If you have a stack of 15 quarters and a stack of 15 nickels, is the volume of the two stacks the same?

The probability that the sample mean would be less than 31,358 miles in a sample of 242 tires if the manager is correct is 0.9925 (or 99.25%).

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

We can use the central limit theorem to approximate the distribution of the sample mean. According to the central limit theorem, if the sample size is sufficiently large, the distribution of the sample mean will be approximately normal with a mean of 30,641 and a standard deviation of sqrt(variance/sample size).

So, we have:

mean = 30,641

variance = 14,561,860

sample size = 242

standard deviation = sqrt(variance/sample size) = sqrt(14,561,860/242) = 635.14

Now, we need to calculate the z-score corresponding to a sample mean of 31,358 miles:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

= (31,358 - 30,641) / (635.14 / sqrt(242))

= 2.43

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 2.43. The probability is approximately 0.9925.

Therefore, the probability that the sample mean would be less than 31,358 miles in a sample of 242 tires if the manager is correct is 0.9925 (or 99.25%).

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There are 48 ways for the driver to load the shipment so that one of the heavier vehicles is directly over the rear axle of the trailer.

In order for one of the heavier vehicles to be directly over the rear axle of the trailer, there are only two options: either the station wagon or the minivan can be in that position. Therefore, we can consider the problem as two separate cases:

Case 1: Station wagon over the rear axle
In this case, we have four vehicles remaining to be loaded onto the trailer: three compact cars and the minivan. The order in which they are loaded onto the trailer does not matter, since the station wagon's position is fixed. Therefore, the number of ways to load the remaining vehicles is simply the number of permutations of 4 items, which is 4! = 24.

Case 2: Minivan over the rear axle
This case is identical to the first case, except that the station wagon is replaced by the minivan. Therefore, the number of ways to load the remaining vehicles is again 4! = 24.

Total number of ways:
Since the two cases are mutually exclusive, we can simply add the number of ways from each case to get the total number of ways:
24 + 24 = 48

Therefore, there are 48 ways for the driver to load the shipment so that one of the heavier vehicles is directly over the rear axle of the trailer.

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A hamburger has 350 calories. So an order of fries has 320 calories, and a hamburger has 50 + 320 = 370 calories.

To solve the problem, you can use algebraic equations. Let x be the number of calories in an order of fries. Then, the number of calories in a hamburger is 50 + x. The problem tells us that 2 hamburgers and 3 orders of fries have a total of 1700 calories. This can be written as:

2(50 + x) + 3x = 1700

Simplifying and solving for x, we get:

100 + 2x + 3x = 1700

5x = 1600

x = 320

So an order of fries has 320 calories, and a hamburger has 50 + 320 = 370 calories.

Explanation:

To solve the problem, we need to set up an equation that relates the number of hamburgers and fries to the total number of calories. We can use algebraic variables to represent the unknown quantities. Let x be the number of calories in an order of fries, and let y be the number of calories in a hamburger.

The problem tells us that each hamburger has 50 + x more calories than each order of fries. This means that the number of calories in a hamburger is equal to the number of calories in an order of fries plus 50:

y = x + 50

We also know that 2 hamburgers and 3 orders of fries have a total of 1700 calories. This can be written as:

2y + 3x = 1700

Now we can substitute the first equation into the second equation to eliminate y:

2(x + 50) + 3x = 1700

Simplifying and solving for x, we get:

2x + 100 + 3x = 1700

5x = 1600

x = 320

So an order of fries has 320 calories. We can substitute this value back into the first equation to find the number of calories in a hamburger:

y = x + 50

y = 320 + 50

y = 370

Therefore, a hamburger has 370 calories.

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The time taken by her for haircut is 21 minutes and to color is 50 minutes.

Assume that

Haircut takes   = x minutes

To Color takes = y minutes

According to the question

The expression for time be,

3x + 4y = 263 ...(i)

The expression for time be,

x + y = 71  ...(ii)

Apply elimination method to solve it,

After equation(i) - 3x(ii) we get,

y = 50 minutes

Now plug it into (ii) we get,

x = 21 minutes.

Hence,

Haircut takes   = 21 minutes

To Color takes = 50 minutes

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5.

4x-6 = 90

4x = 84

x = 21 degrees

6.

The sum of all 3 angles in that triangle = 180.

We know that the right angle = 90.

So the other 2 angles = 90.

(2x+53) + (5x+2) = 90

Combine like terms

7x + 55 = 90

7x = 35

x = 5 degrees

Answer: A

Step-by-step explanation: Okay! So the first thing we notice when looking at the diagram is that the units are in centimeters. We want these in feet. They tell us that 1cm = 4ft. Now we know that the actual scale would have the length be 12 ft, and the width would be 8 ft.

Now, we look at the size they want it increased by: 20%. In order to do this, we must multiply the length and width by 0.2. Then we take THOSE values, and add them to the original.

Let's work it out.

Step 1. Multiplying values by 0.2 (20%)

    Length:  (12ft)(0.2)= 2.4

    Width:    (8ft)(0.2)= 1.6

Step 2. Now that we've found 20% of our original length and width, we must add those values to the original length and width.

    Length: 12ft + 2.4ft = 14.4 ft

    Width:   8ft + 1.6ft= 9.6ft

Those are your final answers! Hope that helps :)

In a simple baseline/offset model y = b0 + b1*x with a dummy-variable predictor x, the coefficient b1 may be interpreted as the difference in the mean value of y between the two groups represented by the dummy variable.

In a simple baseline/offset model with a dummy-variable predictor x, the coefficient b1 represents the difference in the mean value of the response variable y between the two groups represented by the dummy variable. When the dummy variable takes the value of 0, it represents one group, and when it takes the value of 1, it represents the other group.

The coefficient b1 indicates the average change in y when moving from one group to the other, while holding all other variables constant. Therefore, it provides insights into the effect or impact of the group represented by the dummy variable on the response variable.


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The sum ∑ k=1^3 (-1)^k * 1 * sin(pi/k) is an example of a finite series. A series is the sum of the terms in a sequence. In this case, the sequence is defined by the terms (-1)^k * 1 * sin(pi/k) for k=1, 2, 3.

The sum of these terms is calculated by adding up each term one by one, which gives us the total value of the series. In this series, the values of k are limited to the integers 1, 2, and 3. For each value of k, we evaluate the product of (-1)^k, 1, and sin(pi/k) and then add up these values to get the sum.

The sine function sin(pi/k) gives the ratio of the side opposite to the angle pi/k in a right triangle with hypotenuse 1. Since pi is a constant, the value of sin(pi/k) changes as k varies, resulting in different terms for the series. The factor (-1)^k alternates between 1 and -1 as k increases, leading to terms that are positive and negative.

The sum of the series can be computed by adding up all the terms. In this case, we obtain the value 3 - (3/2)sqrt(3). This final value is a real number that represents the total value of the sum of the series.

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There are 462 different ways to select a planning board of 6 scientists from a group of 11 scientists.

The problem requires selecting 6 scientists from a group of 11 scientists. This is a combination problem, and the formula for combination is nCr, where n is the total number of items, and r is the number of items to be selected. The formula is given by:

nCr = n! / (r! * (n-r)!)

Where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.

Using the given formula, the number of ways of selecting a planning board of 6 scientists can be calculated as:

11C₆ = 11! / (6! * (11-6)!)

= (11109876!) / (6! * 54321)

= (1110987) / (5432*1)

= 462

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The slope of the tangent line and the instantaneous rate of change of the function at (4,1) are both equal to [tex]4^{(i-1)}[/tex].

To find the slope of the tangent line, we need to find the derivative of the function y = xi + 7 and evaluate it at x = 4.

(a) To find the derivative, we use the power rule:

so, y' [tex]= 4^{(i-1)}[/tex] when x = 4.

(b) The instantaneous rate of change of the function is also given by the derivative at x = 4. So, the instantaneous rate of change is y' [tex]= 4^{(i-1)}[/tex] when x = 4.

Therefore, the slope of the tangent line at (4,1) is [tex]4^{(i-1)}[/tex] and the instantaneous rate of change of the function at (4,1) is also [tex]4^{(i-1)}[/tex].

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Suppose that v1, v2, v3 is an orthogonal basis for w. Then, we have:

v1 · v2 = 0 (v1 and v2 are orthogonal)

v1 · v3 = 0 (v1 and v3 are orthogonal)

v2 · v3 = 0 (v2 and v3 are orthogonal)

To show that multiplying v3 by a non-zero scalar c gives a new orthogonal basis v1, v2, cv3, we need to show that v1, v2, and cv3 are mutually orthogonal.

First, note that v1 and v2 are still orthogonal to each other, as c does not affect their inner product.

Now, let's check the inner products between v1, v2, and cv3:

v1 · cv3 = c(v1 · v3) = c(0) = 0 (v1 and v3 are orthogonal)

v2 · cv3 = c(v2 · v3) = c(0) = 0 (v2 and v3 are orthogonal)

(cv3) · (cv3) = c^2(v3 · v3) ≠ 0 (v3 is a non-zero vector)

So, v1, v2, and cv3 are mutually orthogonal, except for the fact that cv3 is no longer a unit vector. However, we can normalize cv3 to get a unit vector u3:

u3 = (1/|cv3|)cv3 = (1/|c|)cv3

Then, we have the new orthogonal basis v1, v2, u3. Note that this basis spans the same subspace as the original basis v1, v2, v3, since multiplying v3 by a non-zero scalar does not change the span of the basis.

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Lani uses the fraction 1/3 of a yard of ribbon for each bow.

Fractions represent a part of a whole, and are used to express values that are not whole numbers.

To find the required fraction divide the total amount of ribbon by the number of bows to find the amount of ribbon used per bow.

We also use the concept of fractions to represent the amount of ribbon used per bow as a part of a yard.

Here we have

Lani uses 2 yards of ribbon to make 6 bows. each bow uses the same amount of ribbon.

To find the fraction of a yard of ribbon used for each bow, we need to divide the total length of ribbon used by the number of bows.

Hence, The amount of ribbon used for each bow is:

=> 2 yards/ 6 bows

= 1 yards/3bow

Therefore,

Lani uses the fraction 1/3 of a yard of ribbon for each bow.

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Initially, when a bank has a required reserve ratio of 20%, and no excess reserves, if $10,000 is deposited into the bank, the bank will be required to hold 20% of the deposit as required reserves, which amounts to $2,000.

The remaining $8,000 can be used to make loans or acquire additional assets, such as bonds.

The required reserve ratio is the percentage of deposits that a bank is required to hold in reserve, either in cash or on deposit with the Federal Reserve Bank. The required reserve ratio is set by the Federal Reserve and is used as a tool to regulate the money supply and control inflation.

When a bank receives a deposit, it must keep a portion of that deposit in reserve to ensure that it has enough cash on hand to meet the demands of its customers who wish to withdraw their money.

In this scenario, the bank will hold $2,000 in reserves and can use the remaining $8,000 to make loans or acquire additional assets. This process is known as the money multiplier effect, where the original deposit is multiplied through the banking system as it is loaned out and deposited into other accounts. The money multiplier effect can be used to increase the money supply and stimulate economic growth.

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The correct answer is (a) there is enough evidence to conclude that age and drink preference is dependent.

Using the formula for the chi-square test of independence, we can calculate the test statistic as:

X² = Σ (O-E)^2 / E

Performing this calculation on the given data, we get:

X² = (50-62.5)²/62.5 + (100-87.5)²/87.5 + (200-250)²/250 + (200-200)²/200 + (50-50)²/50 + (200-150)²/150 + (50-37.5)²/37.5 + (150-162.5)²/162.5 + (200-250)²/250 + (50-50)²/50 = 34

Using a chi-square distribution table with (2-1)*(4-1)=3 degrees of freedom and a significance level of 0.05, the critical value is 7.815.

Since the calculated test statistic of 34 is greater than the critical value of 7.815, we can reject the null hypothesis of independence and conclude that there is enough evidence to support the alternative hypothesis that age and drink preference are dependent.

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The lines that have an x-intercept of (3,0) and a y-intercept of (0,-4) are:

y = 4/3x - 4

y + 4 = 4/3(x - 3)

To find a line with a given x-intercept and y-intercept, we can use the slope-intercept form of a line, which is:

y = mx + b

where m is the slope of the line, and b is the y-intercept (the y-coordinate where the line intersects the y-axis).

Both of these lines pass through points (3,0) and (0,-4), so they have the desired x- and y-intercepts.

The other lines do not pass through both of these points

y = -4/3x - 4 does not pass through (3,0)

y = 3x - 4 does not pass through (0,-4)

Y=4/3(x-3) does not pass through (0,-4)

y+4=4/3x does not pass through (3,0)

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The first premise states that Newton, Maxwell, and Einstein worked with physics. This means that they were all involved in the study and exploration of physical phenomena and natural laws. Newton's laws of motion, Maxwell's equations of electromagnetism, and Einstein's theory of relativity are all significant contributions to the field of physics. This premise is important in understanding the cartoon's message that even the greatest minds in physics could not have predicted the events of 2020. It is a reminder that science and knowledge are constantly evolving and that we must remain open to new discoveries and possibilities.

The translation of the first premise is a statement about the involvement of Newton, Maxwell, and Einstein in the field of physics. It acknowledges their contributions to the study of physical phenomena and natural laws. It is a recognition of their status as some of the most influential scientists in history, whose work has had a profound impact on our understanding of the world around us.

The first premise of the cartoon highlights the importance of physics and the contributions of some of its most prominent figures. It underscores the idea that science and knowledge are constantly evolving and that we must remain open to new discoveries and possibilities. It is a reminder that even the greatest minds in physics could not have predicted the events of 2020, and that we must continue to push the boundaries of our understanding of the world around us.

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Answer:

False

Step-by-step explanation:

No we can't find the square root of negative number.

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The volume of the solid after dilation when its surface area is 224 square units is 96 cubic units

Before dilation

Volume of the solid = 6 cubic units

Surface area of the solid = 14 square units

When solid is dilated:

Volume of the solid = x cubic units

Surface area of the solid = 224 square units

Equate ratio of volume to surface area before and after dilation

6 : 14 = x : 224

6/14 = x/224

cross product

6 × 224 = 14 × x

1344 = 14x

divide both sides by 14

x = 1344/14

x = 96 cubic units

Hence, the volume of the solid is 96 cubic units

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Por lo tanto, la altura del edificio es de 313.6 metros.

Por lo tanto, la velocidad con la que la piedra choca en el suelo es de 78.4 m/s.

Para determinar la altura del edificio y la velocidad de la piedra al chocar en el suelo, necesitamos utilizar las ecuaciones de la caída libre.

a) La altura del edificio se puede calcular utilizando la fórmula de la caída libre:

h = (1/2) * g * t^2

Donde h es la altura del edificio, g es la aceleración debido a la gravedad (aproximadamente 9.8 m/s^2) y t es el tiempo de caída (8 segundos).

Sustituyendo los valores conocidos en la fórmula, obtenemos:

h = (1/2) * 9.8 * (8^2)

h = 1/2 * 9.8 * 64

h = 313.6 metros

b) La velocidad con la que la piedra choca en el suelo se puede calcular utilizando la fórmula de la velocidad en caída libre:

v = g * t

Donde v es la velocidad, g es la aceleración debido a la gravedad (9.8 m/s^2) y t es el tiempo de caída (8 segundos).

Sustituyendo los valores conocidos en la fórmula, obtenemos:

v = 9.8 * 8

v = 78.4 m/s

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To find the displacement of the particle at time t, we need to integrate its velocity function v(t) over the interval [0, t]:

s(t) = ∫v(t) dt

s(t) = ∫(t^2 - 2t - 24) dt

s(t) = (1/3)t^3 - t^2 - 24t + C

where C is the constant of integration.

To find the value of C, we need to use the initial condition that the particle is at the position s(0) = 0. Substituting t = 0 and s(0) = 0 into the above equation, we get:

0 = 0 + 0 - 0 + C

C = 0

Therefore, the displacement of the particle at time t is given by:

s(t) = (1/3)t^3 - t^2 - 24t

To find the displacement over the entire interval [0, 6], we can substitute t = 6 into the above equation:

s(6) = (1/3)(6^3) - 6^2 - 24(6)

s(6) = 36 - 36 - 144

s(6) = -144

Therefore, the displacement of the particle over the interval [0, 6] is -144 meters.

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The error in using s10 as an approximation to the sum of the series is less than or equal to 2.79892 × 10^-5.

The given series is a p-series with p = 5, which means it converges if and only if p > 1. Therefore, the series converges.

To find the tenth partial sum, we need to add up the first ten terms of the series:

s10 = 1/1^5 + 1/2^5 + 1/3^5 + ... + 1/10^5

Using a calculator or computer, we get:

s10 ≈ 1.036393

To estimate the error in using s10 as an approximation to the sum of the series, we need to find the remainder term R10:

R10 = ∑ from n=11 to infinity of (1/n^5)

Since we cannot find the exact value of this infinite series, we can use an estimation method such as the integral test:

∫ from 11 to infinity of (1/x^5) dx = [-1/4x^4] from 11 to infinity = 1/4(11^4)

Therefore, we have:

R10 ≤ ∫ from 11 to infinity of (1/x^5) dx = 1/4(11^4) ≈ 2.79892 × 10^-5

So the error in using s10 as an approximation to the sum of the series is less than or equal to 2.79892 × 10^-5.

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To approximate sin1 correct to four decimal places using the Maclaurin series, we need to determine the number of initial terms needed such that the absolute value of the error term is less than or equal to 0.0001.

The Maclaurin series for sinx is given by:

sin x = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...

To find the error term, we can use the alternating series estimation theorem, which states that the error between the actual value and the approximation using an alternating series is less than or equal to the absolute value of the next term in the series.

So for sin1, we want to find the number of initial terms n such that:

|(1^(2n+1))/(2n+1)!| <= 0.0001

Solving for n using a calculator or computer software, we get n = 5. Therefore, we need at least 6 initial terms of the Maclaurin series for sinx to approximate sin1 correct to four decimal places.

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Answer:

Step-by-step explanation:

ƒ(5)= -4(5)²+7(5)

ƒ(5)= -100+35

ƒ(5)= -65

[tex]\frac{f(5)}{5}[/tex]=[tex]\frac{65}{5}[/tex]

ƒ=13

Taring a kitchen scale before weighing an ingredient is essential to obtain accurate measurements by removing the weight of the container, streamlining the process, and ensuring precise and reliable results in culinary preparations.

Taring a kitchen scale before weighing an ingredient is necessary to accurately measure the weight of the ingredient without including the weight of the container or vessel in which it is placed. Taring essentially resets the scale to zero, accounting for the weight of the container so that only the weight of the ingredient being added is measured.

By taring the scale, you eliminate the need to manually subtract the weight of the container from the final measurement. This allows for more precise and efficient measurements in recipes or other culinary applications.

Taring is particularly important when working with small or precise quantities of ingredients, where even a slight variation in weight can significantly impact the final outcome of a dish. It ensures that the weight of the container does not contribute to the measurement, providing accurate and reliable results.

Additionally, taring simplifies the weighing process by eliminating the need to calculate or estimate the weight of the container separately. It saves time and reduces the chances of errors in measurements, promoting consistency and precision in cooking and baking.

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To maximize utility while purchasing diamonds and water, a consumer should follow option 4: equating the marginal utility per dollar spent on each good.
To achieve this, the consumer should follow these steps:
1. Calculate the marginal utility (MU) of each good, which is the additional satisfaction gained from consuming one more unit of that good.
2. Calculate the price per unit of each good.
3. Divide the marginal utility of each good by its respective price to obtain the marginal utility per dollar (MU/$) for each good.
4. Compare the marginal utility per dollar for diamonds and water, and adjust the consumption of each good until the MU/$ for both goods is equal.
By equalizing the marginal utility per dollar spent on each good, the consumer ensures that they are getting the most satisfaction from their expenditure, as each additional dollar spent on either good yields the same amount of additional utility. This is the most efficient allocation of resources to maximize overall utility.

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Answer:

sin I = 3/5

Step-by-step explanation:

sin I = perpendicular/hypotenuse

      = 18/30

      = 9/15

      = 3/5

In this exercise, a random sample of 30 heights of adult females or adult males living in America was gathered and converted to inches. Confidence intervals were then constructed for the mean height of the sample at 90%, 95%, and 99% confidence levels.

Reflection questions were also answered, including summarizing the characteristics of the sample, finding x (sample mean), s (sample standard deviation), interpreting the confidence intervals, and calculating the percent difference between the sample mean and the average height of the population.

The sample consisted of 30 randomly selected heights of either adult females or adult males living in America. The sample mean (x) was found to be 65.87 inches with a sample standard deviation (s) of 3.18 inches. Confidence intervals were then constructed for the mean height of the sample at 90% (63.95, 67.79), 95% (63.34, 68.4), and 99% (62.39, 69.35) confidence levels. The confidence intervals show that we are 90%, 95%, and 99% confident that the true population mean height lies within these ranges.

According to the National Center for Health Statistics, the average height of adult females in the United States is 63.7 inches, and the average height for adult males is 69.2 inches. Based on this, the percent difference between the sample mean and the population mean for adult females is -2.95%, and for adult males, it is -4.71%. This means that the sample mean height is slightly lower than the population mean height for both groups. It is important to note that the sample was relatively small and may not be entirely representative of the population, and thus the percent difference should be interpreted with caution.

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The volume of the solid generated by revolving the region bounded by y=√sin6x, y=0, and the x-axis, if 0≤x≤π/6 is π/12 cubic units.

To find the volume of the solid, we can use the method of cylindrical shells. We consider a vertical strip of thickness dx at a distance x from the y-axis. The radius of the cylindrical shell is y=√sin6x and its height is dx. The volume of the cylindrical shell is given by 2πydx, where 2π represents the circumference of the circle.

Substituting y=√sin6x, we get the volume of the shell as 2π(√sin6x)dx. We integrate this expression with limits from 0 to π/6 to get the total volume of the solid. Thus,

Volume = ∫[0,π/6] 2π(√sin6x)dx

      = π/12

Therefore, the volume of the solid generated by revolving the region bounded by y=√sin6x, y=0, and the x-axis, if 0≤x≤π/6 is π/12 cubic units.

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The area of the region bounded by the graphs is 6 square units.

Option A is the correct answer.

We have,

To find the area of the region bounded by the graphs of y = 3 - x² and

y = 2x², we need to find the points of intersection between these two curves and calculate the definite integral of the difference between the two functions over the interval where they intersect.

Setting the two equations equal to each other, we have:

3 - x² = 2x².

Rearranging this equation, we get:

3 = 3x².

Dividing both sides by 3, we have:

1 = x²

Taking the square root of both sides, we find:

x = ±1.

So the two curves intersect at x = -1 and x = 1.

To find the area of the region between the curves, we integrate the difference between the upper curve (y = 3 - x²) and the lower curve

(y = 2x²) over the interval [-1, 1]:

A = ∫[-1, 1] (3 - x² - 2x²) dx.

Simplifying the integrand, we have:

A = ∫[-1, 1] (3 - 3x²) dx.

A = ∫[-1, 1] 3(1 - x²) dx.

A = 3 ∫[-1, 1] (1 - x²) dx.

Integrating term by term, we get:

A = 3 [x - (x³/3)] evaluated from -1 to 1.

Plugging in the limits of integration, we have:

A = 3 [(1 - (1³/3)) - ((-1) - ((-1)³/3))].

Simplifying further, we find:

A = 3 [(1 - 1/3) - (-1 - 1/3)].

A = 3 [(2/3) - (-4/3)].

A = 3 [(2/3) + (4/3)].

A = 3 (6/3).

A = 6 square units.

Therefore,

The area of the region bounded by the graphs is 6 square units.

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