Seventy-Two Inc. , a developer of radiology equipment, has stock outstanding as follows: 80,000 shares of cumulative preferred 3% stock, $20 par and 410,000 shares of $25 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $33,000; second year, $72,000; third year, $100,000; fourth year, $100,000. Determine the dividends per share on each class of stock for each of the four years.

Preferred stock (dividends per share)
1st Year 2nd Year 3rd Year 4th Year

Common stock (dividends per share)
1st Year 2nd Year 3rd Year 4th Year

As a result, 67° is the measure of ∠B.

Due to the fact that a triangle contains three sides, three angles, & three vertices, it's a complete, two-dimensional object. A triangle is indeed a polygonal element. Triangle ABC can be seen in the image above. Triangle illustrations. Triangles can be found on a variety of everyday objects, such as sandwiches, traffic signs, clothes hangers, and pool table racks.

Given:

∠A = 32°

∠C = 81°

∠B =?

The sum of all the angles in a triangle, as we all know, is 180 degrees.

∴ ∠A +∠B + ∠C = 180°

⇒ 32° + ∠B + 81° = 180°

⇒ ∠B + 113° = 180°

⇒ ∠B = 180° - 113°

⇒ ∠B = 67°

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Answer:

Your question is not fully completed. People can't solve it because it is not fully completed.

Step-by-step explanation:

The slopes of AB and CD are neither equal nor negative reciprocals of each other, we can conclude that AB and CD are neither parallel nor perpendicular.

To determine if AB and CD are parallel, perpendicular, or neither, we need to find the slopes of both lines.

The slope of AB can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (8, 4) and (x₂, y₂) = (4, 3).

mAB = (3 - 4) / (4 - 8) = -1/4

The slope of CD can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (4, -9) and (x₂, y₂) = (2, -1).

mCD = (-1 - (-9)) / (2 - 4) = 8 / (-2) = -4

If the two lines are parallel, their slopes must be equal. However, mAB = -1/4 and mCD = -4, so the two lines are not parallel.

If the two lines are perpendicular, their slopes must be negative reciprocals of each other. That is, mAB x mCD = -1.

However, mAB x mCD = (-1/4) x (-4) = 1, which is not equal to -1. Therefore, the two lines are not perpendicular either.

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If the company has limited resources or is not particularly concerned with precision, it may decide to forego the additional information and rely on its prior probabilities to make decisions

Bayes TheoremBayes Theorem is a statistical technique that enables one to find the probability of an event given another event that is known to have happened. The theorem states that the probability of an event A happening given that another event B has already occurred is equivalent to the probability of event B happening given that event A has already occurred multiplied by the probability of A happening divided by the probability of B happening. The revised decision tree can be produced to make a decision. However, before that, we need to find the sum of getting a Raise report for each outcome of the prior probabilities. This is shown in the table below:Consultant`s Prediction (in %)Actual Market OutcomePrior ProbabilitiesRiseStableFallRaise0.60.70.20.10.70.140.1260.0280.0140.20.30.20.60.240.0600.0180.1260.03 0.03150.0060.00210.07Total 0.34 0.36 0.30 1.00To revise the consultant's prediction using Bayes theorem, we can use the following formula:P(Stable | Raise) = (P(Raise | Stable) * P(Stable)) / (P(Raise | Stable) * P(Stable) + P(Raise | Rise) * P(Rise) + P(Raise | Fall) * P(Fall)) = (0.140 * 0.30) / (0.140 * 0.30 + 0.126 * 0.34 + 0.028 * 0.36) = 0.2906 or 29.06%The probability of getting a stable report given a raise report is 29.06%. This value can also be calculated for getting a fall report given a raise report using the same formula, which gives a probability of 24.51%.To make a decision on whether to use the consultant firm or not, we can use the revised decision tree. The tree shows that the probability of getting a raise report is only 34%, and given that we get a raise report, the probability of getting a stable report is 29.06% while the probability of getting a fall report is 24.51%.If the company decides to use the consultant firm, they will have to pay for the additional information. This cost needs to be weighed against the benefits of having this information, which will depend on the goals and priorities of the company. If the company values precision and accuracy in its decision-making process and is willing to pay for it, then it may choose to use the consultant firm. However, if the company has limited resources or is not particularly concerned with precision, it may decide to forego the additional information and rely on its prior probabilities to make decisions.

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Answer:

4                      [Yes, really]

Step-by-step explanation:

(8/64)^-2/3      [Wow]

(1/8)^-2/3         [Simplify 8/64 to 1/8]]

(8^-1)^-2/3      [Reformat (1/8) to 8^-1]

8^(-1*(-2/3))      [Rule of exponents: When an exponent is raised to another exponent,  multiply the exponents.]

8^(2/3)             [Simplify (-1(-2/3)) to (2/3)]

64^(1/3)            [8^(2/3) means square the 8 and then take the cube root]

4                      [The cube root of 64 is 4 (4*4*4 = 64]

When these two numbers are subtracted, the difference is 2 3/4, which is the total change in the volume of water in the birdbath after two days. This can be written as a mixed number, which would be 2 3/4.

The total change in the volume of water in the birdbath after two days can be determined by subtracting the starting volume of water (1 1/2) from the ending volume of water (4 1/4).

The total change in the volume of water in the birdbath after two days is an important figure to calculate in order to understand the amount of water that has been added or removed from the birdbath. To calculate this figure, one must subtract the starting volume of water from the ending volume of water. In this scenario, the starting volume of water was 1 1/2 and the ending volume of water was 4 1/4. When these two numbers are subtracted, the difference is 2 3/4, which is the total change in the volume of water in the birdbath after two days. This can be written as a mixed number, which would be 2 3/4. This figure is important to know as it can help one determine how much water has been added or removed from the birdbath over a certain period of time.

the complete question is :

A birdbath is filled to the top. On Day 1, the volume of water in the bowl decreases by 7/8 cup. On Day 2, the volume in the bowl decreases by 3/4 cup. What number represents the total change in the volume of water in the bowl after two days? Write your answer as a mixed number.

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Alexandra's net pay each month, using mathematical operations, is C. $3,648.60.

The net pay is the difference between the gross pay or earning and the total deductions.

The net pay per month can be computed following these steps:

Gross earnings per year = $59,904.00

Monthly taxes = $998.40

Annual taxes = $11,980.80 ($998.40 x 12)

Monthly medical, dental, and vision insurance = $345.00

Annual medical, dental, and vision insurance = $4,140 ($345 x 12)

Total deductions and taxes = $16,120.80 ($11,980.80 + $4,140)

Annual net pay = $43,783.20 ($59,904.00 - $16,120.80)

Monthly net pay = $3,648.60 ($43,783.20/12)

Thus, monthly, Alexandra will earn a net pay of Option C.

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Answer:

The expression to represent the total area as the sum of the areas of each room would be:

Total area = area of kitchen + area of bathroom + area of remaining space

Total area = 7 x 11 + 4 x 11 + (11 - 7 - 4) x 11

Total area = 77 + 44 + 11

Total area = 132 square feet

The sum of the perimeters of all squares is 80 ft.

What is perimeter?

Perimeter is the distance around the outer boundary of a two-dimensional shape, such as a rectangle, square, triangle, or circle. It is the total length of all the sides of the shape.

Starting with a square with a perimeter of 40 ft, we can find the length of one side by dividing the perimeter by 4:

[tex]\frac{40ft}{4} = 10ft[/tex]

So, the original square has a side length of 10 ft.

Connecting the midpoints of the sides of this square creates a new square with half the side length of the original square. Each side of this new square is the hypotenuse of a right triangle with legs equal to half the side length of the original square (i.e., 5 ft).

Using the Pythagorean theorem, we can find the length of each side of the new square:

[tex]s^2 = (5 ft)^2 + (5 ft)^2[/tex]

[tex]s^2 = 50 ft^2[/tex]

[tex]s = \sqrt{50}ft[/tex]

So, the second square has a side length of [tex]\sqrt{50}ft[/tex], which is approximately 7.07 ft.

Continuing this process, each subsequent square will have half the side length of the previous square. Therefore, the side length of the third square will be half the side length of the second square, which is:

[tex]\frac{1}{2}[/tex] * [tex]\sqrt{50}ft[/tex] = [tex]\sqrt{25}ft[/tex] = 5 ft.

The side length of the fourth square will be half the side length of the third square, which is: [tex]\frac{1}{2}[/tex] * 5 ft = 2.5 ft. And so on.

The perimeters of the squares are:

The perimeter of the first square is 40 ft.

The perimeter of the second square is 4 * [tex]\sqrt{50}ft[/tex], which is approximately 28.28 ft.

The perimeter of the third square is 4 * 5 ft = 20 ft.

The perimeter of the fourth square is 4 * 2.5 ft = 10 ft.

We can see that the perimeter of each subsequent square is half the perimeter of the previous square. So, the series for the perimeters of the squares is a geometric series with a first term of 40 ft and a common ratio of 1/2.

Using the formula for the sum of an infinite geometric series, we can find the sum of the perimeters of all squares:

S = a / (1 - r)

where a is the first term (40 ft) and r is the common ratio (1/2). Plugging in these values, we get:

S = 40 ft / (1 - 1/2)

S = 80 ft

Therefore, the sum of the perimeters of all squares is 80 ft.

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Therefore , the solution of the given problem of expressions comes out to be  x ≈ 0.6309.

Calculations that combine joining, removing, and random subdivision must be done with ever-changing factors. They could accomplish the following if they united: An programme, some data, and a mathematical problem. Formulas, components, and arithmetic operations like adds, subtractions, mistakes, and groupings can all be found in a declaration of truth.

Here,

We can rewrite this equation as follows in order to answer it using the properties of logarithms:

We can now use a substitution to simplify the problem. Let y = 8^x.

By finding x, we obtain:

=>  y = (6³ˣ))/8

This equation can be made simpler by applying the formula 8 = 23:

=> y = (6³ˣ))/(2³)

=> y = (3³ˣ)/(2³)

=> 6³ˣ - (3³ˣ)/(2³) = 0

=> (6³ˣ)*(2³) - (3³ˣ) = 0

=> (2³)/(3³ˣ) - 1 = 0

=> log((2³)/(3³ˣ)) = log(1)

=> log(2³) - log(3³ˣ) = 0

Simplifying, we get:

=> 3log(2) - 3xlog(3) = 0

By multiplying both parts by 3log(3), we obtain:

=> x = (log(2))/(log(3))

Using a calculator, we can calculate this expression to four decimal places:

=>  x ≈ 0.6309

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The measure of angle B on the straight line is 22 degrees

When two angles lie along a straight line, they form a straight angle which measures 180 degrees.

The statement from the question can be represented as

m∠A = 4(m∠B + 17.5°)

But we know that the sum of the measures of angles A and B is 180 degrees, since they form a straight angle.

m∠A + m∠B = 180°

Substitute the known values in the above equation, so, we have the following representation

4(m∠B + 17.5°) + m∠B = 180°

Simplifying this equation, we get:

5m∠B + 70° = 180°

Subtracting 70 degrees from both sides, we get:

5m∠B = 110°

Dividing both sides by 5, we get:

m∠B = 22°

Therefore, the measure of angle B is 22 degrees.

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The inequality that represents this situation is (x × y) + (z x n) ≥ $300 and the quantities are true for h when the value is 36.

To find the value of h (the number of hours Chris needs to work), we can rearrange the inequality as follows:

Base wage x Number of hours worked ≥ $300 - Bonus per book x Number of books sold

Number of hours worked ≥ ($300 - Bonus per book x Number of books sold) / Base wage

Now, let's substitute the values we know into this equation. We know that Chris earns a base wage of $7.50 per hour and a $2 bonus for each book sold. We also know that she sold 15 books. Therefore:

Number of hours worked ≥ ($300 - $2 x 15) / $7.50

Number of hours worked ≥ ($300 - $30) / $7.50

Number of hours worked ≥ $270 / $7.50

Number of hours worked ≥ 36

So, the inequality that represents this situation is:

Base wage x Number of hours worked + Bonus per book x Number of books sold ≥ $300

Now, let us consider that x refers the Base wage, y refers the Number of hours worked, z refers the Bonus per book and n refers the Number of books sold, then the resulting inequality is

=>  (x × y) + (z x n) ≥ $300

And the true value of h (the number of hours Chris needs to work) is at least 36 hours.

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The Celsius temperature that has the same value as when converted to a Fahrenheit temperature is -40

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

F = 9/5C + 32

The Celsius temperature that has the same value as F implies that

C = F

Substitute the known values in the above equation, so, we have the following representation

C = 9/5C + 32

So, we have

C - 9/5C = 32

Evaluate the like terms

-4/5C = 32

So, we have

C = -32 * 5/4

Evaluate

C = -40

Hence, the value of C is -40

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For the isolated term the value of f/2  is -2.5

Given the equation f/2+9=4, we need to isolate the term f/2 to solve for the value of f. To do so, we need to perform the same operation on both sides of the equation in order to keep it balanced.

One way to isolate f/2 is to subtract 9 from both sides of the equation. This would give us:

f/2 = -5

By subtracting 9 from both sides, we removed the constant term from the left side of the equation. This operation did not affect the capacity of the equation, as we simply moved a constant value from one side to the other.

Another way to isolate f/2 is to multiply both sides of the equation by 2. This would give us:

f + 18 = 8

By multiplying both sides by 2, we eliminated the denominator on the left side of the equation, and the capacity of the equation remained unchanged.

Next, to isolate the term f, we need to perform the same operation on both sides of the equation, but this time with a different set of values.

To isolate f, we can subtract 18 from both sides of the equation. This would give us:

f = -10

By subtracting 18 from both sides, we removed the constant term from the right side of the equation, and the capacity of the equation remained the same.

We can also isolate f by dividing both sides of the equation by 2. This would give us:

f/2 = -2.5

By dividing both sides by 2, we eliminated the numerator on the left side of the equation, and the capacity of the equation remained unchanged.

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Therefore , the solution of the given problem of unitary comes out to be

option A is correct option.

The task can be finished by combining the data expression obtained to use this nanosection methodology with in all supplemental data from two people who employed a particular variable tactic. In plain English, this indicates that, if the desired result occurs, either the stated individual will be known or, in fact, the colour by both enormous processes would be skipped. A refundable fee of Rupees ($1.01) may be necessary for forty pens.

Here,

Given :

there is a relationship between a person’s age and their preference for a particular style of dress.

So,

The question can be included in the interview

and so,

option A. The questions are acceptable because the researcher is studying the relationship between age and preferred dress style.

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A. The questions are acceptable because the researcher is studying the relationship between age and preferred dress style.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence.

conducting a research study, it is important to carefully consider the questions being asked in the survey to ensure that they are relevant to the research question and that they do not cause any harm or offense to the participants. In the case of the clothing designer's survey, asking about age and dress size is relevant to the study's goal of investigating the relationship between age and preferred dress style. Therefore, including these questions in the survey is acceptable.

However, it is also important to consider the potential concerns or discomfort that some participants may have about answering these questions. To address these concerns, the survey questions should be worded in a respectful and non-intrusive manner.

Therefore, A. The questions are acceptable because the researcher is studying the relationship between age and preferred dress style.

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In this case, the probability of getting a question wrong is 0.5, and there are 16 questions, so the expected value of incorrect answers is 0.5 x 16 = 8.

The expected value of the number of incorrect answers on a 16-question true or false exam with random guessing is 8. This is because there are an equal number of true and false answers, and the chance of getting each one correct is 50%. Therefore, the expected value of incorrect answers is 8.

To calculate the expected value, you need to multiply the probability of getting a question wrong by the number of questions.

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Answer:

range = 60

Step-by-step explanation:

the range of the data set is the difference between the largest and smallest values in the set.

the largest value = 140 ( denoted by the line on furthest right )

the smallest value = 80 ( denoted by line on left )

range = 140 - 80 = 60

Answer:

33

Step-by-step explanation:

First, you multiply 3 into the other equation (remember, anytime there is a parentheses by each like there is shown, it will be multiplication.) So -3 * -7 is 21 because a negative and a negative is a positive. Then -3 * -4 which is 12. Add 21 and 12 together and you get 33!

I hoped this helped <3

Answer:

(-4, -2)      x=−4,  y=−2

Step-by-step explanation:

According to the given information, it will take Hector 15 weeks to reach 10 km if he starts at 2.5 km and adds 0.5 km every week.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equals sign (=), where each side contains an expression that may contain variables, constants, or mathematical operations. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.

The equation that correctly determines how many weeks it will take Hector to reach 10 km is 0.5x + 2.5 = 10, where x is the number of weeks.

To verify, we can solve for x:

0.5x + 2.5 = 10

0.5x = 10 - 2.5

0.5x = 7.5

x = 7.5/0.5

x = 15

Therefore, it will take Hector 15 weeks to reach 10 km if he starts at 2.5 km and adds 0.5 km every week.

The other equations are not equivalent to Hector's weekly addition of 0.5 km:

0.5 – 2.5 = 10x is not equivalent because it does not involve adding 0.5 every week.

2.5x + 0.5 = 10 is not equivalent because it does not take into account Hector's starting distance of 2.5 km.

2.5x – 0.5 = 10 is not equivalent because it does not involve adding 0.5 every week and it also does not take into account Hector's starting distance of 2.5 km.

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Answer:

5 weeks

Step-by-step explanation:

To solve this problem, we can use the idea of proportionality. We know that the number of quizzes Percy takes is directly proportional to the number of weeks he attends school. This means that we can set up a proportion:

12 quizzes / 4 weeks = 15 quizzes / x weeks

We can cross-multiply to get the following:

12x = 60

Then we can solve for x:

x = 60/12 = 5

Therefore, Percy will have to attend 5 weeks of school to take a total of 15 quizzes.

If 87¹/₂ percent of milk is water and a gallon consists of 16 cups, the number of cups of water in a gallon of milk is 14 cups.

A value expressed in percentage implies that it is the quotient multiplied by 100.

The quotient is the result of the division operation involving a portion and the whole value.

The number of cups in a gallon of milk = 16

The percentage of the content that is water = 87¹/₂%

87¹/₂% of 16 = 14 cups (16 x 87¹/₂%)

Thus, we can state that out of 16 cups in a gallon of milk, water consists of 14 cups, which is 87¹/₂ per cent.

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Answer:

[tex]q > 20[/tex]

Step-by-step explanation:

[tex] - q < - 13 - 7[/tex]

[tex]q > 20[/tex]

Answer:

angle=80 degrees

Step-by-step explanation:

if we know the arc is 160 degrees than we know we want to find the interior angle, then we must divide 160/2 to get the measure of the indicated angle.

In the case of the example given, the finance charge is $5.32, which is the amount of money that will be charged for borrowing the money for the given period.

Finance charges refer to the fees and interest associated with borrowing money or making a purchase on credit. Finance charges are usually expressed as a percentage of the total amount borrowed or purchased, and they are calculated based on the interest rate and the length of the loan term. In the case of the example given, the finance charge is $5.32, which is the amount of money that will be charged for borrowing the money for the given period. The finance charge is calculated by multiplying the interest rate by the amount borrowed and then dividing it by the total number of days in the loan term.

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Answer:

the mean is 13

Step-by-step explanation:

the mean is all the numbers added (130) divided the number of numbers in the set(10)

A2AGE, A2HT, A2WGT, A2FTL, A2HC, A2CC, A2NC, A2WC, A2SW, A2SH, A2SKH, A2SEH, A2NHT, A2PPD, A2ARM, A2WH, A2GND

The ANSUR II study was conducted in 2012 and consisted of body measurements from 6068 U.S. Army personnel. In the data set, AGE is in years, WEIGHT is in kilograms (kg), GENDER is identified as 1=male and 0=female, WRITING HAND is 1=right and 2=left and 3=both, and the other body measurements are in millimeters (mm). The following data list names are provided for TI-83/84: A2AGE, A2HT, A2WGT, A2FTL, A2HC, A2CC, A2NC, A2WC, A2SW, A2SH, A2SKH, A2SEH, A2NHT, A2PPD, A2ARM, A2WH, A2GND.

The first five rows of the data set are provided here for reference:

AGE HEIGHT WEIGHT FOOT LENGTH HEAD CIRC CHEST CIRC SHOULDER WIDTH SITTING HT ARM SPAN WRITING HAND GENDER (1=M)
41 1776 81.5 273 583 1074 493 928 1782 1 1
35 1702 72.6 263 568 1021 479 884 1745 2 1
42 1735 92.9 270 573 1120 544 917 1867 2 1
31 1655 79.4 267 576 1114 518 903 1708 1 1
21 1914 94.6 305 566 1048 524 919 2035 1 1

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The expression can be simplified by breaking it down into its individual components. we multiply this by 5 squared, which simplifies to 25 x 5 = 125. Lastly, we subtract 7.3 from 125 to get 117.7, which is the final answer.

First, we can evaluate the expression inside the parentheses, which is -4.5 + 6.87. This evaluates to 2.37. We then divide this by 3 to get 0.79. Next, we multiply this by 5 squared, which gives us 79. Lastly, we subtract 7.3 from 79 to get 71.7, which is the final answer.

The expression can be expanded by breaking it down into its individual parts. First, we have -19, which is already in its expanded form. Next, we can expand the expression inside the parentheses, which is -4.5 + 6.87. This can be expanded to -4 + 0.5 + 6 + 0.87, which simplifies to -4 + 6 + 0.87 = 2.87. We then divide this by 3 to get 0.79. Next, we multiply this by 5 squared, which simplifies to 25 x 5 = 125. Lastly, we subtract 7.3 from 125 to get 117.7, which is the final answer.

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Answer:

=7542,71

Step-by-step explanation:

13 680.00 x 0.551368

=7542,71424

round off to the second decimal place

=7542,71