A high school soccer team is going to Columbus, Ohio to see a professional soccer game. A coordinate grid is superimposed on a highway map of Ohio. The high school is at point (2, 5) and the stadium in Columbus is at point (8, 13). The map shows a highway rest stop halfway between the cities. What is the distance between the high school and the stadium? (One unit = 8.6 miles.)

The equation of circle for both the parts will be as,

(a)  (x-3)² +(y-2)²= 4

(b)   x²+y² = 1

What is circle?

A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.

Main Body:

(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.

 Circle centered at (h, k) with radius r:

 (x -h)² +(y -k)² = r²

The given circle is ...

 (x -2)² +(y -2)² =2²

 (x -2)² +(y -2)² = 4

__

(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:

x²+y² = 1

Hence the equation of circle is such.

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Answer:

p=8

Step-by-step explanation:

y= -5x + b

( -7) = -5(5) + b

-7= -25+b

add 25 both sides

-7+25=-25+25+b

18=b

y= -5x+18

p=-5(2)+18

p=8

The reciprocal of 1 5/9 is 9/14 and the reciprocal of 9/14 is 14/9.

The multiplicative inverse of a number is referred to as the reciprocal.

In other words, 1 divided by a number is the definition of the reciprocal.

Any given number multiplied by its reciprocal will always yield the value 1.

If x is any real number, then 1/x will be the reciprocal of that number.

For instance, 1/8 is the reciprocal of 8, which is 1 divided by 8.

So, the reciprocal of the fractions is:

(A) 1 5/9

9+5/9

14/9

Reciprocal: 9/14

(B) 9/14

Reciprocal: 14/9

Therefore, the reciprocal of 1 5/9 is 9/14 and the reciprocal of 9/14 is 14/9.

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Answer:

C

Step-by-step explanation:

length = 17 + width/2

2×length = 34 + width

width = 2×length - 34

area of a rectangle

length × width = length × (2×length - 34) =

= 2×length² - 34×length

which is the answer option C.

Answer:

i need points

Step-by-step explanation:

For the function that is locate any absolute extreme points over the given interval  h (x) - x 3 - 5x2 - 6x, 10 a we get absolute maximum for x and y  (-0.380, 0.488) (10, 350) and  absolute minimum for x and y (-2, -22) and (4.38, -52.924)

Both critical point lies in domain -2 [tex]\leq[/tex] n [tex]\leq[/tex] 10. We know that h (n) is not define at both side of interval end point so n = -2 and n = 10 are critical point,

The critical point are point where f(n) is defined and its derivative is zero or undefined.

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Answer:

7/30 is your answer.

Step-by-step explanation:

Answers:

Q

Step-by-step explanation:

​Yes, the multiple regression equation should be used for predicting the height of a son based on the height of his father and mother because the​ P-value in the ANOVA table is very low.

Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. A single dependent variable and numerous independent variables can be analyzed using the statistical approach known as multiple regression. In order to forecast the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.

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A linear regression assumes a linear relationship between X and Y.

Option B is correct.

Linear regression analysis is used to predict the value of a variable based on the value of another variable. When data has only 1 independent feature then it’s called simple linear regression.

This assumption says that independent and dependent features are having linear relationship. To check this assumption, we can use a scatter plot and a scatter plot should look like the left graph in the attached image.

Hence, we assume that there is a linear relationship between X and Y.

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Demand elasticity came in at -4.6154. The actual markup was 0.2167 as opposed to the desired markup of 0.5789. The increase was therefore not profitable.

A number is split in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of things being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

Here,

The demand elasticity,

=[(Q1-Q2)/(Q1+Q2)] / [(P1-P2)/(P1+P2)]

[(8000-5000)/(8000+5000)] / [(9.5-10.5)/(9.5+10.5)]

[(3000/13000)] / [-1/20}

60000/-13000

=-4.6154

The desired markup,

(9.5-4) / 9.5

= 0.5789

The actual markup,

1/4.6154

= 0.2167

The demand elasticity was -4.6154. The desired markup was 0.5789 and actual markup was 0.2167. Hence, The increment was not profitable.

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The ratio of the amount of money alice has to the amount bob has 31:9.

Assume the following:

Alice's amount = P

Bob's amount = Q

Amount received = n

If Alice receives $n$ dollars from Bob ;then she will have $4$ times as much money as Bob.

P + n = 4(Q - n)

P + n = 4Q - 4n

P = 4Q - 4n - n

P = 4Q - 5n - - - - (1)

If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob

P - n = 3(Q + n)

P - n = 3Q + 3n

P = 3Q + 3n + n

P = 3Q + 4n - - - - - - (2)

Equating both equations - (1) and (2)

4Q - 5n = 3Q + 4n

4Q - 3Q = 4n + 5n

Q = 9n

Express P in terms of n, use either equation (1) or (2)

From equation 2:

P = 3Q + 4n

Substituting Q = 9n

P = 3(9n) + 4n

P = 27 + 4n

P = 31n

Alice's amount = P, Bob's = Q

Ratio = P:Q

31 : 9

Hence, the ratio of the amount of money alice has to the amount bob has 31:9.

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The volume of the solid formed by revolving an equilateral triangle around any of its sides of length 2 is π /√3 units .

From the diagram we can see that the washer method will be used to calculate the are of the solid formed.

The solid formed is in the form of a cone.

Volume of a cone = 1/3 πr²h

Here the radius of the cone = diameter / 2 = 2/2 = 1 units.

Height of the cone is calculated using the Pythagoras theorem of a right angled triangle

radius² + height² = side ²

or,  height² = 4 - 1

or, height = √3

Volume of the cone = 1/3 πr²h

Substituting the values we get:

V = 1/3 π 1²√3 = π /√3

Therefore the volume of the cone thus formed is  π /√3  cubic units.

A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.

The base may only be a circle, any closed one-dimensional figure, any one-dimensional quadratic form in the plane, or any combination of the above plus all the enclosed points, depending on the author.

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The chi-square distribution serves as the sampling distribution for the goodness of fit test since it quantifies how well the distribution derived from the data fits the empirical distribution.

The sampling distribution is the probability distribution of a statistic that is obtained by repeated sampling of a certain population. The mean or mode of a population's mean or mode of a variable is one example of the many different choices for a statistic that are described in this passage. The sampling distribution of a proportion is obtained by repeating your survey or poll for each possible sample of the population. For instance, instead of asking 1,000 cat owners what cat food they prefer, you could conduct a number of polls.

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Answer:

y -8 = 3(x+8)

Step-by-step explanation:

y-8 = 3(x-(-8)

y - 8 = 3(x+8)

There are several different ways that Brad could arrange the blocks to create an array with the same number of blocks in each row. For example, he could create a 3x6 array by arranging the blocks into three rows of six blocks each. Alternatively, he could create a 6x3 array by arranging the blocks into six rows of three blocks each. He could also create a 2x9 array by arranging the blocks into two rows of nine blocks each. Or he could create a 9x2 array by arranging the blocks into nine rows of two blocks each

TL;DR: 3x6, 6x3, 2x9 and 9x2.

The mathematical program will help the user to provide the data on the Excel sheet and solve accordingly.

The mathematical program to minimize the total cost of constructing the wastewater treatment plants can be expressed as follows:

Minimize z = 50x1 + 100x2 + 100x3 + 50x4 + 50x5 + 100x6 + 100x7

Subject to:

x1 + x2 + x3 + x4 + x5 + x6 + x7 <= 4 (1)

x1 + x2 + x3 + x4 + x5 + x6 + x7 >= 1 (2)

x1 + x4 <= 1 (3)

x2 + x4 <= 1 (4)

x3 + x4 <= 1 (5)

x4 + x5 <= 1 (6)

x4 + x6 <= 1 (7)

x4 + x7 <= 1 (8)

x1, x2, x3, x4, x5, x6, x7 are binary variables (i.e. they can only take on the values 0 or 1)

The objective function (1) minimizes the total cost of constructing the wastewater treatment plants, where the cost of constructing a plant in each city is given in the table. The constraints (2)-(8) ensure that at most four wastewater treatment plants are constructed and that each city is served by at most one wastewater treatment plant.

To solve this problem with Excel, we can create a spreadsheet with columns for the names of the cities, the corresponding costs of constructing a wastewater treatment plant, and the binary variables x1, x2, x3, x4, x5, x6, x7. We can then use Excel's solver tool to minimize the objective function subject to the constraints. The solver tool can be found under the Data tab in the Analyze group.

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The same trip will be 8 hours long if you traveled at 10 mph

Variation is a concept that deals with variability or change in mathematics. Variation is defined as any change in some quantity due to a change in another

Given: The time T it takes to travel some distance varies inversely with the rate r of travel. This implies:

T α 1/r

T = k/r    where k is the constant of proportionality

if it takes 2 hours to get somewhere traveling 40 mph. Then:

2 = k/40

k = 2 x 40 = 80

How long would the same trip take you instead if you traveled 10 mph will be:

T = k/r

T = 80/10

T = 8 hours

Therefore, the same trip take you 8 hours if you traveled 10 mph

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The function which defines the total sales done by Samantha in 'x' number of weeks is: f(x) = 475 + 5x/100.

As per the stated question-

Weekly pay of Samantha = $475.

Sales percentage = 5% of the sales.

Let 'x' be the sales done for the week.

Then, function models for the pay of the week.

f(x) = 475 + 5%x

f(x) = 475 + 5x/100

Thus, the function which defines the total sales done by Samantha in 'x' number of weeks is: f(x) = 475 + 5x/100.

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import java.util.ArrayList;

import java.util.Collections;

import java.util.Comparator;

import java.util.HashMap;

import java.util.Iterator;

import java.util.LinkedList;

import java.util.List;

import java.util.Map;

import java.util.Scanner;

public class Mean {

   static public void main(String args[])

   {

       // Initializing variables

       int[][] a = new int[100][100]; // Array of arrays for holding the inputs

       Map<Integer,ArrayList<Integer>> averagemaps = new HashMap<Integer,ArrayList<Integer>>(); // Map to contain the average and the list of array indexes

       List<Integer> averages = new ArrayList<Integer>(); // List of averages of the arrays

       Scanner sc = new Scanner(System.in);

       // Input for the array of arrays

       System.out.println("Enter the number of arrays: ");

       int noArrays = sc.nextInt();

       for(int i = 0; i < noArrays; i++)

       {

           System.out.println("Enter the number of elements in the array "+i+":");

           int noElements = sc.nextInt();

           int sum = 0;

           int avg = 0;

           System.out.println("Enter the elements of the array "+i+" one by one:");

           for(int j = 0; j < noElements; j++)

           {

               a[i][j] = sc.nextInt(); // Input for each elements in the array.

               sum += a[i][j];    // Calculating the sum of the elements in the array.

           }

           avg = sum/noElements; // calculating average for the array

           // checking if the average is inside the list or not

           if(!averages.contains(avg))

           {    

               // If the average is not already in the list

               // Adding the average into the list

               averages.add(avg);

               // create an array list to

               // hold the list of indices which has the same array

              ArrayList<Integer> a1 =  new ArrayList<Integer>();

               a1.add(i);

               // Mapping the average to the list of indices.

               averagemaps.put(avg, a1);

           }

           else

           {

               // The average is present in the list

               // Adding the index to the array list

               // mapped to it.

               averagemaps.get(avg).add(i);

           }

       }

       // Sorting the index arrays for each average

       // in ascending order

       Iterator itr=averages.iterator();

       int index = 0;

       while(itr.hasNext()){  

             Collections.sort(averagemaps.get(itr.next()));

       }

       // For sorting the array of indices based on their lowest number

       // Since the arrays are in a map, the map needs to be sorted.

       // There is no function to sort the map, Hence the map is converted to

       // a list of entersets.

       List<Map.Entry<Integer,ArrayList<Integer>>> list =

               new LinkedList<Map.Entry<Integer,ArrayList<Integer>>>(averagemaps.entrySet());

       // Using the sort function to sort the list. The list should be sorted based on the minimum

       // element in each array.

       Collections.sort(list, new Comparator<Map.Entry<Integer,ArrayList<Integer>>>() {

           public int compare(Map.Entry<Integer,ArrayList<Integer>> o1,

                              Map.Entry<Integer,ArrayList<Integer>> o2) {

               // since the elements in the arrays are already sorted

               // the element in the index 0 will be the smallest element

               return (o1.getValue().get(0)).compareTo(o2.getValue().get(0));

           }

       });

       // Converting the list back to a hashmap

       averagemaps = new HashMap<Integer,ArrayList<Integer>>();

       for (Map.Entry<Integer,ArrayList<Integer>> entry : list) {

           averagemaps.put(entry.getKey(), entry.getValue());

       }

       // Initializing an array of array for the output

       // The outer array dimension is defined.

       // The inner array dimension can be defined based on the

       // size of the indices array

       int[][] answer = new int[averages.size()][];

       itr = averages.iterator();

       // Iterate through the averages lists

       while(itr.hasNext())

       {

           ArrayList<Integer> i = averagemaps.get(itr.next());

           Iterator iterr=i.iterator();

           answer[index] = new int[i.size()];

           int innerindex = 0;

           while(iterr.hasNext())

               answer[index][innerindex++] = (Integer)iterr.next(); // adding the array of indices into the output array.

           index++;

       }

       // Printing the arrays of arrays.

       System.out.print("[ ");

       for(int i = 0; i < answer.length; i++)

       {

           System.out.print("[ ");

           for(int j = 0;j < answer[i].length; j++)

               System.out.print(answer[i][j]+ ", ");

           System.out.println("]");

       }

       System.out.println("]");

   }

}

Output:

Enter the number of arrays:

4

Enter the number of elements in the array 0:

3

Enter the elements of the array 0 one by one:

-5

2

3

Enter the number of elements in the array 1:

2

Enter the elements of the array 1 one by one:

0

0

Enter the number of elements in the array 2:

1

Enter the elements of the array 2 one by one:

0

Enter the number of elements in the array 3:

2

Enter the elements of the array 3 one by one:

-100

100

[ [ 0, 1, 2, 3, ]

]

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It means that if you run your experiment again you have a good chance of finding no difference between average differences.

What is a confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contains the parameter's true value is what is meant by the confidence level.

If zero is included in a confidence interval for paired data.

It means that if you rerun your experiment you have a good chance of finding no difference between groups.

When performing your statistical test, you will also see that the p-value in each of these situations is high, indicating that the null hypothesis—that there is no association between the variables or difference between the groups—could have produced the same findings.

Hence, finding no difference between average differences.

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Answer: y=20x

Step-by-step explanation: 40/2=20, 80/4=20, etc.

There are 20 per every-one

Answer: 36

Step-by-step explanation:

Since all triangle angles add up to 180 we just add up both the angle measure we know and then subtract by 180.

54+90=144

180-144=36

The acute angle measure is 36 degrees.

answer:

36 degrees

step-by-step explanation:

all the angles of a triangle add up to be 180 degrees. so subtract 90 and 54 degrees to get the answer. hope that helps!

The time series plot is attached below

The parameters for the line that minimizes mse for this time series 119.714 - 4.9286t

What is time series ?

A time series is a group of data points that have been indexed chronologically in mathematics. A time series is most frequently a sequence captured at a series of equally spaced moments in time. As a result, it is a collection of discrete-time data.

These four elements are: -Secular trend, which describes movement over time; -Seasonal variations, which depict seasonal changes; -Cyclical fluctuations, which relate to periodic but not seasonal variations; -Irregular variations, which are additional nonrandom sources of variations in series.

t' = 28 / 7

 = 4

Y' = 700 / 7

   = 100

∑(t - t') (y - y') = -138

∑(t - t')² = 28

b1 = -138 / 28

    = -4.9286

b0 = Y' - b1t'

    = 100 - (-4.9286*4)

    = 119.714

[tex]T_{t}[/tex] = 119.714 - 4.9286t

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The probability of the total being equal to 8 is 1/9 or 11.11%.

To calculate this probability, we must first calculate all the possible combinations of two six-sided dice that add up to 8. Since both the dice are showing an even number, the possible combinations are (2, 6), (4, 4), and (6, 2). the total number of possible combinations for two six-sided dice is 36 (6 x 6). Therefore, the probability of the total being equal to 8 is 3/36 or 1/9 or 11.11%.

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Both of those probabilities decrease, hence Option (B) is the correct answer.

Given, the number of tosses of a fair coin goes up from 10, to 100, to 1,000 and to 10,000.

we have to find the effect on the probability of getting exactly 50% heads.

In 10 tosses,

we have to get heads 5 times,

P(X = 5) = (1/2)^5(1/2)^5

P(X = 5) = (1/2)^10

In 100 tosses,

we have to get heads 50 times,

P(X = 50) = (1/2)^50(1/2)^50

P(X = 50) = (1/2)^100

and so on.

It is clear that the probability of getting 50% heads decreases.

Also, Probability of getting heads between 40% and 60% decreases.

Hence, both of those probabilities decrease.

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The three stages of an annealing process in the sequence is  recovery, recrystallisation, and gain growth.

Sequence:

In math, a series is defined as the sum of the elements of a sequence.

Given,

Here we need to find the are the three stages during annealing when  an annealing process is provided for the sample after cold work.

In order to find the stages of the annealing process, first we have to know the definition of annealing process,

A process which is used to enhance ductility and counter the increase in hardness by cold working is known as annealing.

This one is to deal with residual stresses we first can reheat the glass to a high temperature known as annealing point and let it cool slowly so that the outside and inside cool at about the same rate.

And the resultant will have little to no residual stresses making annealed glass.

In the first stage recovery stage of annealing recovers the physical properties of the metals.

Second stage is recrystallisation, and gain growth.

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Answer:

$38

Step-by-step explanation:

400 ÷ 8 = 50 per person plus admission

minus admission

50 - 12 = 38

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]4x+10y=-140\implies 10y=-4x-140\implies y=\cfrac{-4x-140}{10} \\\\\\ y=\cfrac{-4x}{10}-\cfrac{140}{10}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{5}}x-14\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-2}\implies {\Large \begin{array}{llll} \cfrac{5}{2} \end{array}}}}[/tex]