Find the product of 12 and 8

2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).

Multiplication in elementary algebra is the process of figuring out what happens when a number is multiplied by itself. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication.

Given

Polynomial

(2x³ + 4x² − 5x)(x³ + 2x - 1)

Multiplying by distributive method,

2x³(x³ + 2x - 1) + 4x²(x³ + 2x - 1) - 5x(x³ + 2x -1)

2x⁶ + 4x⁴ - 2x³ + 4x⁵ + 2x³ - 4x² - 5x⁴ + 10x² - 5x

Adding polynomials with same powers

2x⁶ + 4x⁵ + 4x⁴ - 5x⁴ - 2x³ + 2x³ - 4x² + 10x² - 5x

2x⁶ + 4x⁵ - x⁴ + 6x² - 5x

2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).

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An algorithm for navigating or searching through tree or graph data structures is called depth-first search. The algorithm begins at the root node (choosing an arbitrary node to serve as the root node in the case of a graph) and proceeds to investigate each branch as far as it can go before turning around.

Thus, the basic concept is to begin at the root or any other random node, mark that node, then advance to the next nearby node that is not marked. This process is repeated until there are no more adjacent nodes that are unmarked. Then go back and look for more unmarked nodes to cross. Print the path's nodes lastly.

To solve the issue, adhere to the instructions listed below:

Make a recursive function that accepts a visited array and the node's index.

STEP -1

// C++ program to print DFS traversal from

// a given vertex in a given graph

#include <bits/stdc++.h>

using namespace std;

// Graph class represents a directed graph

// using adjacency list representation

class Graph {

public:

map<int, bool> visited;

map<int, list<int> > adj;

// function to add an edge to graph

void addEdge(int v, int w);

// DFS traversal of the vertices

// reachable from v

void DFS(int v);

};

void Graph::addEdge(int v, int w){

adj[v].push_back(w); // Add w to v’s list.}

void Graph::DFS(int v)

{

// Mark the current node as visited and

// print it

visited[v] = true;

cout << v << " ";

// Recur for all the vertices adjacent

// to this vertex

list<int>::iterator i;

for (i = adj[v].begin(); i != adj[v].end(); ++i)

if (!visited[*i])

DFS(*i);

}

// Driver's code

int main()

{

// Create a graph given in the above diagram

Graph g;

g.addEdge(0, 1);

g.addEdge(0, 2);

g.addEdge(1, 2);

g.addEdge(2, 0);

g.addEdge(2, 3);

g.addEdge(3, 3);

cout << "Following is Depth First Traversal"

" (starting from vertex 2) \n";

// Function call

g.DFS(2);

return 0;

STEP- 2

Time complexity: O(V + E), where V is the number of vertices and E is the number of edges in the graph.

Auxiliary Space: O(V), since an extra visited array of size V is required.

Pseudocode:

Depth_First_Search(matrix[ ][ ] ,source_node, visited, value)

{

If ( sourcce_node == value)                

return true // we found the value

visited[source_node] = True

for node in matrix[source_node]:

  If visited [ node ] == false

  Depth_first_search ( matrix, node, visited)

  end if

end for

return false //If it gets to this point, it means that all nodes have been explored.

                   //And we haven't located the value yet.

}

final answer-

A tree data structure or a graph's vertices can be searched using a recursive technique called t. Beginning with the first node of graph G, the depth-first search (DFS) algorithm digs down until it reaches the target node, also known as the node with no children.

The DFS method can be implemented using a stack data structure due to its recursive nature. The DFS algorithm implementation procedure is comparable to that of the BFS algorithm.

The following describes how to implement DFS traversal step-by-step. -

Create a stack with all of the graph's vertices in it first.

Select whatever vertex you want to use as the first vertex in the traverse, and add it to the stack.

uses for the DFS algorithm

The following list of uses for the DFS algorithm includes:

The topological sorting can be implemented using the DFS algorithm.

It can be applied to determine the routes connecting two vertices.

It can also be used to find graph cycles.

DFS technique is also applied to puzzles with a single solution.

If a graph is bipartite or not, it can be determined using DFS.

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The values of the probability in both scenarios are 0

First two dice show aces, and the next three do not

From the question, we have the following parameters that can be used in our computation:

Experiment = rolling of dice

The outcome of an ace is not in the sample space of rolling a die

This means that the probability is 0.

Two of the five dice show aces, and the other three do not

Here, we have

Experiment = rolling of dice

The outcome of an ace is not in the sample space of rolling a die

This means that the probability is 0.

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Answer:5 cm

Step-by-step explanation:

Answer: w=2.5cm

Step-by-step explanation:

when solving for a right triangle, you need to to the length multiplied by the width and then divided by two. You then get (6*5)/2=30/2=15.

When solving for a rectangle, it’s the same, but without dividing by two. But you need them to be equal, and you already have the measure six.
So 5/2=2.5 therefore w=2.5cm.

there you go i think

The best option which describes the p-value is 0.02 < p-value < 0.025.

We know that for the p-value method,

Z = (Sample Mean - Population Mean) / (standard deviation/sqrt (number of selections))

The average GPA for all the college students in the United States as of 2006 = 3.11 (Sample Mean)

The average GPA of randomly selected students at Texas A&M

= 3.27 (Population Mean)

Number of students randomly selected = 47

Standard deviation of them = 0.54

Therefore, Z = (3.27-3.11)/ (0.54/ sqrt(47)) = 2.031

Hence, by right tailed test,

p = 0.024

which implies, 0.02 < p-value < 0.025.

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Thee value of the function f(2) is 70

A function can be defined as an expression, law or rule that stands to explain the comparison between two variables.

These are namely;

From the information given, we have the function as;

f(x)=(3x-1)(2x+10)

To determine the value of the function when x = 2, we have to substitute the value of x as

Now, substitute the value into the function, we have;

f(2) = (3(2) - 1 )(2(2) + 10)

expand the bracket

f(2) = (6 -1)(4 + 10)

Add or subtract the values

f(2) = (5)(14)

Multiply the values, we have

f(2) = 70

Hence, the value is 70

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Because the slope of the supplied line is -4, the needed slope of a line perpendicular to y=-4x-7 is 1/4.

The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope of a line is its steepness as it goes from LEFT to RIGHT. Slope is the ratio of a line's rise, or vertical change, to its run, or horizontal change. The slope of a line is always constant (it never changes) no matter what 2 locations on the line you select. The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b.

Here,

y=mx+c

m=-4

slope of a line perpendicular to y=-4x-7,

m1=1/4

The required slope of a line perpendicular to y=-4x-7 will be 1/4 as the slope of given line is -4.

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The claim of the producer can be accepted at 5% significant level since the 30 hours is within 21.8118 < X < 30.932

The claim of the producer cannot be accepted at 20% significant level since the 30 hours is not within 23.648 < X < 29.102

The claim is done using t score as the sample is less than 30. the formula for t scores is as follows

= x-bar ± t(s/√n)

from the given data the mean is calculated

sample mean, x-bar = (15 + 28 + 33 + 24 + 28 + 25 + 31 + 27) / 8

= 211/8

= 26.375

sample standard deviation, s

variance = (15 - 26.375)² + (28 - 26.375)² + (33 - 26.375)² + (24 - 26.375)² + (28 - 26.375)² + (25 - 26.375)² + (31 - 26.375)² + (27 - 26.375)²) / (8 - 1)

= 207.875 / 7

= 29.696

standard deviation = √variance

= √29.6964

= 5.45

Definition of variables

mean, x-bar = 26.375

standard deviation, s = 5.45

sample size, n = 8

significance level = 5%

confidence level = 1 - significance level = 1 -  0.05 = 0.95 = 95%

z score, z

For sample size less than 30, n < 30. t scores are used

degree of freedom, df = n - 1 = 8 - 1 =7

t score for 95% confidence level and df of 7  = 2.365

substituting into the formula

= x-bar ± t(s/√n)

= 26.375 ± 2.365 (5.45 / √8)

= 26.375 ± 4.557

= 21.8118 < X < 30.932

t score for 20% significant level and df of 7 = 1.415

substituting into the formula

= x-bar ± t(s/√n)

= 26.375 ± 1.415 (5.45 / √8)

= 26.375 ± 2.727

= 23.648 < X < 29.102

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Answer:

x = –24

[tex] \frac{1}{3(x + 6)} = \frac{1}{2(x - 3)} \\ \\ ⇒ \frac{1}{3x + 18} = \frac{1}{2x - 6} \\ \\ ⇒3x + 18 = 2x - 6 \: \\ \\ ⇒3x - 2x = - 6 - 18 \\ \\ ⇒x = - 24 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

Hope it helps you

Answer:

21.

Step-by-step explanation:

[tex]\frac{1}{3} (x+6)=\frac{1}{2} (x-3);\\\\6*\frac{1}{3} (x+6)=6*\frac{1}{2} (x-3);\\2(x+6)=3(x-3);\\2x+12=3x-9;\\x=21.[/tex]

The perimeter of triangle XYZ is 48 units

What is the perimeter of a triangle?

The total of a triangle's sides equals the triangle's perimeter. The space encircled by a triangle's three sides is known as its area.

Here, we have

In The triangle XYZ

A is the midpoint of XY

B is the midpoint of YZ

AB = 1/2 XZ

AB = 5 units

Substitute the value of XZ in AB

5 = 1/2 × XZ

XZ = 10 units

B is the midpoint of YZ

C is the midpoint of XZ

BC =  1/2 XY

XY = 24 units

BC = 1/2 × 24 = 12 units

A is the midpoint of XY

C is the midpoint of XZ

AC = 1/2 YZ

AC = 7

7 = 1/2 YZ

YZ = 14

The perimeter of a triangle = the sum of the lengths of its sides

Perimeter ΔXYZ = XY + YZ + ZX

Perimeter ΔXYZ = 24 + 14 + 10

Hence, the perimeter of triangle XYZ is 48 units

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Answer:

The correct answer to this expression is 9x + 7y. To find this answer, you need to combine like terms. This means that you need to add together any terms that have the same variable and coefficient. In this case, the expression has two terms with the variable x and two terms with the variable y. The coefficients of the x terms are 2 and 7, and the coefficients of the y terms are 3 and 4. To combine these terms, you need to add the coefficients of the x terms together to get 9, and add the coefficients of the y terms together to get 7. Therefore, the combined expression is 9x + 7y.

The equation that represents the total amount is y = 50(4+x).

The mathematical statement that shows two mathematical terms have equal values is known as an equation. An equation simply states that two things are equal.

Equations contain both constant terms and algebraic terms which are combined by operations like Adding and subtraction etc.

Here we have

An electrician charges a callout fee of $ 200 and $ 50 per hour

Given that the total amount charged is y for x hours

As we know the electrician charges $ 50 per hour

=> The charge per x hours = 50x

And callout fee = $ 200

The equation that represents the above situation is

=> y = 200 + 50x

=> y = 50(4+x)

Therefore,

The equation that represents the total amount is y = 50(4+x)

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The pair of Linear angles are 51° and 129°.

When two lines intersect at a point then they will form two linear angles. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.

In other words, if the sum of two adjacent angles is 180° then the pair of angles are said to be Linear Angles.

Here we have

Two angles form linear angles

Let x and y be the two angles

=> x + y = 180 ------ (1)  [ since both are linear angles ]  

Given that the sum of one angle plus 27 is equal to two times the sum of the other angle

=> x + 27 = 2y

=> x = (2y - 27) ---- (2)

Substitute (2) in (1)

=> 2y - 27 + y = 180

=> 3y = 153

=> y = 153/3

=> y =  51  

Now substitute y = 51 in (1)

=> x + 51 = 180

=> x = 180 - 51

=> x = 129

The pair of Linear angles are 51° and 129°.

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Answer:

  (a)  2

Step-by-step explanation:

You want the greatest common factor of 18, 24, 40.

The prime factorization of these numbers is ...

The only common factor is 2.

2 is the greatest common factor of 18, 24, and 40.

If there are too many categories of statistics to present clearly on a graph, then the next best option is a Chart.

Hence, option (a) is the correct choice.

A chart displays data that can be shown as a table, graph, or diagram. It includes a variety of information presentation techniques.

Various Graph and Chart Formats for Data are the following:

Bar Graph: When one data label is lengthy or if there are more than ten things to compare, a bar graph should be used to reduce clutter.

Column Chart.

Line Graph.

Dual Axis Chart.

Area Chart.

Stacked Bar Chart.

Mekko Chart.

Pie Chart.

The chart is one of the most effective ways to categorise the data.

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May be the complete questions should be as follow:

if there are too many categories of statistics to present clearly on a graph, what is the next best option?

Bar graph

Column Chart.

Line Graph.

Stacked Bar Chart.

Mekko Chart.

Answer: 2.795

Step-by-step explanation:

[tex]cos 56= \frac{x}{5}[/tex]

Susie is correct as it is not a right triangle

        Square of the hypotenuse side = 289

        Squares of the other two sides = 12 * 12 = 144

                                                             =9 * 9 = 81

        Sum of the squares of the other two sides = 144 + 81

                                                                               = 225

        So, here 225 ≠ 289

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The value of river garden's common stock is $24.79.

In order to determine the value of the common stock, the constant dividend model would be used.

According to this model, the value of a common stock is determined by its dividend, the growth rate and the required return.

Value of the stock = Dividend / (required return - growth rate)

The first step is to determine the dividend of the common stock.

Dividend = pay out ratio x expected earnings

Dividend = 0.45 x $3.25

Dividend = $1.46250

Value of the stock = $1.46250 / (0.124 - 0.065)

Value of the stock = $24.79

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For part (a), we need to find the derivative of the supply equation with respect to the number of units, x.

The supply equation is given by:

S(x) = 30 + 90p * In(4x + 5)

To find the derivative of S(x) with respect to x, we can use the chain rule:

[tex]\frac{dS(x)}{dx} =\frac{dS(x)}{dp}*\frac{dp}{dx}[/tex]

Since the derivative of S(x) with respect to p is 90 * In(4x + 5), we can substitute this into the equation above:

[tex]\frac{dS}{dx}=(90*ln(4x+5))*(\frac{dp}{dx} )[/tex]

This gives us the expression for the rate of change of supply price with respect to the number of units supplied.

For part (b), we need to find the rate of change of supply price when the number of units is 30. Substituting x = 30 into the equation above gives us:

[tex]\frac{Ds(30)}{dx} = (90*ln(4*30+5))*\frac{dp}{dx}[/tex]

For part (c), we need to approximate the price increase associated with the number of units supplied changing from 30 to 31. To do this, we can use the equation from part (a) to find the rate of change of supply price with respect to the number of units supplied and then multiply this rate by the change in the number of units (from 30 to 31).

The approximate price increase is given by:

[tex]\frac{dS(x)}{dx} *(x2-x1)=\frac{dS(x)}{dx}*(31-30)[/tex]

Substituting the appropriate values into this equation will give us the approximate price increase associated with the number of units changing from 30 to 31.

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The balance of the loan (not made any payments yet) of the bank

be after one year charges 3.8% interest each year is; $7785

There are mainly two types of interest. One which works only on principal(or say initial) amount, and one which works on amount plus interest to be paid till date.

For 1 year case, if interest is applied annually, both interests are same since there is no interest before first year.

For 1 year, interest with R% rate for principal amount P is just R% of P which is; (P/100) * R

We are given that R = 3.8% each year

Since P = $7500, thus, interest for 1 year is 3.8% of $7500 is;

I = 7500/100 * 3.8

I = $285

Thus, total payable amount = Principal amount + interest

Total amount = $7500 + $285 = $7785

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Answer:

Yes this is a resendable prediction

Step-by-step explanation:

Answer:

a) 1 degree above

b) 4 degrees below

c) 12 degrees above

d) 7 degrees above

Step-by-step explanation:

The inequality which represents the possible number of hours , x, the salesperson works this week is 20x + 800 ≥ 1400 where x ≥ 30,

using equation formation steps.

What is an equation ?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation.

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

In given que,

minimum earning = $1400

The possible number of hours = x

No. of cars sold = 8

Price earned by sold cars = $800

Price earned per hour =$20

Price earned for x hours = $20x

So, the total amount = 20x + 800

The equation become 20x + 800 ≥ 1400

Solving inequality que,

20x >= 600

x ≥ 30

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Value of the function given below is f(-4)= -18 , f(-2)= -10 , f(6)= 12 , f(-1)= -6

What is a function?

An algebraic function in mathematics is a function that may be described as the solution to a polynomial problem. Algebraic expressions with a finite number of terms and solely the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power make up algebraic functions rather frequently.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The whole set of values that the function's output can produce is referred to as the range. The set of values that might be a function's outputs is known as the co-domain.

f(-4)  means x =-4 which is less than -1

so the 4x-2 expression will be used

f(-4)= 4(-4)-2

f(-4)= -18

f(-2)  means x =-2 which is less than -1

so the 4x-2 expression will be used

f(-2)= 4(-2)-2

f(-2)= -10

f(6)  means x =6 which is greater than -1

so the x/2 +9 expression will be used

f(6)= 6/2 +9

f(6)= 12

f(-1)  means x =-1

so the 4x-2 expression will be used for x = -1

f(-1)= 4(-1)-2

f(-1)= -6

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Answer: The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of -0.993 indicates a very strong negative relationship, which means that as one variable increases, the other variable decreases. This suggests that you can be quite confident that your predicted value will be reasonably close to the actual value.

The proportionality constant, k, in this case is 0.00043.

a. The proportionality relationship between body mass index (B), weight (w), and height (h) can be expressed as follows:

B ∝ w * [tex]h^{-2[/tex]

where k is the constant of proportionality.

b. To find the value of the constant of proportionality, k, we can substitute the known values into the equation and solve for k.

28.4 = k * 198 * [tex]70^{-2[/tex]

Solving for k gives:

k = 0.00043

Therefore, the proportionality constant, k, in this case is 0.00043.

A proportionality constant is a number that is used to indicate the ratio of two different variables that are proportional to each other. It is also known as a scaling factor or a constant of proportionality. It is usually represented by the letter k.

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The slope of a line that is perpendicular to a line whose equation is; 3y = -4x + 2 is; 3 / 4.

As evident in the task content is; the given equation is; 3y = -4x + 2.

To determine the slope of the given line; the equation can be expressed in slope-intercept form by dividing through by; 3.

y = -4/3x + 2/3

On this note, by comparison with the slope-intercept form of a linear equation; the slope, m is; -4/3.

Therefore, since the product of the slopes of perpendicular lines equal; -1;

The slope of the required line which is perpendicular to the given line can be determined as follows;

Slope of perpendicular; m = -1 ÷ (-4/3)

= -1 × 3 / -4

= -3 / -4

= 3/4.

On this note, the slope of the line perpendicular to the given line is; 3 / 4.

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Answer:

[tex]\boxed{1.1914285714285713}[/tex]

Step-by-step explanation:

Jill earned a total of 9 + 6/7 = <<9+6/7=9.857142857142857>>9.857142857142857 points.

Alice earned a total of 8 + 2/3 = <<8+2/3=8.666666666666666>>8.666666666666666 points.

Therefore, Jill earned 9.857142857142857 - 8.666666666666666 = <<9.857142857142857-8.666666666666666=1.1914285714285713>>1.1914285714285713 more points than Alice. Answer: \boxed{1.1914285714285713}.

Alice earned approximately 1.19 points more than Jill.

To find the difference between the number of points earned by Jill and the number of points earned by Alice, we need to first convert both amounts to a common denominator.

Since the denominators of the fractions representing the number of points earned by Jill and Alice are different, we will need to find a common denominator. To do this, we can find the least common multiple (LCM) of 7 and 3, which is 21.

We can then rewrite the fraction representing the number of points earned by Jill as 9 + 6/7 = (9 * 3 + 6)/21 = 27/21 + 6/21 = 33/21, and the fraction representing the number of points earned by Alice as 8 + 2/3 = (8 * 7 + 2)/21 = 56/21 + 2/21 = 58/21.

To find the difference between the number of points earned by Jill and the number of points earned by Alice, we can subtract the number of points earned by Alice from the number of points earned by Jill:

33/21 - 58/21

We can simplify this expression by combining like terms:

(33 - 58)/21 = -25/21

This represents a difference of -25/21 points, or approximately -1.19 points. Since a negative difference represents a smaller quantity, this means that Alice earned approximately 1.19 points more than Jill.