at a movie theater 4 out of the first 10 customers bought popcorn. based on this imformation , if 180 people go to the movie theater , how many would be expected to buy popcorn

When talking about a limit of a function at a particular point, it's significant to note that this means evaluating the function as the input approaches that point. It's worth noting that the point in question must be a limit point of the domain of the function for the function to have a limit.

An isolated point is one that doesn't have any other points near it in the domain of the function. Because of this, it makes no sense to consider the limit of a function at an isolated point of the domain of the function.

A limit is defined as the value that a function approaches as the input (x) approaches a certain point (c). This definition is simple enough, but it necessitates the function having values near that point in the domain. That is to say, there must be a sufficient number of points near the point c in the domain such that we can talk about the input approaching c without going out of the domain.

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With a budget of R 80,000 and each street name board costing R 134, the municipality can afford to put up approximately 597 new street name boards. After purchasing these boards, there will be R 9,998 remaining in the budget.

To find out how many new street name boards can be put up, we divide the total budget of R 80,000 by the cost of each board, which is R 134. This calculation gives us 597. So, the municipality can put up approximately 597 new street name boards.

To determine how much money will be left in the budget, we subtract the total cost of the boards from the initial budget. The total cost of 597 boards can be calculated by multiplying the cost of each board (R 134) by the number of boards (597), resulting in R 80,098. Subtracting this amount from the initial budget of R 80,000 leaves us with R 9,998 remaining in the budget.

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The box slides along the rough surface for a distance of d meters. At the bottom of the ramp, the box has zero potential energy and maximum kinetic energy.

To determine the distance the box slides along the rough surface, we need to consider the conservation of energy and the effects of friction.

Initially, the box is at a height of 0.25 m and has potential energy given by mgyo, where m is the mass of the box (2.0 kg) and yo is the initial height (0.25 m). As the box slides down the frictionless ramp, the potential energy is converted into kinetic energy. At the bottom of the ramp, the box has zero potential energy and maximum kinetic energy.

Upon reaching the rough horizontal surface, the box encounters friction. The work done by friction results in the conversion of kinetic energy into thermal energy, reducing the box's speed.

To calculate the distance the box slides on the rough surface, we need to determine the work done by friction. The work done by friction is given by the equation work = force × distance. The force of friction can be calculated using the equation force = friction coefficient × normal force, where the normal force is equal to the weight of the box (mg).

Using the given friction coefficient (μ = 0.50) and the mass of the box (m = 2.0 kg), we can calculate the force of friction. Once we have the force of friction, we can calculate the work done by friction.

The work done by friction is equal to the change in kinetic energy of the box. We can equate this work to the initial kinetic energy and solve for the distance traveled (d). The initial kinetic energy is given by (1/2)mv², where v is the velocity of the box at the bottom of the ramp.

By solving the equation for the work done by friction and equating it to the initial kinetic energy, we can determine the distance the box slides along the rough surface (d).

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There are 217 bacteria there now.

A percentage is defined as the ratio that can be expressed as a fraction of 100.

We have:

initial count (P) = 155

growth rate (r) = 40% = 0.4 (from the image)

current count = P(1 + r)

current count = 155(1 + 0.4)

current count = 155(1 .4)

current count = 217

Therefore, 217 bacteria are there now.

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The expected payout is 5.625 cents, and the cost to play the game is 7 cents, it can be concluded that paying 7 cents to play this game is not fair. The expected payout is lower than the cost, resulting in a disadvantage for the player.

In this game, tossing 3 fair coins results in different payouts for the number of heads obtained. The payouts are 12 cents for 3 heads, 7 cents for 2 heads, and 4 cents for 1 head. The question is whether paying 7 cents to play this game is fair.

To determine if the game is fair, we need to compare the expected payout with the cost to play. Let's calculate the probabilities and payouts for each outcome. There are a total of 8 possible outcomes when tossing 3 coins: HHH, HHT, HTH, THH, TTH, THT, HTT, and TTT (H denotes a head, and T denotes a tail).

The probability of getting 3 heads is 1/8, so the payout for this outcome is 12 cents. The probability of getting 2 heads is 3/8 (HHH, HHT, HTH), so the payout for this outcome is 7 cents. The probability of getting 1 head is also 3/8 (TTH, THT, HTT), resulting in a payout of 4 cents. The probability of getting 0 heads (3 tails) is 1/8, resulting in a payout of 0 cents.

Now, let's calculate the expected payout by multiplying each outcome's probability with its corresponding payout and summing them up:

Expected payout = (1/8 * 12) + (3/8 * 7) + (3/8 * 4) + (1/8 * 0) = 1.5 + 2.625 + 1.5 + 0 = 5.625 cents.

Since the expected payout is 5.625 cents, and the cost to play the game is 7 cents, it can be concluded that paying 7 cents to play this game is not fair. The expected payout is lower than the cost, resulting in a disadvantage for the player.

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The fully transformation that maps triangle A to triangle B involves a combination of translation, rotation, and scaling operations.

To map triangle A to triangle B, we can apply a series of transformations. First, we can perform a translation to move triangle A to the desired position. Translation involves shifting the entire triangle in a specific direction. Once the translation is applied, the vertices of triangle A will be in the correct position relative to triangle B.

Next, we can apply a rotation transformation to align the orientation of triangle A with triangle B. Rotation involves rotating the triangle around a specific point or axis. By adjusting the rotation angle, we can ensure that the corresponding vertices of the two triangles match up.

Finally, we can apply a scaling transformation to adjust the size of triangle A to match the size of triangle B. Scaling involves uniformly expanding or shrinking the dimensions of the triangle. By scaling triangle A appropriately, we can ensure that the corresponding sides of the triangles are proportional.

By combining these three transformations—translation, rotation, and scaling—we can fully map triangle A to triangle B, ensuring that the positions, orientations, and sizes of the triangles are aligned.

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The function that represents the difference between the value of Aleka's and Helene's total savings after x years is h(x) = 1000(1.025)^x - 200x.

To determine the function that represents the difference between the value of Aleka's and Helene's total savings after x years, we need to subtract Helene's total savings from Aleka's total savings.

1: The function for Aleka's total savings after x years is f(x) = 2500(1.025)^x.

2: The function for Helene's total savings after x years is g(x) = 1500(1.025)^x + 200x.

3: To find the difference, subtract g(x) from f(x): h(x) = f(x) - g(x).

4: Substitute the expressions for f(x) and g(x) into the equation for h(x):

h(x) = 2500(1.025)^x - (1500(1.025)^x + 200x).

5: Simplify the expression by distributing the negative sign:

h(x) = 2500(1.025)^x - 1500(1.025)^x - 200x.

6: Combine like terms to simplify further:

h(x) = (2500 - 1500)(1.025)^x - 200x.

7: Simplify the coefficients:

h(x) = 1000(1.025)^x - 200x.

Therefore, the function that represents the difference between the value of Aleka's and Helene's total savings after x years is h(x) = 1000(1.025)^x - 200x.

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The equation x^3 = y^5 represents a relationship between two variables, x and y, raised to different exponents. This equation states that the cube of x is equal to the fifth power of y.

To better understand this relationship, we can take the cube root of both sides to isolate x: x = y^(5/3). This equation shows that x is equal to the fifth root of y raised to the power of 5/3.

In simpler terms, it means that if we raise y to the power of 5/3 and then take the cube root of that result, we will obtain x.

This equation allows us to relate x and y and determine the value of one variable based on the value of the other.

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The expression for the time for which a person does both activities in 5 days is 5(m+30) minutes.

We have to write an expression that can help to find out the minutes for which a person does both the activities (homework and TV) each day. Let the time for which the person does homework each day be m minutes.  

Therefore, the expression for time for which a person does both the activities each day is (m+30) minutes.To find out the time for which a person does both the activities for 5 days, we need to multiply the time for which the person does both the activities each day by 5.

Hence, the expression for the time for which a person does both activities in 5 days is:5(m+30) minutes

We have been given that each day, a person does homework for m minutes and watches TV for 30 minutes. We have to find an expression that can help to find out the minutes for which the person does both the activities each day.

Let us begin by defining variables. Let the time for which a person does homework each day be m minutes. Therefore, the expression for time for which a person does both the activities each day is (m+30) minutes.

Now we need to find the time for which the person does both activities in 5 days. To do so, we need to multiply the time for which the person does both the activities each day by 5.

Hence, the expression for the time for which a person does both activities in 5 days is:5(m+30) minutes.Now let’s consider an example to understand this better.Suppose the time for which a person does homework each day is 60 minutes.

Therefore, the expression for time for which a person does both the activities each day is (60+30) minutes = 90 minutes.

In this case, the time for which the person does both activities in 5 days is:

5(60+30) minutes = 5 x 90 minutes = 450 Minutes Therefore, in 5 days, a person will do both activities for 450 minutes.

The expression to find the minutes for which a person does both activities each day is (m+30) minutes. The expression for the time for which a person does both activities in 5 days is 5(m+30) minutes.

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Answer: To find out how much a 5-ounce serving of the frozen Scandinavian vegetable mix costs, we need to calculate the cost per ounce first.

Given that a 2 ¾-pound bag costs $0.88 per pound, we can calculate the cost per pound as follows:

Cost per pound = $0.88

Since there are 16 ounces in a pound, we can calculate the cost per ounce by dividing the cost per pound by 16:

Cost per ounce = Cost per pound / 16

Cost per ounce = $0.88 / 16

Cost per ounce ≈ $0.055

Now, to find the cost of a 5-ounce serving, we can multiply the cost per ounce by 5:

Cost of a 5-ounce serving = Cost per ounce * 5

Cost of a 5-ounce serving ≈ $0.055 * 5

Cost of a 5-ounce serving ≈ $0.275

Therefore, the cost of a 5-ounce serving of the frozen Scandinavian vegetable mix is approximately $0.275, which is closest to option (b) $0.28.

The answer is option C: $609.32.

To calculate the extra amount Cynthia will have to pay in finance charges due to the increased APR, we need to compare the interest charged at the original rate (17%) with the interest charged at the new rate (21%).

Using the formula for calculating compound interest, we can determine the interest charges for both rates over the 24-month period. The original interest charges would be 17% of the $3,265 balance, while the new interest charges would be 21% of the same balance.

By subtracting the original interest charges from the new interest charges, we find that Cynthia will have to pay an extra $609.32 in finance charges due to the increase in her APR.

Therefore, the correct answer is option C: $609.32.

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If Henry uses 1 1/2 cups of corn grits, he will need 3 cups of water.

The recipe calls for 1/4 cup of corn grits for every 1/2 cup of water. To find out how much water Henry will need if he uses 1 1/2 cups of corn grits, we can set up a proportion.

Let's assume x represents the amount of water needed in cups. The proportion can be written as:

1/4 cup of corn grits / 1/2 cup of water = 1 1/2 cups of corn grits / x cups of water

To solve the proportion, we can cross multiply:

(1/4) × x = (1 1/2) × (1/2)

Simplifying the right side of the equation:

(1/4) × x = (3/2) × (1/2)

x/4 = 3/4

To isolate x, we can multiply both sides of the equation by 4:

x = (3/4) × 4

x = 3

Therefore, if Henry uses 1 1/2 cups of corn grits, he will need 3 cups of water.

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The tax revenue that Australia generate each year by instituting a income tax is $96,054,697,991. The Option C.

Tax revenue is the income that is collected by governments through taxation. To know the tax revenue, we will multiply the working population by the average salary and then multiply that by the tax rate.

Tax Revenue = (Working population) * (Average salary) * (Tax rate)

Tax Revenue = 11,565,470 * $26,450 * 0.314

Tax Revenue = $96,054,697,991

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The given information lacks specific values for the lengths of segments MB and MA, as well as the radius of the Earth. Without numerical values, it is not possible to determine the exact lengths of these segments or the radius of the Earth.

The problem states that segments MB and MA, as well as the radius of the Earth, need to be approximated. However, without specific values or additional information, it is not possible to determine the lengths of segments MB and MA or the radius of the Earth accurately.
To calculate the lengths of segments MB and MA, we would need the coordinates of the points M, B, and A or additional information about their positioning or relationships.
Similarly, the radius of the Earth can vary depending on the reference frame or the method of approximation used. The Earth's radius can be approximated using different measurements, such as the equatorial radius or the mean radius. Each approximation yields a slightly different value.
Therefore, without specific numerical values or additional information, it is not possible to determine the approximate lengths of segments MB and MA or the radius of the Earth.

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The author's use of time in "Beyond the Dumpster" is reflected in option C: The story begins in the past and ends in the present time to show how the narrator ended up where he is now.

In "Beyond the Dumpster," the story is structured in a way that transitions between past and present events. It begins with the narrator reflecting on his high school years and his aspirations for a successful future. As the story progresses, the narrative shifts to the present, revealing the current circumstances and challenges the narrator faces.

The author's use of time helps develop the ideas expressed by the narrator by highlighting the contrast between the narrator's past hopes and dreams and his present reality. It shows how the decisions and circumstances from the past have shaped his current situation. This technique allows the reader to understand the narrator's journey and the impact of his choices.

By starting in the past and concluding in the present, the story provides a sense of reflection and growth, emphasizing the theme of self-discovery and the consequences of the narrator's actions. It allows the reader to see the narrator's development over time and how the passage of time has influenced his perspective and understanding of life.

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Yes, the equation y - 250x = 500 represents the same relationship between the distance from the start of the trail and the elevation.

The given equation is y - 250x = 500.
The above equation is of the form y = mx + c, where m = slope of the line and c = y-intercept of the line.
Let us convert the given equation into the form y = mx + c, y - 250x = 500, y = 250x + 500. Now, we can see that this equation is of the form y = mx + c, where m = 250, which means that the slope of the line is 250 and the value of y-intercept is 500.

Thus, the equation y - 250x = 500 represents the relationship between the distance from the start of the trail and the elevation.

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The average yearly temperature in New York is 56°F, while the average yearly temperature in Alaska is -11°F. This is because New York is located in a temperate climate zone, while Alaska is located in an arctic climate zone. The temperate zone has warm summers and cool winters, while the arctic zone has long, cold winters and short, cool summers.

The average temperature in New York is higher because it is closer to the equator and therefore receives more sunlight throughout the year. In contrast, Alaska is farther from the equator and receives less sunlight, leading to colder temperatures. Additionally, Alaska is known for its large snowfall amounts, which contributes to the low average temperature. New York and Alaska are two of the most popular states in the United States of America. The average yearly temperature in New York is 56°F, while the average yearly temperature in Alaska is -11°F. This is because New York is located in a temperate climate zone, while Alaska is located in an arctic climate zone.

The temperate zone has warm summers and cool winters, while the arctic zone has long, cold winters and short, cool summers. The average temperature in New York is higher because it is closer to the equator and therefore receives more sunlight throughout the year. In contrast, Alaska is farther from the equator and receives less sunlight, leading to colder temperatures. Additionally, Alaska is known for its large snowfall amounts, which contributes to the low average temperature. The difference in temperature between these two states is significant and can be attributed to various factors such as geography, climate, latitude, and distance from the equator. These factors impact the amount of sunlight that each state receives and, in turn, affect the overall temperature. Furthermore, these factors also influence other aspects of life, such as plant growth and wildlife, making each state unique.

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If a keyword is "rose steadily," the line segment showing that description should be upward-slanting.

Assuming that "rose steadily" refers to an increase in some quantity over time, the corresponding line segment would be a diagonal line with a positive slope. The horizontal axis represents time, while the vertical axis represents the quantity being measured. As time increases, the quantity also increases, resulting in a steady rise of the line.

When we describe something as "rising" or "increasing steadily," it indicates a consistent and gradual upward movement. In the context of a line segment, an upward-slanting line represents this kind of progression. As we move from left to right along the line segment, the values or quantities associated with it are increasing steadily. The slope of the line segment would be positive, indicating the upward direction.

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The equations smaller number is -2 and the larger number is 3.

The smaller number as "x" and the larger number as "y". Based on the given information the following equations:

Six times the smaller number minus the larger number is -15:

6x - y = -15

Thirteen more than twice the smaller number is three times the larger number:

2x + 13 = 3y

A system of two equations use various methods, such as substitution or elimination.

use the substitution method to solve the system:

From equation 2),

2x - 3y = -13

express 6x from equation 1) in terms of y:

6x = -15 + y

x = (-15 + y) / 6

Substituting this value of x into equation 2)

2((-15 + y) / 6) - 3y = -13

Simplifying and solving this equation

(-30 + 2y) - 18y = -78

-16y = -48

y = 3

Substituting the value of y back into equation 1),  find the value of x:

6x - 3 = -15

6x = -12

x = -2

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A supplement of an angle is six times as large as a complement of the angle. the measure of the angle is 72°.

To find the measure of the angle, we can use the concept of the supplementary angle and the complementary angle. So, Let's consider the angle as "x"∴ Complement of the angle = 90° - x Supplement of the angle = 180° - x According to the given statement,180° - x = 6(90° - x) ⇒ 180° - x = 540° - 6x⇒ 5x = 540° - 180°⇒ 5x = 360°⇒ x = 360°/5⇒ x = 72°.

We are given that, a supplement of an angle is six times as large as a complement of the angle. We need to find the measure of the angle. Let's consider the angle as "x".∴ Complement of the angle = 90° - x Supplement of the angle = 180° - x According to the given statement, we can write,180° - x = 6(90° - x)⇒ 180° - x = 540° - 6x.

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This is the expression written in standard form, where the terms are ordered in descending order of the variables' exponents: 2x^3y - 7y^2x - 3x^2 + 12y

To write the expression 2x^3y - 3x^2 - 7y^2x + 12y in standard form, we rearrange the terms in descending order of the variables' exponents.

The standard form of a polynomial is written as follows:

ax^n + bx^m + ... + cx^2 + dx + e

where a, b, c, d, and e are coefficients, and n, m, and so on represent the exponents of the variables.

Applying this to the given expression:

2x^3y - 3x^2 - 7y^2x + 12y

Rearranging the terms, we get:

2x^3y - 7y^2x - 3x^2 + 12y

This is the expression written in standard form, where the terms are ordered in descending order of the variables' exponents:

2x^3y - 7y^2x - 3x^2 + 12y

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The statement that holds true is that for every 1 1/2 cups of cheese used, there should be 6 ounces of pasta.

Based on the given ratio of 1 1/2 cups of cheese to 6 ounces of pasta in the recipe, the following statement is true:

For every 1 1/2 cups of cheese used, there should be 6 ounces of pasta.

The ratio indicates the proportion or relationship between the amounts of cheese and pasta in the recipe. In this case, for each 1 1/2 cups of cheese, the recipe calls for 6 ounces of pasta. This means that the quantities of cheese and pasta are in a consistent and proportional relationship.

To illustrate this further, if you were to double the amount of cheese used in the recipe, you would also need to double the amount of pasta. For example, if you use 3 cups of cheese, you would need 12 ounces of pasta (2 times 6 ounces).

Therefore, based on the given ratio, the statement that holds true is that for every 1 1/2 cups of cheese used, there should be 6 ounces of pasta.

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When you flip two coins 1,600 times, the best prediction possible for the number of times both coins will land on heads is 400 times. This is based on the probability of the outcome of flipping two coins.

Based on probability theory, there are four possible outcomes when two coins are flipped: heads-heads, heads-tails, tails-heads, and tails-tails. The probability of getting heads on a single coin toss is 1/2, and the probability of getting tails on a single coin toss is also 1/2.

When two coins are flipped, the probability of getting heads on both coins is the product of the probability of getting heads on each coin:1/2 x 1/2 = 1/4Therefore, the probability of getting heads on both coins is 1/4. To find the expected number of times both coins will land on heads when flipping the coins 1,600 times, you can multiply the probability of getting heads on both coins by the total number of times the coins are flipped:1/4 x 1,600 = 400So the best prediction possible for the number of times both coins will land on heads when flipping two coins 1,600 times is 400 times.

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The equation of a line that contains (2,1) and is perpendicular to the line: y=3x-4 can be calculated as follows:Given the line y=3x-4

Then slope of the line will be; y = mx + b (slope-intercept form)

where m = slope of the lineSince the given line is y=3x-4then, slope of the line will be m=3

Then, slope of the line perpendicular to it will be;Perpendicular slopes are negative reciprocal of each other. Therefore, slope of the line perpendicular to the given line will be:m1 = -1/m= -1/3

The given line passes through (2, 1) which means x=2 and y=1

Substituting these values in point-slope form of equation;y - y1 = m(x - x1)y - 1 = (-1/3)(x - 2)

Multiplying by 3 on both sides to get rid of the denominator;3(y - 1) = -1(x - 2)3y - 3 = -x + 2

Rearranging;3y = -x + 5y = (-1/3)x + 5/3

Therefore, the equation of a line that contains (2,1) and is perpendicular to the line: y=3x-4 is y = (-1/3)x + 5/3.

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Compared to a comparable fixed payment loan, the total interest on a fixed principal loan is less.

When comparing a fixed principal loan to a fixed payment loan, the key difference lies in how the interest is calculated. In a fixed principal loan, the interest is based on the initial principal amount and remains constant throughout the loan term.

On the other hand, in a fixed payment loan, the interest is calculated based on the outstanding principal balance, which reduces over time as payments are made. As a result, the interest payments decrease gradually over the loan term.

Due to the nature of a fixed principal loan, where the interest is calculated based on the initial principal amount, the total interest paid over the loan term is lower compared to a fixed payment loan. Since the principal amount remains the same, the interest payments do not decrease over time.

In contrast, a fixed payment loan typically has higher total interest payments because the interest is calculated based on the outstanding principal balance, which is higher at the beginning of the loan term and decreases gradually as payments are made.

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Compared to a comparable fixed payment loan, the total interest on a fixed principal loan is ___.  

a) less

b) more  

c) same

A motorist travels from a town P on a bearing of 150° to a town Q 40km away. From Q he travels to a town R on a bearing of 210° if R you s located directly south of P, how far is R from P? (a)40√3km(b)40√2km(c)40km(d)80km

​Let P be the starting point of the motorist .Let x be the distance of PR .Let PQR be the triangle formed by the towns P, Q, and R. Using the law of cosines, we have:(40)² = x² + (40 + x)² - 2(40)(40 + x)cos(150° + 30°)(40)² = x² + (40 + x)² - 2(40)(40 + x)cos(180° - 150° - 30°)1600 = x² + (40 + x)² + 2(40)(40 + x)cos(150° + 30°)1600 = x² + (40 + x)² + 2(40)(40 + x)cos(30°)1600 = x² + (40 + x)² + 2(40)(40 + x)(√3/2)1600 = x² + (40 + x)² + (40)(40 + x)(√3)800 = x² + (40 + x)² + (20)(40 + x)(√3)800 = x² + 1600 + 80x + x² + 1600 + 80x + 800(√3)1600 = 2x² + 160√3 x + 4000(√3) - 800x² + 240√3 x + 4000(√3)0 = -6x² + 400√3 x + 4000(√3)0 = -2x² + 133.33 x + 1333.33By the quadratic formula:  x = (–b ± √b² – 4ac)/2a x = [–133.33 ± √(133.33)² – 4(–2)(1333.33)]/2(–2)x = [–133.33 ± √(17777.1089)]/–4x ≈ 34.14, –19.61Since x must be positive, x ≈ 34.14km (nearest hundredth)Therefore, the distance between P and R is approximately 34.14 km. Answer: (a)40√3 km.

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The capacity of the cylindrical pipe in the trailer is approximately  10,009 liters

To calculate the capacity of a cylindrical pipe, one need to know the height or length of the pipe as well as the radius.

Given:

So to  calculate the capacity (volume) of a cylindrical pipe, one can:

Volume = π * r² * h,

So to calculate the capacity:

Volume = π x  (0.70 m)^2 * 6.50 m

= π * 0.49 m² x 6.50 m

= 3.14 * 0.49 m² x  6.50 m

≈ 10.009 m³

Since the volume is in cubic meters, to convert it to liters, we multiply it by 1000 (1 cubic meter = 1000 liters):

Capacity = 10.009 m³ x  1000

=  10,009 liters

Therefore, the capacity of the cylindrical pipe in the trailer is approximately  10,009 liters

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The numerical expression, -200 121 3 (4.5), represents the depth of the diver. The expression is to be simplified using the order of operations.

According to the given expression, the diver begins at sea level and dives down 200 feet. Then he ascends at a steady rate of 121/3 feet per minute for 4.5 minutes. The depth is represented by the numerical expression: -200 121/3 (4.5). Here, the expression has to be simplified using the order of operations as follows:

First, we need to simplify 121/3 * 4.5 which is equal to 363/2. Next, we have to multiply -200 with 363/2 to get -72600/2. Finally, -72600/2 can be simplified to -36300. Now, it is evident that the result of the simplified expression in feet is -36300/12 which is equal to -3025/4 or -7550/8 or -1895/2 or -947.5. Therefore, the diver's depth is -255.5 feet.

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To simplify the expression f(x) - g(x) where f(x) = x + 4 and g(x) = x^2 + 3x - 2, we substitute the given functions into the expression and simplify it. The simplified form will be in terms of x and will represent the difference between the two functions.

To simplify f(x) - g(x), we substitute the given functions:

f(x) - g(x) = (x + 4) - (x^2 + 3x - 2)

Expanding the expression, we get:

f(x) - g(x) = x + 4 - x^2 - 3x + 2

Combining like terms, we have:

f(x) - g(x) = -x^2 - 2x + 6

Therefore, the simplified form of f(x) - g(x) is -x^2 - 2x + 6. This expression represents the difference between the functions f(x) and g(x) in its simplest form.

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Araceli had 20 minutes for a 3-problem quiz. She spent 11 7/10 minutes on question A and 3 2/5 minutes on question B, leaving her 5 1/5 minutes for question C. Effective time management is important during tests.

Araceli had 20 minutes to complete a three-problem quiz, and she spent 11 7/10 minutes on question A and 3 2/5 minutes on question B. To find out how much time she spent on question C, we can subtract the time she spent on question A and question B from the total time of 20 minutes:

20 minutes - 11 7/10 minutes - 3 2/5 minutes = 5 1/5 minutes

Therefore, Araceli spent 5 1/5 minutes on question C.

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