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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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-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 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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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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The coefficient of x³y² in the expansion of (2x+y)5 is 80.

Given data :

The coefficients of terms of (p+q)^n can be found by the Pascal's triangle for small values of n.  Pascal's triangle will start with (1,1)  = coefficients of (p,q)^n =1.  For n=2, we add successive terms of the previous value of n.  Thus for n-2, we have (, 1+1,11=(1,2,1), for n=3, we have (1,3,3,1), giving the following pattern:

(1,1)

(1,2,1)

(1,3,3,1)

(1,4,6,4,1)

(1,5,10,10,5,1)

meaning for n=5, the binomial expansion for (P+Q)^5 is

P^5+5P^4Q+10P^3Q^2+10P^2Q^3+5PQ^4+Q^5

Setting P=2x, Q=y in the term 10P^3Q^2, we get a term

10(2x)^3(y)^2

=10(8x^3)(y^2)

=80x^3y^2

So the required coefficient is K=80.

We can also find the coefficient 10 by binomial expansion of

n=5, x=3 in

C(n,x) = n! / (x! (n-x)!) = 5! / (2!3!) = 5*4*3/(1*2*3) = 10

Then again substituting 10(2x)^3(y)^2 = 80x^3y^2

to get the coefficient K=80.

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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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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:

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.

Answer:

[tex]y=\frac{3}{5}x+\frac{1}{5}[/tex]

Step-by-step explanation:

Using the points [tex](3,2)[/tex] and [tex](8,5)[/tex],

[tex]m=\frac{5-2}{8-3}=\frac{3}{5} \\ \\ y-2=\frac{3}{5}(x-3) \\ \\ y-2=\frac{3}{5}x-\frac{9}{5} \\ \\ y=\frac{3}{5}x+\frac{1}{5}[/tex]

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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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 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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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]

How do you find the mean of 4 numbers?

Finding the mean, refers to finding the average. To do this, add the four numbers together and then divide that number by 4.

There are 5 types of line graphs:

1) Simple line graph                                 2) Compound Line Graph

3) Multiple Line Graph                             4)Vertical Line Graph

5) Horizontal Line Graph                         6) Straight Line Graph

1) Simple Line Graph:

A simple line chart is the most basic type of line chart. Only one dependent variable is tracked in this chart, so there is only one line connecting all the data points on the chart. All points in the chart relate to the same element and the sole purpose of the chart is to track changes in these variables over time. Only variables are graphed, so this graph cannot be used to compare one variable to another.

2) Multiple Line Graph:

In a multiple line chart, multiple dependent variables are plotted on a chart and compared against a single independent variable (often time). Different dependent variables are often marked with different colored lines to distinguish each data set. Each row relates only to points in the specified dataset. Lines do not cross between dependent variables.

3) Compound Line Graph:

If information can be subdivided into two or more types of data. This type of line graph is called a compound line graph.  Composite line charts, like multiline charts, use multiple variables. However, variables are often stacked on top of each other to show the sum of all variables. This informs the user not only of the relationship between each variable, but also of how the total is changing.

4) Vertical Line Graph:

A vertical line chart is a chart in which a vertical line extends from each data point to the horizontal axis. A vertical line chart is sometimes called a column chart. A line parallel to the y-axis is called a vertical line.

5) Horizontal Line Graph:

A horizontal line chart is a chart with a horizontal line running parallel to the globe at each data point. Horizontal line charts are sometimes called line charts.

6) Straight Line Graph:

A line parallel to the X axis is called a vertical line. Line charts are often used to solve conditions that change over specific time intervals. The general linear function has the form y = mx + c, where m and c are constants.

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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 )

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 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

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 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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The inverse of a 3x3 matrix is found by creating an Adjugate Matrix.

Step 1 : For any matrix M find the adjoint matrix.

        [tex]\text{Let a matrix }M= \left[\begin{array}{ccc}1&2&3\\0&1&4\\5&6&0\end{array}\right][/tex]

                         [tex]M^{T}= \left[\begin{array}{ccc}1&0&5\\2&1&6\\3&4&0\end{array}\right][/tex]

                       Adj M = [tex]\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right][/tex]

Step 2 :Find Determinant of a 3x3 Matrix

         [tex]M= \left[\begin{array}{ccc}1&2&3\\0&1&4\\5&6&0\end{array}\right][/tex]

       det (M)= 1 (0- 24 ) - 2 (0 - 20 )+3 (0- 5 )

                  = - 24 + 40 -15

                  = 40 - 39

                  = 1

Step 3 : Find inverse matrix [tex]M^{-1}[/tex]

          [tex]M^{-1 } = \frac{1}{det (M)} (Adj M)[/tex]

          [tex]M^{-1 } = \frac{1}{det (M)} (Adj M)\\\\M^{-1 } = \frac{1}{1}\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right]\\\\M^{-1 }=\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right][/tex]

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Answer:

x = 43.25

Step-by-step explanation:

(x + 2 )+ (x + 2) + (2x + 3) = 180(total angles in a triangle)

x + 2 + x + 2 + 2x + 3 = 180

x + x + 2x + 2 + 2 + 3 = 180

4x + 7= 180

4x = 180 – 7

4x = 173

divide both sides by (4)

[tex] \frac{4x}{4} = \frac{173}{4} [/tex]

x = 43.25

i hope this helps

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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Answer:

u-41+u-40=u

2u-u=41+40

u=81

The balance after 5 years would be near around 5661 dollars.

What is compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

According to the given question:

First, convert R as a percent to r as a decimal

r = R/100

r = 2.5/100

r = 0.025 rate per year,

Then solve the equation for A

A = P(1 + r/n)ⁿˣ

A = 5000(1 + 0.025/2)²ˣ⁵

A = 5661.35

Hence the balance after 5 years would be near around 5661 dollars.

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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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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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