if 4y= 2.6,find the value of 20y + 3​

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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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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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 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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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 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 angle measure of the rhombus with one diagonal of a rhombus is a geometric mean of the length of the other diagonal are measured to be 75.5° .

Let d₁ and d₂ be the lengths of the diagonals of the rhombus and s as the side length. We have,

d₁ = s√2 (since the diagonal is the hypotenuse of a right triangle formed by two sides of length s)

d₁ = √d₂s

Combining these two equations, we get,

s√2 = √d₂s

Squaring both sides, we get,

2s² = d₂

Since the diagonals of a rhombus are perpendicular bisectors of each other, we have,

cosθ = (1/2) (where θ is one of the acute angles of the rhombus)

Using the law of cosines with sides s and d₂/2, we have,

(s² + (d₂/2)² - 2sd₂/2cosθ) = s²

Simplifying, we get,

d₂ = 4s cosθ

Substituting this expression for d₂ in 2s² = d₂, we get,

2s² = 4scosθ

Dividing both sides by 2s and simplifying, we get,

s = 2cosθ

Therefore, the angle measures of the rhombus are,

θ = arccos(s/2)

= arccos(cosθ/2)

= arccos(1/4)

= 75.5°

And the other acute angle has the same measure.

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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 point guard has to decide whether to shoot a three-point attempt or pass the ball to another player for a two-point shot. The point guard has a 30% success rate for three-point shots, while the teammate has a 48% success rate for two-point shots.

To determine the best option, we can compare the expected values for each decision. Here's a step-by-step explanation:

1. Calculate the expected value of the point guard's three-point attempt:
  - Success rate: 30% (0.3)
  - Point value: 3
  - Expected value: 0.3 (3 )= 0.9

2. Calculate the expected value of the teammate's two-point shot:
  - Success rate: 48% (0.48)
  - Point value: 2
  - Expected value: 0.48 (2) = 0.96

3. Compare the expected values:
  - Three-point attempt: 0.9
  - Two-point shot: 0.96

Since the expected value of the teammate's two-point shot (0.96) is higher than the point guard's three-point attempt (0.9), it would be a better decision for the point guard to pass the ball to the teammate for a two-point shot.

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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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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.

The percentage of beds that should be specially equipped is 19.0%. The correct option is c.

To be "pretty sure" of having enough specially equipped beds, the hospital wants to have only a 5% chance of running short of these beds, even when the hospital is fully occupied. This means that the probability of having enough beds should be 95%.

Let x be the percentage of beds that should be specially equipped. Then the probability that a patient does not require a specially equipped bed is 100% - 13.95% = 86.05%.

The probability that all 258 beds are occupied by patients who do not require a specially equipped bed is (0.8605)^258 = 0.0501, which is about 5%.

Therefore, the probability that at least one patient requires a specially equipped bed is 1 - 0.0501 = 0.9499, which is about 95%.

We can set up an equation to solve for x:

0.9499 = 1 - (1 - x)^258

Solving for x, we get:

x = 19.0%

Therefore, the percentage of beds that should be specially equipped is 19.0%.

So the answer is C) 19.0%.

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Answer:

The total amount Joe spent on gasoline and oil can be determined by the expression: 2.85g + 3.15c. This expression represents the cost of g gallons of gasoline at $2.85 per gallon plus the cost of c cans of oil at $3.15 per can.

Step-by-step explanation:

The net pay is correct.

To determine if Chloe's net pay is correct, we need to check if all the deductions are calculated correctly. Let's examine each deduction one by one:

1. Social Security tax:
Social Security tax is 6.2% of gross pay.
6.2% of $856 = 0.062 * $856 = $53.07

2. Medicare tax:
Medicare tax is 1.45% of gross pay.
1.45% of $856 = 0.0145 * $856 = $12.41

3. State tax:
State tax is 23% of federal tax.
23% of $80 = 0.23 * $80 = $18.40

Now let's calculate the net pay by subtracting all deductions from the gross pay:
Net pay = Gross pay - (Federal tax + Social Security tax + Medicare tax + State tax)
Net pay = $856 - ($80 + $53.07 + $12.41 + $18.40) = $856 - $163.88 = $692.12

Since all deductions are correct, and the calculated net pay matches the given net pay, the correct answer is:

a. The net pay is correct.

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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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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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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).

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 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 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 cost of the stock for the investor would be calculated as follows:

Cost of 1 share = $98.93
Number of shares purchased = 500

Total cost of the stock = Cost per share x Number of shares
Total cost of the stock = $98.93 x 500
Total cost of the stock = $49,465

The broker charges 2% of the cost of the stock, so the broker's fee would be calculated as:

Broker's fee = 2% x Total cost of the stock
Broker's fee = 2% x $49,465
Broker's fee = $989.30

Therefore, the total cost of the stock for the investor including the broker's fee would be:

Total cost of the stock + Broker's fee = $49,465 + $989.30
Total cost of the stock + Broker's fee = $50,454.30

So the cost of the stock for the investor including the broker's fee is $50,454.30.

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El área de papel utilizada para cada CD es aproximadamente 20.41 cm².

How much paper area is used for each CD?

Para calcular el área de papel utilizado para cada CD, necesitamos determinar el área de la región entre dos círculos concéntricos.

El área de un círculo se calcula utilizando la fórmula A = πr², donde r es el radio. En este caso, tenemos dos círculos con radios diferentes: el radio mayor de 5.8 cm y el radio menor de 0.7 cm.

El área del papel utilizado será la diferencia de áreas entre los dos círculos. Entonces, podemos calcularlo de la siguiente manera:

Área utilizada = Área del círculo mayor - Área del círculo menor

= π(5.8²) - π(0.7²)

= π(33.64) - π(0.49)

≈ 105.72 - 1.54

≈ 104.18 cm²

Por lo tanto, aproximadamente se utilizan 104.18 cm² de papel para cada CD.

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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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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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Lo siento, pero los problemas que ha proporcionado no están relacionados con el cálculo. El problema a) es simplemente una operación de multiplicación y suma, y el problema b) es una operación de multiplicación y suma agrupada. Para crear un problema que pueda resolverse con cálculo, podría plantear algo como:

a) ¿Cuál es la tasa de cambio de la función f(x) = x^2 en el punto x = 3?

b) ¿Cuál es el valor máximo de la función g(x) = 3x^2 - 12x + 5 en el intervalo [0, 4]?

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The surface area of the triangular prism is 4302 mm²

A prism is a solid shape that is bound on all its sides by plane faces. The surface area of a prism is expressed as;

SA = 2B + ph where B is the base area and h is the height of the prism and p is the perimeter of the base.

Base area = 1/2 bh

= 1/2 × 36 × 24

= 36 × 12

= 432 mm²

Perimeter of the base = 36 + 30+30 = 96 mm²

SA = 2 × 432 + 96 × 36

SA = 846 + 3456

SA = 4302 mm²

Therefore the surface area of the triangular prism is 4302 mm².

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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 calculations for break even point is 5000 customers, and the solution to the system of equations were shown. Mr. Bro's Chick-fil-A franchise would be more profitable as it required less initial borrowing, broke even sooner and generated more income than Ms. Kramer's Popeye's franchise.

To solve this problem, we need to set up a system of equations. Let's use "b" to represent the amount each owner had to borrow to open their restaurant, "x" to represent the number of customers, and "y" to represent the total profit.

For Mr. Bro's Chick-fil-A

After 500 customers: y = -4000

After 3000 customers: y = 1000

We can use these two equations to find the slope of the line: m = (1000 - (-4000)) / (3000 - 500) = 1.8

Using the point-slope form of a line y - (-4000) = 1.8(x - 500)

Simplifying, we get: y = 1.8x - 3400

For Ms. Kramer's Popeye's

After 2000 customers: y = -6000

After 4500 customers: y = 1500

We can use these two equations to find the slope of the line: m = (1500 - (-6000)) / (4500 - 2000) = 1.4

Using the point-slope form of a line: y - (-6000) = 1.4(x - 2000)

Simplifying, we get: y = 1.4x - 5400

Now, we can set the two equations equal to each other to find the break-even point

1.8x - 3400 = 1.4x - 5400

0.4x = 2000

x = 5000

This means that both restaurants need to serve 5000 customers to break even.

To compare the total income of the two restaurants, we can find the y-value for both equations when x = 5000

Chick-fil-A: y = 1.8(5000) - 3400 = $5,000

Popeye's: y = 1.4(5000) - 5400 = $1,000

From this analysis, it is clear that owning Chick-fil-A is more profitable than owning Popeye's.

To know more about system of equations:

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