Aleks topic please help

Step-by-step explanation:

The 'mean' is the 'average'

    add all of the heights together .....thien divide by the NUMBER of heights that were used.

The length of the slide is approximately 16.56 feet.

To solve this problem, we can use basic trigonometry.

The angle of elevation refers to the angle between the horizontal ground and the line of sight from the bottom of the slide to the top of the slide.

Given that the angle of elevation is 44 degrees and the height of the top of the slide is 16 feet, we can use the tangent function to find the length of the slide.

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

The opposite side is the height of the slide (16 feet), and the adjacent side is the length of the slide that we want to find (let's call it x).

So, we have:

tan(44 degrees) = 16 feet / x

To solve for x, we rearrange the equation:

x = 16 feet / tan(44 degrees)

Using a calculator, we can find the value of the tangent of 44 degrees, which is approximately 0.9659.

Thus, we can calculate:

x = 16 feet / 0.9659

≈ 16.56 feet

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a) The deepest that the diver went is of: 432 yards deep.

b) It took 12 minutes for the diver to return to the surface.

c) After one minute, the diver was 132 yards deep.

The quadratic function modeling the diver's height after x seconds is given as follows:

d(x) = 12x² - 144x.

The coefficients are given as follows:

a = 12, b = -144, c = 0.

The x-coordinate of the vertex is given as follows:

x = -b/2a

x = 144/24

x = 6.

Item a:

As a > 0, the minimum height for item a is given as follows:

d(6) = 12(6)² - 144(6)

d(6) = -432 feet.

(the minimum height is the y-coordinate of the vertex, as a > 0).

Item b:

The roots of the function for item b are obtained as follows:

12x² - 144x = 0

12x(x - 12) = 0

(coefficient c is of zero, hence there is no need to apply the Pythagorean Theorem).

Hence:

12 - 0 = 12, hence it took 12 minutes for the diver to return to the surface.

Item c:

After one minute, the depth of the diver for item c is given as follows:

d(1) = 12(1)² - 144

d(1) = -132 yards.

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The probability that more than 240 flights in a random sample of 400 commercial airline flights will arrive on time is approximately 1 or 100%.

To solve this problem using a normal approximation, we need to calculate the mean (μ) and standard deviation (σ) of the binomial distribution and then use the normal distribution to approximate the probability.

Given:

Probability of an airline flight arriving on time (success): p = 0.84

Number of trials (flights): n = 400

Number of flights arriving on time (successes): x > 240

First, we calculate the mean and standard deviation of the binomial distribution using the following formulas:

Mean (μ) = n * p

Standard Deviation (σ) = √(n * p * (1 - p))

μ = 400 * 0.84 = 336

σ = √(400 * 0.84 * 0.16) = √(53.76) ≈ 7.33

Now, we can use the normal distribution to find the probability that more than 240 flights will arrive on time. Since we're interested in the probability of x > 240, we will calculate the probability of x ≥ 241 and then subtract it from 1.

To use the normal distribution, we need to standardize the value of 240:

z = (x - μ) / σ

z = (240 - 336) / 7.33

z ≈ -13.13

Now, we can find the probability using the standard normal distribution table or a calculator. Since the value of z is extremely low, we can approximate it as:

P(x > 240) ≈ P(z > -13.13)

From the standard normal distribution table or calculator, we find that P(z > -13.13) is essentially 1 (close to 100%).

Therefore, the probability that more than 240 flights in a random sample of 400 commercial airline flights will arrive on time is approximately 1 or 100%.

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Answer:

The square root of x should lie between 9.2 and 9.3 since it is closer to 9.3, we can assume that x > 9.3^2 = 86.49. Since x is a whole number, the smallest whole number greater than 86.49 is 87. Therefore, the whole number that best approximates the value of x is 87.

Step-by-step explanation:

The whole number best approximates the value of x is 87.

We have the point root x in between 9.3 and 9.4.

If the number line between 9.3 and 9.4 is divided into five equal parts, the red dot would be located one part to the right of 9.3.

This indicates a value of 9.32. To find the square of 9.32 and determine the value of x, we calculate √9.32, which is equal to 86.86.

Among the four given options, 87 is the closest representation of x and provides the best approximation.

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Answer:

(0, -3) and (1, -2)

Step-by-step explanation:

This question essentially asks at which points do these two quadratic functions intersect. By looking at the graph, the two points of intersection are at (0, -3) and (1, -2)

Answer:

The solutions are (0, -3) and (1, -2).

Step-by-step explanation:

The solutions to a graphed system of equations are the points of intersections.

Points of intersection refer to the coordinates where the graphs of the equations intersect on a coordinate plane.

From inspection of the given graphs, we can observe that the blue and red curves intersect at points (0, -3) and (1, -2).

Therefore, the solutions are (0, -3) and (1, -2).

The fire department wants to send booklets on fire hazards to all teachers and homeowners in town. 38000 booklets does it need. The correct answer is (B) 38000.

To determine the number of booklets the fire department needs, we need to consider the total number of homeowners and teachers separately. Additionally, since some teachers are also homeowners, we should avoid duplicating the booklets for those individuals.

Total number of homeowners = 35,000

Total number of teachers = 4,000

Number of teachers who own their own homes = 1,000

To calculate the number of booklets needed, we need to subtract the number of teachers who own their own homes from the total number of teachers. This is because they will receive both the teacher booklet and the homeowner booklet.

Number of booklets needed for homeowners = Total number of homeowners = 35,000

Number of booklets needed for teachers = Total number of teachers - Number of teachers who own their own homes = 4,000 - 1,000 = 3,000

Therefore, the total number of booklets needed is:

Number of booklets for homeowners + Number of booklets for teachers = 35,000 + 3,000 = 38,000

Therefore, the correct answer is (B) 38000.

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The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.

a) We are given the equation 8 tan θ = 3 cos θ.

Dividing both sides of the equation by cos θ, we have:

8 tan θ / cos θ = 3

Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:

8 (sin θ / cos θ) / cos θ = 3

Simplifying further, we get:

8 sin θ / cos^2 θ = 3

Now, multiplying both sides of the equation by cos^2 θ, we have:

8 sin θ = 3 cos^2 θ

Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:

8 sin θ = 3(1 - sin^2 θ)

Expanding the equation, we get:

8 sin θ = 3 - 3 sin^2 θ

Rearranging the terms, we have:

3 sin^2 θ + 8 sin θ - 3 = 0

Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.

b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.

To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.

In this case, the equation factors as:

(3 sin θ - 1)(sin θ + 3) = 0

Setting each factor equal to zero, we have two equations:

3 sin θ - 1 = 0    or    sin θ + 3 = 0

For the first equation, solving for sin θ, we get:

3 sin θ = 1

sin θ = 1/3

Taking the inverse sine (sin^-1) of both sides, we find:

θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)

For the second equation, solving for sin θ, we have:

sin θ = -3

Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).

Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.

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(1) The area of the actual bridge deck in square feet is  5,280 square feet.

(2) The theoretical probability, P(gold), is 25% and the experimental probability, P(gold), is 27.5%.

(1) To find the area of the actual bridge deck, we need to convert the dimensions of the scaled bridge deck from inches to feet, and then scale up by a factor of 60.

48 inches = 4 feet

4 and 2/5 inches = 0.3667 feet (rounded to four decimal places)

Area of the scaled bridge deck = 4 feet x 0.3667 feet = 1.4668 square feet

Scaling up by a factor of 60:

Area of actual bridge deck = 1.4668 square feet x 60^2 = 5,280.48 square feet

Therefore, the area of the actual bridge deck is approximately 5,280 square feet.

(2) Based on the given data,

The theoretical probability of pulling a gold marble from the bag is 25% since there are a total of 40 marbles and 11 of them are gold.

Meanwhile, the experimental probability is calculated by dividing the total number of marbles pulled by the number of times gold was pulled.

As a result, the accurate answer is that the theoretical probability, P(gold), is 25% and the experimental probability, P(gold), is 27.5%.

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Answer:

A = 115°

B = 115°

C = 65°

Step-by-step explanation:

Vertically opposite angles are equal.

A = 115°

Corresponding angles are equal.

B = 115°

Alternate angles add up to 180°.

A + C = 180

C = 180 - A

C = 180 - 115

C = 65°

The recursive formula for the sequence an = { 3/5, 1/10, 1/60, 1/360 } is an = an-1 / (6 - n). So, the recursive formula for the sequence is an = an-1 / (6 - n).

The given sequence an = { 3/5, 1/10, 1/60, 1/360 } can be written as follows: a1 = 3/5

a2 = 1/10

a3 = 1/60

a4 = 1/360

To find the recursive formula for the sequence, we need to find an-1 and an.

We have, a2 = a1 / (6 - 2) = a1 / 4,

which gives us a1 = 4a2a3 = a2 / (6 - 3) = a2 / 3,

which gives us a2 = 3a3a4 = a3 / (6 - 4) = a3 / 2,

which gives us a3 = 2a4

Substituting these values in the above formula, we get: an = an-1 / (6 - n)a2 = a1 / 4 => a1 = 4a2a3 = a2 / 3 => a2 = 3a3a4 = a3 / 2 => a3 = 2a4

Substituting a1, a2, and a3 in the recursive formula, we get: a2 = a1 / 4 => a1 = 4a2 = 4/10 = 2/5a3 = a2 / 3 => a2 = 3a3 = 3/60 = 1/20.  a4 = a3 / 2 => a3 = 2a4 = 2/360 = 1/180. Therefore, the recursive formula for the sequence is an = an-1 / (6 - n).

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Answer:

Let's assume that the total number of students in the school is "x". We can create a proportion to estimate how many students would choose the aquarium based on the given information:

Number of students who chose aquarium / Total number of students in the school = Percentage of students who chose aquarium / 100

We can plug in the values we know:

80 / x = p / 100

where "p" is the percentage of students who would choose the aquarium if the entire school were surveyed.

We can solve for "x" by cross-multiplying and simplifying:

8000 = px

x = 8000 / p

Now, we need to estimate the value of "p". We can do this by finding the average percentage of students who chose the aquarium, science center, planetarium, and farm:

(80 + 60 + 30 + 40) / x = (210 / x) = Average percentage of students who chose an attraction

This tells us that, on average, 210 out of every "x" students would choose one of the attractions. We can estimate that a similar percentage of the entire school would choose the aquarium:

p / 100 = 80 / 210

p = 38.1

So, we can estimate that approximately 38.1% of the students in the whole school would choose the aquarium. To find the estimated number of students who would choose the aquarium, we can plug in this value for "p" in our original proportion:

80 / x = 38.1 / 100

Cross-multiplying and solving for "x", we get:

x = 209.71

Rounding to the nearest whole number, we can estimate that approximately 210 students in the whole school would choose the aquarium.

Step-by-step explanation:

Answer:

The teacher surveyed a total of:

80 + 60 + 30 + 40 = 210 students.

If we assume that the sample of 210 students surveyed is representative of the entire population of 1000 students at Lake Middle School, we can use the relative frequency of students choosing the aquarium in the sample to estimate the number of students in the whole school who would choose the aquarium.

The relative frequency of students choosing the aquarium in the sample is:

80/210 = 0.38

This means that approximately 38% of the students in the sample chose the aquarium.

To estimate the number of students in the whole school who would choose the aquarium, we can multiply the relative frequency by the total number of students at the school:

0.38 x 1000 = 380

Therefore, the teacher can estimate that approximately 380 students out of 1000 at Lake Middle School would choose the aquarium for a field trip.

Chenelle can travel at most 160 miles without exceeding her spending limit of $300.

We have,

To determine the maximum number of miles Chenelle can travel without exceeding her spending limit of $300, we need to subtract the flat rate from her budget and divide the remaining amount by the cost per mile.

So,

Subtract the flat rate from Chenelle's budget:

Budget after subtracting the flat rate.

= $300 - $19.95

= $280.05

Divide the remaining budget by the cost per mile to find the maximum number of miles:

Maximum miles = Budget after subtracting the flat rate / Cost per mile

= $280.05 / $1.75

Using division.

Maximum miles = 160.028571

Therefore,

Chenelle can travel at most 160 miles without exceeding her spending limit of $300.

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The slope (m) is 1 and the y-intercept (b) is 33 for the equation y = x + 33.

The equation y = x + 33 represents a linear equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope (m) is the coefficient of x, which is 1. Therefore, the slope is 1.

The y-intercept (b) is the value of y when x is 0. In the given equation, y = x + 33, when x = 0, we can see that y = 0 + 33 = 33. Hence, the y-intercept is 33.

Therefore, the slope (m) is 1 and the y-intercept (b) is 33 for the equation y = x + 33.

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The angle LKJ in the triangle is 49 degrees.

The sum of angles in a triangle is 180 degrees. The measure of the angle LKJ can be found as follows:

Therefore, the angle LKJ can be found using trigonometric ratios as

follows:

Not the triangle is a right angle triangle. Therefore, one of its angles is 90 degrees.

Hence,

tan x = opposite / adjacent

tan x = 8.9 / 7.7

tan x = 1.15584415584

x = tan ⁻¹ 1.15584415584

x = 49.1346675513

Therefore,

angle LKJ = 49 degrees

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a. The given equation, 9x² + 4y² - 90x + 40y + 289 = 0, is a representation of an ellipse

b.   the equation of the conic section (ellipse) in conic form is

(x - 5)² / 4 + (y + 5)² / 9 = 1.

We will rearrange the equation to be :

9x² - 90x + 4y² + 40y = -289

(9x² - 90x) / (-289) + (4y² + 40y) / (-289) = 1

9(x² - 10x) + 4(y² + 10y) = -28

9(x² - 10x + 25) + 4(y² + 10y) = -289 + 9(25)

We then simplify :

9(x - 5)² + 4(y² + 10y) = -289 + 225

We will complete the square for y by adding (10/2)² = 25.

9(x - 5)² + 4(y² + 10y + 25) = -289 + 225 + 4(25)

9(x - 5)² + 4(y + 5)² = -289 + 225 + 100

9(x - 5)² + 4(y + 5)² = 36

Finally we divide both sides by 36 :

(x - 5)² / 4 + (y + 5)² / 9 = 1

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Answer:

This is an equation of an ellipse.

[tex]\dfrac{(x-5)^2}{4}+\dfrac{(y+5)^2}{9}=1[/tex]

Step-by-step explanation:

The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).

The standard equations for hyperbolas and ellipses all include x² and y² terms, whereas the standard equation for a parabola includes the square of only one of the two variables.

In the equation of an ellipse, the signs of the terms involving x² and y² are both positive, whereas one of the squared terms in the equation of a hyperbola is negative. Therefore, the conic section is an ellipse.

To determine the equation of the ellipse in conic form, rewrite the equation by completing the square.

Given equation:

[tex]9x^2+4y^2-90x+40y+289=0[/tex]

Rearrange the equation so that the constant is on the right side:

[tex]9x^2-90x+4y^2+40y=-289[/tex]

Factor out the coefficient of the squared terms:

[tex]9(x^2-10x)+4(y^2+10y)=-289[/tex]

Add the square of half the x-term and y-term inside their respective parentheses on the left side of the equation, and add their distributed values to the right side:

[tex]9(x^2-10x+25)+4(y^2+10y+25)=-289+9(25)+4(25)[/tex]

Factor the perfect square trinomials on the left side and simplify the right side of the equation:

[tex]9(x-5)^2+4(y+5)^2=36[/tex]

Divide both sides by the constant on the right side so that the equation equals 1:

[tex]\dfrac{9(x-5)^2}{36}+\dfrac{4(y+5)^2}{36}=\dfrac{36}{36}[/tex]

[tex]\dfrac{(x-5)^2}{4}+\dfrac{(y+5)^2}{9}=1[/tex]

Therefore, the equation of the given conic section in conic form is:

[tex]\boxed{\dfrac{(x-5)^2}{4}+\dfrac{(y+5)^2}{9}=1}[/tex]

The distance of A from the house is approximately 29.07 meters.

We can set up the following equation:

tan(32°) = height of house / x

tan(40°) = height of house / (x + 20 + y)

Notice that we added 20 meters to x since Tumpale walked 20 meters towards the house. We can simplify this equation by using the fact that y = x + 20.

tan(40°) = height of house / (2x + 20)

Now we have two equations with two variables (x and the height of the house). We can solve for x by isolating x in the first equation:

x = height of house / tan(32°)

Now we can substitute this expression for x into the second equation:

tan(40°) = height of house / (2(height of house / tan(32°)) + 20)

Simplifying this equation gives us:

tan(40°) = height of house / (2/tan(32°) + 20/(height of house))

We can solve for the height of the house by multiplying both sides by (2/tan(32°) + 20/(height of house)):

height of house = (2/tan(32°)) * tan(40°) / (1 - (40° - 32°) * tan(40°))

x = 17.64 / tan(32°) ≈ 29.07 meters

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Rounding to the nearest hundredth, the probability that the player gets the bonus on the 4th coin collected is approximately 0.07.

To find the probability that the player gets the bonus on the 4th coin collected, we can analyze the situation.

The probability of getting the bonus on any given coin collected is 1/10, since there is a 1 in 10 chance that the last digit of the milliseconds in the game's timer equals 1.

Since the events of collecting each coin are independent, we can use the probability of getting the bonus on a single coin to calculate the probability of not getting the bonus on the first three coins and then getting it on the fourth coin.

The probability of not getting the bonus on a coin is 9/10, as there are 9 out of 10 possible last digits that do not satisfy the condition.

So, the probability of not getting the bonus on the first three coins is (9/10)^3, as each event is independent.

Therefore, the probability of getting the bonus on the 4th coin is:

P(C=4) = (9/10)^3 * (1/10) = 729/10000 ≈ 0.0729.

Hence, rounding to the nearest hundredth, the probability that the player gets the bonus on the 4th coin collected is approximately 0.07.

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Answer:

Step-by-step explanation:

A solution for x would mean that when you plugged in that value for x, the equation will be balanced and equal.  It will make a true statement.  

Ex.  100=100 is a true statement

      whereas if you picked something wrong for x and got 100=50 that is not true.

The medication NT71B caused the patient's hemoglobin count to decrease by an average of 0.32 g/dL per week during the five-week trial.

To determine how much the patient's hemoglobin count decreased each week due to the medication NT71B, we can calculate the average rate of decrease over the five-week trial period.

The initial hemoglobin count was 14.2 g/dL, and the final hemoglobin count after five weeks was 12.6 g/dL. The total decrease in hemoglobin count over the five weeks is:

14.2 g/dL - 12.6 g/dL = 1.6 g/dL

To find the average decrease per week, we divide the total decrease by the number of weeks:

Average decrease per week = Total decrease / Number of weeks

= 1.6 g/dL / 5 weeks

= 0.32 g/dL per week

Therefore, the medication NT71B caused the patient's hemoglobin count to decrease by an average of 0.32 g/dL per week during the five-week trial.

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Answer:

C. f(x) = x

The function f(x) = 2[x - 6] is a linear function where the input value x is multiplied by 2 and then shifted horizontally 6 units to the right. The parent function for this linear function is f(x) = x.

Step-by-step explanation:

Hello!

-4(-5 + 3)

= -4(-2)

Answer:

C

Step-by-step explanation:

-4(-5+3)
20+(-12)

The exponential function that goes through the points [tex]\((0, 5)\)[/tex] and [tex]\((4, 6480)\) is \(y = 5 \cdot 6^x\)[/tex] .

To write the exponential function in the form [tex]\(y = ab^x\)[/tex] that goes through the points [tex]\((0, 5)\) \ and \((4, 6480)\)[/tex], we can use the point-slope form of a linear equation.

First, let's substitute the values of the first point into the equation:

[tex]\(5 = ab^0\)[/tex]

Since any number raised to the power of 0 is 1, the equation simplifies to:

[tex]\(5 = a\)[/tex]

Now, we have the value of \(a\), which is 5.

Next, let's substitute the values of the second point into the equation:

[tex]\(6480 = 5b^4\)[/tex]

Simplifying the equation:

[tex]\(b^4 = \frac{6480}{5}\)\(b^4 = 1296\)[/tex]

Taking the fourth root of both sides:

[tex]\(b = \sqrt[4]{1296}\)\(b = 6\)[/tex]

The concept of finding an exponential function involves determining the values of the coefficients a and b in the equation [tex]y = ab^x[/tex], based on given points. By substituting the coordinates of the points into the equation, we can solve for the values of a and b to define the exponential relationship.

Therefore, the exponential function that goes through the points [tex]\((0, 5)\)[/tex] and [tex]\((4, 6480)\) is \(y = 5 \cdot 6^x\)[/tex] .

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The balance of Jennifer's account after 15 years is given as follows:

$295,243.41.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 145000, r = 0.0475, n = 12, t = 15.

Hence the balance of the equation after 15 years is given as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(15) = 145000\left(1 + \frac{0.0475}{12}\right)^{12 \times 15}[/tex]

A(15) = $295,243.41.

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8a,the answer will be 30-40 or 30-35

b,it will be 5 because it the one that is in the 50th percentile

We can say that the corresponding sides JH is congruent to VX.

We have,

In ΔJHI and ΔWXV,

JI = WV ( given )

HI = WX ( given )

Now,

In two triangles, if two corresponding sides are equal then the remaining corresponding sides will be equal.

So,

JH ≅ VX

Thus,

We can say that the corresponding sides JH is congruent to VX.

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The scenarios that can be considered a seller-based discount are:

A. The offer by Wire and Cable

B. Carfna's Fine Foods

C. Mouser Electronics offer

E. Carchex Car Maintenance

A seller-based discount is a discount that is offered by a seller for the early purchase of a product. The goal of the seller in this case is to get cash as he or she is in an immediate need for cash.

The most outstanding example is that of Carchex Car Maintenance where an offer is made by the seller for the early purchase of products.

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Answer:

D. $5,040

Step-by-step explanation:

Money made during peak season = 1,800,000 * p

1. Expression for money made during peak season:

During peak season, the zoo has about 1,800,000 visitors. To calculate the money made during peak season, we multiply the number of visitors by the price of one peak season ticket (p):

Money made during peak season = 1,800,000 * p

2. Expression for money made during the off season:

The zoo wants to sell tickets in the off season for half the price of tickets in the peak season. Therefore, the price of one off season ticket would be p/2. To calculate the money made during the off season, we multiply the number of visitors by the price of one off season ticket:

Money made during the off season = 1,200,000 * (p/2) = 600,000 * p

3. Inequality for breaking even:

To break even, the zoo needs to make at least as much money as they spent on the animals. Let's represent the amount spent on animals as A. The money made during peak season plus the money made during the off season should be greater than or equal to the amount spent on animals:

1,800,000 * p + 600,000 * (p/2) ≥ A

Simplifying the inequality:

3,600,000p + 300,000p ≥ 2A

3,900,000p ≥ 2A

Solving for p:

p ≥ (2A) / 3,900,000

This determines the minimum price of one peak season ticket to break even.

The price of one off season ticket would be half the price of one peak season ticket, so the off season ticket should be (p/2).

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