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An example of geometric series is  2 + 6 + 18 + 54.

When a set of numbers follow a particular order, they are said to be in sequence.

A set of numbers are said to be in geometric sequence if the ratio between second and first term is same as the ratio between third and second term and so on. The geometric sequence is presented as

Sum of n terms = a, ar, ar², ar³,  ......, arⁿ⁻¹, arⁿ.

where,

The first term is a.

Every two consecutive terms, r is the common ratio.

The number of terms is n.

When the numbers in geometric sequence are added together, it is called a geometric series. The geometric series is presented as

Sum of n terms = a + ar + ar² + ar³ + ...... + arⁿ⁻¹ + arⁿ.

where,

The first term is a.

Every two consecutive terms, r is the common ratio.

The number of terms is n.

Let us take an example.

The numbers 2, 6, 18, 54 are in geometric sequence because 6:2 = 18:6 = 54:18 and when we will write it as 2 + 6 + 18 + 54, it will become a geometric series.

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y = 3x - 2 is an example of a linear function graph.

For graphing linear functions, there are three fundamental techniques. The first method involves tracing a line across a set of points that have been plotted. The second method makes use of the slope and y-intercept. Applying transformations to the identity function f(x)=x f(x) = x is the third step.

Those with a straight-line graph are considered to be linear functions. The following is the form of a linear function. a + bx = y = f(x). In the linear function there are one independent and one dependent variables . X is an independent variable, whereas Y is a dependent variable.

Example: The equation y = 3x – 2 depicts a linear function since it is a straight line in the coordinate plane. This function may be expressed as f(x) = 3x - 2 since y can be substituted with f(x).

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The slope-intercept form is the common representation of a linear function.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function since it is a straight line in the coordinate plane. This function may be written as f(x) = 3x - 2 since y can be substituted with f(x).

A mathematical equation must take the form y=mx+b in order to be classified as a linear function (in which m is the slope and b is the y-intercept). This form cannot be satisfied by a nonlinear function. The variables in a linear equation are appear in first degree only and terms containing products of variables are absent.

This equation generates a straight line because the power of x is always one demonstrating that there is only one x variable. As long as the exponent of x is one, the graph is a straight line. Any other values will yield nonlinear curves.

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The equation of line passing through point (-1,0) and slope 4 in slope intercept is  y = 4x + 4   .

The Slope Intercept form of the line is denoted as " y = mx + c " , c in y intercept and m is slope .

the slope of the line is given to be = 4 ;

and the line passes through the point (-1,0) ,

which can be represented as : 0 = (-1)(4) + c ,

0 = -4 + c .

On simplifying further ,

we get ;

c = 4 .

Substituting the values , we get equation as ⇒ y = 4x + 4 .

Therefore , the equation of line is y = 4x + 4  .

The given question is incomplete , the complete question is

How do you write an equation in slope intercept form with one point and slope ? the point is (-1,0) and slope is 4 .

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When the two sides and one angle of a triangle are given then we can find out the other two remaining angles by the law of sins.

Law of Sin :

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

According to the law of sine s

[tex]\frac{sina}{A}[/tex] = [tex]\frac{sin b}{B}[/tex]

[tex]\frac{sin90}{A}[/tex] = [tex]\frac{sin b}{B}[/tex] ( since it is given that one angle is 90 degrees)

[tex]\frac{1}{A}[/tex] =[tex]\frac{sin b }{B}[/tex]

sin b = B/A

b = [tex]sin^{-1}[/tex](B/A)    where B and A are sides of the triangle and known values.

Remaining angle c = 180- [tex]sin^{-1}[/tex](B/A)

Therefore if one angle and at least two sides are given then we can find out the remaining by the law of sin

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The solution of the system of equations:

2x - 3y = -12

y = (-5/3)x - 3

Is (-3, 2)

Here we have the following system of equations:

2x - 3y = -12

y = (-5/3)x - 3

To solve it graphically, we just need to graph the two lines and see where do they intersect. The graph of the system can be seen below.

We can see that the intersection is at the point (-3, 2), so that is the solution of the system.

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The values of x are -3 and 4.

What is factoring polynomial?

The term "factorization of polynomials" or "polynomial factorization" refers to the process of combining irreducible factors with coefficients in the same domain to express a polynomial with coefficients in a given field or in integers.

Consider, the given equation

x^2 - x = 12

Subtract 12 from both sides

x^2 - x - 12 = 12 - 12

x^2 - x - 12 = 0

Since -12 = -4 x 3

⇒ x^2 - 4x + 3x - 12 = 0

x(x - 4) + 3(x - 4) = 0

(x + 3)(x - 4) = 0

⇒ (x + 3) = 0,   (x - 4) = 0

           x = -3,         x = 4

Hence, the values of x are -3 and 4.

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There are two terms in the given expression 5xy²+ 35xy².

What is meant by term?

Terms comprise expressions. A term may be a constant, a variable, or a combination of variables and constants.

What is an example of a term?

It could be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase. Single-word examples: A single phrase is 3x.

There are two terms in the equation 5xyA ^2 + 35xyA^2 that is separated by an arithmetic operator +.

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Answer:

u-41+u-40=u

2u-u=41+40

u=81

Answer:

$1.60

Step-by-step explanation:

1 pound of rice divided into eight sections. Five sections cost $1, thus divide by 5 and multiply by 8

1/5*8 = $1.6

Answer: $1.60  (I think)

Step-by-step explanation: I'm not sure, but when it said the whole diagram = 1 whole pound of rice. So, we know there are 8 parts. So, if 5 of the 8= $1.00. So, the 100 / 5 = 20, now we can ASSUE each tile = 0.20 cents. So, 0.20 x 8 = $1.60. I hope I am right

To add the two expressions (2x^2+6x−3) and (2x^3 −3x+2), we need to combine like terms. Like terms are terms that have the same variable and exponent.

The two expressions have no like terms, so we can simply add them as follows:

(2x^2+6x−3) + (2x^3 −3x+2) = 2x^2 + 6x − 3 + 2x^3 − 3x + 2

= 2x^2 + 2x^3 + 6x − 3x − 3 + 2

= 2x^2 + 2x^3 + 3x − 3 + 2

= 2x^2 + 2x^3 + 3x − 1

The resulting expression is (2x^2 + 2x^3 + 3x − 1).

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Given equations: 2x^2+6x-3+2x^3-3x+2

                             = 2x^2+2x^3+6x-3x-3+2

                             =2x^3+2x^2+3x-1

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The Median of 2 and 6 will be 4.

What is the Median?

The Median is a midpoint value in an ordered set of numbers, the median is a detailed descriptive statistic that distinguishes between the more significant and lesser halves of the group. The median value for a continuous probability distribution is one where a number has an equal chance of falling above or above it.

How to calculate the Median?

First, sort the numbers in the collection from lowest to highest in order to obtain the median (highest to lowest works just as well). Second, ascertain whether the set's elements are an odd or an even number. Third, there is always a middle point if the number of data points is odd; for example, in the set 1, 2, 3, 4, 5, it is 3. The median is the arithmetic mean of the two points closest to the midpoint in sets with an even number of members. For instance, in the set 1, 2, 3, 4, the median is between 2 and 3, therefore (2 + 3) / 2 = 2.5.

In our question two numbers are given 2 and 6, so the median must be between 2 and 6.

Using our concept, the median of this problem will be (2+6)/2= 4.

So, our final answer will be 4.

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Answer:

B=18 and C=2

Step-by-step explanation:

To find the possible factors of the function, recall that a*c must equal u*v and b must equal u+v:

So,

[tex]a=1\\b=16\\c=-36\\u=-2\\v=18[/tex]

[tex](1)(-36)=-36=(-2)(18)[/tex]

and

[tex]16=(-2)+(18)[/tex]

f(x) can then be rewritten as:

[tex]f(x)=x^2-2x+18x-36\\f(x)=(x^2-2x)+(18x-36)\\f(x)=x(x-2)+18(x-2)\\f(x)=(x+18)(x-2)[/tex]

So,

B=18 and C=2

Answer: geometric

Step-by-step explanation:

the first number, 100, is divided by 2 to become 50, and the second number, 50, is divided by 2 to get 25 and so on

The value of the car when Jane bought it three years ago would be = £52,338.46

The value of a product is the cost or worth of that product which can decrease or increase over time and this can affect it's cost outcome.

The value of the car bought by Jane decreases in the first year = 12.5%

The value of the car decreased next two years by 10% each = 10× 2 = 20%

The total percentage decrease in value = 20+12.5 = 32.5%

The amount decreases to.= £17010

That is 32.5% = £17010

100% = X

Make X the subject of formula;

X = 100 × 17010/32.5

X = 1701000/32.5

X= £52,338.46

Therefore, in conclusion, the value of the new car three years ago = £52,338.46.

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To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Common instruments used to measure angles are:

1. Protractor

2.Compass

3.Digital Angle finder

4.Angle finder

5.Clinometer

6. Inclinometer

You can take the following actions to copy angle ABC:

Create a line segment that will serve as the foundation for the new angle you're going to create.

Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.

Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.

Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.

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32.3 divided 5.6 is 0.173

What is an estimation number?

Estimation of numbers is the process of estimating/approximating or rounding off the numbers in which the value is used for some other purpose in order to avoid complicated calculations.

Change the divisor 32.3 to a whole number by moving the decimal point 1 places to the right.

Then move the decimal point in the dividend the same, 1 places to the right.

Now we have the equations:

56 ÷ 323 = 0.173

and therefore:

5.6 ÷ 32.3 = 0.173

Both calculated to 3 decimal places.

32.3 divided 5.6 is 0.173

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Answer: 4.4 meters per second.

Step-by-step explanation:

To determine the speed of the puck, we can use the equation for calculating final velocity given an initial velocity of zero, a force applied for a certain amount of time, and the mass of the object. This equation is:

v = F * t / m

where v is the final velocity, F is the force applied, t is the time over which the force is applied, and m is the mass of the object.

In this case, the mass of the puck is 0.09 kg, the force applied is 28.8 N, and the time over which the force is applied is 0.12 s. Plugging these values into the equation above gives us:

v = 28.8 N * 0.12 s / 0.09 kg = 4.4 m/s

So, the puck will head toward the goal with a speed of approximately 4.4 meters per second.

The volumes of pyramid as well as a prism are always 1:3 Volume of prism if their bases and heights are the same.

A pyramid is just a three-dimensional object that has faces made of triangles and a base made of polygons.

A prism is indeed a three-dimensional object having two identically shaped and sized polygonal bases and rectangular sides.

Thus, the volumes of a pyramid as well as a prism are always 1:3 Volume of prism if their bases and heights are the same.

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Answer:

[tex]m=\frac{3}{2}[/tex]

Step-by-step explanation:

The x value of the y-intercept must be 0, so let

[tex](x_1,y_1)=(0,1)[/tex]

and

[tex](x_2,y_2)=(4,7)[/tex]

The slope of a line can be found with the following:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So,

[tex]m=\frac{(7)-(1)}{(4)-(0)}\\m=\frac{6}{4}\\m=\frac{3}{2}[/tex]

Answer:

subtract 3 from both sides

6m+3=51

6m+3-3=51-3

simplify

6m=48

divide both sides

6m/6 = 48/6

simplify

divide the numbers

m=8

solution.

M = 8

-12

step by step:

√50-3√2(2√2-5) -5√32​

= 5√2 -12+15√2-5(4)√2

= 5√2 -12+15√2-20√2

= -12

The total surface area of the cylinder is 10635 cm-square

Given, the length of the toilet paper roll = 16 cm

The radius of the toilet paper roll = 6cm

The diameter of the inside roll = 3cm

So, the radius of inside cylinder = diameter/2 = 3/2 = 1.5 cm

We know that the formula for :

The total surface area of a cylinder = 2πrh (h+r)

Here, h = 16 cm

r1 = 6cm and r2 = 1.5 cm

Since there are two cylinders one cylinder inside another so here total surface area will be equal to :

2πr1h (h+r1) - 2πr2h (h+r2)

On calculating, Total surface area = 10635 cm-square

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0.8 is the quotient when 2.4 is divided by 3.

In the end, the quotient is what we obtain when we divide a number. A mathematical procedure called division involves separating objects into equal groups. The letter (÷) is used to symbolize it.

When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction and this can be obtained by reversing its numerator and denominator—is and then dividing the  fractions. Multiply the two numerators after that. Multiply the two denominators after that, After that we need to simplify the fraction to its lowest form.

Mathematically quotient is defined by:

 = 2.4 ÷ 3

=> 2.4/ 3

=>0.8

so 0.8 is the quotient when 2.4 is divided by 3

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Answer:

Step-by-step explanation:

Il est difficile de dire si Maxime a fini de refaire la tapisserie de son salon sans plus de contexte. Pour savoir s'il a fini, il faut connaître la surface totale de la tapisserie et combien de papier il a utilisé en tout. Si la surface de la tapisserie est suffisamment grande et que Maxime n'a pas utilisé assez de papier, il n'a pas fini. S'il a utilisé plus de papier que nécessaire, il a peut-être fini, mais il est possible qu'il ait fait des erreurs ou qu'il ait dû recommencer certains morceaux.

Pour savoir combien de papier Maxime a utilisé en tout, il faut ajouter les quantités de papier qu'il a utilisé chaque jour. Quatre quinzième représentent 4/15 de la surface totale de la tapisserie, deux cinquième représentent 2/5 de la surface totale de la tapisserie et un sixième représentent 1/6 de la surface totale de la tapisserie. Si vous ajoutez ces quantités, vous obtiendrez la quantité totale de papier utilisée par Maxime. Ensuite, vous pouvez comparer cette quantité à la surface totale de la tapisserie pour savoir s'il a fini ou non.

The heart beats normally between 60 and 100 times per minute while at rest. Your heart beats far more quickly than usual if you have ventricular tachycardia, with many individuals reporting heart rates of 170 or more per minute.

64% level: 170 x 0.64 = 109 bpm, and 76% level: 170 x 0.76 = 129 bpm

77% level: 185 x 0.77 = 142 bpm, and 93% level: 185 x 0.93 = 172 bpm

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0.25  is the probability of rolling a five on the first die and a one on the second die

How do you calculate probability?

Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen

Very interesting problem.

1  1

1  2

1  3

1  4

2  1

2  2

2  3

2  4

3  1

3  2

3  3

3  4

4  1

4  2

4  3

4 4

There are 16 possible out comes

1   4

4  1

2  3

3  2

4 out of the 16 outcomes are possible

P(5) = 4/16 = 0.25

The theoretical out come would be 4 times

4/16 = 0.25

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Answer:

(- 2, - 3 )

Step-by-step explanation:

since the dilatation is centred at the origin, then multiply the coordinates by the scale factor.

(- 8, - 12 ) → ([tex]\frac{1}{4}[/tex] (- 8), [tex]\frac{1}{4}[/tex] (- 12) ) → (- 2, - 3 )

Therefore , the solution to this problem is confidence interval 95% is given by Z =1.96.

In frequentist statistics, a confidence interval is the range of estimates for an unknown quantity. 95% is the most frequent confidence level used when calculating confidence intervals, however 90% and 99% are also occasionally used.

a)85 out of 100 paid at the pump using credit card

Thus,

p = proportion of customers who paid at the pump using credit card

  = 85/100

  = 0.850

Estimated Value of the population proportion = 0.850

b)

Given:

p' = 0.85           ....... Sample Proportion

n = 100           ....... Sample Size

For 95% Confidence interval

α = 0.05,      α/2 = 0.025

From z tables of Excel function

Z = [tex]\frac{p'-p}{\sqrt{p(1-p)/n} }[/tex]

we find the z value

z = (0.025) = 1.96

We take the positive value of z

Therefore , the solution to this problem is confidence interval 95% is given by Z =1.96.

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