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Answer:

1 + 1 = 2

Step-by-step explanation:

^

Answer:

no , it's happening to everyone , even I can't see it .

Answer:

C) 24/25

Step-by-step explanation:

did the quiz and got it right

The value of the sine theta in the first quadrant in the diagram given is [tex]\mathbf{\dfrac{24}{25}}[/tex]

The explanation of the trigonometric functions (i.e cosine, sine, tangent) in respect of point coordinates on the unit circle informs us of the signs and meanings of the trigonometric functions for each of the four(4) quadrants, depending on the signs of the x, as well as, y coordinates in each quadrant.

In the first quadrant;

Thus, we have a positive x and y-axis.

Taking the forms x and y, i.e. (x, y) = (cos θ, sin θ)

The value of sine theta in [tex]\mathbf{(\dfrac{7}{25}, \dfrac{24}{25} ) = \dfrac{24}{25} }[/tex]

Learn more about Trigonometric functions here:

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Answer:

33333 x 166667 = 5555511111

I think that is the answer you wanted

Step-by-step explanation:

      166667

     x 33333

5555511111

Hi there! :)

Answer:

Given the information, we can write an equation in slope-intercept form

(y = mx + b) to graph the line:

Plug in the slope for 'm', the y-coordinate of the point given for 'y', and the

x-coordinate given for 'x':

-4 = -2/3(-7) + b

-4 = 14/3 + b

Solve for b:

-12/3 = 14/3 + b

-12/3 - 14/3 = b

-26/3 = b

Therefore, the equation of the line is y = -2/3x - 26/3 (Graphed below)

Some points on the line include:

(-7, -4)

(-4, -6)

(0, -26/3)

(2, -10)

(5, -12)

Answer:

angle JKL =  120 degrees

Step-by-step explanation:

Since arc JL is 60 degrees, the central angle is also 60 degrees.

Point K is the intersection of tanges at J and L, therefore KJM and KLM are 90 degrees.

Consider quadrilateral JKLM whose sum of internal angles = 360.

Therefore

angle JKL + angle KLM + angle LMJ + angle MJK = 360 degrees

angle JKL + 90 + 60 + 90 = 360

angle JKL = 360 - 90 - 60 -90 = 120 degrees

Answer:

120 degrees

Step-by-step explanation:

Since arc JL is 60 degrees, the central angle is also 60 degrees.

Point K is the intersection of tanges at J and L, therefore KJM and KLM are complementary or equal 90 degrees.

look at quadrilateral JKLM whose sum of internal angles = 360.

Therefore

angle JKL plus angle KLM plus angle LMJ plus angle MJK = 360 degrees

angle JKL + 90 + 60 + 90 = 360

Answer:

Optimal production = 600 gold pens

Revenue  = 600*7 = $4200 gold pens

Step-by-step explanation:

The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model.

A. The silver model requires 1 minute in a grinder and 3 minutes in a bonder.

B. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder.

Because of maintenance procedures,

C. the grinder can be operated no more than 30 hours per week and

D. the bonder no more than 50 hours per week.

The company makes

E. $5 on each silver pen and

F. $7 on each gold pen.

How many of each type of pen should be produced and sold each week to maximize profits?

Solution:

We will solve the problem graphically, with number of silver pens, x, on the x axis, and number of gold pens, y, on the y axis, i.e.

1. From A and C, the maximum number of silver pens

x <= 30*60 / 1 = 1800 and

x <= 50*60 /3 = 1000  ....................(1)   bonder governs

2. from A & D, the maximum number of gold pens

y <= 30*60 / 3 = 600 .....................(2) grinder governs

y <= 50*60 / 4 = 750

3. From D,

x + 3y <= 30*60 = 1800  ...................(limit of grinder) ..... (3)

3x + 4y <= 50*60 = 3000 .................(limit of bonder)  .......(4)

Need to maximize profit,

Z(x,y) = 5x+7y, represented by parallel lines y = -5x/7 + k such that all constraints of (3) and (4) are satisfied.

The maximum is obtained when Z passes through (360,480), i.e. at intersection of constraints (3) and (4).  Using slope intercept form,

(y-480) = -(5/7)(x-360)

or y=-(5/7)x + (737+1/7)    [the purple line] which violates the red line, so not a solution.

Next try the point (0,600)

(y-600) = -(5/7)(x-0), or

y = 600 - (5/7)x   [the black line]

As we can see all point on the black (in the first quadrant) satisfy the constraints, so it is a feasible solution, and is the optimal solution, with a revenue of

Revenue  = 600*7 = 4200 gold pens

Answer:

[tex]\boxed{9}[/tex]

Step-by-step explanation:

The two angles are complementary to each other.

That means they add up to 90 degrees.

[tex]5x+15+30=90[/tex]

[tex]5x+45=90[/tex]

[tex]5x=45[/tex]

[tex]x=9[/tex]

Answer:

x = 9

Step-by-step explanation:

So you know that the total is 90 degrees.

What you need to do is create an equation.

5x + 15 + 30 = 90

Then, solve the equation like this.

5x + 15 + 30 = 90

5x + 45 = 90

5x = 90 - 45

5x = 45

x = 45 ÷ 5

x = 9

Hope this helps! :)

Answer: Parents and children ( till the age of 5) of Norway

Step-by-step explanation:

Here, A large study of over 2000 parents and children in Norway found that toddlers who regularly slept less than 10 hours per night or woke frequently (three or more times) at night tended to experience more emotional and behavioral problems when they reached age five.

Since the study involved a large random sample of mothers and children and was conducted over several years.

So, the population of interest in this survey is "Parents and children ( till the age of 5) of Norway".

Answer:

4

Step-by-step explanation:

Answer:

1/8 < 1/6

Step-by-step explanation:

The top is divided into 8 and 1 part is shaded so 1/8

The bottom is divided into 6 and 1 part is shaded so 1/6

Comparing

1/8 < 1/6

Answer:

192

Step-by-step explanation:

There are a total of 15 marbles . When the lavender is left out 14 remain.

Using combinations we find that each of the four color marbles can be chosen in the following way.

2C1*4C1*4C1*6C1= 2*4*4*6=  192

We select  one of the two red marbles , one of the four green marbles, one of the four yellow marbles, one of the 6 orange marbles leaving the lavender out.. We apply combinations and then multiply to get the answer.

Answer:

1

Step-by-step explanation:

We can find the slope using

m= ( y2-y1)/(x2-x1)

   = ( -8 - -4)/( 4 - 8)

   =  ( -8 +4)/( 4 - 8)

   = -4 / -4

   = 1

Answer:

slope equals 1

Step-by-step explanation:

To do this you would need to do an equation that is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex] so in this case -8 would be y2 and -4 would be y1 and 4 would be x2 and 8 would b e x1 so if you plug it into the equation we would get [tex]\frac{-8-(-4)}{4-8}[/tex] and if we simplify we get [tex]\frac{-4}{-4}[/tex] which simplifies to 1 so the slope would equal 1

Answer:

37

Step-by-step explanation:

To find the fifth term , we have to take the value of n as 5

So, F(5)= 6.5 (5) +4.5

= 32.5 + 4.5

= 37

Answer:

x = 65°

Step-by-step explanation:

Naming the sides of the parallelogram formed ABCD as shown in the attached image to this solution.

Angle A = 2x (vertically opposite angles are equal)

Angle A = Angle C (opposite angles of a parallelogram are equal)

Angle A = Angle C = 2x

(Angle C) + 50° = 180° (Sum of angles on a straight line is 180°)

2x + 50° = 180°

2x = 180° - 50° = 130°

x = (130°/2) = 65°

Hope this Helps!!!

Answer:

65 degrees

Step-by-step explanation:

The answer is 47 pounds

Explanation:

1. First, let's calculate the amount of money that was spent on chicken

$5 per pound of chicken x 25 pounds = $125

2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.

$454 (total) - $125 (chicken)  =  $329

3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.

$329 / $7 = 47 pounds

Answer:

A=82°

a= 67.4

c = 60.1

Step-by-step explanation:

For A

A+B+C =180°

A= 180-(B+C)

A= 180-(36+62)

A= 189-(98)

A= 82°

For a

a/sinA= b/sinB

a/sin82= 40/sin36

a= (40*sin82)/sin36

a=( 40*0.9903)/0.5878

a=67.39

Approximately = 67.4

For c

c/sinC= b/sinB

c= (sinC*b)/sinB

c= (sin62*40)/sin36

c =(0.8829*40)/0.5878

c = 60.08

Approximately = 60.1