please help me with this question

A summer camp took a survey of the favorite book genres. Eighteen campers said that their favorite book genre is nonfiction.

What is the total number of campers that were surveyed?

Enter your answer in the box.
__ Campers

The exponential growth function can be written as P0 * [tex]e^(rt)[/tex] where P0 is the initial population, r is the annual growth rate expressed as a decimal, t is the time in years, and e is the mathematical constant e. To estimate the population in 2018, we need to find the value of P(t) when t = 6 (since 2018 is six years after 2012).

An exponential growth function is a mathematical function that models the growth of a quantity at an exponential rate over time.

a) The exponential growth function can be written as:

P(t) = P0 * [tex]e^(rt)[/tex]

where P0 is the initial population, r is the annual growth rate expressed as a decimal, t is the time in years, and e is the mathematical constant e (approximately equal to 2.71828).

In this case, P0 = 5.94 million, r = 0.0377 (3.77% expressed as a decimal), and t is the time in years. Therefore, the exponential growth function for this city is:

P(t) = 5.94 * [tex]e^(0.0377t)[/tex]

b) To estimate the population in 2018, we need to find the value of P(t) when t = 6 (since 2018 is six years after 2012). So, we plug in t = 6 into the exponential growth function:

P(6) = 5.94 * [tex]e^(0.0377 * 6)[/tex] ≈ 7.58 million

Therefore, the estimated population of the city in 2018 was 7.58 million.

c) To find when the population of the city will be 9 million, we need to solve the exponential growth function for t when P(t) = 9. So, we plug in P(t) = 9 into the exponential growth function:

9 = 5.94 * [tex]e^(0.0377t)[/tex]

Divide both sides by 5.94:

1.516835016835017 = [tex]e^(0.0377t)[/tex]

Take the natural logarithm of both sides:

ln(1.516835016835017) = 0.0377t

Solve for t:

t ≈ 8.39

Therefore, the population of the city will reach 9 million approximately 8.39 years after 2012, which is around 2020.

d) The doubling time is the amount of time it takes for the population to double. We can use the exponential growth function to find this time by solving for t when P(t) = 2P0 (twice the initial population):

2P0 = P0 * [tex]e^(rt)[/tex]

Divide both sides by P0:

2 = [tex]e^(rt)[/tex]

Take the natural logarithm of both sides:

ln(2) = rt

Solve for t:

t = ln(2) / r

Substituting r = 0.0377, we get:

t = ln(2) / 0.0377 ≈ 18.38

Therefore, the doubling time for the population of this city is approximately 18.38 years.

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the temperature at 9 P.M. is 38 degrees Fahrenheit, and the equation that represents this temperature is T(9) = 53 - 3(9-4).

How to determine the temperature ?

To determine the temperature at 9 P.M., we need to calculate how much the temperature drops from 4 P.M. to 9 P.M. We know that the temperature drops 3 degrees per hour, and since there are 5 hours between 4 P.M. and 9 P.M., the temperature will have dropped 3 x 5 = 15 degrees.

Therefore, to calculate the temperature at 9 P.M., we need to subtract 15 degrees from the temperature at 4 P.M.:

Temperature at 9 P.M. = Temperature at 4 P.M. - 15

Substituting the given temperature of 53 degrees Fahrenheit at 4 P.M.:

Temperature at 9 P.M. = 53 - 15 = 38 degrees Fahrenheit

Thus, the equation that accurately represents the temperature at 9 P.M. is:

T(9) = 53 - 3(9-4)

Simplifying the equation:

T(9) = 53 - 15

T(9) = 38

In conclusion, the temperature at 9 P.M. is 38 degrees Fahrenheit, and the equation that represents this temperature is T(9) = 53 - 3(9-4).

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Answer:

y ≈ 13,9

Step-by-step explanation:

Use trigonometry:

[tex] \tan(60°) = \frac{y}{8} [/tex]

Cross-multiply to find y:

[tex]y = 8 \times \tan(60°) = 8 \times \sqrt{3} = 8 \sqrt{3} ≈13.9[/tex]

Answer:

y ≈ 13.9

Step-by-step explanation:

using the tangent ratio in the right triangle

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{8}[/tex] ( multiply both sides by 8 )

8 × tan60° = y , then

y ≈ 13.9 ( to the nearest tenth )

Answer:

soln;Here

Given,

f(x)=2x² + 4x - 14

g(x)= x³ + 15x

(f + g)(3)= ?

Now,

(f + g)(3) = f(3) + g(3)

=2×3³- 14 + 3³ + 15 × 3

=2 × 27 - 14 + 27 + 45

= 54 - 14 + 27 + 45

= 54 - 14 + 7

=61 - 14

= 47..

Hence the value of f + g)(3)= 47

The probability that the 4th or 5th student you stop is the first to have the jumper cables is 0.2417 or about 24.17%.

This is an example of a negative binomial probability problem, where we want to know the probability of obtaining a certain number of failures before obtaining a certain number of successes in a series of independent trials. In this case, the "success" is finding a student with jumper cables, and the "failure" is finding a student without jumper cables.

Let p be the probability of success (finding a student with jumper cables) on any given trial, which is 0.18 according to the problem. Let k be the number of successes we want to obtain, which is 1 in this case (since we only need to find one student with jumper cables). Let x be the number of trials it takes to obtain k successes, which is either 4 or 5 in this case.

Then, the probability of finding the first student with jumper cables on the 4th or 5th stop is:

P(X = 4 or X = 5) = P(X = 4) + P(X = 5)

We can calculate these probabilities using the negative binomial distribution formula:

[tex]P(X = x) = (x-1) choose (k-1) * p^k * (1-p)^{x-k}[/tex]

For x = 4:

[tex]P(X = 4) = (4-1) choose (1-1) * 0.18^1 * (1-0.18)^{4-1} = 0.1778[/tex]

For x = 5:

[tex]P(X = 5) = (5-1) choose (1-1) * 0.18^1 *(1-0.18)^{5-1} = 0.0639[/tex]

So, the probability of finding the first student with jumper cables on the 4th or 5th stop is:

P(X = 4 or X = 5) = 0.1778 + 0.0639 = 0.2417

Therefore, the probability that the 4th or 5th student you stop is the first to have the jumper cables is 0.2417 or about 24.17%.

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In order to have $140,000 in 20 years, you should deposit $371 each month.

$89,040 of the $140,000 comes from deposits and $50,960 comes from interest.

In Mathematics and Financial accounting, the periodic deposit (payment) for an investment can be calculated by using the following mathematical equation (formula):

[tex]FV=PMT(\frac{(1+\frac{r}{n})^{nt} -1}{\frac{r}{n} })[/tex]

Where:

By substituting the given parameters into the formula for the periodic deposit (payment), we have:

[tex]140,000=PMT(\frac{(1+\frac{0.0425}{12})^{12 \times 20} -1}{\frac{0.0425}{12} })[/tex]

140,000(0.0425/12) = PMT(1.33613612561)

495.8333333333 = PMT(1.33613612561)

PMT = 495.8333333333/1.33613612561

PMT = $371.0949 ≈ $371.

For the amount that comes from deposits, we have:

Total deposit = $371 × 12 × 20

Total deposit = $89,040

For the amount that comes from interest, we have:

Interest = $140,000 - $89,040

Interest = $50,960.

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Answer:

The answer is 5

Step-by-step explanation:

You divide 175 divided by 7 to find the hourly rate of how many oranges Leah peels. 60 minutes are in a hour. So 12 times 5 is 60. If 175 divided by 7 is 25. And that's hour much she peels in an hour. You divide it by five to find the 12 minute rate, because 12 times 5 is 60 that is equivalent to your hourly rate.

Answer:

Step-by-step explanation:

--> If 7 hrs= 175 oranges

1 hr= 175/7=25

1hr= 60 minutes

So, leah can peal 25 oranges in 60 mins.

Let the number of oranges peeled in 12 mins be x.

60x=25*12

x= 25*12/60

x=300/60

x=5

Leah can peel 5 oranges in 12 minutes,

the population of Bolivia in 2030, if it continues to grow at a rate of 1.6% continuously, will be approximately 14.45 million.

To solve this problem, we need to use the formula for continuous compounding, which is:

[tex]A = Pe^(rt)[/tex]

Where:

A = the final amount

P = the initial amount

r = the annual growth rate (as a decimal)

t = the number of years

We know that Bolivia had a population of 10.5 million in 2010 and a growth rate of 1.6%, or 0.016 as a decimal. We want to find the population in 2030, which is 20 years after 2010.

So, we plug in the values into the formula:

[tex]A = 10.5 million * e^(0.016 * 20)[/tex]

Using a calculator, we get:

[tex]A = 10.5 million * e^(0.32)[/tex]

A = 10.5 million * 1.3775

A = 14.45 million

Therefore, the population of Bolivia in 2030, if it continues to grow at a rate of 1.6% continuously, will be approximately 14.45 million.

Continuous compounding is a mathematical concept used to calculate the growth of a quantity that grows at a constant rate over time. It is different from simple interest, which is calculated based on a fixed rate over a certain period of time. In continuous compounding, the growth rate is applied infinitely many times over an infinite time period, resulting in exponential growth. The formula we used is a standard formula for continuous compounding, and it can be used to calculate the growth of various quantities, such as population, money, or investments.

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Answer: 4 ft 2 in i believe <3

Step-by-step explanation:

Answer: [tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]

Step-by-step explanation:

Half angle formula for sine is  

sin([tex]\frac{x}{2}[/tex])=[tex]\sqrt{1-cosx}/2[/tex]

If x is 150, then sin 75=[tex]\sqrt{1-cos150}/2[/tex] =[tex]\sqrt{1-\frac{cos(180-30)}{2} }[/tex]=[tex]\sqrt{1+cos30}/2[/tex]

=[tex]\sqrt{(1/2)+(\sqrt{3}/4)}[/tex] =[tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]

The shape given below consists of a rectangle and a triangle, and its area is 91 m²

Based on the image, we can see that the shape is composed of a rectangle and a triangle.

In order to find the width of rectangle we have to subtract the height of the triangle from the total length:

9m - 4m = 5 m .

Area of Rectangle:

Length = 13 m

Width = 5 m

Area of Rectangle = Length x Width

= 13 m x 5 m

= 65 m²

Triangle:

Base = 13 m

Height = 4 m

Area of Triangle = (1/2) x Base x Height

= (1/2) x 13 m x 4 m

= 26 m²

Total area of the shape = Area of Rectangle + Area of Triangle

= 65 m² + 26 m²

= 91 m²

Therefore, the area of the shape is 91 square meters (m²)

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The probability of drawing a penny dated 1977 is 0.24 or 24%.

Probability is a branch of mathematics that deals with the study of random events. It is used to measure the likelihood or chance of a particular event occurring.

Probability is expressed as a fraction or a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

The probability of drawing a penny dated 1977 can be found by dividing the number of pennies dated 1977 by the total number of pennies.

Here we have

Total number of pennies = 50

Number of pennies dated 1977 = 12

Probability of drawing a penny dated 1977

= Number of pennies dated 1977 / Total number of pennies

= 12 / 50

= 0.24

Therefore,

The probability of drawing a penny dated 1977 is 0.24 or 24%.

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Answer: The answer is 4.64$

Step-by-step explanation:

9 pencils is 2.25$. and we have 2.39$ for the notebook. 2.25 + 2.39 = 4.64

Step-by-step explanation:

The vertical line exactly between them     x = -1   is the axis of rotation

The two equations that are true for the value x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16.

For x = -2, substituting into equation 1 gives:

(-2)² - 4 = 0

4 - 4 = 0

Adding x = -2 to equation 2 results in:

4(-2)² = 16

4(4) = 16

For x = 2, substituting into equation 1 gives:

(2)² - 4 = 0

4 - 4 = 0

Adding x = -2 to equation 2 results in:

4(2)² = 16

4(4) = 16

Therefore, the equations is true.

The equation 3x² + 12 = 0 is not true for either x = -2 or x = 2 since substituting either value into the equation yields a non-zero result.

The equation 2(x - 2)² = 0 is only true for x = 2, but not for x = -2, since substituting x = -2 yields a non-zero result.

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The slope of the line passing through A(0,-5) and B(3,1) is 2.

what is slope?

In mathematics, slope is a measure of how steep a line is. It is the ratio of the change in the y-coordinates to the change in the x-coordinates between two points on the line.

The slope formula is given by:

slope = (change in y)/(change in x)

The change in y is the difference between the y-coordinates of two points on the line, while the change in x is the difference between the x-coordinates of the same two points. The slope is a single number that represents the degree of steepness of the line.

To find the slope of the line passing through two given points A(0,-5) and B(3,1), we can use the slope formula:

slope = (change in y)/(change in x)

We first need to find the change in y and the change in x between the two points:

change in y = y-coordinate of B - y-coordinate of A

= 1 - (-5)

= 6

change in x = x-coordinate of B - x-coordinate of A

= 3 - 0

= 3

Now, we can substitute these values into the slope formula:

slope = (change in y)/(change in x)

= 6/3

= 2

Therefore, the slope of the line passing through A(0,-5) and B(3,1) is 2.

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Therefore, for every passing hour, the amount of drug in the body is multiplied by approximately 0.7937 or 79.37% based on factor.

The half-life of a drug refers to the amount of time it takes for the concentration of the drug in the body to decrease by half. In this case, with a half-life of 3 hours, we can assume that the concentration of the drug in the body decreases by 50% every 3 hours.

To determine the factor by which the amount of drug in the body is multiplied for each passing hour, we can use the formula:

[tex]b = 0.5^(1/t)[/tex]

where b: factor by which the amount of drug in the body is multiplied for each passing hour, and t: half-life of the drug in hours. Substitute t = 3 hours into formula gives:

[tex]b = 0.5^(1/3) = 0.7937[/tex]

Therefore, for every passing hour, the amount of drug in the body is multiplied by approximately 0.7937 or 79.37%. This means that after one hour, the amount of drug in the body is reduced to 79.37% of its original amount, after two hours it is reduced to 62.86% (0.7937^2), after three hours it is reduced to 50%, and so on.

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Answer: make sure to add options.

The radio station gave away 43 tickets to employees, and they gave away 3 times as many tickets (3x) to listeners, which is 3 * 43 = 129 tickets. We can calculate it in the following manner.

Let's assume that the radio station gave away "x" tickets to employees.

According to the problem, they gave away three times as many tickets to listeners as to employees. So the number of tickets given to listeners would be 3x.

We know that the total number of tickets given away is 172. Therefore, we can set up an equation based on this:

x + 3x = 172

Simplifying and solving for x, we get:

4x = 172

x = 43

Therefore, the radio station gave away 43 tickets to employees, and they gave away 3 times as many tickets (3x) to listeners, which is 3 * 43 = 129 tickets.

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if you purchased one ticket, your expected gross winnings are $0.36.

what is gross winnings  ?

Gross winnings refer to the total amount of money won before any taxes or fees are deducted. In other words, it is the total amount of money won by an individual in a lottery or other type of game of chance, without taking into account any deductions that may be made

In the given question,

To calculate the expected gross winnings, we need to multiply the probability of winning each prize by the value of the prize and then add up these values.

First, let's find the probability of winning each prize:

First prize: There is only one first prize, and there are 15,000 tickets sold, so the probability of winning the first prize is 1/15,000.

Second prize: There are two second prizes, so the probability of winning a second prize is 2/15,000.

Third prize: There are three third prizes, so the probability of winning a third prize is 3/15,000.

Now we can calculate the expected gross winnings:

First prize: The probability of winning the first prize is 1/15,000, and the value of the prize is $3,000, so the expected value of the first prize is (1/15,000) x $3,000 = $0.20.

Second prize: The probability of winning a second prize is 2/15,000, and the value of each prize is $750, so the expected value of a second prize is (2/15,000) x $750 = $0.10.

Third prize: The probability of winning a third prize is 3/15,000, and the value of each prize is $300, so the expected value of a third prize is (3/15,000) x $300 = $0.06.

Now we can add up these value to find the total expected gross winnings:

$0.20 + $0.10 + $0.06 = $0.36

Therefore, if you purchased one ticket, your expected gross winnings are $0.36.

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It is not possible to solve the triangle with the given information.

What is Triangle ?

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is widely used in mathematics, science, and engineering. Triangles can be classified in different ways based on their side lengths, angle measures, and other properties.

To solve a triangle, we need at least three pieces of information, including at least one side length. In this case, we have the side lengths a=100 and b=90, and the angle opposite side a is 29 degrees. However, we don't have enough information to find the remaining angles and side lengths of the triangle.

We can use the Law of Cosines and the Law of Sines to solve a triangle, but we need at least one more piece of information. For example, if we had the length of side c or another angle, we could solve the triangle.

Therefore, It is not possible to solve the triangle with the given information.

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A sum is divisible by 3 if and only if both of the dice rolls are either 1 and 2 or 2 and 1, or both of the dice rolls are either 1

How to solve the problem?

To solve this problem, we first need to determine the total number of possible outcomes when rolling the die twice. Each roll has six possible outcomes, so the total number of outcomes when rolling the die twice is 6 x 6 = 36.

Next, we can create a table to list all possible outcomes and their corresponding sums:

Die 1 Die 2 Sum

1 1 2

1 2 3

1 3 4

1 4 5

1 5 6

1 6 7

2 1 3

2 2 4

2 3 5

2 4 6

2 5 7

2 6 8

3 1 4

3 2 5

3 3 6

3 4 7

3 5 8

3 6 9

4 1 5

4 2 6

4 3 7

4 4 8

4 5 9

4 6 10

5 1 6

5 2 7

5 3 8

5 4 9

5 5 10

5 6 11

6 1 7

6 2 8

6 3 9

6 4 10

6 5 11

6 6 12

Using this table, we can calculate the probability of each event:

Event A: The sum is greater than 9.

There are four possible outcomes where the sum is greater than 9: 10, 11, and 12. The probability of getting each of these outcomes is:

P(sum = 10) = 3/36

P(sum = 11) = 2/36

P(sum = 12) = 1/36

Therefore, the probability of Event A is:

P(Event A) = P(sum = 10) + P(sum = 11) + P(sum = 12)

= (3/36) + (2/36) + (1/36)

= 6/36

= 1/6

Event B: The sum is not divisible by 3.

A sum is divisible by 3 if and only if both of the dice rolls are either 1 and 2 or 2 and 1, or both of the dice rolls are either 1

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Answer:

u = 12;

v = 6

Step-by-step explanation:

Use trigonometry:

[tex] \tan(60°) = \frac{6 \sqrt{3} }{v} [/tex]

Use the property of proportion to find v:

[tex]v = \frac{6 \sqrt{3} }{ \tan(60°) } = \frac{6 \sqrt{3} }{ \sqrt{3} } = 6[/tex]

Use the Pythagorean theorem to find u:

[tex] {u}^{2} = {v}^{2} + ( {6 \sqrt{3}) }^{2} [/tex]

[tex] {u}^{2} = {6}^{2} + ( {6 \sqrt{3}) }^{2} = 36 + 36 \times 3 = 36 + 108 = 144[/tex]

[tex]u > 0[/tex]

[tex]u = \sqrt{144} = 12[/tex]

The definite integrals associated with the piecewise function have the following values:

Case 1: 1.5

Case 2: - 2 + 0.5π

Case 3: 5.5

In this problem we find the representation of a piecewise function formed by four parts, whose definite integrals must be determined by means of the following formulas:

[tex]I = \int\limits^b_a {f(x)} \, dx[/tex]

Graphically speaking, the definite integral is equal to the area below the curve.

Case 1

I = 0.5 · 2² - 0.5 · 1²

I = 1.5

Case 2

I = - 2 · 1 + 0.5π · 1²

I = - 2 + 0.5π

Case 3

I = - 0.5 · 0.5 · 1 + 0.5 · 1.5 · 3 + 1 · 3

I = - 0.25 + 2.75 + 3

I = 5.5

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a) Pedro's car completes 110 laps while Noor's car completes 100 laps.

b) Pedro's car completes 110% of the number of laps that Noor's car completes.

A lap refers to a complete circuit or rotation around a racetrack or other designated course. It is a standard unit of distance used in racing and other related sports. The length of a lap can vary depending on the specific track or course being used. In general, completing more laps than your competitors in a race is an indication of better performance and can help you win the race.

a)We can start by setting up a proportion to represent the relationship between the number of laps Pedro's car completes and the number of laps Noor's car completes:

2.2 laps / 2 laps = x laps / 100 laps

We can solve for x by cross-multiplying:

2.2 laps * 100 laps = 2 laps * x laps

220 laps = 2x

Dividing both sides by 2, we get:

x = 110 laps

b)If Pedro's car completes 2.2 laps for every 2 laps Noor's car completes, then we can find the ratio of the number of laps Pedro's car completes to the number of laps Noor's car completes as follows:

2.2 laps / 2 laps = 1.1

This means that Pedro's car completes 1.1 laps for every 1 lap Noor's car completes.

To find the percentage that Pedro's car completes compared to Noor's car, we can multiply this ratio by 100:

1.1 * 100 = 110%

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Answer:

The overall gain is $604.30.

Step-by-step explanation:

A summary of two stocks is shown.

52W high 52W low Name of Stock Symbol High Low Close

37.18 29.39 Zycodec ZYO 39.06 32.73 34.95

11.76 7.89 Unix Co UNX 16.12 12.11 15.78

Last year, a stockholder purchased 40 shares of Zycodec at its lowest price of the year and purchased 95 shares of Unix at its highest price of the year. If the stockholder sold all shares of both stocks at their respective closing price, what was the overall gain or loss?

The overall loss is $604.30.

The overall gain is $604.30.

The overall loss is $660.35.

The overall gain is $660.35.

Got It Right.

Answer: Don't use the other message below it's AI generated..

Step-by-step explanation:

The percentage of the project that has been completed 29.5%.

What is percenatge?

Percentage is a way of expressing a fraction or a portion of a whole as a number out of 100. The word "percent" comes from the Latin phrase "per centum", which means "by the hundred".

Based on the information given, Indiana Company began a construction project in 2024 with a contract price of $161 million to be received when the project is completed in 2026. During 2024, Indiana incurred $36 million of costs and estimates an additional $86 million of costs to complete the project.

Indiana Company recognizes revenue over time and for this project recognizes revenue over time according to the percentage of the project that has been completed. This means that Indiana Company will recognize a portion of the revenue each year based on the percentage of the project that has been completed.

To calculate the percentage of the project that has been completed, we need to divide the total costs incurred by Indiana Company by the estimated total costs of the project.

Total costs incurred in 2024 = $36 million

Estimated total costs of the project = $36 million + $86 million = $122 million

Therefore, the percentage of the project that has been completed in 2024 is:

Percentage of project completed = Total costs incurred / Estimated total costs

Percentage of project completed = $36 million / $122 million

Percentage of project completed = 0.295 or 29.5%

Based on this calculation, Indiana Company can recognize 29.5% of the total contract price as revenue for 2024.

Revenue recognized in 2024 = 29.5% x $161 million

Revenue recognized in 2024 = $47.5 million

So, Indiana Company can recognize $47.5 million in revenue for 2024. However, it is important to note that this is only an estimate and the actual revenue recognized may differ based on the progress of the project.

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Answer:

3,3,0,3

Step-by-step explanation:

because it's right

After answering the presented question, we can conclude that This equation also has solutions x = -5 and x = -1: |x + 5| - |x + 1| = 4

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

[tex]|x + 3| - 2 = 0\\|x + 3| = 2\\x + 3 = 2 or x + 3 = -2\\x = -5 or x = -1\\|x + 2| + 4 = 1\\|x + 2| = -3\\|x + 5| - |x + 1| = 4\\[/tex]

This equation also has solutions x = -5 and x = -1:

|x + 5| - |x + 1| = 4

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For the given figure the absolute value equation | [tex]x+3[/tex] | = [tex]2[/tex] has the solution set x={[tex]-5,-1[/tex]}.

An absolute value equation is an equation that involves an absolute value expression. An absolute value expression is denoted by enclosing the expression inside vertical bars, like this: |expression|. The absolute value of a real number x is defined as:

|x| = x if x is non-negative (i.e.,[tex]x\geq 0[/tex])

|x| = -x if x is negative (i.e., [tex]x < 0[/tex])

A quadratic equation is a second-degree polynomial equation of the form:

[tex]ax^{2} +bx +c = 0[/tex]

where a, b, and c are constants, and x is the variable. The highest power of the variable x is[tex]2[/tex], which means that the equation represents a curve called a parabola. The constant a is called the leading coefficient and determines the shape and direction of the parabola.

According to the given information

An absolute value equation with solution set x={[tex]-5,-1[/tex]} can be written as:

| [tex]x+3[/tex] | = [tex]2[/tex]

To see why this equation has the given solution set, we can substitute [tex]-5[/tex] and [tex]-1[/tex] for x and check that they satisfy the equation:

| [tex]-5+3[/tex] | = [tex]2[/tex], which is true since |[tex]-2[/tex]| = [tex]2[/tex]

| [tex]-1+3[/tex] | = [tex]2[/tex] which is also true since |[tex]2[/tex]| = [tex]2[/tex]

Therefore, the absolute value equation | [tex]x+3[/tex] | = [tex]2[/tex] has the solution set x={[tex]-5,-1[/tex]}.

Learn more about quadratic equations here:

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