Scenario The height, in feet, of an object shot upwards into the air with an initial velocity, in feet per second, of v. after t seconds is given by the formula: h = - 161² + vt Use the equation above to answer questions about a model rocket is launched from the ground into the air with an initial velocity of 320 feet per second. Use the graph below to help answer the questions. Height in Feet Н. Starting Point Highest Point Time in Seconds Landing Point : Assessment Instructions Show and explain all steps in your responses to the following parts of the assignment using the Algebra concepts discussed within the course. All mathematical steps and explanations must be typed up and formatted using the equation editor. Part 1: Create the equation for the height of the rocket after t seconds. Part 2: Find the time it takes for the rocket to reach a height of 0. Interpret both solutions. Part 3: Find the time it takes to reach the top of its trajectory. Part 4: Find the maximum height. Part 5: Find the time it takes to reach a height of 800 feet. Round your answer to the nearest tenth.​

The ratio of the amount of money Alice has to the amount Bob has is approximately 3.36 : 1.

According to the problem, two equations can be set up:

If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. This gives us the equation:

A + n = 7(B - n)

If Alice gives n dollars to Bob, then she will have 2 times as much money as Bob. This gives us the second equation:

A - n = 2(B + n)

We can rearrange these equations to make them easier to solve:

8n = 7B - A

3n = A - 2B

Setting these equal to each other, since they are both equal to 24n, gives:

21B - 3A = 8A - 16B

37B = 11A

A / B = 37 / 11

= 3. 36

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the number of adults who bought tickets is 25.

Answer:

the answer is,

[tex]p(x) = \sqrt[3]{2-x} \\[/tex]

Step-by-step explanation:

The values of the missing values in the triangle given are :

A.)

Using Trigonometry, the marked angle B can be related in the following ways:

Hypotenus = 9.43

Opposite = 5

Adjacent = 8

SinB = opposite / hypotenus = 5/9.43

CosB = Adjacent / Hypotenus = 8/9.43

TanB = opposite / Adjacent = 5/8

B.)

Angle A can be obtained using the relation :

CosA = Adjacent / Hypotenus

CosA = 47/61 = 0.770

A =

[tex] {cos}^{ - 1} (0.770)[/tex]

A = 39.6°

Hence, A = 39.6° to the nearest degree.

C.)

Using Trigonometry, the length of side x :

Tan D = opposite / Adjacent

Tan28 = 21/x

0.5317 = 21/x

x = 21/0.5317

x = 39.5 mm

Therefore, the value of x is 39.5mm

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Answer:

20[tex]c^{6}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

given

(- 4c³)(- 5c³) ← remove parenthesis

= - 4 × c³ × - 5 × c³

= - 4 × - 5 × c³ × c³

= 20 × [tex]c^{(3+3)}[/tex]

= 20[tex]c^{6}[/tex]

The fraction 13/7 lies between the fractions 6/6 and 6/7.

We have,

Between the fractions 6/6 and 6/7, there are infinitely many fractions.

To find a fraction that lies between these two fractions, we can take their average.

The fraction 6/6 simplifies to 1, and the fraction 6/7 cannot be simplified further.

To find the average, we add the two fractions and divide the sum by 2:

(6/6 + 6/7) / 2

To add the fractions, we need a common denominator, which is the least common multiple (LCM) of 6 and 7, which is 42.

Converting the fractions to have a common denominator:

(6/6) x (7/7) + (6/7) x (6/6) / 2

Simplifying the expression:

(42/42 + 36/42) / 2

Combining the numerators:

(78/42) / 2

Dividing:

78/42 = 13/7

Thus,

The fraction 13/7 lies between the fractions 6/6 and 6/7.

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Answer:

T1=-12

T2=-19

T3=-26

Step-by-step explanation:

Determine which term will have a value of -6998

-7n-5=-6998

-7n=-6998+5

-7n=-6993

-7n/-7=-6993/-7

n=999

The expression that represents the side length of the triangle in this problem is given as follows:

10x + 3.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The perimeter for this problem is given as follows:

30x + 9.

The triangle is an equilateral triangle, meaning that all side lengths are the same, hence the side length is given as follows:

(30x + 9)/3 = 30x/3 + 9/3 = 10x + 3.

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The acquisition of the patent can be recorded in the books such that it takes the form of:

Date                      Account title                                Debit                Credit

April 1.                  Patents                                        $115,200

                             Cash                                                                 $115,200

To record the purchase of a patent, you would typically debit the Patents asset account and credit the Cash (or Accounts Payable if purchased on credit) account.

Here's the journal entry:

Date: [Date of purchase]

Debit: Patents [Cost of the patent]

Credit: Cash [Amount paid]

If the patent was purchased on credit instead of cash, the entry would be:

Date: [Date of purchase]

Debit: Patents [Cost of the patent]

Credit: Accounts Payable [Amount owed]

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Rest of the question :

Record the acquisition of patent. If an amount box does not require an entry, leave it blank.

Answer:

[tex]\cos G=\dfrac{2}{3}[/tex]

[tex]\csc E=\dfrac{3}{2}[/tex]

[tex]\cot G=\dfrac{2}{\sqrt{5}}[/tex]

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

[tex]\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}[/tex]

Therefore:

[tex]\hrulefill[/tex]

To find cos G, use the cosine trigonometric ratio:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

[tex]\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]

[tex]\hrulefill[/tex]

To find csc E, use the cosecant trigonometric ratio:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

[tex]\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}[/tex]

[tex]\hrulefill[/tex]

To find cot G, use the cotangent trigonometric ratio:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

[tex]\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}[/tex]

The length of AC is [tex]4\sqrt(2)[/tex].

Create a diagram using the information provided.

As per the diagram, give the points and circles names.

Find the lengths of AD, AE, and EC using the provided information.

Use the Pythagorean Theorem to calculate the length of AC.

The following diagram displays the details:

Diagram illustrating the points at which two circles with radii of 10 and 6 cross.

A common tangent, which connects the two circles, runs through the larger circle at point D and the smaller circle at point E.

Stretched to point C, where it intersects the larger circle, is the line segment DE.

The following equations can be used to determine the lengths of AD, AE, and EC:

AD = 10 - 6 = 4

AE = 6 - 6 = 0 EC = 10 - 6 = 4

[tex]AC = \sqrt(32) = 4\sqrt(2)[/tex]

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Note: The complete question is- A larger circle with radius 10 and a smaller circle with radius 6 intersect each other at two points. A common tangent of the two circles is drawn, which intersects the larger circle at point D and the smaller circle at point E. The line segment DE is extended to intersect the larger circle at point C. Find the length of AC.

Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

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Answer:

62) B

63) D

Step-by-step explanation:

62

Angles N and U are congruent.

The sum of the interior angles of a triangle add to 180.

To find N :

180 - 142 - 24 = 14

This means that angle U is also 14

2x - 50 = 14  Add 50 to both sides

2x = 64  Divide both sides by 2

x = 32 This is answer B

63

We know that side NP is congruent to side Su

2x - y = 13  Substitute 32 for x and solve for y

2(32) - y = 13

64 -y = 13  Subtract 64 from both sides

-y = -51  Multiple both sides by -1

y = 51  The answer is D.

Helping in the name of Jesus.

Answer:

The binomial distribution formula is given by:

P(X = k) = (nCk) * p^k * q^(n-k)

where:

P(X = k) is the probability of getting exactly k successes

n is the number of trials

k is the number of successes

p is the probability of success in a single trial

q is the probability of failure in a single trial (1 - p)

(nCk) is the binomial coefficient, calculated as n! / (k!(n-k)!)

In this case, we have n = 15, p = 0.45, and q = 0.55.

Now, let's calculate the probability of getting fewer than 3 successes (0, 1, or 2).

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 0) = (15C0) * (0.45^0) * (0.55^15)

P(X = 1) = (15C1) * (0.45^1) * (0.55^14)

P(X = 2) = (15C2) * (0.45^2) * (0.55^13)

Using the binomial coefficient formula (nCk) = n! / (k!(n-k)!), we can calculate:

P(X = 0) = (1) * (1) * (0.55^15)

P(X = 1) = (15) * (0.45) * (0.55^14)

P(X = 2) = (15C2) * (0.45^2) * (0.55^13)

By substituting the given values and evaluating these equations, we can find the probability of fewer than 3 successes.

Step-by-step explanation:

The amount you need to deposit in an account now  is $4444.44

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

Amount = $6000

Duration = 5 years

interest = 7%

The amount can be calculated as

Principal amount = Amount/(1 + Rate * Time)

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

Principal amount = 6000/(1 + 7% * 5)

Evaluate

Principal amount = 4444.44

Hence, the amount is $4444.44

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To complete the table with tally marks and frequencies, we'll assume the range of values for the frequencies is from 1 to 5. Here's the completed table:

Subjects                              Tally Marks                                Frequency                          

Mathematics                       |                                                         1

Science                               ||                                                        2

Filipino                               |||                                                       3

English                               ||||                                                      4

Araling Panlipunan       |||||                                                     5

Now, let's assign tally marks and frequencies to each subject:

Mathematics:

For a frequency of 1, we can use a single tally mark: |

So, the tally marks for Mathematics would be: |

Science:

For a frequency of 2, we can use two tally marks: ||

So, the tally marks for Science would be: ||

Filipino:

For a frequency of 3, we can use three tally marks: |||

So, the tally marks for Filipino would be: |||

English:

For a frequency of 4, we can use four tally marks: ||||

So, the tally marks for English would be: ||||

Araling Panlipunan:

For a frequency of 5, we can use five tally marks: |||||

So, the tally marks for Araling Panlipunan would be: |||||

By filling in the tally marks and frequencies, the table is now complete.

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Answer: C

Based on the information given, one might conclude that the population mean is probably greater than 85 minutes. So, the correct answer would be C. The population mean is probably greater than 85 minutes.

Answer:

C. Has to be greater than 85

Step-by-step explanation:

The reciprocal of 7 is 1/7 or approximately 0.142857142857...

The reciprocal of a number is found by taking the inverse of that number. To find the reciprocal of 7, we divide 1 by 7.

Reciprocal of 7 = 1/7

When we divide 1 by 7, we get the fraction 1/7. This means that if we multiply 7 by its reciprocal, the result will be 1. The reciprocal of a number is often used in various mathematical operations, such as solving equations involving fractions or finding the multiplicative inverse of a number.

In decimal form, the reciprocal of 7 is approximately 0.142857142857... The decimal representation of the reciprocal continues infinitely without repeating, as it is a non-terminating decimal.

Therefore, the reciprocal of 7 is 1/7 or approximately 0.142857142857...

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1. Mean = 33.61

2. Standard Deviation = 11.3284

3. Variance = 128.33

The given data are: [tex]22.8, 49.8, 17.5, 44.1, 33.2, 20.6, 43.2, 37.7[/tex]

To get mean, we will sum up all the numbers and divide by the total count. The mean is:

= (22.8 + 49.8 + 17.5 + 44.1 + 33.2 + 20.6 + 43.2 + 37.7) / 8

= 268.9 / 8

= 33.62

Standard Deviation: [tex]\sqrt((22.8 - 33.61)^2 + (49.8 - 33.61)^2 + (17.5 - 33.61)^2 + (44.1 - 33.61)^2 + (33.2 - 33.61)^2 + (20.6 - 33.61)^2 + (43.2 - 33.61)^2 + (37.7 - 33.61)^2) / 8[/tex]

= [tex]\sqrt{128.3336}[/tex]

= 11.3284420818

= 11.3284

Variance = (Standard Deviation)^2

Variance = [tex]11.3284 ^2[/tex]

Variance = 128.33264656

Variance = 128.33.

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The answers are as follows : V = length * width * height, 63 bento boxes, 63 times the volume of one bento box, equal.

Using the formula for the volume of a rectangular prism, the manager can calculate the volume of the container.

A rectangular prism's volume can be calculated using the formula V = length * width * height.

The container in this instance has the following measurements: 7/2 feet by 3/2 feet by 3/2 feet. As a result, the container's volume can be determined as V = (7/2) * (3/2) * (3/2) = 63/8 cubic feet.

The worker is correct in estimating how many bento boxes can fit inside the container.

We must determine the volume of a bento box in order to determine how many can be used to fill the container. As each bento box is a cube with edges that are half a foot long, its volume may be determined as follows:

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A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

Answer:

how do you find the measure of an angle? Using a Protractor The best way to measure an angle is to use a protractor. To do this, you'll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle's measurement to the nearest degree.

Step-by-step explanation:

The perimeter of the parallelogram ABCD is equal to 136

A parallelogram is a geometric shape with four sides, where opposite sides are parallel and have equal lengths. Its opposite angles are also equal in measure.

AB is equal to DC so;

5x - 18 = 2x + 12

5x - 2x = 18 + 12 {collect like terms}

3x = 30

x = 30/3 {divide through by 3}

x = 10

AB = 2(10) + 12 = 32

BC = 3(10) - 6 = 36

perimeter of parallelogram = 2(32 + 36)

perimeter of parallelogram = 2 × 68 = 136

Therefore, the perimeter of the parallelogram ABCD is equal to 136

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Statements 1, 3, and 4 are true, while statements 2 and 5 are false.

Among the given statements, the following are true:

1. If you take any number and multiply it by i-squared, the sign(s) will change.

This statement is true. The complex number i is defined as the square root of -1. When we multiply any real or complex number by i-squared, it is equivalent to multiplying it by -1. Multiplying by -1 changes the sign of the number.

3. If you take any real number and multiply it by i-squared, it will stay a real number.

This statement is also true. Multiplying any real number by i-squared is equivalent to multiplying it by -1. Since -1 is a real number, the result will also be a real number.

4. If you take any number and multiply it by i-squared, nothing will change.

This statement is false. Multiplying any number by i-squared results in a change because i-squared is equal to -1. The multiplication by -1 changes the sign of the number.

As for the remaining statements:

2. Any imaginary number can be written as a real number.

This statement is false. Imaginary numbers, which involve the imaginary unit i, cannot be written as real numbers because they do not have a real component. They can only be expressed in the form of a real number multiplied by i.

5. Any real number can be written as an imaginary number.

This statement is false. Real numbers do not have an imaginary component, so they cannot be written as imaginary numbers. Imaginary numbers have a unique form with the imaginary unit i in the expression.

To summarize, statements 1, 3, and 4 are true, while statements 2 and 5 are false.

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Kevin takes to complete the remaining work alone:

3 + 1 = 4 days in total.

Let's calculate the rates at which Kevin and David can paint the house individually.

Kevin's rate of work is 1/6 of the house per day (since he can complete the house in 6 days), and David's rate is 1/9 of the house per day (since he can complete the house in 9 days).

When they work together for 3 days, their combined rate is:

(1/6 + 1/9) of the house per day = 5/18 of the house per day.

In 3 days, they complete:

3 * (5/18) = 5/6 of the house.

The remaining work is 1 - (5/6) = 1/6 of the house.

Now, since Kevin is completing the remaining work alone, his rate is 1/6 of the house per day.

To determine how many days it takes for Kevin to complete the remaining work, we divide the remaining work (1/6) by Kevin's rate (1/6):

(1/6) / (1/6) = 1 day.

Therefore, it will take Kevin 1 additional day to complete the remaining work alone.

The total number of days taken to paint the house is the initial 3 days they worked together plus the additional day Kevin takes to complete the remaining work alone:

3 + 1 = 4 days in total.

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The highest point for the quadratic function for the height of the object, h(t) = -16·t² + 224·t + 816, indicates that the interval over which the height of the object is increasing is; (-∞, 7]

The shape of the graph of a quadratic function is a parabola.

The function for the height of the object in question 3 is; h(t) = -16·t² + 224·t + 816

Where;

t = The time in seconds

The height of the object is increasing in the interval to the left of the highest point, which can be found as follows;

The x-coordinate of the highest point of the quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)

Therefore, the x-coordinates of the highest point of the object is; -224/(2 × (-16)) = 7

Therefore, the height of the object is increasing in the interval; -∞ < t ≤ 7

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The value of x in the parallelogram is 112°.

In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.

To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.

Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.

Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.

Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.

This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.

For the given question, we know x° + 68° = 180°.

Then x° = 180° - 68°

x° = 112°

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Answer: A sphere and a cylinder have the same radius and height. The volume of the cylinder is 50 feet cubed. A cylinder with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? Start Fraction 50 Over 3 End Fraction feet cubed Start Fraction 100 Over 3 End Fraction feet cubed 75 feet cubed 100 feet cubed

Step-by-step explanation: Because first you need to find the radius and height, Next you will have to find the volume of both, We know h= height and r=radius, so then you plug everything in.

The following are six measures of solvency or profitability that can be determined from the given data of Gates Inc.:Debt ratio: The debt ratio measures the proportion of total assets that are financed by the creditors. It is calculated as: Debt ratio = Total liabilities / Total assets= 3,000,000 / 7,000,000= 0.43 or 43%

Debt-to-equity ratio: The debt-to-equity ratio measures the amount of debt financing in relation to the amount of equity financing. It is calculated as: Debt-to-equity ratio = Total liabilities / Total stockholders' equity= 3,000,000 / 5,000,000= 0.6 or 60%Interest coverage ratio:

The interest coverage ratio measures the number of times the company can cover its interest expenses with its earnings before interest and taxes (EBIT). It is calculated as:Interest coverage ratio = EBIT / Interest expense= (18,900,000 - 120,000 - (1,570,000 + 930,000 - 100,000 - 400,000)) / 120,000= 174,760 / 120,000= 1.5 or 1.5 timesCash coverage ratio:

The cash coverage ratio measures the number of times the company can cover its interest expenses with its cash flow from operations. It is calculated as:Cash coverage ratio = (EBIT + Depreciation) / Interest expense= (18,900,000 - 120,000 - (1,570,000 + 930,000 - 100,000 - 400,000) + 3,200,000 / 10) / 120,000= 764,760 / 120,000= 6.4 or 6.4 times Return on assets (ROA):

The return on assets ratio measures the company's ability to generate earnings from its assets. It is calculated as:ROA = Net income / Total assets= 930,000 / [(7,000,000 + 3,000,000) / 2]= 930,000 / 5,000,000= 0.186 or 18.6%Return on equity (ROE): The return on equity ratio measures the company's ability to generate earnings from its equity financing. It is calculated as: ROE = Net income / Total stockholders' equity= 930,000 / 5,000,000= 0.186 or 18.6%

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Answer: all are 8

Mean:8
Median:8

Mode: 8

Step-by-step explanation:

Mean is the average: add all them up and divide by how many numbers there are

Median: is basically the middle number: put the line in number order and find the number in the middle

Mode: most frequent number

Answer:

Mean = 8

Median = 8

Mode = 8

Step-by-step explanation:

Finding the mean:

The mean is the sum of all the data points divided by the total number of data points.  Since there are 8 data points in total, we can find the sum and divide it by 8 to find the mean:

Mean = (2 + 12 + 8 + 15 + 8 + 7 + 3 + 9) / 8

Mean = (64) / 8

Mean = 8

Thus, the mean of the given data is 8.

Finding the median:  

The median is the value that lies in the middle of the data.  First, we must arrange the data in ascending numerical order:

2, 3, 7, 8, 8, 9, 12, 15.

Because there are 8 data points, we have two numbers in the middle, namely 8 and 8.  In order to find the mean, we find the average of these two numbers:

Median = (8 + 8) / 2

Median = 16 / 2

Median = 8

Thus, the median of the given data is 8.

Finding the mode:

The mode is the most frequently occurring value in a data set.  8 occurs most frequently so the mode of the given data is 8.