What is an advantage of using graphing to solve a system of equations?.

The wine quality score for a wine that has an alcohol content of 10% is 73.4. So the option a is correct.

In the given question, this study examined the relationship between wine quality score (winescore) and alcohol content (alcohol) for 160 bottles of red wine.

Wine quality score ranges from 0-100 points, with a higher score indicating a higher quality wine. Alcohol content is measured in percent alcohol content and ranges from 8.4 - 13.6 (e.g. alcohol=9.5 would mean an alcohol content of 9.5%).

The data and question is given below;

We have to predict the wine quality score for a wine that has an alcohol content of 10%.

So, wine quality = 59.3 + 1.41*Alcohol Content

wine quality = 59.3 + 1.41*10

wine quality = 59.3 + 14.1

wine quality = 73.4

Hence, the wine quality score for a wine that has an alcohol content of 10% is 73.4. So the option a is correct.

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The cost of adult tickets is £17.00 and child tickets cost £9.00

What is an equation?

An equation is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here, we have

The Smith family of two adults and three children pays £61.

The Jone family of three adult and five children pay £96.

By using this, we get the following equations:

2a + 3c = 61.....(1)

2a = 61 - 3c

a = 30.5 - 1.5c

3a + 5c = 96....(2), By putting the value of a in (2), we get

3(30.5-1.5c)+5c = 96

91.5-4.5c+5c = 96

91.5+0.5c = 96

0.5c = 4.5

c = 9, and since a = 30.5 - 1.5c

a = 17

Hence, adult tickets cost £17.00 and child tickets cost £9.00.

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To solve the quadratic equation by completing the square 11.25 needs to be added to the equation.

The given equation is x²+13x+31 = 0

Let us now solve it by completing the square:

x² + 13x + 31 = 0

or, x² + 2x × 6.5 +6.5² -6.5²+ 31 = 0

or, (x +6.5)² -42.25+31 = 0

or,  (x +6.5)² -11.25 = 0

Therefore we have to add 11.25 to the equation to solve the quadratic equation.

The roots or zeros of the expression on the left side of the equation are the values of x that satisfy the equation. There can only be two possible solutions to a quadratic problem. If there is only one solution, a problem is said to have a twofold root.

The only choices are one real double root, two distinct solutions that are complex conjugates of one another, two real solutions, or two real solutions if all the coefficients have real values.

If complex roots are taken into account, a quadratic equation will always have two roots; a double root counts as two. An equivalent equation can be created by factoring a quadratic equation.

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The proof for congruent triangles is as follows.

What is congruent triangles?

Congruence of triangles: 2 triangles are same to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure.

Main body:

SSS (Side-Side-Side)-

If all the 3 sides of 1 triangle are corresponding to the corresponding 3 sides of the second triangle, then the 2 triangles area unit aforesaid to be congruent by independent agency rule.

SAS (Side-Angle-Side)

If any 2 sides and also the angle enclosed between the perimeters of 1 triangle ar corresponding to the corresponding 2 sides and also the angle between the perimeters of the second triangle, then the 2 triangles ar aforementioned to be congruent by SAS rule.

ASA (Angle-Side- Angle)

If any 2 angles and therefore the facet enclosed between the angles of 1 triangle ar corresponding to the corresponding 2 angles and facet enclosed between the angles of the second triangle, then the 2 triangles ar aforesaid to be congruent by ASA rule.

AAS (Angle-Angle-Side)

AAS stands for Angle-Angle-Side. once 2 angles and a non-included facet of a triangle square measure adequate to the corresponding angles and sides of another triangle, then the triangles square measure aforementioned to be congruent.

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Fatality related to motor vehicle traffic is the number one cause of accidental death and motor vehicle collisions are the leading cause of death for people ages 3 to 33

The fatality related to motor vehicle is not common in the US. The US ranked 11th position in the collision vehicle death. Therefore the number one cause of accidental death and motor vehicle collisions are the leading cause of death for a lot people. From the data it is clear that most of the people were in the age of 3 to 33. The younger population dying in crashes of motor vehicles. So it is the leading cause of death of younger people in the united state

Hence,  Fatality related to motor vehicle traffic is the number one cause of accidental death and motor vehicle collisions are the leading cause of death for people ages 3 to 33

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The agile principle definition is, they outlined a number of fundamental ideas that should be prioritized by businesses, such as client satisfaction, teamwork, flexibility, and more.

What is the Agile cycle?

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The project management approach a team decides on will have a small impact on the Agile life cycle. For instance, Scrum teams work in sprints, which are brief timeframes akin to iterations. They also have responsibilities that are precisely defined, like Scrum master. Kanban teams, on the other hand, operate more continuously and don't have set roles. Another illustration is Extreme Programming, where teams frequently work in shorter iterations and give engineering practices more attention. Self-organized teams can better adapt to business requirements with a lightweight strategy. All agile frameworks use iterative and incremental development and have a set, defined iteration duration. They also all take a lightweight approach that enables self-organized teams to better adapt to business needs. It's a term for methods used in software development.

Hence,

The agile principle definition is, they outlined a number of fundamental ideas that should be prioritized by businesses, such as client satisfaction, teamwork, flexibility, and more.

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The concept of Linear Regression including the difference between the dependent and independent variable is given below .

In the question ,

we have to explain the concepts of Linear Regression ,

the term Linear regression is defined as the relationship between the dependent and one independent variable through a linear equation.

It is called Simple Linear Regression when only one independent variable is used and

it is called Multiple Linear Regression when two or more independent variables are used .

the dependent variable is the variable that is being studied or that we want to predict, and

the independent variable is the variable which is independent in nature and used to predict  dependent variable .

Therefore , the concepts about Linear Regression are explained .

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The three angles opposite the three equal sides are equal in size because the three sides are equal.

Given,

An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. It is also known as an equiangular triangle since each angle is 60 degrees.

A right-angled triangle has one angle that is 90 degrees, thus if we define an equilateral triangle as having all angles that are 90 degrees, their sum would be 270 degrees, which is not conceivable because the sum of all the angles in a triangle is 180 degrees.

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4 number can be arranged in 4! ways and to remove repetitions of 3 nines divide by 3!.

What is permutation and combination?

A set of items can be divided into subsets in two different ways: combination and permutation.

                                  The subset's components can be listed in any order when combined. The subset's components are listed in a permutation in a specific order.

(a) Strings with no repetition of digit is 9 * 9 * 8 * 7

b) Strings which end with an even digit : 9 * 9 * 9 * 5

5 -- > because of 5 even numbers. In the other places can digit can be displayed

c) Strings with exactly three digits that are 9s = 9 * 4! / 3!

4 number can be arranged in 4! ways and to remove repetitions of 3 nines divide by 3!.

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The angular velocity of tip is 5.42/√L rad/s and the speed of the tip of rod is 5.42√L m/s.

In the given question, a long, thin rod of mass M and length L is standing straight up on a table. Its lower end rotates on a frictionless pivot. A very slight push causes the rod to fall over.

Applying conservation of rotational energy to this situation.

At the start, there is only Potential Energy(PE) and no Kinetic Energy(KE) just before impact, all the PE has converted to KE.

In the starting, the center of mass is half way up, so;

The PE of this system is 1/2 MgL;

where L is the length,

The KE at the end is 1/2 Iw^2

where I is the moment of inertia and w is the angular velocity.

I for a stick pivoted at an end I = 1/3 mL^2, so we have

1/2×m×g×L = 1/2×1/3×m×L^2×w^2

1/2×g = 1/6×lw^2

w = √[3g/L]

A) We have to find the angular velocity.

As we know g=9.8 m/sec^2

w = [tex]\sqrt{3\times9.8/L}[/tex]

w = √(29.4/L)

w = 5.42√L

The angular velocity of tip is 5.42/√L rad/s.

B) We have to find the speed of the tip of the rod.

The speed of the Tip , v = l×w

v = L × 5.42√L

v = 5.42 × √L

The speed of the tip of rod is 5.42√L m/s.

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Proof:

The slope of (0,0) to (1,0) is undefined (the denominator is 0). Same with (1,1) to (0,1).

The slope of (0,0) to (0,1) and (0,1) to (1,1) is 0.

There are two parallel lines, and the slope are negative reciprocals of each other, meaning they're perpendicular.

The distance of the points are all 1.

Therefore, it fits the requirements of a square.

The correct answer is option D.

ag=bg

What is the work of the bisector?

Bisector cuts something in 1/2 of. An attitude bisector is a line that cuts a given attitude in 1/2 of. The perpendicular bisector of a line phase is the road that cuts the given phase in 1/2 of and is at proper angles to it.It is for this reason that line CD is bisecting the facet AB in triangle ABE.

Bisecting a line phase method that diving a line phase into  same parts. So, whilst CD bisects facet AB at factor G it method that:AG = BG.and AE = BG

Since the line bisects at point g therefore ag=bg

It is given that line CD is bisects the side AB in triangle ABE

and AE = BE .

Bisecting a line segment means that dividing a line segment into two equal parts. So, when CD bisects side AB at point G it means that:

AG = BG

Hence, the correct answer is option D.

ag=bg

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The proportion and the standard deviation of the sample proportion for samples of size 100 are 0.047.

A statistic's probability distribution is called a sampling distribution when it is calculated from a larger number of samples taken from a particular population. The distribution of frequencies for a variety of outcomes that could possibly occur for a statistic of a population is known as the sampling distribution of that population.

it is given that,

Population size = 1000

sample size = 100

so, proportion = 0.5

the standard deviation of the sample proportion = [tex]\sqrt{\frac{N-n}{N-1} . \frac{P(1-P)}{n} }[/tex]

= √{( 1000-100)/(1000-1) × (0.5 × 0.5/100)}

= √0.002252

= 0.047

thus, the proportion and the standard deviation of the sample proportion are 0.5 and 0.047.

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Being able to inspect and adapt at scale is more what enterprise agile is all about.

What is enterprise ?

Despite being another word for a for-profit business or organization, the word "enterprise" is most frequently related to entrepreneurial endeavors. Those who are successful in business are frequently referred to as "enterprising." Legal businesses come in a variety of shapes and sizes, but the most popular ones in the US.

At the executive level, it's about placing smaller wagers. It involves being able to balance the sales and marketing side of the business with your capacity to develop useful products and then sustainably support those products.

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The addition doubles fact used here is 4+4 =8 or 5+5=10

Given,

Double facts;-

Remind your kids that a double fact is a mathematical expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16. Give children the chance to practize combining groups of the same number using manipulatives or other classroom supplies.

Here,

We have to find the  addition doubles fact that can help us to solve 4 + 5

Then,

⇒4+5

=4+4+1----[5=4+1]

=2 × 4 +1

=8+1

= 9

Now,

→4+5

=(5-1)+5

=5+5-1

=10-1

=9

Therefore,

The addition doubles fact used here is;

→4+4 =8

or

→5+5=10

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Answer:   x2− y2

x al Cuadrado 2. Y al cuadrado 2

espero que te ayude

Step-by-step explanation:

Yes, all equilateral triangles also isosceles triangles. No, all isosceles triangles are not equilateral triangles. Any two sides that are equal have equal opposite angles since every equilateral triangle is likewise an isosceles triangle.

A triangle is a two-dimensional shape with three sides, three internal angles, and three vertices that is used in geometry.

Given,

All equilateral triangles can also isosceles triangles are all isosceles triangles also equilateral triangles,

Any two sides that are equal have equal opposite angles since every equilateral triangle is likewise an isosceles triangle. As a result, because an equilateral triangle has equal lengths on each of its three sides, its three angles are also equal. As a result, every equiangular triangle is an equilateral triangle.

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The size of the angle θ in degrees to the nearest integer will be;

⇒ θ = 65°

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In the triangle,

The perpendicular length = 13 cm

The base = 6 cm

Now,

We know that;

⇒ tan θ = Perpendicular / Base

Substitute all the values, we get;

⇒ tan θ = 13 / 6

⇒ tan θ = 2.16

⇒ θ = 65.15

⇒ θ = 65°

Thus, The size of the angle θ in degrees to the nearest integer will be;

⇒ θ = 65°

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In the given reaction, oxygen is the limiting reagent and carbon disulfide is the excess reagent.

According to our question-

a) The limiting reactant is Oxygen  

b) There will remain 0.667 moles of Carbon disulfid  

c) 0.333 moles of Carbon dioxide and 0.667 moles of Sulfur dioxide will be formed.  

1 mole of Carbon disulfide need 3 moles of Oxygen to produce 1 moles of Carbon dioxide and 2 moles of sulfur dioxide.  

Number of moles of  Carbon disulfide = 1.00 mol  

Number of moles of Oxygen = 1.00 mol    

Calculate the limiting reactant    

Oxygen is the limiting reactant. It will completely be consumed.(1.00 mol).  

(B) Carbon disulfide is excess reactant. There will react with

Carbon disulfide react with 0.33 moles of Oxygen.

The remaining excess reagent:

0.667 moles of Carbon disulfide will remains.  

Calculate moles of products:

1 mole of Carbon disulfide need 3 moles of Oxygen to produce 1 moles of Carbon dioxide and 2 moles of sulfur dioxide.  

For 1.00 mol of oxygen =  1.00/3 = 0.333 moles Carbon dioxide.  

For 1.00 mol of Oxygen  = 1.00 /(3/2) = 0.667 moles of sulfur dioxide.

Hence, In the given reaction, oxygen is the limiting reagent and carbon disulfide is the excess reagent.

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James has a total of 62 dimes and 100 quarters in his collection

The given parameters in the question are:

Total count of coins = 162

Worth of coins = $31.20

Represent the dimes with x and the quarters with y

So, we have the following representations

Dimes in dollars = 0.1x

Quarters in dollars = 0.25y

Solving further, we have the following equations

x + y = 162

0.1x + 0.25y = 31.20

Make x the subject in the equation x + y = 162

So, we have the following representation

x = 162 - y

Substitute x = 162 - y in 0.1x + 0.25y = 31.20

0.1(162 - y) + 0.25y = 31.20

Evaluate

16.2 - 0.1y + 0.25y = 31.20

So, we have

0.15y = 15

Divide both sides by 0.15

y = 100

Recall that

x = 162 - y

So, we have

x = 162 - 100

Evaluate

x = 62

Hence, the number of dimes is 62

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Possible question

James has dimes and quarters saved up in his change jar. He has a total of 162 coins totaling $31.20.

What is the number of dimes and quarters in James collection?