4. materials science a machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 inches. a bearing is acceptable if its diameter is within 0.004 inches of this target value. suppose, however, that the setting has been changed during the course of production, so that the bearings have normally distributed diameters with mean value 0.499 inches and standard deviation 0.002 inches. what percentage of the bearings produced will not be acceptable?

The pοssible dimensiοns (length and width) οf the rectangular plοt are:

Length = 21 meters, width = 8.05 meters

Length = 8.05 meters, width = 21 meters

Let the length οf the rectangular plοt be L and the width be W. Then we knοw that the perimeter οf the rectangular plοt, which is equal tο the length οf fencing Baο has, is given by:

2L + W = 39

Alsο, the area οf the rectangular plοt is given by:

L × W = 169

We can use these twο equatiοns tο sοlve fοr L and W. First, we can sοlve the equatiοn 2L + W = 39 fοr W:

W = 39 - 2L

Substituting this into the equation for the area, we get:

L × (39 - 2L) = 169

Expanding and rearranging this equation, we get a quadratic equation in terms of L:

[tex]-2L^2 + 39L - 169 = 0[/tex]

We can solve for L using the quadratic formula:

[tex]L = [ -39 \± sqrt(39^2 - 4(-2)(-169)) ] / (2(-2))\\L = [ -39 \± sqrt(1681) ] / 4\\L = [ -39 \± 41 ] / 4[/tex]

L = 1/2 or L = 21

If L = 1/2, then W = 38, which gives a negative area and is therefore not possible.

If L = 21, then W = 169/21, which simplifies to W = 8.05 (rounded to two decimal places).

Therefore, the possible dimensions (length and width) of the rectangular plot are:

Length = 21 meters, width = 8.05 meters

Length = 8.05 meters, width = 21 meters

Note that these are the only possible dimensions, as the sum of the length and width must be less than or equal to 19.5 meters (half of the available fencing).

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the range of the function is at least $400 plus $50 for each month after the purchase. The average monthly cost of owning the cell phone can be represented as:

C(t) = 400 + 50t

Where t is the number of months after the purchase.

Since C(t) is a linear function, its range is all real numbers greater than or equal to 400, since the initial cost of the phone is 400 and the monthly cost is a positive constant. Therefore, the range of C(t) is:

Range of C(t) = {C(t) | C(t) ≥ 400} or [400, ∞)

In other words, the range of the function is all possible average monthly costs of owning the phone, which is at least $400 plus $50 for each month after the purchase.

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Suppose that IQ scores have a bell-shaped distribution with a mean of 96 and a standard deviation of 17. Using the empirical rule, 15.87 percentage of IQ scores are less than 79.

The empirical rule says that for a normal distribution, almost all of the data will fall within three standard deviations of the mean.

Specifically:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Almost all (99.7%) of the data falls within three standard deviations of the mean.
Given that the mean of IQ scores is 96 and the standard deviation is 17.

Hence the Z score can be calculated as
z=(x−μ)/σ=(79−96)/17=−1
From the standard normal distribution table, the percentage of the data that is less than z = -1 is 15.87%.
Hence the percentage of IQ scores that are less than 79 is approximately 15.87%.

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Answer:

The 99% confidence interval will be wider than the 95% confidence interval because it encompasses a greater range of possible values, meaning that there is a lower chance of the true population parameter falling outside the interval. The 95% confidence interval means that if the study was repeated many times, 95% of the intervals constructed would contain the true population parameter, whereas the 99% confidence interval means that 99% of the intervals constructed would contain the true population parameter.

Step-by-step explanation:

I'm sorry, 35 is not a measure of angle and therefore cannot be rounded to the nearest degree. Are you asking for the sine, cosine, or tangent of 35 degrees?

Answer:

Step-by-step explanation:

3x^16

Answer:

3x^16

Step-by-step explanation:

Stephen Dubner and Steven Levitt are the authors of the essay, and as they develop their essay, they use a great deal of quantification.

The following are three specific examples that they used: They write, "If a martini is made with 4 ounces of gin, that’s 2.8 standard drinks. "They also said, "Let's consider the five most unsafe hours for driving, which are Saturday and Sunday mornings from 1 am to 6 am. In the middle of this time period, 3 am on Saturday morning, the likelihood of an accident is three times higher than at noon on a weekday. "In another instance, they note that "The average person who has been murdered has approximately 300 friends and relatives, which means that a homicide victim’s personal network is quite extensive. "The authors use these specific numbers to make their argument more convincing. Using quantification provides an air of authority to the author's claims. By providing specifics, the author can communicate more information than would otherwise be possible.

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The standard deviation for a chi square distribution for given degree of freedom is 7.0711.

The chi-square distribution is parameterized by the number of degrees of freedom (df). As the number of degrees of freedom increases, the shape of the distribution becomes more symmetrical and approaches a normal distribution.

The standard deviation (σ) of a chi-square distribution with k degrees of freedom is given by the formula:

σ = sqrt(2k)

Therefore, for a chi-square distribution with 25 degrees of freedom:

σ = sqrt(2(25)) = sqrt(50) ≈ 7.0711

Rounding this to four decimal places gives a standard deviation of approximately 7.0711.

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The value of the constant C is 3/4.

Probability is a branch of mathematics that deals with the likelihood or chance of an event occurring. It is a measure of the likelihood that a specific event will occur, expressed as a value between 0 and 1

The sum of the probabilities for all possible values of X should equal 1

P(1) + P(2) + P(3) + P(4) = 1

Substituting the given values, we get:

C/4 + 1/2 + 1/8 + C/4 = 1

Simplifying the equation, we get:

C/2 + 5/8 = 1

Move 5/8 to right hand side of the equation

C/2 = 3/8

C = (3/8) x 2

C = 3/4

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In response to the stated question, we may state that therefore, the expressions value of vector will be n = 25.73.

An expression in mathematics is a collection of numbers, variables, and mathematical (such as addition, reduction, multiplication, division, exponentiation, etc.) that express a quantity or value. Expressions might be as basic as "3 + 4" or as complicated as "(3x2 - 2) / (x + 1)". They may also contain functions like "sin(x)" or "log(y)". Expressions can also be evaluated by substituting values for the variables and performing the mathematical operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

to find vector and magnitude we have

[tex]n^2 = (22.5)^2 + (12.5)^2\\n^2 = 506.25 + 156.25\\n^2 = 662.5\\n = \sqrt(662.5)\\n = 25.73[/tex]

therefore, the value of vector will be n = 25.73.

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Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.

To calculate how much money Mr. Kha Lipat should invest today to receive $400.00 one year from now at an 8% interest rate, we can use the formula for calculating simple interest though compound intrest:

I = P * r * t

where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate (as a decimal), and t is the time period (in years).

We know that Mr. Kha Lipat wants to earn $400.00 in interest, the interest rate is 8% or 0.08 (as a decimal), and the time period is 1 year. We can plug these values into the formula and solve for P:

I = P * r * t

400 = P * 0.08 * 1

400 = 0.08P

P = 400 / 0.08

P = 5000

Therefore, Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.

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Answer: 28x+8y+2

Step-by-step explanation:

Remove parentheses: -2(14x-4y-1)

Solution: 28x+8y+2

Answer:

28x+8y+2

Step-by-step explanation:

The value of x that makes the given image to be a rectangle is: x = 2.5

The length of the diagonals of a rectangle are equal and congruent to each other. It is also pertinent to note that the diagonals of a rectangle bisect each other at the center. Thus:

From the given parameters, we see that half of the diagonals have been labelled and as such we have:

8x - 3 = 4x + 7

Rearrange to have like terms on same side and so we have:

8x - 4x = 7 + 3

4x = 10

x = 10/4

x = 2.5

Thus, the value of x from the calculation above of the rectangle is 2.5

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The solution of the match is

(1) Orthocenter          (C) The point at which the altitudes of a triangle                                                

                                              meet.

(2) Centroid                 (D) The point at which the medians of a triangle

                                             meet.

(3) Circumcenter         (A) The point of intersection of the perpendicular                  

                                             bisectors of the sides of a triangle.

(4) Incentre                 (B) The point at which the three angle bisectors      

                                             of a triangle meet.

The orthocenter of a triangle is the point where the altitudes of the triangle intersect. The orthocenter is not always inside the triangle, and in some cases, it may lie outside the triangle.

The centroid of a triangle is the point where the three medians of the triangle intersect. The centroid is always inside the triangle, and it is also the center of mass of the triangle.

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect.  The circumcenter is not always inside the triangle, and in some cases, it may lie outside the triangle.

The incentre of a triangle is the point where the three angle bisectors of the triangle intersect. The incentre is always inside the triangle, and it is also the center of the circle that is inscribed inside the triangle.

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Complete Question:

Match the following.

(1) Orthocenter         (A) The point of intersection of the perpendicular                  

                                             bisectors of the sides of a triangle.

(2) Centroid                 (B) The point at which the three angle bisectors of

                                             a triangle meet.

(3) Circumcenter         (C) The point at which the altitudes of a triangle

                                              meet.

(4) Incentre                 (D) The point at which the medians of a triangle

                                             meet.

The final equation of motion for the system is: x(t) = [(8v0 - 2x0)/6]*[tex]e^{(-2t)} + [(2x0 - 8v0)/6]*e^{(-8t).[/tex]

To determine the initial conditions and equations of motion, we can use the following steps:

Write down the equation of motion for the system. The equation of motion for a mass-spring-damper system is given by:

m * [tex]d^2x/dt^2[/tex] + c * dx/dt + k * x = 0

where m is the mass, c is the damping coefficient, k is the spring constant, x is the displacement from the equilibrium position, and t is time.

In this case, the mass is 1 kg, the spring constant is 16 N/m, and the damping coefficient is 10 times the instantaneous velocity, or 10 * dx/dt.

Substituting these values into the equation of motion, we get:

1 * [tex]d^2x/dt^2[/tex] + 10 * dx/dt + 16 * x = 0

Determine the initial conditions. The initial conditions refer to the position and velocity of the mass at time t = 0.

Let x(0) be the initial displacement of the mass from the equilibrium position, and let v(0) be the initial velocity of the mass. Then the initial conditions are:

x(0) = ?

v(0) = ?

These values are typically given in the problem statement.

Solve the differential equation. To solve the differential equation, we can use the characteristic equation method. First, we assume that the displacement of the mass is of the form:

x(t) = A[tex]e^{(rt)[/tex]

where A and r are constants to be determined.

Taking the first and second derivatives of x(t), we get:

dx/dt = Are^(rt)

d^2x/dt^2 = Ar^2*e^(rt)

Substituting these expressions into the equation of motion, we get:

A * ([tex]r^2[/tex] + 10r + 16) * [tex]e^{(rt)[/tex]= 0

Since [tex]e^{(rt)[/tex]is never zero, we can divide both sides by it and simplify to obtain the characteristic equation:

[tex]r^2 + 10r + 16 = 0[/tex]

Solving for r using the quadratic formula, we get:

r1 = -2

r2 = -8

Therefore, the general solution for the displacement of the mass is:

[tex]x(t) = Ae^{(-2t)} + Be^{(-8t)[/tex]

where A and B are constants determined by the initial conditions.

To find A and B, we use the initial conditions x(0) = x0 and v(0) = v0. Taking the derivative of x(t) and setting t = 0, we get:

v(0) = -2A - 8B

Using the second initial condition, we get:

x(0) = A + B = x0

Solving for A and B, we get:

A = (8v0 - 2x0)/6

B = (2x0 - 8v0)/6

Therefore, the final equation of motion for the system is:

[tex]x(t) = [(8v0 - 2x0)/6]*e^{(-2t)} + [(2x0 - 8v0)/6]*e^{(-8t)[/tex]

Complete question: A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. Determine the equations of motion if (a) the mass is initially released from rest from a point 1 meter below the equilibrium position, and then (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s.

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The statement that best describes the use of spaces in folders and files names in ArcGIS is "Using spaces in folder and file names in ArcGIS is permitted but strongly discouraged."

ArcGIS is a geographic information system software that is used for creating, editing, analyzing, and sharing spatial data. The software is widely used by GIS professionals, environmental scientists, geographers, and other experts to manage and analyze spatial data.

In ArcGIS, it is possible to use spaces in folder and file names, but it is not recommended. This is because spaces can cause problems when the software tries to access files with spaces in their names. Therefore, it is better to use underscores or hyphens instead of spaces when naming folders and files in ArcGIS. This helps to avoid issues when working with data in ArcGIS.
The statement "Using spaces in folder names in ArcGIS is permitted but strongly discouraged" is the best description of the use of spaces in folder and file names in ArcGIS.

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The decrease in the time spent exercising is 0.74.

A scatter plot is a type of data visualization that is used to display the relationship between two continuous variables. It consists of a set of data points, each representing an observation, plotted as a point on a two-dimensional graph with one variable on the x-axis and the other variable on the y-axis.

Scatter plots are often used to identify patterns or relationships between two variables, such as correlation or causation. If the points on the plot tend to form a pattern, such as a straight line, then there may be a relationship between the two variables. If the points do not form a pattern, then there may be no relationship between the two variables.

The answers are quite straightforward.

(a) Here, we substitute x=4

(b) Again, we substitute x= 0

(c) Here, if y1=y2-y1= (-0.74x- 0.74+8.54)-(-0.74x + 8.54)= y2-y1= -0.74x- 0.74+8.54 + 0.74x + 8.54= y2- y1= 0.74.

Thus, the decrease in the time spent exercising is 0.74.

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The complete question is

The probability P(Xˉ−2<114<Xˉ+2) is approximately 0.95. (Option 3)

We know that the population mean is 114 and the standard deviation is 6. We also know that the sample size is 36, which is large enough to apply the central limit theorem. Thus, the distribution of sample means follows a normal distribution with a mean of 114 and a standard deviation of 6/√36=1.

Now, we need to calculate the z-score for the lower and upper bound of the inequality.

z1=(114-2-114)/1=-2

z2=(114+2-114)/1=2

Using a standard normal distribution table, we can find that the area to the left of -2 is 0.0228 and the area to the left of 2 is 0.9772. Thus, the area between -2 and 2 is approximately 0.9772-0.0228=0.9544, which is approximately 0.95.

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Complete Question:

In 2022, NBA teams score 114 points per game on average with a standard deviation of 6 points per game. Suppose that we randomly sample 36 NBA scores from this season and consider the sample mean (

Xˉ ); the average points per game scored in this sample.

Calculate P( Xˉ 2<114< Xˉ +2)

Answer: 5 Gallons of gas

Step-by-step explanation: Start with 9, and subtract that by how much he lost within those two hours (2t = 2(2) = 4, 9 - 4 = 5)

After driving for 2 hours, Brody would have 5 gallons of gas left in the tank. The formula to find gas left after tt hours is gas left = 9 - 2tt.

To find out how much gas would be in Brody's tank after driving for 2 hours, we need to subtract the amount of gas used in 2 hours from the initial amount of gas in the tank. Each hour, Brody's car uses up 2 gallons of gas, so in 2 hours it would use up 2 x 2 = 4 gallons. Therefore, after driving for 2 hours, Brody would have 9 - 4 = 5 gallons of gas left in the tank.

To find out how much gas would be left after tt hours, we can use the formula: gas left = initial gas - gas used in tt hours. In this case, initial gas is 9 gallons, and gas used in tt hours is 2 x tt gallons. So the formula becomes: gas left = 9 - 2tt.

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Answer:

a)

[tex]y = - \frac{1}{2} x - 1[/tex]

b)

[tex]2x - y = - 9[/tex]

Step-by-step explanation:

a)

[tex]m = \frac{3 - ( - 7)}{ - 8 - 12} = \frac{10}{ - 20} = - \frac{1}{2} [/tex]

[tex] - 7 = - \frac{1}{2} (12) + b[/tex]

[tex] - 7 = - 6 + b[/tex]

[tex]b = - 1[/tex]

[tex]y = - \frac{1}{2} x - 1[/tex]

b) Slopes of perpendicular lines are negative reciprocals of each other, so if the original line has slope -1/2, the perpendicular line will have a slope of 2.

[tex]5x - 6y + 54 = 0[/tex]

[tex]5x - 6y = - 54[/tex]

We see that the y-intercept of this line is at (0, 9), so in slope-intercept form, we have

[tex]y = 2x + 9[/tex]

Putting this in standard form:

[tex] - 2x + y = 9[/tex]

[tex]2x - y = - 9[/tex]

The probability of drawing an ace and a queen from a pack of cards without replacement is 1/78. This can be explained as follows:

In a standard pack of 52 cards, there are 4 aces and 4 queens. When two cards are drawn without replacement, the probability of drawing an ace and then a queen is 4/52 x 3/51 = 12/2652. This can be simplified to 1/78.

Without replacement means that the card that is drawn is not replaced in the deck before the next card is drawn. In this case, when the first card is an ace, there are only 3 queens left in the deck so the probability of the second card being a queen is 3/51.

To put it another way, the chances of drawing an ace and a queen when the cards are drawn without replacement can be thought of as a ratio of the favorable outcomes to the total number of possible outcomes. There is only one favorable outcome (ace-queen) out of a total of 78 possible outcomes (4 aces and 4 queens combined with the remaining 44 cards). Thus, the probability of drawing an ace and a queen is 1/78.

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Solution: x + 12

Step-by-step explanation:

first simplify then distribute!

Answer:x+12

Step-by-step explanation:

we have to multiply number outside of brackets to each of the numbers inside it:

2(2x+5)=4x+10

-(3x-2)=-1(3x-2)=-3x+2

4x+10-3x+2=x+12

The data shown in the dot plots above doesn't support Merrell's claim that he randomly assigned rats to treatment groups. It doesn't support it because the dot plots are not similarly distributed.

There are a few discrepancies in the data that are not possible if rats were randomly assigned to treatment groups.

Difference between the two dot plots:

There is a noticeable difference between the two dot plots.

The dot plot on the left shows that most rats in Group 1 weigh between 200 and 240 grams.

On the other hand, in Group 2, most rats weigh between 240 and 280 grams.

The two groups' data are not similarly distributed, and there is an overlap in the weight of rats in the two groups. Furthermore, the data suggests that heavier rats were placed in Group 2 while lighter rats were placed in Group 1.

This difference implies that rats were not randomly assigned to treatment groups.

Other information should be considered:

The information shown in the dot plots alone is not enough to conclude that the rats were not randomly assigned to treatment groups.

We must investigate further and gather more information to confirm our assumptions about the rats' treatment groups. Randomization guarantees that each rat has an equal probability of being assigned to a treatment group.

The two groups must be equivalent in every aspect except for the treatment they get.

Therefore, it's essential to confirm that there was no selection bias in the rat selection process.

This means that rats were picked randomly from a large population, and no specific rat characteristics influenced the selection process.

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Answer:

The probability of selecting a number at random from the sample space {1, 2, 3, 4, 5, 6, 7, 8} that is positive is:

There are 8 possible outcomes in the sample space, and 4 of them are positive (1, 2, 3, 4).

Therefore, P(the number is positive) = 4/8 = 1/2 = 0.5

The probability of selecting a number at random from the sample space {1, 2, 3, 4, 5, 6, 7, 8} that is even is:

There are 8 possible outcomes in the sample space, and 4 of them are even (2, 4, 6, 8).

Therefore, P(the number is even) = 4/8 = 1/2 = 0.5

So the probability of selecting a number at random from the sample space {1, 2, 3, 4, 5, 6, 7, 8} that is positive is 0.5 and the probability of selecting a number at random from the same sample space that is even is also 0.5.

Answer:

The last option.

Adding their polynomials together results in a polynomial with degree 7, but subtracting one polynomial from the other results in a polynomial with degree 5.

Step-by-step explanation:

Both polynomials are of degree 7.

The 7th degree terms are both x^7.

When you add the polynomials, the x^7 term of one polynomial will be added to the x^7 term of the other polynomial resulting in 2x^7. The sum of the polynomials is also of degree 7.

When  you subtract the polynomials, the x^7 term of one polynomial subtracted from the other x^7 term of the other polynomial will eliminate the x^7 terms. The difference of the polynomials will have a 3x^5 or a -3x^5 term resulting in a 5ht degree polynomial.

Answer: The last option.

Answer:

1/20

Step-by-step explanation:

because you turn the denominators to 40, then subtract walk from run and you got your answer

The resultant vector is 7 units to the left and 5 units down. As a result, graphs option (c) a vector pointing to the left 7 units and down 5 units is the correct answer.

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle

We can add vectors geometrically by setting the starting point of the second vector at the terminal point of the first vector and drawing a vector from the first vector's initial point to the second vector's terminal point.

Next we align the starting point of vector v with the terminal point of vector u and draw a vector from the initial point of vector u to the terminal point of vector v:

The resultant vector is 7 units to the left and 5 units down. As a result, option (c) a vector pointing to the left 7 units and down 5 units is the correct answer.

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[tex]y=\frac{7}{2.4} x-6[/tex] ; if estimated then : [tex]y=\frac{7}{2.5} x-6[/tex]

Explination:

Y-intercept is -6, (0,-6)

The rise over run it [tex]\frac{7}{2.4} x[/tex]. The denominator is 2.4 because it nearly 2.5.

The two numbers in the system of equation is 5 and 13.

A group of multiple-variable equations that must all be solved concurrently make up a system of equations. Finding values for the variables that satisfy every equation in a system of equations is the objective. Each equation in the system reflects a connection between the variables. In order to find a singular solution or a group of solutions, systems of equations can be solved using a variety of methods, such as substitution or elimination. In many disciplines, including mathematics, physics, engineering, and economics, systems of equations can occur.

Let us suppose the two numbers as x and y.

x + y = 18

x - y = -8

The second equation can be written as:

x + 8 = y

Substitute the value of y in equation 1:

x + x + 8 = 18

2x = 10

x = 5

Substitute the value of x to get y:

x + y = 18

5 + y = 18

y = 13

Hence, the two numbers in the system of equation is 5 and 13.

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To maximize the area of a rectangular field with one side along a stream using 1100 feet of fencing, the dimensions should be 183.33 feet by 550 feet.

Let's call the length of the field that runs parallel to the stream "x" and the width of the field that runs perpendicular to the stream "y".

The total amount of fencing that the farmer has available is 1100 feet, and we know that three sides of the rectangular field will be fenced. Since one side of the field is already bordered by the stream and does not require fencing, we can set up the following equation:

2x + y = 1100 - x

Simplifying this equation, we get:

3x + y = 1100

We want to maximize the area of the field, which is given by the formula:

A = xy

We can use the equation we derived earlier to solve for y in terms of x:

y = 1100 - 3x

Substituting this into the area formula, we get:

A = x(1100 - 3x)

Expanding the parentheses, we get:

A = 1100x - 3x^2

To find the maximum area, we need to find the value of x that maximizes this equation. We can do this by taking the derivative of A with respect to x and setting it equal to zero:

dA/dx = 1100 - 6x = 0

Solving for x, we get:

x = 183.33 feet

We can use this value of x to find the corresponding value of y:

y = 1100 - 3x = 550 feet

Therefore, the dimensions of the rectangular field that maximize the area are 183.33 feet by 550 feet.

To know more about maximize the area:

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