Point EE is located at (-6,1)(−6,1) on the coordinate plane. Point EE is reflected over the yy-axis to create point E'E


′
. Point E'E


′


is then reflected over the xx-axis to create point E''E


′′
. What ordered pair describes the location of E''?E


′′


?



E= ?, ?

In order to find that quadrilateral PYRX is a parallelogram, we have to show that its opposite sides are parallel.

Therefore, member QS is a  slant in parallelogram PQRS, it divides the parallelogram into two  harmonious triangles triangle QSP and triangle RQS. Then, angle QSP is  harmonious to angle RQS.  

Since angle SXR is  harmonious to angle PYQ, we can say that that angle QSP is  harmonious to angle RXP. This is due to angles QSP and PYQ are alternate interior angles, and angles RQS and SXR are alternate interior angles, so now they are considered  harmonious.

 Then, we have dyads of  contrary angles that are  harmonious angle QSP is  harmonious to angle RXP, and angle QPS is  harmonious to angle RXS.   Applying  discourse of the binterior angles theorem, we can come to the conclusion that member PS is  resemblant to member RX, and member PQ is  resemblant to member XY.  

Since PY and RX are  contrary sides of quadrilateral PYRX and are  resemblant to member PS, they have to be  resemblant to each other. also, since RX and PQ are  contrary sides of quadrilateral PYRX and they're both  resemblant to member XY, they should be  resemblant to each other.

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The features of function g(x) are: Domain of (4, ∞) Range of (8, ∞) X-intercept at (-4 + 1/256, 0) Y-intercept at (0, 10). Vertical asymptote of x=-4.

Since they enable us to convert an exponential equation into a logarithmic equation and vice versa, logarithmic functions are employed to solve equations involving exponents. They are also used in a variety of disciplines, including science, finance, and engineering.

The common logarithm, indicated by log, is the base that is most frequently used in logarithmic functions, and it is equal to 10. (x). The natural logarithm, indicated by ln, is provided through the use of another frequently used base, e. (x). The product rule, quotient rule, and power rule are among the characteristics of logarithmic functions that are similar to those of exponential functions.

When the function is transformed according to the given translation we have:

The domain of g(x) is (4, inf).

The vertical asymptote of f(x) is x=0, which corresponds to the y-axis.

The x-intercept is:

g(x) = f(x+4) + 8 = 0

f(x+4) = -8

[tex]2^{(f(x+4))} = 2^{(-8)}[/tex]

x+4 = 1/256

x = -4 + 1/256

Therefore, the x-intercept of g(x) is (-4 + 1/256, 0).

The y intercept is g(0) = f(4) + 8

= log∨2 4 + 8

= 2 + 8

= 10

Therefore, the y-intercept of g(x) is (0, 10).

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Answer:

24π cm²

Concepts Applied:

SA (TSA) of a cone = π · r · ( l+r )

Relation between l, h, and r i.e. l²=h²+r²

(h: cone height, r: base radius, l: slant height)

Step-by-step explanation:

Calculating the Slant height:

l²=h²+r²

l = sqrt(h²+r²)

l = sqrt(16+9)

l = sqrt(25)

l = +5 cm (distance is a scalar quantity)

Calculating the TSA:

= π · 3 · (5+3)

= 24π cm²

Answer:

34π cm^2 is the correct answer

Answer:

  a) 149,270 m³

  b) 4 hours 9 minutes

Step-by-step explanation:

You want to know the volume of air in a 4 km tunnel 8 m high and 5 m wide with a semicircular cross section at the top. And you want to know the replacement time for that air if it is exchanged at 10 m³ per second.

The area of the semicircular top of the tunnel is ...

  A = π/8d²

  A = π/8·(5 m)² = 25π/8 m²

The area of the rectangular bottom of the tunnel is ...

  A = LW

  A = (5 m)(8 -2.5 m) = 27.5 m²

So the total cross sectional area of the tunnels is ...

  (25π/8 +27.5) m² ≈ 37.317477 m²

The volume of the tunnel is ...

  V = Bh

  V = (37.317477 m²)(4000 m) ≈ 149269.9 m³

The volume of the air in the tunnel is about 149269.9 m³.

At 10 m³ per second, the air will be replaced after ...

  (149269.9 m³)/(10 m³/s) = 14926.99 s ≈ 4 hours 9 minutes

The given pump takes 4 hours 9 minutes to replace the air in the entire tunnel.

__

Additional comment

This tunnel would not meet any standard of safety.

A typical building is supposed to have about 5 air exchanges per hour. That's about 21 times the rate given here. Some tunnel structures need to have the air exchanged once per minute. (Here, that would mean the wind in the tunnel is 149 mph.)

The breathing requirements of the tunnel occupants need to be considered, as well as removal of air pollutants.

There are 3600 seconds in 1 hour.

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Answer:

(x-6)^2+(y-4)^2=10

Step-by-step explanation:

use the equation of a circle ( x- x coordinate of center)^2+(y-y coordinate of the center)^2=radius squared.

to solve for the radius, make a right triangle from the center to the point on the circle. 1^2+3^2=r^2. So r^2 is 10

The judge in this scenario is acquitting all defendants regardless of the evidence.

If the judge decides to acquit all defendants, regardless of the evidence, then the probability of a Type I error would be 1, meaning that the judge will always reject the null hypothesis (that the defendant is guilty) when it is actually true.

A Type I error occurs when we reject a null hypothesis that is actually true. In the context of a criminal trial, this would mean that the judge is acquitting a defendant who is actually guilty.

In statistical hypothesis testing, we typically set a threshold (called the "level of significance") for the probability of making a Type I error. The most commonly used level of significance is 0.05, which means that we are willing to accept a 5% chance of making a Type I error.

However, if the judge in this scenario is acquitting all defendants regardless of the evidence, then the probability of making a Type I error would be 1, which is much higher than the typically acceptable level of significance.

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The correct answer to this question is C, 100ft/min.

The rate of climbing can be calculated by dividing the increase in elevation (100 ft) by the time it takes to make that increase (2 min).

This gives a rate of 50ft/min. Therefore, the class is climbing at a rate of 100ft/min since the question asks for the rate of their climbing.

It's important to pay attention to the wording of the question to ensure that the correct answer is selected. In this case, the question specifically asks for the rate of climbing, not the rate of increase in elevation.

Always read the question carefully and make sure to include all given information when solving problems with content loaded.

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We know that the length of TU to the nearest tenth is 6.9 in

The figure is tangent to the circle at point U. Using the information given in the figure, we can conclude that segment ST is tangent to the circle at point T.

To find the length of TU, we can use the formula for the length of a tangent segment from a point outside the circle:

TU^2 = TS x TR

We know that TS = ST = 4 in. To find TR, we can use the Pythagorean theorem:

TR^2 = RS^2 - TS^2
TR^2 = 8^2 - 4^2
TR^2 = 48
TR = sqrt(48)

Now we can substitute the values we have found into the first formula:

TU^2 = 4 x sqrt(48)
TU = sqrt(4 x sqrt(48))
TU ≈ 6.9 in.

Therefore, the length of TU to the nearest tenth is 6.9 in.

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The missing angle for x by the measures add up to 90° is 53°

Complementary angles are pairs of angles whose measures add up to 90°. In this problem, we are given two angles, one of which measures 37°, and the other of which has an unknown measure that we will call x. We are also told that these angles are complementary, which means that their measures add up to 90°.

So, we can set up an equation to represent this relationship:

37 + x = 90

We can simplify this equation by subtracting 37 from both sides:

x = 90 - 37

x = 53

Now we know that the measure of the second angle is 53°. But we can go further and solve for x to get a more complete solution.

In the problem statement, we are also given an expression for the second angle in terms of x:

5x + 3

We know that this angle measures 53°, so we can set up another equation to represent this relationship:

5x + 3 = 53

We can solve for x by first subtracting 3 from both sides:

5x = 50

Then, we can divide both sides by 5 to isolate x:

x = 10

Now we know that x has a value of 10, and we can substitute this value back into the expression for the second angle to find its measure:

= 5x + 3

= 5(10) + 3 = 53

Therefore, the missing angle is 53°, and x has a value of 10.

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The sample regression equation for salary and education is Salaryˆ= 32.67 + 4.46Education. For each additional year of education, an individual's salary is predicted to increase by $4,460. Predicted salary for 7 years of education is $63,845.

Using the provided data, we can calculate the sample regression equation for the model  Salary = β0 + β1Education + ε by using linear regression. The result is Salaryˆ= 32.67 + 4.46Education.

The coefficient for Education is 4.46, which means that as Education increases by 1 year, an individual’s annual salary is predicted to increase by $4,460.

To find the predicted salary for an individual who completed 7 years of higher education, we substitute Education = 7 into the regression equation: Salaryˆ= 32.67 + 4.46(7) = $63,845. Therefore, the predicted salary for an individual who completed 7 years of higher education is $63,845.

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The calculated value of the actual area of the playground is 5625π

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

A scale drawing of a playground had a scale of 15

This means that

Scale factor = 15/1

Evaluate

Scale factor = 15

The actual area of the park in meters squared is calculated as

Area = Area of scale * Scale factor²

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

Area = Area of scale * 15²

Using the area of circle, we have

Area = π5² * 15²

Evaluate

Area = 5625π

Hence, the actual area is 5625π

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The time series plot shows a generally increasing trend with some seasonality.

a. To construct a time series plot, we plot the data points on a graph with the x-axis representing the quarters and the y-axis representing the values. Each data point is marked on the graph to show the value for each quarter. Based on the plot, we can observe a seasonal pattern in the data, where the values tend to fluctuate in a regular pattern over the quarters.

b. To account for seasonal effects, we can use a multiple regression model with dummy variables. We create three dummy variables, Qtr1, Qtr2, and Qtr3, representing the quarters. These variables take a value of 1 if the corresponding quarter is present and 0 otherwise. The equation for the model would be:

Value = β0 + β1 * Qtr1 + β2 * Qtr2 + β3 * Qtr3

c. To compute quarterly forecasts for the next year based on the model developed in part b, we substitute the values of the dummy variables for the corresponding quarters of the next year into the equation and calculate the forecasted values.

d. To account for both trend and seasonal effects, we can use a multiple regression model with dummy variables and a variable t representing the time. The equation for the model would be:

Value = β0 + β1 * t + β2 * Qtr1 + β3 * Qtr2 + β4 * Qtr3We create the variable t, which takes values from 1 to 12, representing the quarters in the three years. By including both the dummy variables and the variable t in the model, we can capture the combined effects of trend and seasonality on the data.

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The ratios are 1. Current ratio = 2.90, 2. Acid-test ratio = 2.22, 3. Inventory turnover ratio = 3.57, 4. Debt to equity ratio = 0.77, 5. Return on equity ratio = 15%.

The ratios to be computed are:

1. Current ratio

2. Acid-test (quick) ratio

3. Inventory turnover ratio

4. Debt to equity ratio

5. Return on equity ratio

1. Current ratio = Current assets / Current liabilities

Current assets = Cash + Accounts receivable + Inventory = $17,205 + $80,290 + $68,820 = $166,315

Current liabilities = Accounts payable = $57,350

Current ratio = $166,315 / $57,350 = 2.90

2. Acid-test (quick) ratio = (Cash + Accounts receivable) / Current liabilities

Acid-test ratio = ($17,205 + $80,290) / $57,350 = 2.22

3. Inventory turnover ratio = Cost of goods sold / Average inventory

Average inventory = (Beginning inventory + Ending inventory) / 2

Beginning inventory = $57,350

Ending inventory = $68,820

Average inventory = ($57,350 + $68,820) / 2 = $63,085

Inventory turnover ratio = $225,600 / $63,085 = 3.57

4. Debt to equity ratio = Total liabilities / Total equity

Total liabilities = Accounts payable + Mortgage payable = $57,350 + $114,700 = $172,050

Total equity = Common stock + Retained earnings = $160,580 + $63,085 = $223,665

Debt to equity ratio = $172,050 / $223,665 = 0.77

5. Return on equity ratio = Net income / Average equity

Average equity = (Beginning equity + Ending equity) / 2

Beginning equity = Common stock + Retained earnings = $137,640 + $45,880 = $183,520

Ending equity = Common stock + Retained earnings + Net income - Dividends = $160,580 + $63,085 + $31,100 - $21,700 = $232,065

Average equity = ($183,520 + $232,065) / 2 = $207,793

Return on equity ratio = $31,100 / $207,793 = 0.15 or 15%

Therefore, the ratios are:

1. Current ratio = 2.90

2. Acid-test ratio = 2.22

3. Inventory turnover ratio = 3.57

4. Debt to equity ratio = 0.77

5. Return on equity ratio = 15%

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Answer: (18, 4)

Part 1:

The cost of seeds and dried fruit together is $22:

1.5x + 2.5y = 22

Hunter plans to spend all of his money on seeds and dried fruit:

x + y = 22

Part 2:

We can use substitution method to solve the system of equations:

x = 22 - y   (from the second equation)

1.5(22 - y) + 2.5y = 22   (substitute x into the first equation)

33 - 1.5y + 2.5y = 22

y = 4

Substituting y = 4 into x + y = 22, we get x = 18.

Therefore, the ordered pair representing the number of seeds and dried fruit that Hunter bought is (18, 4).

The probability of choosing a ball numbered 25 is 0.

The lottery game contains only 24 balls numbered from 1 to 24. There is no ball numbered 25, so the probability of choosing a ball numbered 25 is 0. The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.

In this case, the number of favorable outcomes is 0 because there is no ball numbered 25, and the total number of possible outcomes is 24 since there are 24 balls in the game. Therefore, the probability of choosing a ball numbered 25 is 0/24, which simplifies to 0.

Mathematically, the probability of choosing a ball numbered 25 can be calculated as:

P(choosing ball numbered 25) = number of favorable outcomes / total number of possible outcomes

= 0 / 24

= 0

Therefore, the probability of choosing a ball numbered 25 is 0.

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Rounding to the nearest whole number, the linear speed of a point on Uranus' equator is approximately 139,424 miles/day.

(a) To find the angular speed of a point on Uranus' equator, we need to convert the rotation period from hours to days and then calculate the angle rotated in one day.

In one day (24 hours), Uranus rotates:

24 hours ÷ 17.2 hours/rotation ≈ 1.3953 rotations

The angle rotated in one day is:

1.3953 rotations × 2π radians/rotation ≈ 8.7674 radians/day

So the angular speed of a point on Uranus' equator is approximately 8.7674 radians/day.

(b) To find the linear speed of a point on Uranus' equator, we can use the formula:

linear speed = radius × angular speed

where the radius is given as 15,881 miles and the angular speed is 8.7674 radians/day (from part (a)).

Substituting these values, we get:

linear speed = 15,881 miles × 8.7674 radians/day ≈ 139,424 miles/day

Rounding to the nearest whole number, the linear speed of a point on Uranus' equator is approximately 139,424 miles/day.

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The area of the composite figure is equal to 104 square feet.

In this question we have a composite figure formed by a part of a rectangle and an entire triangle. The area formulas for a rectangle and a triangle are introduced below:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

Now we proceed to determine the area of the mural:

A = (10 ft) · (8 ft) - 0.5 · (10 ft) · (5 ft) + 0.5 · (14 ft) · (7 ft)

A = 104 ft²

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To save $220 per month while working a job that pays $8.50 per hour with deductions of 26.15%, you would need to work approximately 43 hours per month, rounded up to the nearest whole hour.

To calculate how many hours you would need to work, you need to first determine your hourly pay after deductions. To do this, subtract the percentage of deductions (26.15%) from 100% (100% - 26.15% = 73.85%). Then, multiply your hourly rate by this percentage to get your effective hourly rate after deductions: $8.50 x 0.7385 = $6.27.

To save $220 per month, you need to earn at least $220 more than your expenses from your second job. Assuming a 4-week month, your expenses would need to be at most $55 per week ($220/4 weeks = $55/week).

To earn $55 per week, you need to work for $55/$6.27 = 8.77 hours per week. Rounded up to the nearest whole hour, you would need to work approximately 9 hours per week.

Multiplying this by 4 weeks gives you a total of 36 hours. However, since you need to earn slightly more than $55 per week to account for taxes and rounding, you would need to work approximately 43 hours per month.

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Answer:

The polar form of the rectangular coordinates (0, 6√3) with a positive value of r, over the interval 0 ≤ θo < 27 and in terms of radians, is (6√3, 1.58).

Step-by-step explanation:

To convert the rectangular coordinates (0, 6√3) to polar form, we can use the following formulas:

r = √(x^2 + y^2)

θ = tan^(-1)(y/x)

Substituting the given values, we get:

r = √(0^2 + (6√3)^2) = 6√3

θ = tan^(-1)((6√3)/0) = π/2

However, note that the angle θ is not well-defined since x=0. We can specify that the point lies on the positive y-axis, which corresponds to θ = π/2 radians.

Thus, the polar form of the rectangular coordinates (0, 6√3) is:

r = 6√3

θ = π/2

To express the angle θ in terms of θo, where 0 ≤ θo < 27 and in radians, we can write:

θ = π/2 = (π/54) × 54 ≈ (0.0292) × 54 ≈ 1.58 radians

Therefore, the polar form of the rectangular coordinates (0, 6√3) with a positive value of r, over the interval 0 ≤ θo < 27 and in terms of radians, is (6√3, 1.58).

We can make 24 bouquets of flowers for a wedding, each with 10 roses and 7 lilies.

To determine the largest number of identical bouquets that can be made using 240 roses and 168 lilies, we need to find the greatest common factor (GCF) of these two numbers.

The prime factorization of 240 is 2^4 x 3 x 5, while the prime factorization of 168 is [tex]2^3 * 3 * 7[/tex]. To find the GCF, we can take the product of the common prime factors raised to the smallest exponent they appear in either number. Therefore, the GCF of 240 and 168 is [tex]2^3 * 3[/tex] = 24.

This means that we can make 24 identical bouquets using 240 roses and 168 lilies. To do so, we would use 10 roses and 7 lilies in each bouquet, since 10 and 7 are the largest numbers that divide both 240 and 168 without remainder, respectively. So, we can make 24 bouquets, each with 10 roses and 7 lilies.

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Kareem drove the truck for 150 miles.

As areem rented a truck for one day. there was a base fee of $19.99 , and there was an additional charge of 83 cents for each mile driven we will let the number of miles driven by Kareem be represented by 'x'. The total cost, including the base fee, can be represented as:

Total cost = Base fee + Additional charge per mile * Number of miles driven

$135.36 = $19.99 + $0.83x

Subtracting $19.99 from both sides and then dividing by $0.83, we get:

x = (135.36 - 19.99) / 0.83

x = 150

Therefore, Kareem drove the truck for 150 miles.

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For the line segment, the measure of angle BOD is 90°.

We will draw a circle passing through points A, B, C, and D. Since AC is parallel to BD, this circle will be the circumscribed circle of quadrilateral ABCD.

Now, let's consider the angles formed by the intersection of the circle and the lines AB and CD. We know that angle CAB is equal to half the arc AC of the circle, and angle CDB is equal to half the arc BD.

Since AC is parallel to BD, arc AC is congruent to arc BD. Therefore, angle CAB is equal to angle CDB.

Using this information, we can find the measure of angle AOB, which is equal to angle CAB + angle CDB. Substituting the given values, we get angle AOB = 35° + 55° = 90°.

Finally, we can use the fact that angle AOB and angle COD are supplementary angles (they add up to 180°) to find the measure of angle BOD.

Angle BOD = 180° - angle AOB

Substituting the value of angle AOB, we get

Angle BOD = 180° - 90° = 90°

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Complete Question:

Line segments AB and CD intersect at O such that AC∣∣DB. If ∠CAB=35° and ∠CDB=55°, find ∠BOD.

The exponential growth function V(t) is:
V(t) ≈ 35,000 * (1.068)^t

To find the exponential growth rate k and the exponential growth function V(t), we can use the formula:

V(t) = V₀ * (1 + k)^t

where V(t) is the value of the painting at time t, V₀ is the initial value of the painting, k is the growth rate, and t is the number of years after 1950.

Given:
Initial value, V₀ = $35,000 (in 1950)
Final value, V(54) = $92,906,000 (in 2004, which is 54 years after 1950)

We can now solve for k:

92,906,000 = 35,000 * (1 + k)^54

Divide both sides by 35,000:

2,654.457 = (1 + k)^54

Now take the 54th root of both sides:

1.068 = 1 + k

Subtract 1 from both sides to find k:

k ≈ 0.068

Now, we can plug k back into the exponential growth function formula:

V(t) = 35,000 * (1 + 0.068)^t

So, the exponential growth function V(t) is:

V(t) ≈ 35,000 * (1.068)^t

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To find the surface area C of the birdhouse, we need to find the area of each face and add them together.

First, let's find the area of the square base:

Area of base = side^2 = 16^2 = 256 in^2

Next, let's find the area of each triangular face:

Area of each triangular face = 1/2 * base * height

Since the base is 16 in and the slant height is 10 in, the height can be found using the Pythagorean theorem:

height^2 = slant height^2 - base^2/4

height^2 = 10^2 - 16^2/4

height^2 = 100 - 64

height^2 = 36

height = 6

So the area of each triangular face is:

1/2 * 16 * 6 = 48 in^2

There are four triangular faces, so the total area of the triangular faces is:

4 * 48 = 192 in^2

Finally, we add the area of the base and the area of the triangular faces to find the total surface area:

256 + 192 = 448 in^2

Therefore, the surface area of the birdhouse is 448 square inches, which is closest to option A: 262 in^2.

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Answer:

x = -10 (zeros), vertex = infinity..?

Step-by-step explanation:

The graph is a straight line, not a parabola. I would assume the vertex would be infinity, and the zeros would be x = -10.

The company’s earnings per share reported in its financial statements for the year ended December 31, 2020 is $1.45. The correct option is c.

To calculate earnings per share, we need to take the company's net income and divide it by the weighted average number of shares outstanding during the year.

First, let's adjust for the stock dividend on July 31. Since the dividend was 100%, we can double the number of shares outstanding to 416,000:

Jan. 1: 200,000 shares
Feb. 1: 8,000 new shares
July 31: 200,000 shares doubled to 400,000 shares
Dec. 31: 416,000 shares

Next, we need to calculate the weighted average number of shares outstanding during the year. We can do this by taking the number of shares outstanding for each period and multiplying it by the number of months those shares were outstanding:

Jan. 1 to Jan. 31: 200,000 shares x 1 month = 200,000
Feb. 1 to July 31: (200,000 + 8,000) shares x 6 months = 1,248,000
Aug. 1 to Dec. 31: 416,000 shares x 5 months = 2,080,000

Total weighted average shares outstanding: 3,528,000

Finally, we can divide the net income of $560,000 by the weighted average shares outstanding of 3,528,000 to get earnings per share of $0.1585. Multiplying this by 9 (since there are 9 months of the year remaining after February 1) gives us earnings per share of $1.4265. Rounded to the nearest penny, the answer is $1.45.

Thus, The correct option is c.

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The exact value for each trigonometric function are -12/13, -5/13 and 12/5

To find the reference angle, we can use the properties of right triangles. We can draw a line from the point (-5, 12) to the x-axis to form a right triangle. The hypotenuse of the triangle is the distance from the point (-5, 12) to the origin, which is the square root of the sum of the squares of the x and y coordinates:

√((-5)² + 12²) = 13

The reference angle is the acute angle between the x-axis and the adjacent side of the triangle, which is the x-coordinate of the point (-5, 12) divided by the hypotenuse:

cosθ = -5/13

θ = arccos(-5/13)

θ ≈ 2.214 radians

The angle's standard form is given by the equation:

θ = n(2π) ± α

where n is an integer, and α is the angle's reference angle. Since the point (-5, 12) is in the second quadrant, the angle's terminal side intersects the unit circle at an angle of θ = π + α. Therefore, the standard form of the angle is:

θ = (2n + 1)π - arccos(-5/13)

To find the exact value of the trigonometric functions of this angle, we can use the properties of the unit circle. Since the sine function is positive in the second quadrant, we have:

sinθ = sin(π + α) = -sinα = -12/13

Similarly, since the cosine function is negative in the second quadrant, we have:

cosθ = cos(π + α) = -cosα = -5/13

Finally, since the tangent function is the ratio of the sine and cosine functions, we have:

tanθ = tan(π + α) = -tanα = 12/5

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In a bag containing 5 red, 3 blue, and 12 yellow marbles, we will predict the number of times Hazel will select a blue marble out of 500 trials.

Step 1: Calculate the total number of marbles in the bag:
Total marbles = 5 red + 3 blue + 12 yellow = 20 marbles

Step 2: Determine the probability of selecting a blue marble:
Probability of selecting a blue marble = (number of blue marbles) / (total marbles) = 3 blue / 20 marbles = 3/20

Step 3: Predict the number of times Hazel will select a blue marble in 500 trials:
Predicted blue marbles selected = (probability of selecting a blue marble) x (total trials) = (3/20) x 500

Step 4: Perform the calculation:
(3/20) x 500 = 75

In conclusion, we predict that Hazel will select a blue marble 75 times out of 500 trials, given that the bag contains 5 red, 3 blue, and 12 yellow marbles.

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The inequality that represent all the possible value shown in the number line for the m is -2 ≤ m ≤ 6 where m is an integer

The possible values on the number line is -2,-1,0,1,2,3,4,5,6

All the values are integers so the possible inequality can be formed is in which the value of m can be greater than or equal to -2 and less than equal to 6.

Inequalities are the mathematical expressions in which both sides are not equal it tells the relation between two values.

It can be represented the form

-2 ≤ m ≤ 6 where m is an integer

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The given question is incomplete complete question is :

The number line shows all the values passible values of m.

create an in equality that represents all the possible value of m.