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, $31,000; second year, $73,000; third year, $80,000; fourth year, $120,000. Determine the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "0.00". 1st Year 2nd Year 3rd Year 4th Year Preferred stock (dividends per share) $fill in the blank 1 $fill in the blank 2 $fill in the blank 3 $fill in the blank 4 Common stock (dividends per share)

Answer:

math = 227.98

programming = 42.55

Step-by-step explanation:

We have
3m + 4p = 854.14 -eq(1)

8m + 1p = 1866.39 -eq(2)

rq(2) x 4: 32m + 4p = 7465.56 -eq(3)

eq(3)-eq(1):

32m + 4p = 7465.56

- ( 3m + 4p = 854.14)

--------------------------------

29m = 6611.42

--------------------------------

⇒ m = 6611.42/29

m = 227.98

sub in eq(1)

3(227.98) + 4p = 854.14

4p = 854.14 - 683.94

4p = 170.2

p = 170.2/4

p = 42.55

Answer:

x = 5

Step-by-step explanation:

We can solve for x in this proportion, or an equation of ratios, by multiplying both sides by 20.

[tex]{/}\!\!\!\!\!{20}\cdot \dfrac{5}{{/}\!\!\!\!\!20}=\dfrac{x}{{/}\!\!\!\!\!20} \cdot {/}\!\!\!\!\!20[/tex]

We can see that the 20s cancel in the numerator and denominator in both sides, and the equation is solved for x:

[tex]x = 5[/tex]

Answer:

20 dimes

Step-by-step explanation:

1 dime = $0.1

1 quarter = $0.25

Let there be x dimes

Then the number of quarters is 32-x

Also, $5 = 0.1x + 0.25(32-x)

⇒ 5 = 0.1x + 8 - 0.25x

⇒ 0.25x - 0.1x = 8 - 5

⇒ 0.15x = 3

⇒ x = 3/0.15

⇒ x = 20

Note that the longest segment in the shapes shown is DC (Option B).

The longest side of a triangle is opposite to greatest angle.

To determine the longest side in a triangle, compare the lengths of all three sides. The side with the greatest length is the longest side.

You can use a ruler or a measuring tool to measure the lengths of the sides or compare the numerical values if they are provided.

In this case,

∠A = ∠DBA = 60°

So ∠ ABD is an equilateral triangle.

So, AB = BD = AD

Since

AB = BC

Then

∠BDC = ∠C ∠ 38°

so ∠DBC > 90°

This means that DC is the longest side.

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Answer:

x = 110°

Step-by-step explanation:

The opposite angles are equal in a parallelogram

3x - 60 = 2x + 50

⇒ 3x - 2x = 60 + 50

⇒ x = 110°

Answer:

x = 110°

Step-by-step explanation:

As the top and bottom line segments of the given shape are the same length and parallel (indicated by the tick marks and arrows), the shape is a parallelogram.

As the opposite angles of a parallelogram are equal, to find the value of the variable x, equate the two angle expressions and solve for x:

[tex]\begin{aligned}3x-60^{\circ}&=2x+50^{\circ}\\3x-60^{\circ}-2x&=2x+50^{\circ}-2x\\x-60^{\circ}&=50^{\circ}\\x-60^{\circ}+60^{\circ}&=50^{\circ}+60^{\circ}\\x&=110^{\circ}\end{aligned}[/tex]

Therefore, the value of x is 110°.

Note: There must be an error in the question. If x = 110°, each angle measures 270°, which is impossible since the sum of the interior angles of a quadrilateral is 360°.

Answer:

-2097152 is the 20th term

Step-by-step explanation:

Write geometric sequence as an explicit formula

[tex]-4,8,-16,32\rightarrow-4(-2)^0,-4(-2)^1,-4(-2)^2,4(-2)^3\\a_n=a_1r^{n-1}\rightarrow a_n=-4(-2)^{n-1}[/tex]

Find the n=20th term

[tex]a_{20}=-4(-2)^{20-1}=-4(-2)^{19}=4(-524288)=-2097152[/tex]

The point of intersection is (-1, 0). Therefore, the correct answer is C. (-1, 0).

To find the solution to the system of equations graphed below, we need to identify the point where the two lines intersect.

The equations of the lines are:

y = -x - 1

y = x + 1

To find the point of intersection, we can set the two equations equal to each other and solve for x:

-x - 1 = x + 1

Adding x to both sides:

-1 = 2x + 1

Subtracting 1 from both sides:

-2 = 2x

Dividing both sides by 2:

x = -1

Now that we have the x-coordinate, we can substitute this value back into either equation to find the y-coordinate. Let's use the second equation:

y = x + 1

y = -1 + 1

y = 0

Therefore, the point of intersection is (-1, 0).

Among the given options, the closest point to (-1, 0) is option C: (-1, 0).

Therefore, the correct answer is C. (-1, 0).

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Answer:

Its b i bealive

Step-by-step explanation:

Answer: seconds

Step-by-step explanation:

The statement that is true about the function is "The function is negative for all real values of x where x < -2."

To determine the statement that is true about the function f(x) = (x + 2)(x + 6) based on the given graph, we can analyze the behavior of the graph and identify the regions where the function is positive or negative.

Looking at the graph:

The function intersects the x-axis at x = -6 and x = -2.

The graph is below the x-axis between x = -6 and x = -2, and above the x-axis outside of that interval.

From this information, we can conclude that the function is negative for all real values of x where x < -2. This is because the graph is below the x-axis in that region.

Therefore, the statement that is true about the function is:

"The function is negative for all real values of x where x < -2."

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The system has exactly one solution. The solution is (13, 8)

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

Country A: -x + 20y = 147

Country B: -x + 10y = 67

Country C: y = 8

So, we have

-x + 20y = 147

-x + 10y = 67

y = 8

Substitute 8 for y in the first and second equations

So, we have

-x + 20 * 8 = 147

-x + 10 * 8 = 67

Evaluate the products

-x + 160 = 147

-x + 80 = 67

So, we have

x = 160 - 147

x = 80 - 67

Evaluate

x = 13

x = 13

Hence, the solution to the system of equations is (13, 8)

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The equation of the new function after shifting 6 units right and 4 units down is f(x) = (x + 6)² - 4.

If we are to apply the changes below to the quadratic parent function, F(x) = x², what is the equation of the new function, given that we are to shift 6 units to the right and 4 units down? We will approach this question by following the steps outlined below.

Step 1: Identify the parent function F(x) = x² and its transformations

Step 2: Write the equation of the new function

Step 3: Simplify the new equation of the function.Step 1: Identify the parent function F(x) = x² and its transformations

Here, we are given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down.

The general equation for the horizontal and vertical shifts of a quadratic function is given by:f(x) = a(x - h)² + k, where a, h, and k are constants.

The value of a determines the direction of opening of the parabola, while (h, k) represents the vertex of the parabola.

If a > 0, the parabola opens upwards, while a < 0, the parabola opens downwards. If the values of (h, k) are positive, the parabola is shifted right and up, respectively. On the other hand, if the values of (h, k) are negative, the parabola is shifted left and down, respectively.

Therefore, given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down, we can represent these changes by the following:

a = 1 (since the parabola opens upwards)h = -6 (since we are shifting the parabola 6 units to the right)k = -4 (since we are shifting the parabola 4 units down)

Step 2: Write the equation of the new function Now that we have identified the constants a, h, and k, we can write the equation of the new function as follows:f(x) = a(x - h)² + kf(x) = 1(x - (-6))² + (-4)Replacing the constants a, h, and k in the equation, we have:f(x) = (x + 6)² - 4

Step 3: Simplify the new equation of the function.f(x) = (x + 6)² - 4= (x + 6)(x + 6) - 4= x² + 12x + 36 - 4= x² + 12x + 32Therefore, the equation of the new function after shifting 6 units right and 4 units down is f(x) = x² + 12x + 32.

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The height of the building is approximately 32 meters.

To determine the height of the building, we can use the tangent function, which relates the angle of depression to the height and the length of the shadow.

Let's denote the height of the building as h.

Given that the angle of depression is 36 degrees and the length of the shadow is 44 m, we can set up the following trigonometric equation:

tan(36°) = h / 44

Now, we can solve for h by multiplying both sides of the equation by 44:

h = 44 * tan(36°)

Using a calculator, we find that tan(36°) is approximately 0.7265.

Substituting the value, we get:

h = 44 * 0.7265

Calculating the value, we find:

h ≈ 32 meters

Consequently, the building stands about 32 metres tall.

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Geno read 36 pages during the first and second hour, and 1.5 times that, which is 54 pages, during the third hour.

Let's break down the information given:

Geno read 126 pages in 3 hours.

He read the same number of pages each hour for the first 2 hours.

Geno read 1.5 times as many pages during the third hour as he did during the first hour.

Let's solve this:

Let's assume that Geno read x pages during the first hour.

Since he read the same number of pages each hour for the first 2 hours, he also read x pages during the second hour.

During the third hour, Geno read 1.5 times as many pages as he did during the first hour, which is 1.5x pages.

To find the total number of pages he read, we can add up the pages from each hour: x + x + 1.5x = 126.

Combining like terms, we have 3.5x = 126.

Divide both sides of the equation by 3.5 to solve for x: x = 36.

Therefore, Geno read 36 pages during the first and second hour, and 1.5 times that, which is 54 pages, during the third hour.

In summary, Geno read 36 pages during each of the first two hours and 54 pages during the third hour, for a total of 126 pages in 3 hours.

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Answer:

x = - 3 , x = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

to find the x- intercepts let y = 0 , that is

(x + 3)(6x - 2) = 0

equate each factor to zero and solve for x

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

6x - 2 = 0 ( add 2 to both sides )

6x = 2 ( divide both sides by 6 )

x = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

the x- intercepts are then x = - 2 and x = [tex]\frac{1}{3}[/tex]

The correct statements are: B. Circle F and circle D are similar and D. The center of circle F is (0, 3).

Explanation:

A. The radius of circle F is not 28. When a circle is translated, the radius remains the same. So, circle F has the same radius as circle D, which is 7.

B. Circle F and circle D are similar. Similarity means that the two shapes have the same shape but possibly different sizes. Since circle F is a translation of circle D, it has the same shape and proportions as circle D. Therefore, they are similar.

C. Circle F and circle D are not congruent. Congruence means that two shapes are identical in both shape and size. While circle F and circle D have the same shape, they have different positions due to the translation. Thus, they are not congruent.

D. The center of circle F is (0, 3). When a circle is translated horizontally by a certain amount, the x-coordinate of the center changes, while the y-coordinate remains the same. Since circle F is translated 2 units to the right, the x-coordinate of the center of circle F would be 2 + 0 = 2. As the y-coordinate remains the same, the center of circle F is (2, 3). Therefore, the statement is incorrect.

In summary, the correct statements are B and D. Circle F and circle D are similar, and the center of circle F is (0, 3). Therefore, Option B and D are correct.

The question was incomplete. find the full content below:

According to these three facts, which statements are true?

• Circle D has center (2, 3) and radius 7.

• Circle F is a translation of circle D, 2 units right.

• Circle F is a dilation of circle D with a scale factor of 4.

Select each correct answer.

A. The radius of circle F is 28.

B. Circle F and circle D are similar.

C. Circle F and circle D are congruent.

D. The center of circle F is (0, 3)

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Answer:

Step-by-step explanation:Angle EDH=Angle FDH, so A must be correct.

Also, we don't have more information to prove B, C, D is right

Answer:

A.

Step-by-step explanation:

An angle bisector is a line, ray, or segment that divides an angle into two equal parts. It divides the angle into two congruent or equal angles. The angle bisector originates from the vertex of the angle and extends towards the interior of the angle. It essentially cuts the angle into two smaller angles of equal measure.

Answer:

x = 11.62

Step-by-step explanation:

opp / adj would be tangent, so the equation would be 4*tan(71) giving us 11.616, and rounding to the nearest hundredth gives you 11.62

Hope this helps :)

The equation y = -6x + 2 (option c) is parallel to the graph of y = -6x + 3.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the graph in the question:

y = -6x + 3

To determine which of the given options:

a) y = (1/6)x + 3

b) y = -(1/6) + 3

c) y = -6x + 2

d) y = 3x - 6

is parallel to the graph of y = -6x + 3, we need to compare their slopes.

The given equation of the graph is y = -6x + 3:

Slope of the graph is -6.

Now, lets check each option:

a) y = (1/6)x + 3

This equation has a slope of 1/6, which is not equal to -6.

Therefore, it is not parallel to y = -6x + 3.

b) y = -(1/6) + 3

This equation also has a slope of 1/6 (the negative sign doesn't affect the slope), it is not parallel to y = -6x + 3.

c) y = -6x + 2

This equation has a slope of -6, which is the same as the slope of y = -6x + 3. Therefore, it is parallel to the given graph.

d) y = 3x - 6

This equation has a slope of 3, which is not equal to -6. Thus, it is not parallel to y = -6x + 3.

Therefore option C) y = -6x + 2 is the correct answer.

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To show that ΔJKL ≅ ΔMNR by SAS (Side-Angle-Side), we need the additional information that the lengths of the corresponding sides JK and MN are equal.

To prove ΔJKL ≅ ΔMNR using the SAS congruence criterion, we need to establish that two corresponding sides and the included angle of the triangles are congruent.

1. Given information:

  - KL ≅ NR (corresponding sides)

  - JL ≅ MR (corresponding sides)

  - ∠J ≅ ∠M (included angle)

  - ∠L ≅ ∠R (corresponding angles)

  - ∠K ≅ ∠N (corresponding angles)

  - ∠R ≅ ∠K (corresponding angles)

2. Additional information needed:

  - We need to know if JK ≅ MN (corresponding sides) to establish the SAS congruence criterion.

3. Possible scenarios:

  - If JK ≅ MN, then we can establish that ΔJKL ≅ ΔMNR by SAS.

  - If JK is not equal to MN, then we cannot apply the SAS congruence criterion, and additional information or a different congruence criterion would be needed to prove the triangles congruent.

In summary, the lengths of the corresponding sides JK and MN need to be equal to prove ΔJKL ≅ ΔMNR by SAS. Without this information, we cannot conclude the congruence of the triangles using the SAS criterion alone.

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The linear inequality represented by the graph is y < 3x + 2. Option A.

To determine the linear inequality represented by the graph, let's analyze the given information and the slope-intercept form of a linear equation (y = mx + b), where m represents the slope and b represents the y-intercept.

We are given two points on the line: (-3, -7) and (0, 2). Using these points, we can calculate the slope (m) as follows:

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

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

= 9 / 3

= 3

Therefore, the slope of the line is 3.

Next, we can substitute the slope and one of the given points into the slope-intercept form to find the y-intercept (b). Let's use the point (0, 2):

y = mx + b

2 = 3(0) + b

2 = b

So, the y-intercept (b) is 2.

Now we have the equation of the line: y = 3x + 2.

The shaded region is to the left of the line. To express this region as an inequality, we need to find the inequality symbol. Since everything to the left of the line is shaded, we need the inequality to represent values less than the line.

Therefore, the correct inequality is y < 3x + 2.

Hence, the linear inequality represented by the graph is y < 3x + 2. So Option A is correct.

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Note the complete question is

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.

Which linear inequality is represented by the graph?

A.) y < 3x + 2

B.) y > 3x + 2

C.) y < 1/3x + 2

D.) y > 1/3x + 2

Answer:

27)  34.29 in²

28)  If I get an A, then I studied for my final.

Step-by-step explanation:

To calculate the area of the trapezoid, we need to find its perpendicular height.

As the given diagram shows an isosceles trapezoid (since the non-parallel sides (the legs) are of equal length), we can use Pythagoras Theorem to calculate the perpendicular height.

Identify the right triangle formed by drawing the perpendicular height from the vertex of the bottom base to the top base (this has been done for you in the given diagram).

As the two base angles of an isosceles trapezoid are always congruent, the base of the right triangle is half the difference between the lengths of the parallel bases, which is (8 - 6)/2 = 1 inch.

The hypotenuse of the right triangle is the leg of the trapezoid, which is 5 inches.

Use Pythagoras Theorem to find the perpendicular height (the length of the other leg):

[tex]h^2+1^2=5^2[/tex]

[tex]h^2+1=25[/tex]

      [tex]h^2=24[/tex]

        [tex]h=\sqrt{24}[/tex]

        [tex]h=2\sqrt{6}[/tex]

Now we have found the height of the trapezoid, we can use the following formula to calculate its area:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Area of a trapezoid}\\\\$A=\dfrac{1}{2}(a+b)h$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area.\\ \phantom{ww}$\bullet$ $a$ and $b$ are the parallel sides (bases).\\\phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

The values to substitute into the area formula are:

Substituting these values into the formula we get:

[tex]A=\dfrac{1}{2}(8+6) \cdot 2\sqrt{6}[/tex]

[tex]A=\dfrac{1}{2}(14) \cdot 2\sqrt{6}[/tex]

[tex]A=7\cdot 2\sqrt{6}[/tex]

[tex]A=14\sqrt{6}[/tex]

[tex]A=34.29\; \sf in^2\;(nearest\;hundredth)[/tex]

Therefore, the area of the isosceles trapezoid is 34.29 in², rounded to the nearest hundredth.

[tex]\hrulefill[/tex]

Given conditional statement:

The hypothesis is "I studied for my final", and the conclusion is "I will get an A".

The converse of a conditional statement involves switching the hypothesis ("if" part) and the conclusion ("then" part) of the original statement.

Therefore, the converse of the statement would be:

49.87 because I searched it up

Answer:

16cm

Step-by-step explanation:

perimeter for C is 44cm

perimeter for A and B 60cm

60cm-44cm=16cm

Hope this helps

The graph in this problem is the graph of y = 2sin(x), not y = x, as it has a amplitude of 2.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function in this problem has an amplitude of 2, with no phase shift, no vertical shift and period of 2π, hence it is defined as follows:

y = 2sin(x)

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The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

8

Step-by-step explanation:

Substitute the values in the expression, we have:

[tex]\displaystyle{|-1-3|+4}[/tex]

Evaluate:

[tex]\displaystyle{|-4|+4}[/tex]

Any real numbers in the absolute sign will always be evaluated as positive values. Thus:

[tex]\displaystyle{|-4|+4 = 4+4}\\\\\displaystyle{=8}[/tex]

Hence, the answer is 8. A quick note that z-value is not used due to lack of z-term in the expression.

Based on the data and the one-sample t-test, at the 0.05 level of significance, there is sufficient evidence to conclude that the average bear sales per store at Wal-Mart is significantly higher than $500

.

To determine if there is evidence that the average bear sales per store at Wal-Mart is more than $500 at the 0.05 level of significance, we can conduct a one-sample t-test. Let's go through the steps:

State the null and alternative hypotheses:

Null hypothesis (H₀): The average bear sales per store is equal to or less than $500.

Alternative hypothesis (H₁): The average bear sales per store is greater than $500.

Set the significance level (α):

In this case, the significance level is given as 0.05 or 5%.

Collect and analyze the data:

The weekly sales of bears in 10 stores are as follows:

8, 11, 0, 4, 7, 8, 10, 583

Calculate the test statistic:

To calculate the test statistic, we need to compute the sample mean, sample standard deviation, and the standard error of the mean.

Sample mean ([tex]\bar X[/tex]):

[tex]\bar X[/tex] = (8 + 11 + 0 + 4 + 7 + 8 + 10 + 583) / 8

[tex]\bar X[/tex] ≈ 76.375

Sample standard deviation (s):

s = √[Σ(x - [tex]\bar X[/tex])² / (n - 1)]

s ≈ 190.687

Standard error of the mean (SE):

SE = s / √n

SE ≈ 60.174

Now, we can calculate the t-value:

t = ([tex]\bar X[/tex] - μ₀) / SE

Where μ₀ is the hypothesized population mean ($500).

t = (76.375 - 500) / 60.174

t ≈ -7.758

Determine the critical value:

Since we are conducting a one-tailed test and the alternative hypothesis is that the average bear sales per store is greater than $500, we need to find the critical value for a one-tailed t-test with 8 degrees of freedom at a 0.05 level of significance. Looking up the critical value in the t-distribution table, we find it to be approximately 1.860.

Compare the test statistic with the critical value:

Since -7.758 is less than -1.860, we have enough evidence to reject the null hypothesis.

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Using row operations to write the augmented matrix, the value of x, y and z are 2, -12 and 11

To solve the system using row operations, we'll write the augmented matrix and perform row operations to transform it into row-echelon form. Here are the steps:

1. Write the augmented matrix for the system of equations:

  [1  1  -1  |  1]

  [4  -1  1  |  9]

  [1  -3  2  |  -14]

2. Perform row operations to transform the matrix into row-echelon form:

  R2 = R2 - 4R1

  R3 = R3 - R1

  [1  1   -1  |  1]

  [0  -5  5   |  5]

  [0  -4  3   |  -15]

3. Perform row operations to further transform the matrix into row-echelon form:

  R2 = -R2/5

  R3 = -4R2 + R3

  [1  1   -1  |  1]

  [0  1   -1  |  -1]

  [0  0   -1  |  -11]

4. Perform row operations to obtain a diagonal of 1s from left to right:

  R1 = R1 + R3

  R2 = R2 + R3

  [1  1   0  |  -10]

  [0  1   0  |  -12]

  [0  0   -1 |  -11]

5. Perform row operations to transform the matrix into reduced row-echelon form:

  R3 = -R3

  [1  1   0  |  -10]

  [0  1   0  |  -12]

  [0  0   1  |  11]

The resulting matrix corresponds to the system of equations:

x + y = -10

y = -12

z = 11

Therefore, the solution to the given system of equations is x = -10 - y, y = -12, and z = 11.

So, the solution is x = -10 - (-12) = 2, y = -12, and z = 11.

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