The high temperature in Jackson, WY, on July 13 was 80°F. Use the formula, C = (F - 32), where C is Celsius degrees and


Fis Fahrenheit degrees, to convert 80°F to Celsius degrees. Round to the nearest tenth of a degree

The sphere must be emptied into the cylinder 3 times to completely fill it with water.

We will use the formulas for theSo, the sphere must be emptied into the cylinder 3 times to completely fill it with water. and the volume of a cylinder to find out how many times the sphere needs to be emptied into the cylinder until it is full.

Step 1: Find the volume of the sphere.
The formula for the volume of a sphere is V_sphere = (4/3)πr^3, where r is the radius.
Given that the radius of the sphere is 6 inches, we can calculate its volume:
V_sphere = (4/3)π(6)^3 = (4/3)π(216) ≈ 904.78 cubic inches

Step 2: Find the volume of the cylinder.
The formula for the volume of a cylinder is V_cylinder = πr^2h, where r is the radius and h is the height.
Given that the radius of the cylinder is 6 inches and the height is 18 inches, we can calculate its volume:
V_cylinder = π(6)^2(18) = π(36)(18) ≈ 2038.51 cubic inches

Step 3: Determine how many times the sphere must be emptied into the cylinder.
To find out how many times the sphere needs to be emptied into the cylinder, divide the volume of the cylinder by the volume of the sphere:

Number_of_times = V_cylinder / V_sphere = 2038.51 / 904.78 ≈ 2.25 times
Since we cannot empty the sphere partially, we'll round up to the nearest whole number:
Number_of_times = 3 times

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Answer:

(x-2.75)^2=4.25

Step-by-step explanation:

2x^2-11x+14=0

divide through by two

x^2-5.5x+7=0

x^2-5.5x=-7

x^2-5.5x+(-5.5/2)^2=-7+(-5.5/2)

(x-2.75)^2=4.25

If Mateo jogged 25 9/10 miles last week and jogged the same course all 7 days, then he jogged an average of (25 9/10) / 7 = 3 11/14 miles per day.

To convert this mixed number to an improper fraction, we can multiply the whole number by the denominator of the fraction and add the numerator, then place the result over the denominator:

3 * 14 + 11 = 53

53/14

So, Mateo jogged an average of 53/14 miles per day last week

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The woman performed 100 joules of work to push the cart of groceries over a distance of 10 meters.

To find the work performed by the woman, we will use the work-energy theorem which states that work (W) is equal to the change in energy. In this case, the woman applies a 10 Newton force and uses 100 joules of energy. The formula for work is:

W = F × d × cos(θ)

Where W is work, F is force, d is the distance over which the force is applied, and θ is the angle between the force and the direction of motion. Since the woman used 100 joules of energy, we can rewrite the equation as:

100 J = 10 N × d × cos(θ)

We don't have information about the angle θ, but if we assume that she applied the force horizontally, which is in the same direction as the motion, the angle θ would be 0 degrees, and the cosine of 0 is 1. Therefore, the equation becomes:

100 J = 10 N × d

To find the distance (d), we can now solve for d:

d = 100 J / 10 N

d = 10 meters

So, 100 joules of work was performed by the women to push the cart of groceries over a distance of 10 meters.

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The correct answer is: b

8 points within any 36-month period

6 points within any 24-month period

4 points within any 12-month period

In most US states, drivers are assigned points for certain traffic violations or accidents. If a driver accumulates too many points within a certain period of time, they may be labeled as a "negligent operator" and face penalties such as license suspension or revocation. The point thresholds for being labeled as a negligent operator may vary by state, but the options given in the question are generally accurate.

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The relationship between the areas of the three squares is that square A plus square B equals the area of square C.

The Pythagorean theorem is a fundamental idea in geometry that states that for any right-angled triangle, the square of the length of the longest side (opposite the right angle) is equal to the sum of the square of the lengths of the two remaining sides. This equation can be expressed as:

[tex]a^2 + b^2 = c^2[/tex]

Thus, the relationship between the areas of the three squares is that square A plus square B equals the area of square C.

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Since ln(1/6) is a finite value, the sequence does not diverge. It converges to ln(1/6) as n approaches infinity.

To determine if the sequence diverges, we need to take the limit of the expression as n approaches infinity.

Using the logarithmic identity ln(a/b) = ln(a) - ln(b), we can simplify the expression as follows:

[tex]ln(n^3 8) - ln(6n^3 13n) = ln(n^3) + ln(8) - ln(6n^3) - ln(13n)[/tex]

= [tex]ln(n^3) - ln(6n^3) + ln(8) - ln(13n)[/tex]

= [tex]ln(n^3/6n^3) + ln(8/13n)[/tex]

=[tex]ln(1/6) + ln(8/13n)[/tex]

As n approaches infinity, ln(8/13n) approaches 0, so the limit of the expression is:

lim n→∞ [ln(1/6) + ln(8/13n)]

= ln(1/6)

Since ln(1/6) is a finite value, the sequence does not diverge. It converges to ln(1/6) as n approaches infinity.

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After about 15.7 months, the apartment complex will have 800 occupied units.

Logistic growth is a type of growth in which the growth rate of a population decreases as the population size approaches its maximum value. In this case, the apartment complex has a maximum capacity of 1500 units.

Starting with 15 occupied units and growing at a rate of 10% per month, the number of occupied units can be modeled by a logistic function.

To find the number of months it takes to reach 800 occupied units, we need to solve for the time when the logistic function equals 800.

Let P(t) be the number of occupied units at time t (in months), then we have:

P(t) = 1500 / (1 + 1485[tex]e^{(-0.1t)}[/tex])

We want to find t such that P(t) = 800. Solving for t, we get:

t = -10 ln(1 - 4/37) ≈ 15.7 months

This means that after about 15.7 months, the apartment complex will have 800 occupied units.

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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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Answer:

mean decreases by 15

median stays the same

To use Newton's method to approximate a root of the equation

In (4x) = arctan(x -0.1),

we will need to find the first derivative of the function f(x) = In(4x) - arctan(x-0.1). f(x) = In(4x) - arctan(x-0.1) f'(x) = 4/(4x) - 1/(1+(x-0.1)^2) Using the initial approximation x1 = 0.1,

We can find the second approximation x2: x2 = x1 - f(x1)/f'(x1) x2 = 0.1 - [In(4*0.1) - arctan(0.1-0.1)] / [4/(4*0.1) - 1/(1+(0.1-0.1)^2)] x2 = 0.1076

We can repeat this process to find the third approximation x3: x3 = x2 - f(x2)/f'(x2) x3 = 0.1076 - [In(4*0.1076) - arctan(0.1076-0.1)] / [4/(4*0.1076) - 1/(1+(0.1076-0.1)^2)] x3 = 0.1078

Now we can find the fourth approximation x4: x4 = x3 - f(x3)/f'(x3) x4 = 0.1078 - [In(4*0.1078) - arctan(0.1078-0.1)] / [4/(4*0.1078) - 1/(1+(0.1078-0.1)^2)] x4 = 0.1078

Finally, we can find the fifth approximation x5: x5 = x4 - f(x4)/f'(x4) x5 = 0.1078 - [In(4*0.1078) - arctan(0.1078-0.1)] / [4/(4*0.1078) - 1/(1+(0.1078-0.1)^2)] x5 = 0.1078

Therefore, the fourth approximation x4 is 0.1078 and the fifth approximation x5 is also 0.1078.

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There is a high probability that Somil will be assigned at least one of his preferred topics.

To calculate the probability of Somil getting at least one of his preferred topics, we can use the complement rule. That is, we calculate the probability of Somil not getting any of his preferred topics and then subtract that probability from 1.

Let's first calculate the total number of ways to assign the topics to the students. We can think of this as distributing 34 distinct objects (the topics) into 9 distinct groups (the students), where each group gets 3 objects. We can use the multinomial coefficient formula to compute this:

C(34, 3, 3, 3, 3, 3, 3, 3, 3) = (34!)/(3!)^9

where C(n, k1, k2, ..., km) denotes the multinomial coefficient, which is the number of ways to divide n distinct objects into m groups with k1, k2, ..., km objects in each group.

Next, let's calculate the number of ways to assign the topics such that Somil does not get any of his preferred topics. We can think of this as first choosing 5 topics that Somil does not want, and then distributing the remaining 29 topics among the 9 students. The number of ways to choose 5 topics out of 29 is C(29, 5), and the number of ways to distribute the remaining 29 topics among 9 students is C(29, 3, 3, 3, 3, 3, 3, 3, 2) (since 2 topics are already assigned to Somil). Therefore, the total number of ways to assign the topics such that Somil does not get any of his preferred topics is:

C(29, 5) * C(29, 3, 3, 3, 3, 3, 3, 3, 2)

To calculate the probability of this event, we divide the above expression by the total number of ways to assign the topics:

P(Somil does not get any preferred topic) = [C(29, 5) * C(29, 3, 3, 3, 3, 3, 3, 3, 2)] / [(34!)/(3!)^9]

Finally, we can use the complement rule to find the probability that Somil gets at least one of his preferred topics:

P(Somil gets at least one preferred topic) = 1 - P(Somil does not get any preferred topic)

Plugging in the values, we get:

P(Somil gets at least one preferred topic) = 1 - [C(29, 5) * C(29, 3, 3, 3, 3, 3, 3, 3, 2)] / [(34!)/(3!)^9]

This evaluates to approximately 0.782, or 78.2%. Therefore, there is a high probability that Somil will be assigned at least one of his preferred topics.

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If combine harvester able to cut a 2450 square meters field in 5 hours and other one can do the same job in 7 hours then the area that the two combines cut in 9 hours is equals to the 7,560 square meters.

We have two harvester which can cut a area into different time.

The time taken by first harvester cuts into 2450 square meters field =5 hours.

The time taken by second harvester cuts into 2450 square meters field = 7 hours.

We have to determine the area can the two combines cut in 9 hours.

Here, total work = 2450 square meters

Work ability or efficiency of first harvester = 2450/5 = 490

Work efficiency of second harvester

= 2450/7= 350

Efficiency of both harvester in combine

= 350 + 490 = 840

So, area they cut into 9 hours = 840 × 9

=7560 square meters

Hence, required area is 7,560 square meters.

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Based on the results of Corey repeating his process 10 more times, a possible reason for this outcome with 3 green balls, 2 orange balls, and 5 purple balls could be that there is a higher probability of selecting a purple ball compared to the other colors.

Here's a step-by-step explanation:

1. Corey conducted an experiment where he repeated a process 10 times.
2. During these trials, he obtained the following results: 3 green balls, 2 orange balls, and 5 purple balls.
3. The distribution of colors suggests that there is a higher probability of selecting a purple ball (5/10) than a green ball (3/10) or an orange ball (2/10).
4. This outcome could be due to factors such as a larger number of purple balls in the pool from which Corey is selecting or some other bias in the process that increases the likelihood of selecting a purple ball.

In conclusion, the possible reason for the outcome with 3 green balls, 2 orange balls, and 5 purple balls is that there might be a higher probability of selecting a purple ball during Corey's repeated trials.

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The area of the circle is  12. 56 square units

The formula for calculating the area of a circle is expressed as;

A = πr²

This is so such that the parameters of the equation are;

From the information given, we have that;

Area = unknown

Radius = 2 units

Now, substitute the values into the formula, we have;

Area = 3.14 ×2²

Find the square

Area = 3.14 × 4

Multiply the values, we have;

Area = 12. 56 square units

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Both √203 and √96 are irrational numbers since the numbers inside the roots are not perfect squares.

To determine whether a root is rational or irrational, we need to know if the number inside the square root is a perfect square or not. If it is not, then the root is irrational.

For √203, we can determine that 203 is not a perfect square, since the last digit is 3, which is not a perfect square. Therefore, √203 is an irrational number.

For √96, we can simplify the expression as follows:

√96 = √(16*6) = √16 * √6 = 4√6

Since 6 is not a perfect square, 4√6 is an irrational number.

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Answer:

[tex] \sqrt{20n} = \sqrt{4} \sqrt{5n} = 2 \sqrt{5n} [/tex]

C is the correct answer.

The value of a is -16

If α and β are zeroes of the quadratic equation x²-6x+a, then we know that:

α + β = 6

α * β = a

We are also given that 3α + 2β = 20.

3α + 2β = 20

3(α + β) - α = 20

3(6) - α = 20

18 -α = 20

18 - 20 = α

α = -2

Substituting α = -2 into the equation α + β = 6, we get:

- 2 + β = 6

beta = 8

Therefore, α = -2 and β = 8, and we can find a using the equation α * β = a:

a = α * β

= - 2 * 8

= 16

Therefore, the value of a is -16

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The graph that represents a function is the graph (b)

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

Graphs A to D

As a general rule of the vertical line test

For a graph to represent a function, a line drawn from the x-axis must intersect with the graph at most once

Using the above as a guide, we have the following:

The graph b would intersect with a line from the x-axis at most once

Hence, the graph that represents a function is (b)

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The actual interest paid by Anita is $2949.44 - $2600 = $349.44 (rounded to the nearest cent).

In this case, we have:

P = $2600

r = 0.14 (14%)

n = 12 (compounded monthly)

t = 1 (one year)

Plugging in the values, we get:

A = $2600(1 + 0.14/12)^(12*1)

= $2600(1.0116667)^12

= $2949.44

Interest refers to the amount of money charged by a lender to a borrower for the use of borrowed funds. It is typically expressed as a percentage of the amount borrowed and is usually charged over a specified period of time, such as a month or a year.

Interest can be either simple or compound. Simple interest is calculated only on the principal amount borrowed, while compound interest is calculated on the principal amount as well as any accumulated interest. This means that with compound interest, the borrower ends up paying more in interest over time. Interest rates can vary depending on a range of factors, such as the borrower's credit score, the length of the loan, and prevailing market conditions. In general, higher-risk borrowers are charged higher interest rates, while lower-risk borrowers are charged lower rates.

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To prevent loan or credit card payment default, borrowers must make a minimum monthly payment.

Based on the outstanding debt amount, this payment includes interest and other fees along with portions of principal. The lender/creditor typically sets these payments to ensure progress towards paying off existing debt.

However, by making just minimum payments, borrowers may end up shelling out significantly more in added interest over the lifetime of the debt. Furthermore, prolonging the repayment time is another possible outcome to such a practice; hence, it remains crucial to determine suitable ways of meeting higher than expected monthly payments on debts.

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Each box has a mass of 90 grams, which is found by setting up a proportion using the ratio of cans to boxes and the known mass of each can.

To solve this problem, we need to use proportions. We know that 3 cans have the same mass as 9 identical boxes, which means that the ratio of cans to boxes is 3:9 or simplified to 1:3.

We also know that each can has a mass of 30 grams. Therefore, we can set up the proportion:

1 can / 30 grams = 1 box / x grams

where x is the mass, in grams, of each box.

To solve for x, we can cross-multiply:

1 can * x grams = 30 grams * 1 box

x grams = 30 grams / 1 can * 1 box

Since the ratio of cans to boxes is 1:3, we can substitute 3 for the number of boxes:

x grams = 30 grams / 1 can * 3 boxes

x grams = 90 grams

Therefore, the mass of each box is 90 grams.

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The equation for the company's profit, P(x), is P(x) = 6.6x - 2,300, where x is the number of items sold.

To find the equation P(x) for the company's profit, we can first determine the slope (m) and the y-intercept (b) of the linear equation P(x) = mx + b.

1. Calculate the slope (m) using the given information:

m = (P2 - P1) / (x2 - x1)
m = ($30,700 - $24,100) / (5000 - 4000)
m = $6,600 / 1000
m = $6.6

2. Use one of the points to find the y-intercept (b):

P(x) = mx + b
$24,100 = $6.6(4000) + b
$24,100 = $26,400 + b
b = -$2,300

3. Write the equation for P(x):

P(x) = 6.6x - 2,300

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The cat is 3/8 inches taller than the dragon.

To find the difference in height between the cat and the dragon, we need to subtract the height of the dragon from the height of the cat.

The cat is 7/8 inch tall, and the dragon is 1/2 inch tall.

To subtract fractions, we first need a common denominator. The least common denominator (LCD) of 2 and 8 is 8.

So, we'll convert the fractions to equivalent fractions with a denominator of 8.

1/2 = 4/8 (multiply both the numerator and the denominator by 4)

Now, we can subtract the fractions:

(7/8) - (4/8) = (7 - 4)/8 = 3/8

So, the cat is 3/8 inches taller than the dragon.

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Elijah and Riley are playing a board game. Elijah chooses the dragon for his game piece, and Riley chooses the cat for hers. The dragon is about 1 2 inch tall, and the cat is about 7 8 inch tall. How much taller is the cat than the dragon?

The surface area of the rectangular prism in the image above is determined as:

236 square meters.

The prism given above in the image is a rectangular prism. The formula for finding the surface area of the prism is given as:

surface area of the prism = 2(lh + lw + hw), where:

h is the height

w is the width

l is the length of the prism.

Given the following:

length (l) = 6 m

width (w) = 5 m

height (h) = 8 m

Plug in the values:

Surface area of the prism = 2·(5·6 + 8·6 + 8·5) = 236 square meters.

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The expression (1/2 x 12 / (2 - 2 + 11) + 10) will give a value of 13.

We have,

One possible way to use parentheses to make the value of the expression equal to 13 is:

1/2 x (12 / (2 - 2 + 11))

Here's how the expression evaluates step by step:

- The expression inside the parentheses (2 - 2 + 11) evaluates to 11.

- The expression inside the innermost parentheses (12 / 11) evaluates to approximately 1.090909...

- The expression outside the parentheses (1/2) multiplied by 1.090909... evaluates to approximately 0.5454545...

- Finally, the subtraction of 2 and the addition of 11 to 0.5454545... gives a value of approximately 9.5454545...

However, this value is not 13.

So, we need to modify the expression further.

One way to do this is to add a constant inside the outermost parentheses to adjust the value of the expression.

For example:

(1/2 x 12 / (2 - 2 + 11) + 10)

Therefore,

The expression (1/2 x 12 / (2 - 2 + 11) + 10) will give a value of 13.

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The surface area is 72 square inches.

To find the surface area of a square pyramid, we need to calculate the area of the base and the four triangular faces.

Given that the base is 4 inches wide, the area of the square base is:
Base area = side² = 4² = 16 square inches.

The slant height is 7 inches. To find the area of one triangular face, we use:
Triangle area = (base * slant height) / 2

Each triangle has the same base length as the square base, which is 4 inches. Therefore, the area of one triangular face is:
Triangle area = (4 * 7) / 2 = 14 square inches.

Since there are four triangular faces, their total area is:
4 * Triangle area = 4 * 14 = 56 square inches.

Finally, add the base area and the total area of the triangular faces to get the surface area:
Surface area = Base area + Total triangular faces area = 16 + 56 = 72 square inches.

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The greater number is 455.

There are 197 women in the party.

The geometric ratio of the old and current price of the suit is 25/27.

The first problem requires the application of geometric ratios and algebraic manipulation to determine the greater of the two numbers. Geometric ratios are ratios between two quantities that are constant throughout.

We are also given that their difference is 35, which can be expressed as x - y = 35. We can use algebraic manipulation to solve for the values of x and y.

From the first equation, we can express x in terms of y as x = (13/6)y. Substituting this value of x into the second equation, we get (13/6)y - y = 35. Simplifying this equation, we get y = 210.

To find the value of x, we can substitute y = 210 into the equation x/y = 13/6, giving us x = 455. Therefore, the greater number is 455.

The second problem involves using ratios to find the number of women in a party. We are given that the ratio of men to women is 9 to 7, which can be expressed as 9x/7x, where x is a constant. We are also told that there are 45 men. We can use this information to solve for the number of women.

Therefore, the total number of parts is 45/9 = 5.

We can use this information to find the number of women, which is 7 parts of the ratio, or

=>  7x = (7/16) * 5 * 45 = 196.875.

Since we cannot have a fraction of a person, we round this value up to the nearest whole number, which is 197.

Therefore, there are 197 women in the party.

The third problem involves finding the geometric ratio of the old and current price of a men's suit. We are given that the suit cost $250,000 last year and that a dozen of these suits cost $3,250,000 this year. We can use the information provided to find the geometric ratio.

Since a dozen of the suits cost $3,250,000, one suit costs $3,250,000/12 = $270,833.33. The ratio of the old price to the new price is 250,000/270,833.33, which simplifies to 25/27.

Therefore, the geometric ratio of the old and current price of the suit is (25/27)¹ = 25/27.

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Complete Question:

The geometric ratio of two numbers is 13/6 and their difference is 35. What is the greater number?

At a party the ratio of men to women is 9 to 7. If 45 men are counted, how many women are there?

A men's suit cost $250,000 last year. This year a dozen of these suits cost $3,250. 000 What is the geometric ratio of the old and current price of the suit?

a. The marginal cost is constant at $102 per unit.

b. The profit function is 149 + 52q/Inq.

c. The profit from one more unit sold when 8 units are sold is $4.50.

a. To find the marginal cost, we need to take the derivative of the cost function: C'(q) = 102. So the marginal cost is constant at $102 per unit.

b. The profit function is given by:

[tex]P(q) = R(q) - C(q) = (102q + 52q/Inq) - (102q - 97) = 149 + 52q/Inq.[/tex]

c. To find the profit from one more unit sold when 8 units are sold, we need to find the difference between the profit from selling 9 units and the profit from selling 8 units.

Profit from selling 9 units: P(9) = 149 + 52(9)/In9 = 149 + 104 = $253.

Profit from selling 8 units: P(8) = 149 + 52(8)/In8 = 149 + 108.5 = $257.50.

The profit from one more unit sold when 8 units are sold is the difference between these two profits: $253 - $257.50 = -$4.50. This means that selling one more unit when 8 units are sold will result in a loss of $4.50.

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The per capita birth rate of the given population of manned wolves 246 with number of birth as 83 is equals to 0.34  births per individual per year.

Number of births = 83

Initial population = 246

Time period = 1 year

Number of deaths = 42

The per capita birth rate is calculated as the number of births per individual in the population.

Typically expressed as a rate per unit time.

Per capita birth rate as follows,

Per capita birth rate

= (Number of births / Initial population) × (Time period / 1 year)

Substituting these values into the formula, we get,

Per capita birth rate

= (83 / 246) × (1 / 1)

= 0.3374

Rounding this to the hundredths place, we get,

Per capita birth rate = 0.34

Therefore, the per capita birth rate for this population of maned wolves is 0.34 births per individual per year.

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