In this lesson, you sketched polynomial functions using factors and rewrote them in general form.
1 Use the factors to sketch each cubic function and label the zeros. Then rewrite the function
in general form.
F(x) = (x+3)(-x + 5)2 - 2x)

The value of x is -7.

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We are given the equation as

[tex]8^{x + 3} = 2 ^{x - 5}[/tex]

Solving the equation as;

[tex]8^{x + 3} = 2 ^{x - 5}\\\\2^{3(x + 3)} = 2 ^{x - 5}[/tex]

Then we have;

3x + 9 = x - 5

2x = -14

x = -7

The value of x is -7.

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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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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 probability of having 2 boys and 1 girl would be  [tex]\frac{3}{8}[/tex]

What is Probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given that:

family with 3 children.

Condition: Girl is as likely as a boy at each birth.

s will be the sample space.

The sample space has 8 elements:

s = {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}

n(s) =  [tex]\frac{1}{8}[/tex]

We need 2 boys and 1 girl, regardless of order,

sample space for 2 boys and 1 girl, regardless of order would be 3.

s = 3

Then, probability will be

      [tex]Probability \ of\ having\ 2 \ boys\ and \ 1\ girl =\frac{3}{8}[/tex]

Hence, The probability of having 2 boys and 1 girl would be  [tex]\frac{3}{8}[/tex]

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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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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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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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Answer:

7/30 is your answer.

Step-by-step explanation:

Answers:

Q

Step-by-step explanation:

A rotation matrix has two complex eigenvalues e−iθ and eiθ.

These are matched by complicated eigenvectors.

We are aware that the rotational axis is represented by the eigenvector with the eigenvalue 1 in it. how to demonstrate that the angle of rotation is represented by the complex eigenvalue.

It is simple to compare it with a rotation matrix for rotation about the x, y, or z axes, but how can one draw this conclusion for a general R that belongs to SO (3).

In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix rotates points in the xy plane counterclockwise through an angle θ with respect to the positive x axis about the origin of a two-dimensional Cartesian  Plane.

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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].

In 700 years the population of Transylvania will double  

What is growth rate ?

the typical annual rate of population change during a particular period for a certain nation, region, or geographic area. In most cases, a factor of 100 is used to describe the ratio between the annual growth in population size and the total population for the year.

Growth rate equals Absolute Change divided by Previous Value. Calculate the percentage of change: Percent of change = Growth rate x 100 is the formula that may be used to calculate the percent of change.

To calculate in how many years the population of Transylvania double

= 70 / 0.1

= 700 years

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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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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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Answer: $117

Step-by-step explanation: 1st subtract 3 then divide by 2 then subtract 3 again and divide by 2 again

Answer:

  rectangle, square, triangle

Step-by-step explanation:

Given the coordinates of the vertices of a rectangle, triangle, and square, you want to sort them in order of increasing perimeter.

In general, the length of a side can be found using the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

This shows you that if the x-coordinates are the same, the distance is the positive difference of the y-coordinates, and vice versa.

The attachment shows the side lengths for the figures, computed using this formula. Each row shows the distance from the point on that row to the point on the next row. (You will notice the last point is a copy of the first point.)

The perimeter of each figure is the sum of the side lengths. This is the number below the Distance column in each of the tables.

In increasing order, the perimeters are ...

__

Additional comment

When the computations are repetitive, it is often convenient to let a spreadsheet do them. The formula can be entered once and copied where needed. The problem then reduces to one of data entry, which you generally have to do for any but mental arithmetic.

Answer: 21 miles

Step-by-step explanation:

We know that it travels 2016 miles in 96 hours.

So we just need to get 2016 divided by 96 = 21 miles/ per hour

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Hence, the miles does the balloon travel in one hour is [tex]21[/tex] miles/ per hour.

What is the miles?

Mile is a customary unit used for measuring length or distance. More About Mile Mile is denoted by the symbol 'mi'.

Here given that,

A hot-air balloon travels [tex]2,016[/tex] miles in [tex]96[/tex] hours. It travels the same number of miles each hour.

As we know that it travels [tex]2016[/tex] miles just only in [tex]96[/tex] hours.

[tex]\frac{2016}{96}=21[/tex] miles/ per hour

Hence, the miles does the balloon travel in one hour is [tex]21[/tex] miles/ per hour.

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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 maximum number of electrons in an atom that can have the given sets of quantum numbers n=4 is 32.

In the given question we have to find the maximum number of electrons in an atom that can have the given sets of quantum numbers n=4.

As we know that;

A negatively charged subatomic particle known as an electron can either be free or attached to an atom (not bound). One of the three main types of particles within an atom is an electron that is bonded to it; the other two are protons and neutrons. The nucleus of an atom is made up of electrons, protons, and neutrons altogether.

So the maximum number of electrons in an atom is;

Number of Electron = 2*n^2

Number of Electron = 2*(4)^2

Number of Electron = 2*16

Number of Electron = 32

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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]

Answer:

y -8 = 3(x+8)

Step-by-step explanation:

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

y - 8 = 3(x+8)

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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For the given data, a) The mass at the time t = 3 is 14.13 kg. and b) The mass remaining after 20 days is 10.05 kg.

What is radioactive decay?

The spontaneous breakdown of an atomic nucleus of a radioactive substance resulting in the emission of radiation from the nucleus is known as Radioactive decay.

The Radioactive Formula is given by

                     [tex]N = N_{0} e^{-\lambda T}[/tex]

Given, [tex]m(t) = 15e^{-0.02t}[/tex]

where m(t) is measured in kilograms

a) To find the mass at time t=3, then

m(3) = [tex]15e^{-0.02*3}[/tex] = [tex]15e^{-0.06}[/tex] = 14.13 kg

Therefore, the mass at the time t=3 is 14.13 kg.

b)  To find how much of the mass remains after 20 days,

m(20) = [tex]15e^{-0.02*20}[/tex] = [tex]15e^{-0.4}[/tex] = 10.05 kg

Therefore, the mass remaining after 20 days is 10.05 kg.

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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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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.

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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Answer:

$38

Step-by-step explanation:

400 ÷ 8 = 50 per person plus admission

minus admission

50 - 12 = 38

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:

12. impact

13. environment

14. unique

15, destination

16. provide

17. designed

19. local

20. conservation

Step-by-ste1p explanation:

ur welcome

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.

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.  

To learn more about probability link is here

brainly.com/question/26911497

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