One hundred people purchase lottery tickets. Three winning tickets will be selected at random. If first prize is $100, second prize is $50, and third prize is $25, in how many different ways can the prizes be awarded?.

Answer:

y -8 = 3(x+8)

Step-by-step explanation:

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

y - 8 = 3(x+8)

Answer:

7/30 is your answer.

Step-by-step explanation:

Answers:

Q

Step-by-step explanation:

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

The transformation of f(x) to g(x) is,

f(x) is reflected over the x-axis and then shifted 3 steps to the right.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

f(x) = x

g(x) = -x + 3

g(x) is the transformation of f(x).

When f(x) is reflected along the x-axis we get,

g(x) = -x

Now,

g(x) is shifted 3 steps to the right we get,

g(x) = -x + 3

Thus,

The transformation of f(x) to g(x) is,

f(x) is reflected over the x-axis and then shifted 3 steps to the right.

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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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Mathematically, the expected payback is $9.5.

Below, this is further discussed.

What is the anticipated return?

In general, the likelihood times the value are multiplied together to calculate the projected payback.

E(x) = p(x_1)*x_1 + p(x_2)*x_2 + .....

We have two different repayment alternatives in this situation.

Winning

The payback is $500 - $10 = $490

x_1 = 490

The likelihood of winning is one in a thousand (since the choices are 0 to 999)

p(x 1) = 1/1000

Losing

Due to the fact that the person did not win anything, they actually lost $8.

x _2 = -10

The other 999 numbers are regarded as losing numbers because there is only one number that can win.

p(x 2) = 999/1000

E(x) = p(x 1)*x 1 + p(x 2)*x 2 = (1/1000)* 490+ is the expected payback as a result.

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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:

12. impact

13. environment

14. unique

15, destination

16. provide

17. designed

19. local

20. conservation

Step-by-ste1p explanation:

ur welcome

Answer:

1) [tex]\dfrac{1}{2}[/tex]

2) [tex]\dfrac{7}{10}[/tex]

3) [tex]\dfrac{7}{8}[/tex]

Step-by-step explanation:

Any decimal can be written as a fraction by just putting the given number over 1.

For example, take the first problem.

0.5 can be written as:

[tex]\dfrac{0.5}{1}[/tex]

Then, to simplify it, multiply both the top and bottom by 2.

[tex]\dfrac{0.5 \times 2}{1 \times 2}[/tex]

[tex]= \dfrac{1}{2}[/tex]

The reason this doesn't change the value of the fraction is because any number over itself is 1. Look at the 2's we just multiplied by in the numerator and denominator. We are really just multiplying the entire fraction by 2/2, which equals 1. Here's a way of writing the above step that makes it clearer:

[tex]\dfrac{0.5}{1} \times \dfrac{2}{2}[/tex]

[tex]=\dfrac{1}{2}[/tex]

So, the answer to the first problem is [tex]\dfrac{1}{2}[/tex].

We can repeat these steps for the second problem.

[tex]0.7 = \dfrac{0.7}{1}[/tex]

But this time, multiply by 10/10 instead of 2/2. Remember that 10/10 is still equal to 1.

[tex]= \dfrac{0.7}{1} \times \dfrac{10}{10}[/tex]

[tex]= \dfrac{7}{10}[/tex]

So, the answer to the second problem is [tex]\dfrac{7}{10}[/tex].

Finally, repeat the steps from the previous problems.

[tex]0.875 = \dfrac{0.875}{1}[/tex]

But this time, multiply by 1,000/1,000.

[tex]= \dfrac{0.875}{1} \times \dfrac{1,000}{1,000}[/tex]

[tex]= \dfrac{875}{1,000}[/tex]

And this time, some extra simplification is necessary. Divide by 25/25.

[tex]= \dfrac{875}{1,000} \div \dfrac{25}{25}[/tex]

[tex]= \dfrac{35}{40}[/tex]

Then, divide by 5/5.

[tex]= \dfrac{35}{40} \div \dfrac{5}{5}[/tex]

[tex]= \dfrac{7}{8}[/tex]

So, the answer to the third problem is [tex]\dfrac{7}{8}[/tex].

Ok, so, this implies h=0 when the pebble hits the ground.

So, - 16t^2 + 24t + 1300 = 0

If we find t, we obtain two solutions, one negative and one positive, so the positive is correct.

Then, t = 9.7950 s

Therefore, it would take about 9.7950 seconds for the pebble to hit the ground.

Answer:

it would have a 50% or 0.5 probability of rolling an even number on the dice

Step-by-step explanation:

A dice has six numbers, three have them are odd and three are even so we would calculate it as 3/6.

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 distance the jet can fly in 9 hours is 1950 miles.

The distance the jet can fly in 6 hours is 1300 miles.

The first step is to determine the rate of the jet. The rate measures how fast the jet travels with respect to time. It is the total distance travelled divided by the total time.

Rate = distance / time

Rate  = 650 / 3

Rate  = 216.67 miles per hour

Distance travelled = rate x time

Distance travelled in 9 hours  = 216.67 miles per hour x 9 = 1950 miles

Distance travelled in 6 hours = 216.67 miles per hour x 6 = 1300 miles

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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]

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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Answer:

$38

Step-by-step explanation:

400 ÷ 8 = 50 per person plus admission

minus admission

50 - 12 = 38

After solving the given expression the values for x will be equal to x = 1 and x = 13.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given information in the question,

The given equation is,

(x - 7)² = 36

x - 7 = √36

x = ±6

Then the values for x will be,

x1 = 6 + 7 = 17

x2 = -6 + 7 = -1

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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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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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Answer:

6pi

Step-by-step explanation:

1.) Figure out the total circumference of the circle. The circumference of a circle is equal to 2*pi*r, which is equal to 8pi.

2.) Figure out the portion of the circle that the arc is by using the angle. Since the angle is 90 degrees, and the total measure in a circle is 360 degrees, that means that the cut out part is 90/360, which is 1/4 of the circle.

3.) Now, since the cut out part is 1/4, that means that the remaining part is 3/4 of the circle.
4.) Now, we multiply 8pi * 3/4, which is equal to 6pi.

Answer:  10.169

Step-by-step explanation: To add decimals like this we have to line up them in order.

2.859

+

7.31 =

10.169

Above I have to line them up in order.

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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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12 students like chocolate and vanilla, if there are 55 people in the class.

In the given question, in a class, there are 30 students who like chocolate, 25 students who like vanilla, and 12 students who like neither.

If there are 55 people in the class, then we have to find how many students like chocolate and vanilla.

The number of students who like chocolate, n(C)=30

The number of students who like vanilla, n(V)=25

The number of students who like neither chocolate and vanilla, n(C∪V)′=12

Total number of students, n(U)=55

Now,

The number of students who like vanilla or chocolate;

n(C∪V) = n(U)-n(C∪V)’

n(C∪V) = 55-12

n(C∪V) = 43

Since, we have to find how many students like chocolate and vanilla, if there are 55 people in the class. So

n(C∩V)=n(C)+n(V)- n(C∪V)

n(C∩V)=30+25- 43

n(C∩V)=12

Hence, 12 students like chocolate and vanilla, if there are 55 people in the class.  

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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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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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​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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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 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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Answer:

315 children attend the play.

Answer:

c=315

Step-by-step explanation:

we know c is equal to 21a so we can insert it into the second equation

a+21a=330

22a=330

/22. /22

a=15

now we inset a to find c

21(15)=c

315=c

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