The Island Loop Ferry takes the same route multiple times a day. It starts at the port of
Seabreeze Village and travels due south for 8 miles to the town of Oceanview. From there, it travels due east for 15 miles to Portlandville. Finally, it makes a straight-line journey back to Seabreeze Village. If the ferry can travel 5 miles on a gallon of fuel, how many gallons does the ferry use to complete the route one time?

To rewrite the integral ∫(2x)\(e^{4x^{2} }\)dx using integration by parts, we'll consider the function f(x) = (2x) and g'(x) = \(e^{4x^{2} }\).

Integration by parts states that ∫u dv = uv - ∫v du, where u and v are functions of x.

Let's assign:

u = (2x) => du = 2 dx

dv = \(e^{4x^{2} }\) dx => v = ∫\(e^{4x^{2} }\) dx

To evaluate the integral of v, we need to use a technique called the error function (erf). The integral cannot be expressed in terms of elementary functions. Hence, we'll express the integral as follows:

∫\(e^{4x^{2} }\) dx = √(π/4) × erf(2x)

Now, we can rewrite the integral using integration by parts:

∫(2x)\(e^{4x^{2} }\) dx = uv - ∫v du

= (2x) × (√(π/4) × erf(2x)) - ∫√(π/4) × erf(2x) × 2 dx

= (2x) × (√(π/4) × erf(2x)) - 2√(π/4) × ∫erf(2x) dx

The integral ∫erf(2x) dx can be further simplified using substitution. Let's assign z = 2x, which implies dz = 2 dx. Substituting these values, we get:

∫erf(2x) dx = ∫erf(z) (dz/2) = (1/2) ∫erf(z) dz

Therefore, the final expression becomes:

∫(2x)\(e^{4x^{2} }\) dx = (2x) × (√(π/4) × erf(2x)) - √(π/2) × ∫erf(z) dz

Please note that the integral involving the error function cannot be expressed in terms of elementary functions and requires numerical or tabulated methods for evaluation.

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Answer:

Step-by-step explanation:

61.24 * 3.5 = 214.34

Option 2)

Answer:241.34

Step-by-step explanation:

61.24 * 3.5 = 214.34

The type of variable required is Qualitative with two possible outcomes.

An estimate level of uncertainty is expressed by a range of values known as a confidence interval.

Keeping in mind, the z-score and other data's decimal places should be preserved when generating the confidence interval upper and lower bounds. The responses will be accurate and round-off errors will be prevented.

Also, the confidence interval boundaries are expressed in percentages. The maximum value of 0.8740, for instance, is 87.4% in decimal notation.

Make sure to specify the confidence level, the percentage of the population that the confidence interval actually captures, and the bounds expressed in percentages when expressing the meaning of the confidence interval.

Hence, the type of variable required to construct a confidence interval for a population​ proportion is Qualitative with 2 possible outcomes.

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Answer:

i dont know

Step-by-step explanation:

Answer: x_>6

Step-by-step explanation:

1) Find the curved surface area of a cylinder with the height and radius 4 CM and 7 CM respectively.

\( \underline{\small\bf Solution}\)

In this question we are provided with the radius of a cylinder and a height of the cylinder. We are asked to calculate the curved surface area of the cylinder.

We know,

Curved surface area = 2πrh

Where,

Substituting the values we get

Curved surface area = (2 × 3.14 × 4 × 7) cm²

→ Curved surface area = (6.28 × 28) cm²

→ Curved surface area= 175.84 cm²

2) Find the circular surface area of the cylinder when the radius is 14 CM.

\( \underline{\small\bf Solution }\)

In this question we are provided with the radius of the cylinder. We are asked to calculate the area of the cylinder.

We know,

Area of a cylinder = πr²

Where,

Area = (3.14 × 14²) cm²

→ Area = 3.14 × 14 × 14

→ Area = 615.44cm²

3) Find the circular surface area of the cylinder when the diameter is 7CM.

\( \underline{\small\bf Solution}\)

In this question we are provided with the diameter of the cylinder. We are asked to calculate the area.

First we will calculate the radius

Radius = Diameter/ 2

Substituting the values we get

Radius = 7/2 cm

Radius = 3.5 cm

Now we will calculate the area of the cylinder

We know,

Area of the cylinder = πr²

Area = 3.14 × 3.5²

→ Area = 3.14 × 3.5 × 3.5

→ Area = 38.465 cm²

Answer:

The slope is 1.

You can also graph these points and connect them to find out that they increase by 1 unit per each x.

Step-by-step explanation:

The slope formula is y2 - y1 divided by x2 - x1

So you can plug in the values

-13 - (-10)  /  3 - 6

-13 + 10 / -3

-3 / -3

= 1

Answer:

slope = change in y/change in X

y2 - y1 / X2 - x1

where y2 = -13 and y1 = -10

where X2 = 3 and x1 = 6

from the formula of slope

y2 - y1 / X2 - x1

-13 - -10/ 3 - 6

-3/-3

==> 1

The nonresponse caused the results of the survey to be biased as C. Those who did not respond caused a violation of the assumption of independence.

It should be noted that each person in a simple random sample of 1,200 received a survey, and 325 people returned their survey. How could nonresponse cause the results of the survey to be biased?

In this case, the nonresponse caused rhe results of the survey to be biased as those who did not respond caused a violation of the assumption of independence. Those who did not respond may differ in some important way from those who did respond

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Answer:

Right and Isosceles

Step-by-step explanation:

The triangle is right because it has a 90-degree angle. It is also Isosceles because it has two side lengths that are equal.

The values of a, b, c are 152°, 28°, 152° respectively.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn.

The sum of angles at a point will give 360°.

This means that a + b + c + 28 = 360

c +28 = 180° ( angle on a straight line)

c = 180 -28

c = 152°

c = a( alternate angles are equal)

therefore the value of a = 152°

b = 28( alternate angles are equal)

therefore the value of b is 28

therefore the values of a, b, c are 152°, 28°, 152° respectively

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The probability that a randomly selected household with a savings account has no checking account is approximately 0.149, or 14.9%.

To compute the probability that a randomly selected household with a savings account has no checking account, we can use Bayes' theorem. Let S denote the event that a household has a savings account, and C denote the event that a household has no checking account.

We want to find P(C | S), the probability that a household with a savings account has no checking account.

Using Bayes' theorem, we have:

P(C | S) = P(S | C) * P(C) / P(S)

We know that 40% of households with no checking accounts have savings accounts, so P(S | C) = 0.4. We also know that 21.5% of households have no checking accounts, 66.9% have regular checking accounts, and 11.6% have NOW accounts, so P(C) = 0.215.

Finally, we can use the law of total probability to find P(S), the overall probability of a household having a savings account:

P(S) = P(S | C) * P(C) + P(S | regular checking) * P(regular checking) + P(S | NOW) * P(NOW)

= 0.4 * 0.215 + 0.716 * 0.669 + 0.793 * 0.116

≈ 0.576

Substituting these values into the equation for Bayes' theorem, we get:

P(C | S) = 0.4 * 0.215 / 0.576

≈ 0.149

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Complete question is:

A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.

Compute the probability that a randomly selected household with a savings account has no checking account.

Answer:

21 inches squared

Step-by-step explanation:

i think thats the answer???

Answer:3x7=21

Step-by-step explanation:

multiply 3x7 and its 21

Answer: The playground should be repaired and expanded even if that means raising the entrance fee to the park thinking it as socialy desirable or feel pressured

Two ways that this question may lead to response bias are:

1. The question may be framed in a way that makes the respondent feel like they have to answer a certain way in order to be seen as socially desirable. For example, if the question is framed as "Do you think the playground should be repaired and expanded so that all children can enjoy it?" the respondent may feel pressure to answer "yes" even if they don't truly believe it.

2. The question may be framed in a way that presents false information or assumptions that the respondent feels they have to accept in order to answer the question.

For example, if the question is framed as "Given that the playground is in dire need of repair and expansion, do you think it's worth raising the entrance fee to the park?" the respondent may feel pressured to accept the assumption that the playground is in dire need of repair and expansion, even if they don't actually believe it.

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Answer:

-5/4

Step-by-step explanation:

slope = rise/run

Start at the lower right point. Go up 5. The rise = 5. Go left 4. The run -4.

slope = 5/-4 = -5/4

Treatment Group:

$\mu = 22, \sigma = 2.30$

Placebo Group:

$\mu = 22, \sigma= 0.77$

Answer:

It's C and E i just took the test trust me

Answer:

the person above me has the same name as my sister

Step-by-step explanation:

The number of square units enclosed by the polygon is 18.

First, count the number of dots that are enclosed by the polygon (including those on the boundary). There are 14 such dots.Next, count the number of dots on the boundary of the polygon. There are 8 dots on the boundary.Each of the dots on the boundary corresponds to a line segment of the polygon.

So, the perimeter of the polygon is 8 units (the length of each of these line segments).Now, we can use Pick's theorem to find the area of the polygon. Pick's theorem states that A = i + b/2 - 1, where A is the area of the polygon, i is the number of dots inside the polygon, and b is the number of dots on the boundary of the polygon.

So, plugging in the values we have: A = 14 + (8/2) - 1 = 14 + 4 - 1 = 17

Therefore, the area of the polygon is 17 square units.However, we have to remember that the dots are spaced one unit apart, horizontally and vertically.

Therefore, each square that is enclosed by the polygon has an area of 1 square unit. We counted 17 such squares, so the total area enclosed by the polygon is 17 square units.

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The​ p-value is the probability of getting a test statistic at least as extreme as the one representing the sample​ data, assuming that the null hypothesis is true.

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The total number of posts in the fence is 300.

A community garden is surrounded by a fence. The total length of the fence is 3000 feet. For every 40 8 PM defense, there are four posts.

To find the total number of posts in the fence, first, we need to find out the number of fence segments. Each segment has 1 post at the start and 1 post at the end. The number of posts between any two segments is given by 40/4 = 10 posts per segment.

We can then use this information to solve the problem as follows:Let the number of fence segments be n.Each segment is 8 pm = 1/3 day long.The total length of the fence is 3000 feet.So, the length of one segment of the fence = (3000/n) feet.There are 10 posts per segment.

So, the number of posts in one segment of the fence = 10 x (1/3) = (10/3) posts.Since there is one post at the start and end of each segment, the total number of posts in one segment of the fence = (10/3) + 2 = (16/3) posts.

So, the total number of posts in the fence, n = Total length of the fence / Length of one segmentNumber of segments = n = 3000 / (3000/n)Number of segments = n = (3000 * n) / 3000Number of segments = n = n

Number of segments = n²

Number of segments = 900/16 = 56.25 ~ 56

The total number of posts in the fence = Number of segments x Number of posts per segmentTotal number of posts = 56 x (16/3)Total number of posts = 299.67 ~ 300 posts.

Therefore, the total number of posts in the fence is 300.

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Answer:

X=2,4,6,8,10

Step-by-step explanation:

i think this answer is correct

cool

The expression of time in terms of r is T = 85/9r. If he walked at an average speed of 3 miles per hour. Then the time taken by nick to reach the shopping mall will be 3 hours and 60 minutes.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

Nick walked 5 miles to reach his aunt's house.

From there he traveled 8 miles to the shopping mall on a bicycle.

He traveled 80% faster on the bicycle than on foot.

Let r represent his rate of walking in miles per hour. Then the 1.8r will be the rate of cycling in miles per hour.

Then the number of hours nick took to reach the shopping mall in terms of r will be

T = t₁ + t₂

Where t₁ is the time taken to reach his aunt's house and t₂ is the time taken to reach the shopping mall from his aunt's house. Then we have

T = 5 / r + 8 / 1.8r

T = 1/r (5 + 8/1.8)

T = 85/9r

If r is 3 miles per hour, then the time taken by nick to reach the shopping mall will be

T = 85 / (9 x 3)

T = 3.15 hours

T = 3 hours and 9 minutes

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a) To find the extreme points and determine if they are minimum or maximum, we need to take the derivative of the function and set it equal to zero.

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

Taking the derivative:

f'(x) = 2x + 1

Setting it equal to zero and solving for x:

2x + 1 = 0

2x = -1

x = -1/2

To determine if it is a minimum or maximum, we can examine the concavity of the function. Since the coefficient of x^2 is positive (1), the function opens upward and the critical point at x = -1/2 is a minimum.

b) f(x) = x^3 + x^2

Taking the derivative:

f'(x) = 3x^2 + 2x

Setting it equal to zero and solving for x:

3x^2 + 2x = 0

x(3x + 2) = 0

This gives two critical points:

x = 0 and x = -2/3

To determine if they are minimum or maximum, we need to examine the concavity of the function. Since the coefficient of x^3 is positive (1), the function opens upward. The critical point at x = 0 is a minimum, while the critical point at x = -2/3 is a maximum.

b) Graphical method:

To solve the problem graphically, we will draw a graph representing the constraints and find the feasible area. Then we will identify the corner point feasible solutions (CPFS) and determine if there is an optimal solution.

a) Maximize subject to:

x1 + x2

2x1 + 5x2 <= 5

x1 + x2 <= 5

3x1 + x2 <= 15

x1, x2 >= 0

b) Minimize subject to:

x1 + x2

-x1 + x2 <= 5

x2 <= 3

3x1 + x2 >= 7

x1, x2 >= 0

Unfortunately, the given optimization problems are incomplete as there are no objective functions specified. Without an objective function, it is not possible to determine an optimal solution or solve the problem graphically.

Please provide the objective function for the optimization problems so that we can proceed with the graphical solution and find the optimal solution, if any.

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a) The extreme point for the function f(x) = x² + x - 6 is a minimum point.

b) The extreme point for the function f(x) = x³ + x² is neither a minimum nor a maximum point.

Step 1: For the function f(x) = x² + x - 6, to find the extreme points, we can take the derivative of the function and set it equal to zero. By solving for x, we can identify the x-coordinate of the extreme point. Taking the second derivative can help determine if it is a minimum or maximum point. In this case, the extreme point is a minimum because the second derivative is positive.

Step 2: For the function f(x) = x³ + x², finding the extreme points follows the same process. However, after taking the derivative and solving for x, we find that there are no critical points. Without any critical points, there are no extreme points, meaning there are no minimum or maximum points for this function.

In summary, for the function f(x) = x² + x - 6, the extreme point is a minimum, while for the function f(x) = x³ + x², there are no extreme points.

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Answer:

1. 1760

2. 1400

Step-by-step explanation:

2^5 = 32

32 × 5 = 160

160 × 11 = 1760

2^3 = 8

5^2 = 25

8 × 25 = 200

200 × 7 = 1400

The calculated measure of RST in the circle is (b) 62

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

The circle

Assuming that all lines which appear tangent are actually tangent, we have the following equation

RST = 1/2 * (47 + 77)

The above equation is theorem of angle between two chords

So, we have

RST = 1/2 * 124

Evaluate

RST = 62

Hence, the value of RST in the circle is (b) 62

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Answer:

y=-2/3x-6

Step-by-step explanation:

we know that

Two angles are complementary, if their sum is equal to 90 degrees

Example

If A and B are complementary

A+B=90 degrees

If A=30 degrees

then

The value of B is

B=90-30=60 degrees

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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The expression (A) $20 – (9)($1.10) will correctly represents the given situation.

So, the expression that represents the given situation will be:

Then, the expression will be:

Therefore, the expression (A) $20 – (9)($1.10) will correctly represents the given situation.

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