Write a quadratic equation with the given solutions.
13. 4 and -5
14.-6 and 0
15.3 and 8

a) To obtain the potential pressure drop in the wellbore, we can use the hydrostatic pressure equation.

The potential pressure drop is equal to the pressure gradient multiplied by the length of the wellbore. The pressure gradient can be calculated using the equation: Pressure gradient = (density of oil × acceleration due to gravity) × sin(θ), where θ is the deviation angle of the wellbore from horizontal flow. In this case, the pressure gradient would be (48 lbm/ft^3 × 32.2 ft/s^2) × sin(15°). Multiplying the pressure gradient by the wellbore length of 6,000 ft gives the potential pressure drop.

b) To determine the frictional pressure drop in the wellbore, we can use the Darcy-Weisbach equation. The Darcy-Weisbach equation states that the pressure drop is equal to the friction factor multiplied by the pipe length, density, squared velocity, and divided by the pipe diameter. However, to calculate the friction factor, we need the Reynolds number. The Reynolds number can be calculated as (density × velocity × diameter) divided by the oil viscosity. Once the Reynolds number is known, the friction factor can be determined. Finally, using the friction factor, we can calculate the frictional pressure drop.

c) To calculate the in-situ oil velocity, we need to consider the total volume of the pipe, including both oil and gas. The total pipe volume is calculated as the pipe cross-sectional area multiplied by the wellbore length. Subtracting the gas volume from the total volume gives the oil volume. Dividing the oil volume by the total time taken by the oil to flow through the pipe (converted to seconds) gives the average oil velocity.

d) The flow regime of the two-phase flow can be determined based on the oil and gas mixture properties and flow conditions. Common flow regimes include bubble flow, slug flow, annular flow, and mist flow. These regimes are characterized by different distribution and interaction of the oil and gas phases. To determine the specific flow regime, various parameters such as gas and liquid velocities, mixture density, viscosity, and surface tension need to be considered. Additional information would be required to accurately determine the flow regime in this scenario.

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To determine the appropriate sample size for estimating the true average time to within 5 minutes with a 95% confidence level, we can use the formula for sample size calculation in estimating the mean.

The formula is given by:

n = (Z * σ / E)²

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of approximately 1.96)

σ = standard deviation of the distribution (unknown in this case)

E = maximum error or margin of error (in this case, 5 minutes)

Since the standard deviation (σ) is unknown, we can use a conservative estimate by assuming the worst-case scenario, which is σ = (440 - 320) / 6, where (440 - 320) is the range of the distribution and 6 is a rough approximation of the standard deviation.

Substituting the values into the formula:

n = (1.96 * (440 - 320) / 6 / 5)²

n ≈ 4.83²

n ≈ 23.33

Rounding up to the nearest whole number, the appropriate sample size for estimating the true average time within 5 minutes with a 95% confidence level is 24.

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Answer:

Based on the information given the rate of return is 10.8%.

First step is to find the shares of stock price:

Shares of stock price=25 shares×$30/share

Shares of stock price= $750

Second step is to calculate the total sold price:

Total sold price= $825+$6

Total sold price= $831

Third step is to calculate the Rate of return:

Rate of return=$831-750/$750×100

Rate of return=$81/$750×100

Rate of return=10.8%

Inconclusion the rate of return is 10.8%.

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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Answer: 37°

Step-by-step explanation:

The solution to the linear system of equation is x = 3, y = 5, and z = -0.5

A system of linear equations is a set of linear equations that involve the same variable and which work or are operated (simultaneously) together

The system of linear equation is presented as follows;

2·x - 3·y + 6·z = -12...(1)

5·x + 2·y - 8·z = 29...(2)

7·x + 6·y + 4·z = 49...(3)

Multiplying equation (1) by 5 and equation (2) by 2, we get;

5 × Equation (1) ⇒ 10·x - 15·y + 30·z = -60...(4)

2 × Equation (2) ⇒ 10·x + 4·y - 16·z = 58...(5)

Subtract equation (4) from equation (5), to get;

10·x - 10·x + 4·y - (-15·y) - 16·y - 30·z = 58 - (-60) = 118

19·y - 46·z = 118...(6)

Multiplying equation (1) by 7 and equation (3) by 2, we get;

7 × Equation (1) ⇒ 14·x - 21·y + 42·z = -84...(7)

2 × Equation (3) ⇒ 14·x + 12·y + 8·z = 98...(8)

Subtracting equation (7) from equation (8), we get;

14·x - 14·x + 12·y - (-21·y) + 8·z - 42·z = 98 - (-84) = 182

33·y - 34·z = 182...(9)

Multiplying equation (6) by 33 and equation (9) by 19, we get;

627·y - 1,518·z = 3,894...(10)

627·y - 646·z = 3,458...(11)

Subtracting equation (10) from equation (11), we get;

627·y - 627·y -646·z - (-1,518·z) = 3,458 - 3,894 = -436

872·z = -436

z = -436 ÷ 872 = -0.5

z = -0.5

From equation (6), we have;

19·y - 46·z = 118

19·y - 46 × (-0.5) = 118

19·y - 46 × (-0.5) = 118

19·y = 118  + 46 × (-0.5) = 95

y = 95 ÷ 19 = 5

y = 5

From equation (1), we get;

2·x - 3·y + 6·z = -12

2·x - 3 × 5 + 6 × (-0.5) = -12

2·x = -12 + 3 × 5 - 6 × (-0.5) = 6

x = 6 ÷ 2 = 3

x = 3

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Answer:

10

Step-by-step explanation:

Answer:

10 km

Step-by-step explanation:

total no of km covered=400

total no of trips=40

distance in each trip= 400/40

=10km

Answer:B

Step-by-step explanation:

it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

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Answer:

5,6,8,11,15,20,26,33

Step-by-step explanation:

I THINK IM NOT SURE

Answer:

14 is the rate of change; he can harvest 14 acres per day

Step-by-step explanation:

Here the equation is

Compare to slope intercept form

We get

As its rate of change so it must be price of milk change

The equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100. Option C is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Amount of ammonia in the solution 16%  x 22 gallons  =  3.52 gallons

The proportion of ammonia remains the same as the water evaporates, but the total composition of the solution is decreased by the amount of water that evaporates.

Quantity of ammonia = 3.52 gallons

Quantity of water after evaporation = 22 - n

Composition of ammonia after evaporation of water, 24% = 24/100

Now the percentage of ammonia after evaporates
Quantity of ammonia / Remaining water = 24%
3.52 / (22 - n) = 24 / 100

Thus, the equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100.

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Answer:

1 7/10

Step-by-step explanation:

3 1/2 - 1 4/5 = ?

3 5/10 - 1 8/10 = ?

2 5/10 - 8/10 = ?

1 15/10 - 8/10 = 1 7/10

The solution to the questions posed are :

Percentage = (887 / 1135) * 100

Calculating this expression gives us:

Percentage ≈ 78.06%

Percentage = (1135 / 887) * 100

Calculating this expression:

Percentage ≈ 128.02

Percentage increase = ((2001 value - 2000 value) / 2000 value) * 100

Let's calculate it:

Percentage increase = ((1135 - 887) / 887) * 100

= (248 / 887) * 100

= 0.2798 * 100

Therefore, homicide rate increased by about 28% between 2000 and 2001.

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There are 6 different ways to set up the tournament.

We can make two pairs of teams (a,b and c,d) and then arrange each pair in two different ways (ab, cd and cd, ab). Thus, there are a total of 6 combinations.

(b) There are 8 different outcomes for this tournament. Each pair of teams (a,b and c,d) can play in either the first or second round, and each team can either win or lose. We can calculate the number of outcomes by multiplying the different combinations of the first round (6) with the number of outcomes in the second round (2x2). Therefore, total number of outcomes = 6x2x2 = 8.

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The function y = (x - 4)^2 is not a one-to-one function. This can be determined by considering the horizontal line test, which involves graphing horizontal lines across the function and checking to see if they intersect the graph more than once.

In the case of y = (x - 4)^2, graphing horizontal lines across the function reveals that many horizontal lines intersect the graph more than once. Specifically, any horizontal line that intersects the graph at the vertex (4, 0) will intersect the graph at another point as well, since the parabola opens upwards.

If any horizontal line intersects the graph at more than one point, then the function is not one-to-one. Therefore, the function y = (x - 4)^2 is not a one-to-one function.

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The required area of the circle is 50.24cm².

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, we have the circumference:

8π

Now, calculate for π as follows using the circumference formula (2πr):

8π = 2πr

8π/2π = r

4 = r

Now, calculate the area when r = 4cm (πr²) as follows:

πr²

π(4)²

16π

50.24

Therefore, the required area of the circle is 50.24cm².

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Complete question:
The circumference of a circle is 8π cm. what is the area in square centimeters?

The given linear programming problem is: Maximize: z=15x+7y subject to: 7x+4y≤28, 10x+y≤28, x≥0,y≥0

To maximize the above objective function z=15x+7y subject to the constraints:

7x + 4y ≤ 28 ...................(1)

10x + y ≤ 28 ...................(2)

x ≥ 0, y ≥ 0.

First, plot the lines: 7x + 4y = 28 ...................(1)

10x + y = 28 ...................(2)

Find the corner points A, B, C, and D as shown in the figure by solving the pairs of equations which represent the lines of the constraints: Corner points: A(0, 0), B(0, 7), C(4, 4), D(2, 6)

We have to check which of these points maximizes the objective function z=15x+7y. Therefore, substitute each of the corner points in the given objective function to find the maximum value of z. Corner point A(0, 0): z = 15x + 7y = 15(0) + 7(0) = 0

Corner point B(0, 7): z = 15x + 7y = 15(0) + 7(7) = 49

Corner point C(4, 4): z = 15x + 7y = 15(4) + 7(4) = 68

Corner point D(2, 6): z = 15x + 7y = 15(2) + 7(6) = 72

Thus, the maximum value of z = 72 is obtained at the corner point D(2, 6). The given linear programming problem is: Maximize: z=13x+8y subject to: 8x+6y≤48, 13x+y≤48, x≥0,y≥0

To maximize the above objective function z=13x+8y subject to the constraints: 8x + 6y ≤ 48 ...................(1)

13x + y ≤ 48 ...................(2)

x ≥ 0, y ≥ 0

First, plot the lines: 8x + 6y = 48 ...................(1)

13x + y = 48 ...................(2)

Find the corner points A, B, C, and D as shown in the figure by solving the pairs of equations which represent the lines of the constraints: Corner points: A(0, 0), B(0, 8), C(3.69, 3.23), D(3.08, 3.69)

We have to check which of these points maximizes the objective function z=13x+8y. Therefore, substitute each of the corner points in the given objective function to find the maximum value of z.

Corner point A(0, 0): z = 13x + 8y = 13(0) + 8(0) = 0

Corner point B(0, 8): z = 13x + 8y = 13(0) + 8(8) = 64

Corner point C(3.69, 3.23): z = 13x + 8y = 13(3.69) + 8(3.23) ≈ 54.47

Corner point D(3.08, 3.69): z = 13x + 8y = 13(3.08) + 8(3.69) ≈ 53.23. Thus, the maximum value of z ≈ 54.47 is obtained at the corner point C(3.69, 3.23).

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The measure of the missing length is 32

To determine the value of the missing side of the triangle, we need to know the Pythagorean theorem

The Pythagorean theorem is a mathematical theorem stating that the square of the longest side of a given triangle is equal to the sum of the squares of the other two sides of the triangle

From the information given, we have that;

40² = x² + 24²

Collect the like terms, we have;

40²- 24² = x²

Find the square values, we have;

x² = 1600 - 576

subtract the values, we get;

x² = 1024

Find the square root of both sides, we have;

x = √1024

x = 32

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The most the salon would be willing to pay that groomer is $25×4 = $100.

The unitary method is a technique that determines the worth of a single unit from value of multiple units, as well as the quality of multiple units from value of a single unit.

Some key features regarding the unitary method are-

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Answer:

(2) The statement is true.

-1 < r < 1

For the Binomial(5, 0.4) distribution and the Binomial(5, 0.6) distribution, we can observe that as the probability of success increases, the probability of getting a higher number of successes in a certain number of trials increases and the probability of getting a lower number of successes decreases.

To find the relationship between the Binomial(5, 0.4) distribution and the Binomial(5, 0.6) distribution, follow these steps:

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The expression that is equivalent to (4mn/m^-2n^6)^-2 is \(\frac{n^{10}}{16m^{6}}\)

The expression is given as:

(4mn/m^-2n^6)^-2

Apply the law of indices

\((4m^{1 + 2}n^{1-6})^{-2\)

Evaluate the sum and the differences

\((4m^{3}n^{-5})^{-2\)

Apply the negative exponent

\(\frac{1}{16m^{2*3}}}n^{5*2}\)

Evaluate

\(\frac{1}{16m^{6}}n^{10}\)

Rewrite as:

\(\frac{n^{10}}{16m^{6}}\)

Hence, the expression that is equivalent to (4mn/m^-2n^6)^-2 is \(\frac{n^{10}}{16m^{6}}\)

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the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

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Answer:

A) The wall is larger than you, so no force is exerted

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

vertex = -4

The three segments cannot form a triangle as their lengths are 4, 9, 15, 1, and 9. This is because the sum of any two of the segments’ lengths must be greater than the length of the third segment for a triangle to be formed.

The sum of any two of the segments must be greater than the third segment's length in order to form a triangle. 4 + 9 = 13, which is less than 15, so this cannot form a triangle. 9 + 15 = 24, which is also less than 1, so this cannot form a triangle either. Lastly, 15 + 1 = 16, which is less than 9, so this cannot form a triangle either. Therefore, these three segments cannot be used to form a triangle.In order for three segments to form a triangle, the sum of any two of the segments must be greater than the length of the third segment. In this case, the lengths of the three segments are 4, 9, 15, 1, and 9. If we take the sum of any two of the segments, we find that 4 + 9 = 13, which is less than 15. We also find that 9 + 15 = 24, which is less than 1, and 15 + 1 = 16, which is less than 9. Therefore, these three segments cannot form a triangle as they do not meet the criteria of having the sum of any two of the segments greater than the third segment. This is why these three segments cannot be used to form a triangle.

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Answer:

Step-by-step explanation: a) S = (50:360) × 0.5×3² = 0.625

b) (80:360) × 0.5×5² = \(\frac{25}{9}\)

Answer:

13 blocks per hour

Step-by-step explanation:

52/4=13

hope this is helpful

Answer:

13 blocks per hour

Step-by-step explanation:

52/4 = 13

He was walking really slow apparently