6h/3 algebra simplify expression

How likely something is to occur is known as its probability.Probability when die rolled 1st time is 6C1 i.e. (1,2,3,4,5,6).

How likely something is to occur is known as its probability.We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.

Probability when die rolled 1st time=6C1 i.e. (1,2,3,4,5,6) suppose 1 comes, then 2nd time it should not be .as it is given that no 2 people will roll same number.

so 2nd time probability=5C1 i.e. (2,3,4,5,6). same way 3rd and 4th time probability=4C1 and 3C1 respectively.Probability that no one rolls the same no. = 6*5*4*3and total possibility =6^4 

p(same number)= 6*5*4*3/ 6^4

= 5/18

p(no same number will roll)=1-5/18

=13/18

To learn more about probability refer

https://brainly.com/question/25870256

#SPJ4

n is number of sides of polygon

#b

put n=60

π=3.14159

Difference

Answer:

Given expression:

\(n \times \sin\left(\dfrac{360}{2n}\right)\)

a)  The \(n\) stands for the number of sides of a regular polygon.

b)  If \(n=60\)

\(\implies 60 \times \sin\left(\dfrac{360}{2(60)}\right)=60 \sin(3)=3.140157375...\)

Therefore, the difference between the perimeter and π is:

\(\implies \pi - 60 \sin(3)=0.001435279013...\)

Answer:

3003

Step-by-step explanation:

This is a combination since the order doesn't matter

15 C 10

The formula

15!

-------

10! (15-10)!

15*14*13*12*11

--------------------

5*4*3*2*1

3003

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(y= \stackrel{\stackrel{m}{\downarrow }}{4}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line whose slope is 4 and passes through (1 , 6)

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{4}(x-\stackrel{x_1}{1})\)

\(y-6=4x-4\implies y=4x\underset{\stackrel{\uparrow }{b}}{+2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

To find the area of the surface generated by revolving the curve y = 4 - x^2, -1 ≤ x ≤ 1, about the y-axis, we can use the formula for the surface area of revolution:

\(A = 2π ∫[a,b] f(x) √(1 + (f'(x))^2) dx\)

In this case, we have \(f(x) = 4 - x^2 and f'(x) = -2x.\)

Plugging these into the formula, we get:

\(A = 2π ∫[-1,1] (4 - x^2) √(1 + (-2x)^2) dx\)

Simplifying the expression inside the square root:

\(A = 2π ∫[-1,1] (4 - x^2) √(1 + 4x^2) dx\)

Now, we can integrate to find the area:

\(A = 2π ∫[-1,1] (4 - x^2) √(1 + 4x^2) dx\)

Note: The integral for this expression can be quite involved and may not have a simple closed-form solution. It may require numerical methods or specialized techniques to evaluate the integral and find the exact area.

To know more about curve click the link below:

brainly.com/question/31388450

#SPJ11

Answer:

Step-by-step explanation:

1. If PQ = PQ then PQ ≅ PQ

 Reflexive Property of congruence

2. If K is between J and L, then JK + KL = JL

 Segment addition property

3. EF ≅ EF

 Definition of congruence

4. If RS = TU, then RS + XY = TU + XY

 Addition property of equality

5. If AB = DE, then DE = AB

 Symmetric property of equality

Based on the two expressions, the statement that describes the comparison of the distance that Edward ran and the distance that Richard ran is A) A) The distance that Edward ran is 4 times the distance that Richard ran.

An expression is a mathematical combination of variables, numbers, constants, mathematical operands, without the equal symbol (=).

The mathemaical expressions representing the total distances covered by Richard and Edward are:

The distance Richard ran = x + 5

The distance Edward ran = 4x + 20

When 4x + 20 is factored:

4x + 20 = 4(x + 5)

4(x + 5) ÷ (x + 5) = 4

Thus, the expression 4x + 20 is 4 times the expression x + 5.

Learn more about mathematical expressions at https://brainly.com/question/1859113.

#SPJ4

Richard ran a distance represented by the expression x + 5. Edward ran a distance represented by the expression 4x + 20. Which describes the comparison of the distance that Edward ran and the distance that Richard ran?

A) The distance that Edward ran is 4 times the distance that Richard ran.

B) The distance that Edward ran is 2 times the distance that Richard ran.

C) The distance that Edward ran is 3 times the distance that Richard ran.

D) The distance that Edward ran is 5 times the distance that Richard ran.

The three angles above the bottom line are supplementary, so they add up to 180° in measure:

2x° + 90° + x° = 180°

3x° + 90° = 180°

3x° = 90°

x = 30

The angles with measure x° and 2y° are congruent, since they form a pair of interior angles that alternate with respect to the transversal (in this case, this is the ray that starts from the bottom line and point up and to the right, and passes through the parallel upper line). So

2y° = x°

2y° = 30°

y = 15

Below the upper line, the two angles 2y° and z° are supplementary, so

2y° + z° = 180°

30° + z° = 180°

z = 150

Sam has 7/8 m of rope left.

What is fraction ?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

To derive a solution, you have to subtract the meter of rope that Sam has from the meter of rope he cut for a project.  

Therefore,

1½ - 5/8,  

Since the meter of rope Sam had is represent with a mixed fraction, we have to convert it to an improper fraction, and therefore 1½ can also be written as 3/2

Therefore, we have

3/2 – 5/8

To solve this fraction, you need to find the smallest number that can divide the denominator (2 and 8), which is 8.  

Now divide the denominators with 8 and multiply the answers you get by the numerators.

Therefore, we have

3/2 -5/8

= 12/8 – 5/8

= 7/8 m.

Therefore, Sam has 7/8 m of rope left.

The smallest number used to divide the denominators is also known as the lowest common denominator (LCD).

A fraction has 2 parts, which are numerator and denominator. The numerator is the number at the top in a fraction while the denominator is the number below in a fraction.  

To learn more about fraction from the given link

https://brainly.com/question/78672

#SPJ1  

Answer:

C

Step-by-step explanation:

\((a^{-2}*8^{7})^2 = a^{-2*2}*8^{7*2} = a^{-4}*8^{14}\)

This is the UML diagram for the development of the program, in which Shapes 2D is the superclass and Circle, Square, Triangle, Rectangle, Rhombus, and Parallelogram are subclasses.

​​​​​​​This is the program in C++ demonstrating the above classes.

#include<iostream>

using namespace std;

class shapes

{

public:

   string name;

   string color;

   virtual void getAttributes()=0;

};

class Circle: public shapes

{

public:

   float radius;

   Circle(string n,string c, float r)

   {

       name=n;

       color=c;

       radius=r;

   }

   float getPerimeter()

   {

       return(2*(3.142)*radius);

   }

   float getArea()

   {

       return((3.142)*(radius*radius));

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Square:public shapes

{

public:

   float side;

   Square(string n,string c, float s)

   {

       name=n;

       color=c;

       side=s;

   }

   float getPerimeter()

   {

       return(4*side);

   }

   float getArea()

   {

       return(side*side);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Triangle:public shapes

{

public:

   float base;

   float height;

   float side1;

   float side2;

   float side3;

   Triangle(string n,string c)

   {

       name=n;

       color=c;

   }

   float getPerimeter()

   {

       cout<<"Enter side1\n";

       cin>>side1;

       cout<<"Enter side2\n";

       cin>>side2;

       cout<<"Enter side3\n";

       cin>>side3;

       return(side1+side2+side3);

   }

   float getArea()

   {

       cout<<"Enter base\n";

       cin>>base;

       cout<<"Enter height\n";

       cin>>height;

       return((0.5)*base*height);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Rectangle:public shapes

{

public:

   float length;

   float breadth;

   Rectangle(string n,string c, float l,float b)

   {

       name=n;

       color=c;

       length=l;

       breadth=b;

   }

   float getPerimeter()

   {

       return(2*(length+breadth));

   }

   float getArea()

   {

       return(length*breadth);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Rhombus:public shapes

{

public:

   float diagonal1;

   float diagonal2;

   float side;

   Rhombus(string n,string c)

   {

       name=n;

       color=c;

   }

   float getPerimeter()

   {

       cout<<"Enter Side\n";

       cin>>side;

       return(4*side);

   }

   float getArea()

   {

       cout<<"Enter diagonal 1\n";

       cin>>diagonal1;

       cout<<"Enter diagonal 2\n";

       cin>>diagonal2;

       return((0.5)*diagonal1*diagonal2);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Parallelogram:public shapes

{

public:

   float base;

   float height;

   Parallelogram(string n,string c, float b,float h)

   {

       name=n;

       color=c;

       base=b;

       height=h;

   }

   float getPerimeter()

   {

       return(2*(base+height));

   }

   float getArea()

   {

       return(base*height);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

int main()

{

   int choice;

   while(1)

   {

       cout<<"\n\nEnter your choice :";

       cout<<"\n1 for Circle\n";

       cout<<"2 for Square\n";

       cout<<"3 for Triangle\n";

       cout<<"4 for Rectangle\n";

       cout<<"5 for Rhombus\n";

       cout<<"6 for Parallelogram\n";

       cin>>choice;

       system("cls");

       switch(choice)

       {

       case 1:

           {

               float r;

               cout<<"Enter radius\n";

               cin>>r;

               Circle c("Circle","Yellow",r);

               c.getAttributes();

               cout<<"Perimeter : "<<c.getPerimeter()<<endl;

               cout<<"Area : "<<c.getArea()<<endl;

           }break;

       case 2:

           {

               float side;

               cout<<"Enter side\n";

               cin>>side;

               Square s("Square","Red",side);

               s.getAttributes();

               cout<<"Perimeter : "<<s.getPerimeter()<<endl;

               cout<<"Area : "<<s.getArea()<<endl;

           }break;

       case 3:

           {

               Triangle t("Triangle","Green");

               t.getAttributes();

               cout<<"Perimeter : "<<t.getPerimeter()<<endl;

               cout<<"Area : "<<t.getArea()<<endl;

           }break;

       case 4:

           {

               float l,b;

               cout<<"Enter Length and breadth\n";

               cin>>l>>b;

               Rectangle r("Rectangle","Blue",l,b);

               r.getAttributes();

               cout<<"Perimeter : "<<r.getPerimeter()<<endl;

               cout<<"Area : "<<r.getArea()<<endl;

           }break;

       case 5:

           {

               Rhombus r("Rhombus","Purple");

               r.getAttributes();

               cout<<"Perimeter : "<<r.getPerimeter()<<endl;

               cout<<"Area : "<<r.getArea()<<endl;

           }break;

       case 6:

           {

               float b,h;

               cout<<"Enter base\n";

               cin>>b;

               cout<<"Enter height\n";

               cin>>h;

               Parallelogram p("Parallelogram","Pink",b,h);

               p.getAttributes();

               cout<<"Perimeter : "<<p.getPerimeter()<<endl;

               cout<<"Area : "<<p.getArea()<<endl;

           }break;

       }

   }

}

To learn more about objects and classes,

https://brainly.com/question/21113563

#SPJ4

Answer:

$282.50

Step-by-step explanation:

He will be charged $7.50 for 3 months, which is a total of 7.5 * 3 = $22.50.

Subtract this from the amount in his account to find the amount of money he has at the end of the three months:

305 - 22.5 = 282.5

The answer is therefore $282.50.

Answer: 892.5

Step-by-step explanation:

Answer:  1 8/9

Step-by-step explanation: you convert 1 1/3 to 1 3/9 then add 5/9 to 1 3/9 to get a total of 1 8/9

The quotient is x + 6 with a remainder of 15/(x - 1). We can write the original expression as: (x^2 + 5x + 4)/(x - 1) = x + 6 + 15/(x - 1)

Synthetic division is a shorthand method of dividing polynomials that involves using only the coefficients of the terms. To use synthetic division, the polynomial must be written in standard form with descending powers of x, and the divisor must be of the form (x - a), where a is a constant.

In this problem, we want to divide the polynomial x^2 + 5x + 4 by x - 1 using synthetic division.

First, we write the coefficients of the polynomial in standard form:

1 5 4

1

Next, we bring down the first coefficient (1) to the second row of the synthetic division table:

1 5 4

1 |

Then, we multiply the value in the second row by the divisor (x - 1) and write the result in the third row:

1 5 4

1 | 6

To get the next value in the third row, we add the value in the second row to the value in the third row:

1 5 4

1 | 6

|-------

| 11

We repeat this process until we have all the coefficients of the quotient polynomial. In this case, we only need one more step:

1 5 4

1 | 6

|-------

| 11 15

The final row of the synthetic division table gives us the coefficients of the quotient polynomial:

x^2 + 5x + 4 = (x - 1)(x + 6) + 15/(x - 1)

Note that the remainder term is a rational function with a vertical asymptote at x = 1. It is important to keep track of the remainder term when dividing polynomials, as it can provide additional information about the behavior of the function near the divisor.

Learn more about polynomial at: brainly.com/question/11536910

#SPJ11

Solve Using Synthetic Division: (x2+Solve Using Synthetic Division: (x2+5x+4)÷(x-1)5x+4)÷(x-1)

Answer:

4.32 francs

Step-by-step explanation:

45p × £/(100p) × 9.6 francs / £ = 4.32 francs

Answer:

The supplementary angle of the first angle is 180 degrees minus the measure of the angle, which would be 156 degrees. The supplementary angle of the second angle is 180 degrees, so the sum of the two supplementary angles is 336 degrees.

\(f+44^{\circ}\) and \(71^{\circ}\) are opposite angles.

Therefore

\(f+44^{\circ}=71^{\circ}\\f=27^{\circ}\)

27°

Using information about angles, we can create an equation to solve for f.

Verticle Angles

There is a special angle relationship known as vertical angles. Vertical angles are opposite angles made by interesting lines. The left angle  (made up of f and 44°) and the right angle (71°) are vertical angles. We know this because they are opposite each other and formed by the same interesting lines. Verticle angles are always congruent. This means that their measurements are equal.

Solving for f

We can use the information above to create an equation. Since we know that the left and right angles are congruent, we can set the equal to each other.

Now, we can subtract 44 from both sides and solve for f.

So, angle f must equal 27°.

The sides of the triangle as vectors are,

AB = (3, 1) = 3i + j

BC = (- 2, 3) = - 2i + 3j

CA = (- 1, - 4) = - i - 4j

We have to give that,

Vertices of the triangle are,

A(2, 2), B(5, 3) , and C(3, 6)

Hence, the sides of the triangle as vectors are,

AB = (5, 3) - (2, 2) = (5 - 2, 3 - 2) = (3, 1)

BC = (3, 6) - (5, 3) = (3 - 5, 6 - 3) = (- 2, 3)

CA = (2, 2) - (3, 6) = (2 - 3, 2 - 6) = (- 1, - 4)

Therefore, the sides of the triangle as vectors are,

AB = (3, 1) = 3i + j

BC = (- 2, 3) = - 2i + 3j

CA = (- 1, - 4) = - i - 4j

To learn more about the triangle visit;

brainly.com/question/1058720

#SPJ4

Answer:

1

Step-by-step explanation:

Answer: The answer is 56

explanation: 7*8 is the same as 8+8+8+8+8+8+8 or 7+7+7+7+7+7+7+7 and if you do the math it equals 56

y+43°= 180°( straight angle)

=>y= 180°-43°

=>y=137°

Answer:

85%

Step-by-step explanation:

17 divided by 20, times 100 = 85%

So, 85% of the sheep had black wool.

Answer:

\( y = 10x \)

Step-by-step explanation:

Finding the slope (m) of the line the following points in the line, (0, 0) and (2, 20):

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{20 - 0}{2 - 0} = \frac{20}{2} = 10 \)

y-intercept (b) is 0. The line intercepts the y-axis at 0. Thus, b = 0.

Substitute m = 10 and b = 0 in \( y = mx + b \)

The equation in slope-intercept form for the graph would be:

✅\( y = 1x + 0 \)

\( y = 10x \)

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

Learn more about circle here

brainly.com/question/11878555

#SPJ4

The correct force equilibrium equation along the y direction is ∑Fy = Cy + 450sin40° - 300 = 0.

The force equilibrium equation is used to find the unknown forces or force components that keep an object stationary, i.e. in equilibrium.

A force is defined as the push or pull on an object that results from its interaction with another object. The force equilibrium equation is based on the principle that for an object to be in equilibrium, the sum of all the forces acting on it must be equal to zero.

This equation is a vector equation that can be resolved into its x and y components. The correct force equilibrium equation along the y direction is ∑Fy = Cy + 450sin40° - 300 = 0.

Learn more about force equilibrium equation at

https://brainly.com/question/30426299

#SPJ11

The inequality that Matt could solve to find out how many more miles he can run if he keeps his current pace is less than 6 miles.

It should be noted an inequality is used to show the expressions that are not equal.

In this case, Matthew wants his run today to take no more than 90 minutes and he already has run 30 minutes at a pace of 10 minutes per mile.

Therefore, the appropriate inequality will be;

Let miles = m

m <= 90/10 - 30/10

m <= 9 - 3

m <= 6

He has about 6 miles more.

Learn more about inequalities on:

brainly.com/question/11613554

#SPJ1

Answer:

See Explanation

Step-by-step explanation:

Given

\(a = b\)

Required

Match proper type of equality

Each of the equality properties can easily be identified with their names; For multiplication property of equality, same term must be multiplied on both sides;

For addition, same term  must be added on both sides;

Same thing implies for division and subtraction

Multiplication:

\(a(c) = b(c)\)

Subtraction

\(a - c = b - c\)

Addition

\(a + c = b + c\)

Division

\(a/c = b/c\)