Given the following perfect square trinomial, find the missing term: ___x2 40x 100 1 2 4 10.

The statement that is NOT true about the relationship between a function and its inverse is option B: "The domain of a function is the range of the inverse of the function."

In general, the domain of a function consists of all possible input values, while the range represents the set of all possible output values. When finding the inverse of a function, the roles of the domain and range are interchanged. Therefore, the range of the original function becomes the domain of its inverse, and vice versa.

The other options are true:

A. The graph of the inverse of a function is indeed the reflection across the line y = x of the graph of the function. This means that if you plot the function and its inverse on a coordinate plane, they will be symmetric with respect to the line y = x.

C. The range of a function does correspond to the domain of its inverse. The outputs of the original function become the inputs of its inverse.

D. The inverse of a function is not always a function. For a function to have an inverse, it must be one-to-one, meaning that each input value maps to a unique output value and vice versa. If a function fails to satisfy this criterion, it does not have an inverse. Here, option B is the statement that is not true. Therefore, Option B is correct.

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La function f(x) = x^2 - 1 se puede evaluar para los valores de x desde -3 hasta 3 sustituyendo cada valor en la expresión y calculando el resultado. Aquí están los cálculos para cada valor:

Para x = -3: f(-3) = (-3)^2 - 1 = 9 - 1 = 8

Para x = -2: f(-2) = (-2)^2 - 1 = 4 - 1 = 3

Para x = -1: f(-1) = (-1)^2 - 1 = 1 - 1 = 0

Para x = 0: f(0) = (0)^2 - 1 = 0 - 1 = -1

Para x = 1: f(1) = (1)^2 - 1 = 1 - 1 = 0

Para x = 2: f(2) = (2)^2 - 1 = 4 - 1 = 3

Para x = 3: f(3) = (3)^2 - 1 = 9 - 1 = 8

Entonces, los valores de la function f(x) = x^2 - 1 para x En el rang de -3 a 3 son: 8, 3, 0, -1, 0, 3, 8 respectivamente.

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The coordinates after applying a dilation with a scale factor of 1/5 and centered at the origin to the line segment MN with endpoints M(-2, -4) and N(1, 5) are as follows:

   M: (-2, -4) → (-2/5, -4/5)

   N: (1, 5) → (1/5, 1)

So, the matching coordinates for the points are:

M (-2, -4) → (-2/5, -4/5)

N (1, 5) → (1/5, 1)

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The possible values for x that make the statement true are x = -1 or x = 1.5.

Let's solve the equation step by step to find the possible values for x. We start with the given equation:

5.6 = 3.1 - 12.5|1 - 0.8x|

We can begin by isolating the absolute value expression:

2.5 = -12.5|1 - 0.8x|

Next, divide both sides of the equation by -12.5:

-0.2 = |1 - 0.8x|

Now we have two cases to consider, one where the absolute value is positive and another where it is negative.

Case 1: 1 - 0.8x is positive:

-0.2 = 1 - 0.8x

Solving this equation:

-0.8x = -1.2

x = 1.5

Case 2: 1 - 0.8x is negative:

-0.2 = -(1 - 0.8x)

Solving this equation:

0.2 = 1 - 0.8x

-0.8x = -0.8

x = -1

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a. To find the number of units produced with 300 units of labor (x) and 200 units of capital (y), we substitute these values into the production function:

P = (60^0.75)(200^0.25) = 60^0.75 * 200^0.25 ≈ 31.62 * 5 ≈ 158.10

Therefore, approximately 158 burgers would be produced with 300 units of labor and 200 units of capital.

b. The marginal productivity of labor (MPL) is the partial derivative of the production function with respect to labor (x), while the marginal productivity of capital (MPK) is the partial derivative with respect to capital (y). Taking the partial derivatives, we have:

MPL = 0.75 * 60^0.75 * 200^0.25 / 60 ≈ 0.75 * 31.62 ≈ 23.72

MPK = 0.25 * 60^0.75 * 200^0.25 / 200 ≈ 0.25 * 31.62 ≈ 7.90

c. Evaluating the marginal productivities with x = 300 and y = 200:

MPL = 0.75 * 60^0.75 * 200^0.25 / 60 ≈ 0.75 * 31.62 ≈ 23.72

MPK = 0.25 * 60^0.75 * 200^0.25 / 200 ≈ 0.25 * 31.62 ≈ 7.90

d. The marginal productivity of labor (MPL) represents the additional output gained by increasing the amount of labor while keeping capital constant. In this case, for every additional unit of labor, approximately 23.72 burgers will be produced.

The marginal productivity of capital (MPK) represents the additional output gained by increasing the amount of capital while keeping labor constant. For every additional unit of capital, approximately 7.90 burgers will be produced.

e. If the constraint x + y = 500 is applied, we can use the Lagrange multiplier method to find the maximum production. By maximizing the production function subject to this constraint, we can determine the optimal combination of labor and capital that yields the maximum production.

f. The Lagrange multiplier (λ) represents the rate of change of the production function subject to the constraint x + y = 500. Its value indicates how the maximum production is affected by changes in the constraint. The interpretation of λ in this context is that it quantifies the trade-off between labor and capital to achieve the highest production level while satisfying the given constraint of limited labor and capital resources.

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To apply a dilation to AC with a scale factor of 2 and a center at the point 0, we first need to understand what a dilation is. A dilation is a transformation that stretches or shrinks an object without changing its shape.

It is defined by a scale factor, which determines how much the object is scaled, and a center of dilation, which is the fixed point about which the object is enlarged or reduced. In this case, AC is a line segment, and the scale factor is 2 with the center at the point 0. To perform the dilation, we multiply the length of AC by the scale factor of 2. The center at 0 means that AC is being stretched or shrunk relative to the origin The result of the dilation would be a new line segment, let's call it A'C', where the length of A'C' is twice the length of AC, and the orientation and direction of the line segment remain the same. The points A' and C' would be located at positions that are twice the distance from the origin compared to the original points A and C, respectively.

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b = -15.

Thus, for any value of a = 6 and b = -15, any value of x would be a solution of the equation 3(2x-5) = ax + b.

To find the values of a and b for which any value of x would be a solution of the equation 3(2x-5) = ax + b, we need to consider the properties of the equation.

In the equation 3(2x-5) = ax + b, the left side represents a linear expression that simplifies to 6x - 15. We can equate this to the right side, ax + b.

So, we have the equation 6x - 15 = ax + b.

For any value of x to be a solution, the left side and the right side of the equation should always be equal, regardless of the value of x.

To achieve this, we need the coefficients of x to be equal on both sides of the equation. This means that the coefficient of x on the left side (which is 6) should be equal to the coefficient of x on the right side (which is a).

Therefore, a = 6.

Additionally, the constant term on the left side (-15) should be equal to the constant term on the right side (which is b).

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The blimp will be directly overhead of Ethan in 9.94 minutes.

To determine how long it will take for the blimp to be directly overhead of Ethan, we can use the information about the blimp's altitude and speed.

First, let's find the horizontal distance covered by the blimp in the time it takes to be directly overhead. Since the blimp is moving at a speed of 15 mph, we need to convert this to feet per minute:

15 mph * (5280 ft / 1 mile) * (1 hour / 60 minutes) = 1320 ft/minute

So, the blimp is moving at a rate of 1320 feet per minute horizontally.

Now, let's calculate the vertical distance the blimp needs to cover to be directly overhead of Ethan. This is equal to the altitude of the blimp, which is given as 1150 feet.

Since Ethan is looking up at an angle of 5 degrees, we can use trigonometry to find the horizontal distance covered by the blimp when it reaches the altitude of 1150 feet.

tan(5 degrees) = vertical distance / horizontal distance

We want to solve for the horizontal distance, so rearranging the equation:

horizontal distance = vertical distance / tan(5 degrees)

horizontal distance = 1150 ft / tan(5 degrees)

Using a calculator, we find:

horizontal distance ≈ 13129.01 ft

Now, we can determine the time it takes for the blimp to cover this horizontal distance at a rate of 1320 feet per minute:

time = horizontal distance / rate

time = 13129.01 ft / 1320 ft/minute

Calculating this, we get:

time ≈ 9.94 minutes

Therefore, the blimp will be directly overhead of Ethan in approximately 9.94 minutes.

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The number 6.373 x 10^5 can be written in standard notation as 637,300. This can be explained by understanding the concept of scientific notation and converting it back to its standard form.

Scientific notation is a way to represent very large or very small numbers using powers of 10. In scientific notation, a number is expressed as a coefficient multiplied by 10 raised to a certain power.

In the given number, 6.373 x 10^5, the coefficient is 6.373, and the exponent is 5. This means that we take the coefficient and multiply it by 10 raised to the power of 5.

To convert it back to standard notation, we perform the following calculation:

6.373 x 10^5 = 6.373 * 10 * 10 * 10 * 10 * 10

Simplifying the calculation, we get:

6.373 * 10 * 10 * 10 * 10 * 10 = 6.373 * 100,000

Multiplying 6.373 by 100,000, we obtain:

6.373 * 100,000 = 637,300

Therefore, the number 6.373 x 10^5 can be expressed in standard notation as 637,300, which is the final result.

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When a store advertises sales on different combinations of goods, they are engaging in price discrimination. In this case, the holiday store is practicing second-degree price discrimination because it has different prices for different quantities of bows and wrapping paper.

According to the signs in the store, there are two different deals on bows and rolls of wrapping paper. One sign says that one bow and one roll of wrapping paper can be purchased for $6.00. This means that the store is offering a bundle deal that gives a discount if you purchase both items together. The second sign offers five bows and one roll of wrapping paper for $10.00.

This means that the store is offering an even larger discount for customers who purchase a larger quantity of bows.The fact that the store is offering different prices based on the quantity of goods purchased is an example of price discrimination. Specifically, the store is practicing second-degree price discrimination because it is offering different prices for different quantities of goods.

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Congruent arcs determine equidistant chords in the same circle or in congruent circles.

This means that if two arcs in a circle are congruent, then any chords associated with those arcs will also be equidistant from the center of the circle. In other words, the distance from the center of the circle to any point on the chord will be the same for both chords.

So, the correct choice is "Equidistant".Let's break down the concept of congruent arcs and equidistant chords in more detail.

In a circle, an arc is a curved section of the circumference. When two arcs in the same circle or in congruent circles are congruent, it means they have the same measure or length. In other words, they span the same angle or distance along the circumference.

Now, when we talk about chords, we are referring to line segments that connect two points on the circle. A chord is formed by selecting any two points on the circle and joining them with a straight line.

When we say that congruent arcs determine equidistant chords, it means that if two arcs in a circle are congruent, then any chords associated with those arcs will have the same distance from the center of the circle.

In simpler terms, imagine you have two congruent arcs in a circle. Now, draw a chord for each of those arcs. The key point is that the distance from the center of the circle to any point on one chord will be equal to the distance from the center to any point on the other chord.

This property holds true because congruent arcs subtend the same angle at the center of the circle. Since the distances from the center to the chords are equal, the chords themselves are said to be equidistant.

To summarize, when two arcs in a circle are congruent, the chords associated with those arcs will be equidistant from the center of the circle. This is a fundamental property of circles and is true for any pair of congruent arcs in the same circle or in congruent circles.

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The person can rent the car for 5 days and drive a maximum of 1800 miles within the $450 budget.

To determine the number of days the person can rent the car, we divide the remaining budget of $450 by the daily rental cost of $45. This gives us 10, indicating that the person can rent the car for up to 10 days. However, the goal is to spend the entire budget, so renting the car for the maximum number of days would exceed the budget.

Next, we need to calculate the maximum distance the person can drive within the budget. Since the cost is $0.25 per mile, we divide the remaining budget by $0.25 to find the maximum number of miles. This results in 1800 miles.

Therefore, the person can rent the car for 5 days and drive a maximum of 1800 miles within the $450 budget. By renting the car for 5 days and driving within this mileage limit, the person will spend the entire budget without exceeding it.

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The required potters purchased 33 cans of Pepsi.

The potters purchased a total of 50 cans of soda.

34% of the purchased soda was Coke.

To find the number of cans of Pepsi purchased, we need to subtract the number of Coke cans from the total number of cans.

Number of Coke cans = 34% of 50 cans = 0.34 * 50 = 17 cans

Number of Pepsi cans = Total number of cans - Number of Coke cans

Number of Pepsi cans = 50 cans - 17 cans

Number of Pepsi cans = 33 cans

Therefore, the potters purchased 33 cans of Pepsi.

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Here's an explanation to help you understand the problem. Remy stands on the dock represented by point C. He plans to swim from C to A, then from A to B, and then from B back to C. Now, from Remy to the swim route AB¯¯¯¯¯¯¯¯, the shortest distance is 60 meters, which is measured from C to D.

From the diagram ,AC = x meters and BD = y meters Since Remy swims from C to A and then to B, he swims a distance equal to AB. Thus, the total distance that he swims can be given as follows: AB + BA + BC, where BA is equal to 2x, and BC is equal to 2y.Then, the distance that Remy swims can be given by AB + 2x + 2yNow, we know that Remy swims from C to D at a distance of 60 meters. Therefore, we can represent x in terms of y using the Pythagorean theorem as shown below:x² + y² = 60² ... (Equation 1)Also, we know that Remy plans to swim back to point C. Therefore, the total distance that he will swim is given by: AB + 2x + 2y + AC Substituting AB with 2x, we have:4x + 2y + AC ... (Equation 2)Also, substituting Equation 1 into Equation 2, we get:4x + 2y + √(3600 - y²)Simplify the expression by multiplying both sides by 2:8x + 4y + 2√(3600 - y²)Now, substituting 2x with AB and 2y with BD, we get:2(AB) + AB + 2(BD) + BD + 2√(3600 - y²)Simplify the expression:4AB + 4BD + 2√(3600 - y²)Therefore, the total distance that Remy swims is equal to:4AB + 4BD + 2√(3600 - y²)Therefore, the correct answer is 4AB + 4BD + 2√(3600 - y²).

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Rounded to the nearest tenth of a gram, the amount of the original sample that is still radioactive after half an hour is approximately 17.7 grams.

To model the decay of carbon-11 over time, we can use the exponential decay formula A = A₀ * (1/2)^(t/h), where A is the amount remaining, A₀ is the initial amount, t is the time elapsed, and h is the half-life. In this case, the initial amount is 50 grams and the half-life is 20 minutes. Using this model, we can determine the amount of carbon-11 remaining after a half-hour (30 minutes). Using the exponential decay model A = A₀ * (1/2)^(t/h), we can calculate the amount of carbon-11 remaining after a certain time. For a half-life of 20 minutes, the equation becomes A = 50 * (1/2)^(t/20). To find the amount remaining after half an hour (30 minutes), we substitute t = 30 into the equation:

A = 50 * (1/2)^(30/20)

A = 50 * (1/2)^(3/2)

A = 50 * (√1/2)^3

A = 50 * (√1/8)

A = 50 * (1/2√2)

A = 25/√2

To determine the decimal value of the amount remaining, we can approximate √2 as 1.414. Therefore:

A ≈ 25/1.414 ≈ 17.68 grams

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The correct answer is B (31,50), which shows the location of the new point Mr. Fisher must plot.

To determine the location of the new point Mr. Fisher must plot, let's analyze the given information:

The extra student scored 25 points higher than the student who was absent for 6 days.

This extra student was absent for 5 fewer days than the student who scored 55.

Let's assign variables to the relevant values:

Let "A" represent the number of days the absent student was absent for.

Let "S" represent the score of the student who scored 55.

From the given information, we can determine the following relationships:

The extra student's score = S + 25.

The extra student's number of absent days = A - 5.

Now, let's analyze the answer choices:

A (3,80): This point does not match the given information, as it does not fulfill the conditions related to the absent days and scores.

C (80,3): This point does not match the given information, as it does not fulfill the conditions related to the absent days and scores.

B (31,50): This point satisfies the given conditions: the extra student was absent for 5 fewer days than the student who scored 55, and the extra student's score is 25 points higher.

D (90,3): This point does not match the given information, as it does not fulfill the conditions related to the absent days and scores.

The correct option is b.

The complete question is:

Mr. Fisher remembered that he had one more exam to grade. The extra student scored 25 points, higher than the student who was absent for 6 days. This extra student was absent for 5 fewer days than the student who scored 55. Which shows the location of the new point Mr. Fisher must plot?

A (3,80)

C (80,3)

B (31,50)

D (90,3)

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For a distribution that is skewed right, the median is typically less than the mean and is located to the left of the distribution's peak.

It represents the middle value when the data is arranged in ascending order and is less affected by extreme outliers compared to the mean. The median provides a measure of central tendency that is more representative of the "typical" value in a positively skewed distribution.

In a skewed right distribution, the tail of the distribution extends towards the higher values. This indicates that there are relatively more lower values and fewer higher values in the dataset. As a result, the mean is pulled towards the higher values, making it larger than the median.

The median, on the other hand, represents the middle value in the dataset when arranged in ascending order. It is less sensitive to extreme outliers compared to the mean because it focuses on the middle value rather than the overall distribution. Therefore, in a skewed right distribution, the median tends to be smaller than the mean and is located to the left of the peak of the distribution.

The use of median in a skewed right distribution helps provide a more robust measure of central tendency, as it is less influenced by extreme values and better represents the typical value in the data.

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The mean height of the players on the girls' basketball team, rounded to the nearest whole number, is 68 inches.

The mean height of the players on the girls' basketball team, rounded to the nearest whole number, is X inches.

To find the mean height, we sum up the heights of all the players and divide it by the total number of players.

Given the heights of the players: 66, 68, 69, and 70 inches, we can calculate the mean height.

66 + 68 + 69 + 70 = 273

Next, we divide the sum of the heights by the total number of players, which is 4 in this case.

273 / 4 = 68.25

Rounding the mean height to the nearest whole number, we get X = 68 inches.

Therefore, the mean height of the players on the girls' basketball team, rounded to the nearest whole number, is 68 inches.

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Answer:

Step-by-step explanation:

Ms. Watson paid a flat fee of $110 for the first year and $10 monthly for the membership. As we know, Ms. Watson has to pay for 12 months of membership. The total cost of membership for the year is $230. We can calculate the cost of membership for the year as follows:

Yearly cost = Flat fee + Monthly fee for 12 months

Yearly cost = $110 + ($10 x 12)

Yearly cost = $110 + $120

Yearly cost = $230

Therefore, Ms. Watson has to pay $230 for her membership for the year. Ms. Watson is planning to join Planet Fitness for the first time. She has to pay a flat fee for the first year and a monthly fee for the membership. The flat fee is $110, and the monthly fee is $10. Ms. Watson needs to know the total membership cost for the year. We can calculate the total cost of the membership by using simple arithmetic.

The membership for the first year is a flat fee of $110. This fee is payable only once for the first year. After that, Ms. Watson needs to pay a monthly fee of $10. The membership is valid for 12 months. Therefore, we need to calculate the total cost of 12 months of membership for Ms. Watson.

We can do this by multiplying the monthly fee of $10 by 12 months. Ms. Watson must pay a flat fee of $110 for the first year and a monthly fee of $10. She needs to pay this fee for 12 months of membership. Therefore, the total cost of membership for the year is $230.

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The 95% two-proportion z confidence interval (0.1181, 0.2057) in the given problem indicates that there is a 95% probability that the true difference in proportions between the two polls falls within the range of 0.1181 to 0.2057.

This means that the proportion of registered voters who favor candidate X in the first poll is estimated to be between 11.81% and 20.57% higher than the proportion in the second poll.

The confidence interval is a statistical tool that provides a range of values within which the true difference between the proportions is likely to lie. The interval is constructed based on the sample data and takes into account the variability in the estimates. In this case, it suggests that there is evidence to support the claim that candidate X was more favored by registered voters in the first poll compared to the second poll.

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The actual distance between Cucumber City and Pickleville is 70.4 miles.

To find the actual distance between Cucumber City and Pickleville, we can use the given scale on the map and set up a proportion.

According to the map scale, 2.5 inches represents 22 miles. This means that for every 2.5 inches on the map, the actual distance in the real world is 22 miles.

Let's denote the actual distance between Cucumber City and Pickleville as 'x' miles. We know that on the map, these two cities are 8 inches apart.

Using the proportion:

(2.5 inches) / (22 miles) = (8 inches) / (x miles)

2.5 inches * x miles = 8 inches * 22 miles

2.5x = 8 * 22

2.5x = 176

x = 176 / 2.5

x = 70.4

Therefore, the actual distance between Cucumber City and Pickleville is 70.4 miles.

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The final volume of the gas, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is approximately 142.55 ml.

The final volume of the gas in milliliters, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is unknown ml.

To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. The equation for Boyle's Law is:

P1 * V1 = P2 * V2

where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Given that P1 = 0.428 atm, V1 = 240 ml, and P2 = 0.72338 atm, we can plug these values into the equation and solve for V2:

(0.428 atm) * (240 ml) = (0.72338 atm) * V2

103.2 atm * ml = 0.72338 atm * V2

V2 = (103.2 atm * ml) / 0.72338 atm

V2 ≈ 142.55 ml

Therefore, the final volume of the gas, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is approximately 142.55 ml.

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The property of rectangles where opposite sides are equal in length to determine the length of Line AC. By equating AE and BD and solving for X, we found that X = 6. Substituting this value back into AE, we found that Line AC has a length of 8 units.

To determine the length of Line AC, we need to consider the properties of rectangles.

In a rectangle, opposite sides are equal in length. Since AE and BD are opposite sides of the rectangle, they must be equal.

Given that AE = X + 2 and BD = 4X - 16, we can set up an equation:

AE = BD

X + 2 = 4X - 16

To solve for X, we can simplify the equation:

2 + 16 = 4X - X

18 = 3X

Dividing both sides by 3:

X = 6

Now that we have the value of X, we can substitute it back into the expression for AE to find its length:

AE = X + 2

AE = 6 + 2

AE = 8

Therefore, the length of Line AC, which is equal to AE, is 8 units.

In summary, we utilized the property of rectangles where opposite sides are equal in length to determine the length of Line AC. By equating AE and BD and solving for X, we found that X = 6. Substituting this value back into AE, we found that Line AC has a length of 8 units.

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The upthrust on the object would be 5N.

Given data:

One quarter of the object is submerged under water, the volume of water displaced is one quarter of the object's total volume.

According to Archimedes' principle, the upthrust is equal to the weight of the water displaced.

Weight of the fluid displaced = (1/4) * Weight of the object

= (1/4) * 20N

= 5N.

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The question asks about the recovery time for a randomly selected patient from a surgical procedure. This recovery time follows a normal distribution with a mean of 4 days and a standard deviation of 1.9 days.

To answer questions about probabilities or specific values of the recovery time, we can use the properties of the normal distribution.

Standardize the variable: Convert the recovery time value (X) into a standard score or z-score using the formula: z = (X - μ) / σ, where μ is the mean and σ is the standard deviation.

Use the standard normal distribution table or a calculator to find the corresponding probability or value associated with the standardized z-score.

For example, if you want to find the probability that a randomly selected patient has a recovery time less than a certain number of days (X), you would calculate the z-score, look up the corresponding probability in the standard normal distribution table, and round the answer to four decimal places.

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The function that represents the amount of money the student saves after x months is y = 12x + 15.

In the given scenario, the student initially has $15. Every month, the student saves an additional $12. This means that the amount of money saved after x months can be calculated by multiplying the number of months (x) by the monthly savings of $12 and adding the initial amount of $15. Therefore, the function y = 12x + 15 represents the amount of money (y) the student saves after x months. For example, after 3 months, the student would have saved $12 * 3 + $15 = $51. The function allows for easy calculation of the savings based on the number of months elapsed.

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Based on the information provided by the box-and-whisker plot, the range of the given data (2, 5, 12, 13) is 5.

To determine the range of the data from the given box-and-whisker plot, we need to consider the highest and lowest values represented in the plot.

The whiskers in the plot extend from 102 to 115. This means that the lowest value in the data is 102, and the highest value is 115.

The box in the plot ranges from 109 to 114. The lower boundary of the box represents the 25th percentile (Q1), which is the median of the lower half of the data. In this case, Q1 is 109. The upper boundary of the box represents the 75th percentile (Q3), which is the median of the upper half of the data. In this case, Q3 is 114.

The line dividing the box at 111 represents the median (Q2), which is the middle value when the data is sorted in ascending order. So, Q2 is 111.

Now, let's analyze the given data values: 2, 5, 12, and 13.

Based on the box-and-whisker plot, we can see that the data range from the lowest whisker (102) to the highest whisker (115). However, the given data values fall within the range of the box, which is from 109 to 114.

Therefore, the range of the given data is from the lowest value within the box (109) to the highest value within the box (114). The range can be calculated as:

Range = Highest value - Lowest value

Range = 114 - 109

Range = 5

So, the range of the given data is 5.

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To make each pair of radicals similar by reducing the radicand, we need to simplify the radicands to their lowest terms. Simplifying radicals involves finding the largest perfect square factor of the number under the radical sign and rewriting it. Let's take an example:

Pair 1: √50 and √32

To make these radicals similar, we simplify the radicands:

√50 = √(25 × 2) = 5√2

√32 = √(16 × 2) = 4√2

Now, both radicals have the same simplified radicand, which is √2. The pair becomes 5√2 and 4√2, making them similar.

Similarly, you can apply the same process to any other pairs of radicals, simplifying the radicands to their lowest terms and making the pairs similar by having matching simplified radicands.

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The article about endangered species occupies approximately 1/2 of the cover page.

To determine the portion of the cover page occupied by the article about endangered species, we need to calculate the product of the fractions representing the text and photographs.

First, we find the portion of the cover page occupied by text: 3/8.

Next, we find the portion of the text occupied by photographs: 2/3.

To find the portion of the cover page occupied by the article about endangered species, we multiply these two fractions: (3/8) * (2/3) = 6/24 = 1/4.

Therefore, the article about endangered species occupies 1/4 of the cover page, which is equivalent to 1/2 when simplified.

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