Each segment of an oil pipeline is 30 feet long. If a segment of the pipeline leaks, repair workers reach the leak by opening the pipeline at the nearest end of the segment. The probability of a leak is distributed continuously and uniformly through each segment.


Required:

a. How far can repair workers expect to travel to reach a leak?

b. There is a 0.30 probability repair workers will travel between three feet and how many feet to reach a leak?

Answer:

16cm^2

Step-by-step explanation:

8*4=32

32/2 = 16

Don's null hypothesis is that there is no statistically significant difference between the mean debt of students who attended private college and the mean debt of students who attended public colleges, represented as H₀: μ₁ - μ₂ = 0

The null hypothesis (H0) is a statement of "no difference" or "no effect" and is typically represented as "there is no statistically significant difference between the mean debt of students who attended private college and the mean debt of students who attended public colleges." Therefore, in this case, Don's null hypothesis can be stated as

H₀: μ₁ - μ₂ = 0

where μ₁ represents the population mean debt for students who attended private college, and μ₂ represents the population mean debt for students who attended public colleges.

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The characteristic equation of a closed-loop control system with a proportional-integral (PI) controller is given by:

s^2 + (k_i/k_p)s + (1/k_p) = 0

where k_p is the proportional gain and k_i is the integral gain of the PI controller. To find the roots of the characteristic equation, we can use the quadratic formula:

s = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation. Therefore, the roots of the characteristic equation depend on the values of k_p and k_i, which in turn depend on the specific feedback process being controlled.

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if the bill was $23.60, and the tip was 15%, kim will earn $3.54. the overall total of the meal would be $27.14 :)

Anwser will be $3.54

15% = .15 ( to convert percent to decimal, change the % to . and move the decimal two places to the left)

23.60 * .15 = 3.54

Answer:

7.75

Step-by-step explanation:

By Geometric mean property:

\( GH = \sqrt {a \times b} \)

\( GH = \sqrt {3 \times 20} \)

\( GH = \sqrt {60} \)

\( GH = 7.74596669\)

\( GH \approx 7.75\)

Answer:

1/104

Step-by-step explanation:

The probability of choosing a red king is 2/52 since there are only two red kings in a deck of 52 cards...the probability of choosing a club would be 13/52 since there are 13 club cardsin a deck of 52 cards

Therefore the probability of choosing both by replacing the king would be 2/52 × 13/52 giving us 1/104

Step-by-step explanation:

The numbers between the squares are the possible answers.

For example, 2/3 ÷ 3/4 is either 1/2 or 8/9.

2/3 ÷ 3/4

2/3 × 4/3

8/9

The answer is 8/9, so you'll move up to the next square.

Answer:

x=−3 is your answer :)

Step-by-step explanation:

Steps for Solving Linear Equation

7x+4=−3x−26

Add 3x to both sides.

7x+4+3x=−26

Combine 7x and 3x to get 10x.

10x+4=−26

Subtract 4 from both sides.

10x=−26−4

Subtract 4 from −26 to get −30.

10x=−30

Divide both sides by 10.

x=

10

−30

Divide −30 by 10 to get −3.

x=−3

5*12 + 2*10 + 5*9 + 4*6

60 + 20 + 45 + 24

80 + 69

149 sides in total

Answer:

false

Step-by-step explanation:

4/9 is smaller than 3/4.

Answer:

k=-2

Step-by-step explanation:

2(6k+8)-6k=4

12k+16-6k=4

6k+16=4

6k=-12

k=-2

Answer: x^6+6x^4+8x^2+2

Step-by-step explanation:

Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in

(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2

The limit definition of a derivative is a mathematical method used to calculate the instant rate of change of a characteristic at a particular point. it is based at the idea of the limit of a function because the input techniques a certain cost.

The limit definition of a derivative is expressed as follows:

\(f'(x) = lim (h → 0) [f(x + h) - f(x)] /h\)

Wherein f'(x) represents the derivative of the function f(x) at a particular factor x. The expression \(( f(x + h) - f(x)) / h\) represents the common price of alternate of the characteristic over a small interval of size h, focused at x. The limit of this expression as h approaches 0 represents the instant fee of change of the characteristic at x, or the slope of the tangent line to the function at that factor.

The limit definition of a derivative is a fundamental concept in calculus and is used to calculate the slopes of tangent lines, to find maximum and minimum factors, and to clear up optimization issues in a huge variety of packages.

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Answer:  The length of one side is 9m.

Step-by-step explanation:

If area is 81 square meters, that means A = 81 m^2.

Since A = s^2, we can substitute s^2 for A.  Then

(s^2) = 81 m^2

Take the square root of both sides to solve for s:

(s^2)^(1/2) = (81 m^2)^(1/2)

s = 9 m

Answer:

f( g ( - 2 ) ) = - 14

Step-by-step explanation:

f(x) = - 2x + 4

g(x) = 3x² - x - 5

f( g ( - 2 ) ) = ?

g( - 2 ) = 3( - 2 )² - ( - 2 ) - 5 = 12 + 2 - 5 = 9

f(9) = - 2 × 9 + 4 = - 14

f( g ( - 2 ) ) = - 14

Answer:

B

Step-by-step explanation:

Answer:

14-5=9, then 34 / 9 x 2, 9x2=18, 34 / 18= 1.888888 orrrr 34 / 9= 3.7777 that x 2 = 7.55555554

To determine the number of terms we need to add in order to find the sum of the series with an error less than or equal to 0.002, we can use the concept of the Alternating Series Estimation Theorem.

The Alternating Series Estimation Theorem states that for an alternating series with terms decreasing in absolute value, the error in approximating the sum of the series by the sum of a finite number of terms is less than or equal to the absolute value of the next term.

In the given series, ∑n=1[infinity](−1)n−1n^2, the terms are decreasing in absolute value as n increases, so we can apply the Alternating Series Estimation Theorem.

The next term in the series, which determines the error, is given by (-1)^n * (n+1)^2. To ensure the error is less than or equal to 0.002, we need to find the smallest value of n such that:

|(-1)^n * (n+1)^2| ≤ 0.002

We can solve this inequality by testing values of n until we find the smallest value that satisfies it. Starting with n = 1:

|(-1)^1 * (1+1)^2| = 4 > 0.002

The inequality is not satisfied for n = 1.

Let's continue testing values of n:

|(-1)^2 * (2+1)^2| = 9 > 0.002

|(-1)^3 * (3+1)^2| = 16 > 0.002

|(-1)^4 * (4+1)^2| = 25 > 0.002

|(-1)^5 * (5+1)^2| = 36 > 0.002

|(-1)^6 * (6+1)^2| = 49 > 0.002

...

After testing a few values, we can see that the smallest value of n that satisfies the inequality is n = 9:

|(-1)^9 * (9+1)^2| = 100 > 0.002

Therefore, we need to add at least 9 terms in order to find the sum of the series with an error less than or equal to 0.002.

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Answer:

answer attached in pic ture

Answer:

1/16

Step-by-step explanation:

it is the same as

\(\frac{1}{8^\frac{4}{3}} = \frac{1}{ {(\sqrt[3]{8})}^4} = \frac{1}{2^4} = \frac{1}{16}\)

The percentage of all possible values of the variable that are less than 12 is 22.66%.

A variable is normally distributed with mean 15 and standard deviation 4 . a. find the percentage of all possible values of the variable that lie between and . b. find the percentage of all possible values of the variable that exceed . c. find the percentage of all possible values of the variable that are less than.Variables are unknown quantities that can take on different values.

In statistics, a variable can be a numeric or non-numeric value that can differ from one measurement to the next.A normal distribution is a type of probability distribution where the probability of each value of the variable is proportional to the distance of the value from the mean, and the distribution is symmetrical about the mean. The normal distribution is described by two parameters, the mean (μ) and the standard deviation (σ).a) To find the percentage of all possible values of the variable that lie between 10 and 20, first find the z-scores for 10 and 20.z-score for 10 = (10 - 15) / 4 = -1.25 z-score for 20 = (20 - 15) / 4 = 1.25 Using a standard normal distribution table, find the area between the z-scores of -1.25 and 1.25 Area = 0.7887 or 78.87%

Therefore, the percentage of all possible values of the variable that lie between 10 and 20 is 78.87%.b) To find the percentage of all possible values of the variable that exceed 22, first find the z-score for 22.z-score for 22 = (22 - 15) / 4 = 1.75 Using a standard normal distribution table, find the area to the right of the z-score of 1.75 Area = 0.0401 or 4.01%Therefore, the percentage of all possible values of the variable that exceed 22 is 4.01%.c) To find the percentage of all possible values of the variable that are less than 12, first find the z-score for 12.z-score for 12 = (12 - 15) / 4 = -0.75 Using a standard normal distribution table, find the area to the left of the z-score of -0.75 Area = 0.2266 or 22.66%Therefore, the percentage of all possible values of the variable that are less than 12 is 22.66%.

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To find the total number of minutes used, divide $175 by the $.25 per minute charge. This equals 650 minutes, meaning the user had used 650 minutes throughout the month.

$50 initial fee + $.25 per minute = $225

$225 - $50 = $175

$175 / $.25 = 650 minutes

The initial fee for the phone plan was $50, and for every minute used, an additional $.25 was charged. Last month's bill was $225, so subtracting the $50 initial fee from the total cost of the bill leaves $175, which is the cost of the minutes used. To find the total number of minutes used, divide $175 by the $.25 per minute charge. This equals 650 minutes.

The phone plan charges an initial fee of $50 for the month, as well as an additional $.25 for every minute used. Last month's bill was $225, so to find the total number of minutes used, subtract the $50 initial fee from the total cost of the bill. This results in $175, which is the cost of the minutes used. To find the total number of minutes used, divide $175 by the $.25 per minute charge. This equals 650 minutes, meaning the user had used 650 minutes throughout the month.

A user's phone plan last month costed $225, which included an initial fee of $50 plus $.25 for every minute used. After subtracting the initial fee from the total bill cost, $175 was left which was the cost of the minutes used. Dividing this number by the $.25 per minute charge reveals that the user had used 650 minutes.

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Answer:   84.5%

==========================================================

Work Shown:

A = area of the smaller square

A = (5.98)^2

A = 35.7604 square cm which is exact

B = area of the larger square

B = (15.2)^2

B = 231.04 square cm which is exact

C = the chances of landing in the smaller square

C = A/B

C = 35.7604/231.04

C = 0.15478012465373 which is approximate

C = 0.154780

D = the chances of landing in the blue region

D = 1 - C

D = 1 - 0.154780

D = 0.84522

D = 84.522%

D = 84.5%

Answer:

The answer is A) 4.84 cm :P

Step-by-step explanation:

Gwen wants to create a congruent shape, so, all the sides have to be the same size. And if its a pentagon like in your situation , a pentagon has 5 sides so you have to divide 24.2 cm because it's your regular pentagon by 5 (sides) (24.2 cm ÷ 5 sides = 4.84 cm )

I hope I helped you :P

Answer:

The answer is A.

Step-by-step explanation:

a) The standard error of the mean is 0.90

b) The marginal error is 1.76

Given,

Number of samples in the population, n = 60

Sample mean of the population, μ = 25

Standard deviation of the population, σ = 7

We have to find the standard error of the mean and the margin of error at 95% confidence.

Here,

a) The standard error of the mean = Standard deviation / root of sample

= σ / √n

= 7/√60

= 0.90

b) The margin error;

Zₐ/₂ ×  σ / √n

= Zₐ/₂ × 7/√60

= 1.96 × 0.90

= 1.76

Therefore,

a) The standard error of the mean is 0.90

b) The marginal error is 1.76

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Minimization of  f(x) = |x+3| + x^3 at the endpoints (-2 and 6)  the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}

within the given interval.

To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.

First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:

|x+3| =

x+3 if x+3 >= 0

-(x+3) if x+3 < 0

Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.

Case 1: x+3 >= 0

In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3

Case 2: x+3 < 0

In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3

Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.

Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.

Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.

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Given system is: dx1/dt = 2x1 + 2x2 + tdx2/dt = x1 + 3x2 - 2tNow we will use matrix notation, let X = [x1 x2] and A = [2 2; 1 3]. Then the given system can be written in the form of X' = AX + B, where B = [t - 2t] = [t, -2t].Now let D = |A - λI|, where λ is an eigenvalue of A and I is the identity matrix of order 2.

Then D = |(2 - λ) 2; 1 (3 - λ)|= (2 - λ)(3 - λ) - 2= λ² - 5λ + 4= (λ - 1)(λ - 4)Therefore, the eigenvalues of A are λ1 = 1 and λ2 = 4.Now let V1 and V2 be the eigenvectors of A corresponding to eigenvalues λ1 and λ2, respectively. Then AV1 = λ1V1 and AV2 = λ2V2. Therefore, V1 = [1 -1] and V2 = [2 1].Now let P = [V1 V2] = [1 2; -1 1]. Then the inverse of P is P⁻¹ = [1/3 2/3; -1/3 1/3]. Now we can find the matrix S(t) = e^(At) = P*diag(e^(λ1t), e^(λ2t))*P⁻¹, where diag is the diagonal matrix. Therefore,S(t) = [1 2; -1 1] * diag(e^(t), e^(4t)) * [1/3 2/3; -1/3 1/3])= [e^(t)/3 + 2e^(4t)/3, 2e^(t)/3 + e^(4t)/3; -e^(t)/3 + e^(4t)/3, -e^(t)/3 + e^(4t)/3].Now let Y = [y1 y2] = X - S(t).

Then the given system can be written in the form of Y' = AY, where A = [0 2; 1 1] and Y(0) = [x1(0) - (1/3)x2(0) - (e^t - e^4t)/3, x2(0) - (2/3)x1(0) - (2e^t - e^4t)/3].Now let λ1 and λ2 be the eigenvalues of A. Then D = |A - λI| = (λ - 1)(λ - 2). Therefore, the eigenvalues of A are λ1 = 1 and λ2 = 2.Now let V1 and V2 be the eigenvectors of A corresponding to eigenvalues λ1 and λ2, respectively.  Therefore, V1 = [1 -1] and V2 = [2 1].Now let P = [V1 V2] = [1 2; -1 1]. Then the inverse of P is P⁻¹ = [1/3 2/3; -1/3 1/3]. Now we can find the matrix Y(t) = e^(At) * Y(0) = P*diag(e^(λ1t), e^(λ2t))*P⁻¹ * Y(0), where diag is the diagonal matrix. Therefore,Y(t) = [1 2; -1 1] * diag(e^(t), e^(2t)) * [1/3 2/3; -1/3 1/3]) * [x1(0) - (1/3)x2(0) - (e^t - e^4t)/3, x2(0) - (2/3)x1(0) - (2e^t - e^4t)/3]= [(e^t + 2e^(2t))/3*x1(0) + (2e^t - e^(2t))/3*x2(0) + (e^t - e^4t)/3, -(e^t - 2e^(2t))/3*x1(0) + (e^t + e^(2t))/3*x2(0) + (2e^t - e^4t)/3].Therefore, the general solution of the system is X(t) = S(t) + Y(t), where S(t) = [e^(t)/3 + 2e^(4t)/3, 2e^(t)/3 + e^(4t)/3; -e^(t)/3 + e^(4t)/3, -e^(t)/3 + e^(4t)/3] and Y(t) = [(e^t + 2e^(2t))/3*x1(0) + (2e^t - e^(2t))/3*x2(0) + (e^t - e^4t)/3, -(e^t - 2e^(2t))/3*x1(0) + (e^t + e^(2t))/3*x2(0) + (2e^t - e^4t)/3].

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Answer:

-4.6 Repeating

Step-by-step explanation:

This will be a repeating Decimal. :)

Answer:

0.6666

Step-by-step explanation:

you divide 2 by three and then you get your answer

Answer:

Hey there the best answer would be A.=

Step-by-step explanation: