what do you mean by arithmetic series?​

The explicit formula for the given sequence 8, 20, 50, 125, 312.5, ... is a_n = 8 × 2.5^(n-1)

To find an explicit formula for the given sequence, we first need to identify the pattern or rule that generates the terms.

Looking at the sequence, we can see that each term is obtained by multiplying the previous term by a fixed factor and then adding a constant.

To find this factor and constant, we can use the general form of a geometric sequence:

a_n = a_1 × r^(n-1)

where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the index of the term.

Using the first two terms of the sequence, we can find the common ratio:

r = a_2 / a_1 = 20 / 8 = 2.5

Now we can use the first term and the common ratio to find the constant term

a_1 = 8 = a_1 × 2.5^(1-1) + c

c = 8 - a_1 = 0

Therefore, the explicit formula for the given sequence is:

a_n = 8 × 2.5^(n-1)

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Answer:

(fog)(x) = 726x^2 + 924x + 295, and (fog)(-3) = 6,817.

Answer:

[tex]\frac{m}{11}[/tex]

Step-by-step explanation:

To write the given expression as a fraction, put m in the numerator and 11 in the denominator as shown: [tex]\frac{m}{11}[/tex]

This would be the quotient of m and 11 expressed as a fraction!

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If e = 12 and the equation is true, then the answer to the equation is 12.

You can solve the equation as before if it has the form axe + b = c, where x is the variable. Addition and subtraction should be "undone" first, followed by multiplication and division.

We insert e = 12 into the equation and check to see if the equation is true to see if the given value of the variable is a solution of the equation 9 = (3/4)e, where e = 12.

9 = (3/4)e

9 = (3/4)(12)

9 = 9

If e = 12 and the equation is true, then the answer to the equation is 12.

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Therefore, on average, each cow produced 169.41 ml of milk today.

The average, also known as the arithmetic mean, is a statistical measure that is calculated by adding together a set of numbers and then dividing the sum by the total number of values in the set. The result is a single value that represents the central tendency of the data set.

Given by the question.

To find the average amount of milk produced by each cow, we need to divide the total amount of milk by the number of cows.

Average milk produced by each cow = (Total milk produced)/ (Number of cows)

Total milk produced = 2090 ml + 780 ml = 2870 ml

Number of cows = 17

Therefore,

Average milk produced by each cow = 2870 ml/17

= 169.41 ml

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Answer:

8, 11, 16, 23, 32, and 43.

Step-by-step explanation:

When n = 1:

n² + 7 = 1² + 7 = 8

When n = 2:

n² + 7 = 2² + 7 = 11

When n = 3:

n² + 7 = 3² + 7 = 16

When n = 4:

n² + 7 = 4² + 7 = 23

When n = 5:

n² + 7 = 5² + 7 = 32

When n = 6:

n² + 7 = 6² + 7 = 43

Therefore, the first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.

Answer:

When n = 1, n² + 7 = 1² + 7 = 8

When n = 2, n² + 7 = 2² + 7 = 11

When n = 3, n² + 7 = 3² + 7 = 16

When n = 4, n² + 7 = 4² + 7 = 23

When n = 5, n² + 7 = 5² + 7 = 32

When n = 6, n² + 7 = 6² + 7 = 43

The first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.

Step-by-step explanation:

ᓚᘏᗢ

hope u have a good day man

The answer that is NOT true when two relations Rand S are union-compatible is: Rand S must have the same number of tuples.

A relation is a set of attributes that describe a set of entities (or elements). The union-compatible operation allows you to combine two relations into one with the same attribute set.

The union-compatible operation is performed on two relations that have the same number of attributes and the same domain in each attribute. The union-compatible operation is sometimes known as the union operation.

Assume that two relations Rand S are union-compatible. Then it implies that both relations have the same number of attributes and the domain of the i-th attribute of R must be the same as the domain of the i-th attribute of S.

Thus, the correct option is D and A i.e.

"The domain of the i-th attribute of R must be the same as the domain of the i-th attribute of S".

In relational algebra, the difference operation (-) is used to find the differences between two relations. When two relations R and S are union-compatible, then we can perform the difference operation. Hence, option (b) is true. But option (c) is false as there is no compulsion that two relations Rand S must have the same number of tuples.

Note: The union-compatible operation is one of the three basic operations of relational algebra that includes the selection operation and the projection operation.

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Answer:

Percent questions can be estimated using models by dividing the given number by the total number of parts in the model. For example, if there are ten students in a classroom and 30 candy bars, then each student would get three candy bars. Another example would be if there are ten students in a classroom and 30 candy bars, and one student takes five candy bars, then the remaining nine students would get two candy bars each.

Answer:

Percent questions can be estimated using models by dividing the given number by the total number of parts in the model. For example, if there are ten students in a classroom and 30 candy bars, then each student would get three candy bars. Another example would be if there are ten students in a classroom and 30 candy bars, and one student takes five candy bars, then the remaining nine students would get two candy bars eac

Step-by-step explanation:

The width of the rectangular field is 51 meters

To find the width of the rectangular field, we need to use the formula for the perimeter of a rectangle, which is:

Perimeter = 2 × (length + width)

We are given that the perimeter of the rectangular field is 292 m and the length is 95 m. So, we can plug in these values into the formula and solve for the width:

292 = 2 × (95 + width)

First, we can simplify the right side of the equation:

292 = 190 + 2 × width

Next, we can isolate the variable (width) on one side of the equation by subtracting 190 from both sides:

292 - 190 = 2 × width

102 = 2 × width

Finally, we can solve for the width by dividing both sides by 2:

width = 51 m

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The total number of students which attend the art class is 52 which is 89.75 of the total enrolled students that is 58.

A Latin word with the meaning "out of one hundred" is percentage.

Working with parts of 100 is much easier than working with thirds, twelfths, and other fractions, especially since many fractions lack a consistent (non-recurring) decimal equivalent.

Significantly, this also makes comparing percentages more simpler than comparing fractions with various denominators. This contributes to the widespread usage of the metric measuring system and decimal currencies.

Total students enrolled for art class = 58

Percentage of cancelled students = 10.3%

Then, Percentage of non-cancelled students = 100 - 10.3 = 89.7%

So,

Attended students = 89.7% of 58.

= 89.7*58 / 100

= 52.06

= 52 (approx)

Thus, the total number of students which attend the art class is 52 which is 89.75 of the total enrolled students that is 58.

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Answer:

$0.02

Step-by-step explanation:

0.60/30

The calculation shows that 9,000 scientists have seen the deep ocean through Alvin's windows; and

a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.

1) If on each of the 4,500 dives Alvin carried a new pilot and two new scientists, then the total number of scientists who have seen the deep ocean through Alvin's windows is:

4,500 dives x 2 scientists per dive = 9,000 scientists

Therefore, 9,000 scientists have seen the deep ocean through Alvin's windows.

2) To calculate the total number of people who traveled in Alvin, we can add the number of pilots and scientists on each dive and multiply by the number of dives:

4,500 dives x (1 pilot + 2 scientists)

= 4,500 x 3

= 13,500 people

Therefore, a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.

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The total advertising cost for the campaign is $59,200,000.

To calculate the total cost for each advertising medium, we need to multiply the number of impressions by the cost per thousand impressions (CPM) and divide by 1000 to get the total cost in dollars.

Adding up all of the costs, we get $12,750,000 + $87,500 + $15,000 + $62,500 = $12,915,000.

However, we need to remember that the digital advertising has a CPM of $4.69 instead of the listed cost, so we need to recalculate its cost to be $32000000 x $4.69 CPM / 1000 = $150,080. Adding this to the total cost gives $12,915,000 + $150,080 = $13,065,080. This is the cost before the GRPS and CPP discounts are applied.

To apply these discounts, we need to multiply the total cost by (1 - GRPS) and then divide by CPP. Plugging in the values given, we get ($13,065,080 x (1 - 0.25)) / 1500 = $48,928.50. Finally, we need to multiply this by the total number of impressions to get the overall cost of the campaign, which is $48,928.50 x 1,200,000,000 / 1000 = $59,200,200, or approximately $59,200,000.

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Answer:

54

Step-by-step explanation:

Answer:

y=54

as x=3

so y=2*x^3

y= 2*3^3

y=2*27

y=54

these are the whole statements: Cosine function has a 24-period period. The cosine function's midline has the equation y = 19.25. The cosine function has a 15.25 amplitude.

A mathematical equation, such as 6 x 4 = 12 x 2, states that two amounts and values are equal. two. Countable noun. A scenario known as an equation means that two or more components must be taken into account in order to comprehend or understand the overall situation.

Midline = (34.5 Plus 4) / 2 (34.5 + 4) = 19.25 Maximum value plus Minimum value

As a result, the following equation represents the data's model for the midline of a cosine function:

y = 19.25

The biggest deviation from the function's midline is its amplitude in the cosine function. The maximum amount of v(x) was 34.5 cm/s, and the minimum is 4 cm/s, according to the data provided. The cosine function used to model the data has the following amplitude:

Amplitude is calculated as (highest value – minimum values) / 2 (or 34.5 - 4) / 2 (or 15.25).

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Answer: I couldn't honestly help with that I would if I could

Step-by-step explanation:

Answer:

x = 10

y = -9

Step-by-step explanation:

x = -3y - 17

2x + 3y = -7

Plug in x

2 (-3y - 17) + 3y = -7

-6y - 34 + 3y = -7

-3y = 27

y = -9

Plug in the value you got for y back into the equation to find the x value

x = -3(-9) - 17

x = 10

The number of ways of doing both things is N = m × n

Since there are m ways of doing one thing and n ways of doing another, to find how many ways are there to do both, we proceed as follows.

Since there are m ways of doing one thing and n ways of doing another, to find the number of many ways to do both things,we multiply both numbers together.

So, then number of ways of doing both things is N = m × n

So, there are m × n ways of doing both things

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Answer:

f(x) = (5/6)x - (1/4)

f(-8) = (5/6)(-8) - (1/4)

f(-8) = (5/3)(-4) - (1/4)

f(-8) = (-20/3) - (1/4)

f(-8) = (-80-3)/12

f(-8) = -83/12

The given augmented matrix is equivalent to a system of linear equations with 1 equation and 3 variables. The system is underdetermined and the solution to the system is [tex](x, y, z)[/tex]= (0, 0, 0).

The given augmented matrix is in row-reduced form and is equivalent to a system of linear equations. The matrix has 3 columns and 1 row, so there is 1 equation and 3 variables in the corresponding system of linear equations. Since there is only one equation, the system is underdetermined and has infinitely many solutions.

The solution to the system can be stated as: (x, y, z) = (0, 0, 0). The solution is a point where all the variables are equal to zero. Since the matrix is in row-reduced form, this is the only solution to the system. If the augmented matrix was not in row-reduced form, then the solution would be stated as a parameter, such as (x, y, z) = (0, 0, t), where t is a parameter.

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Answer:

Step-by-step explanation:

For the given augmented matrix, you want to know the number of equations and variables it represents, whether the system is under- or over-determined, and the solution, using parameters as required.

  [tex]\left[\begin{array}{ccc|c}1&\dfrac{1}{4}&-\dfrac{1}{4}&1\\\vphantom{\dfrac{T}{q}}0&0&0&0\end{array}\right][/tex]

Each column of the augmented matrix is the coefficient of the variable in a linear equation represented by the row. The first row of the matrix represents the equation ...

  [tex]1x +\dfrac{1}{4}y-\dfrac{1}{4}z=1[/tex]

The second row of the matrix represents the tautology ...

  0x +0y +0z = 0

It contributes no information about the relationships between the variables.

The matrix represents 1 equation in 3 variables.

For there to be a unique solution to a linear system, there must be as many consistent and independent equations as there are variables. Here, there are fewer equations than variables. This system is underdetermined.

The solution to an underdetermined system can be written in terms of parameters of free choice. We will need as many parameters as there are missing equations: 2.

Here, the coefficients of y and z suggest we choose parameters that let us represent those values as multiples of 4.

Parameters: s, t

Let y = 4s, z = 4t. Then the equation becomes ...

  x +1/4(4s) -1/4(4t) = 1

  x +s -t = 1

  x = 1 +t -s

Now, the solution can be written as ...

  (x, y, z) = (1 +t -s, 4s, 4t)

Answer:

So 3 blue buckets and 4 white buckets were purchased

Step-by-step explanation:

We can solve this by algebra

Let B = number of blue buckets bought

Let W = number of white buckets bought

Total buckets bought:
B + W = 7    (1)

Each blue bucket can hold 2 gallons of water
So B blue buckets can hold 2B gallons of water

Each white bucket can hold 5 gallons of water
So W white buckets can hold 5W gallons of water

Totally they can hold
2B + 5W gallons

We are given that they both can hold  26 gallons of water

So our second equation is
2B + 5W = 26   (2)

By eliminating one of the variable terms we can solve for the other variable term

Let's eliminate the term for variable B

Multiply equation (1) by 2

(1) x 2 ==> 2(B + W) = 2(7)

2B + 2W = 14    (3)

Subtract (3) from (2); B terms are same so they cancel out

(2) - (3):
2B + 5W = 26    [tex]\bold{-}[/tex]
2B + 2W = 14
---------------------
0    +  3W = 12
------------------------

3W = 12
W = 12/3

W = 4

Substitute W= 4 in equation 1
B + W = 7
=> B + 4 = 7

B = 3

So 3 blue buckets and 4 white buckets were purchased

The answer is d please

The three pairs are (AB = 6, BC = 6) (AB = 4, AC = 4√2) and (BC = 2√2, AC = 4). So, First option, Option 5. and Option 6 are correct answers.

Since we know that,

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

The formula for a 30-60-90 triangle is this:

1) Side opposite to 30 will be value a.

2) Side opposite to 60 will be value a√3

3) Hypotenuse will be 2a.

AB is opposite of the angle with 30 degree measurement.

BC is opposite of the angle with 60 degree measurement.

The sides of an isosceles right triangle are in the ratio,

1:1:√2

where √2 is the hypotenuse.

For the example, BC = 2√2, then AC = 2√2  x √2 = 4.

Therefore, the three pairs are;

1. (AB = 6, BC = 6)

5. (AB = 4, AC = 4√2)

6.(BC = 2√2, AC = 4).

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The complete question is attached below:

Answer: $318/mo

Step-by-step explanation:

First, we get the remainder, which is the difference between $9, 632 and $2,000. That gives us $7, 632.

Then, since we know she will pay in 24 months, we assume she pays the same amount each month and divide $7, 632 by 24 = $318/mo

Answer: This statement is known as the Law of Sines and can be proven using trigonometry and the properties of similar triangles.

Consider a triangle ABC with sides of lengths a, b, and c opposite to the angles A, B, and C respectively. Let's draw an altitude from vertex A to side BC, splitting side BC into two segments: BD of length x and CD of length c-x.

Using the Pythagorean theorem, we can write:

a^2 = x^2 + h^2 (1)

b^2 = (c-x)^2 + h^2 (2)

where h is the length of the altitude from A to BC.

Dividing equation (1) by sin^2(A) and equation (2) by sin^2(B), we get:

a^2 / sin^2(A) = x^2 / sin^2(A) + h^2 / sin^2(A)

b^2 / sin^2(B) = (c-x)^2 / sin^2(B) + h^2 / sin^2(B)

Since angles A and B are complementary (i.e. A + B = 90 degrees), we have sin(A) = cos(B) and sin(B) = cos(A). Substituting these identities and rearranging the equations, we get:

a^2 / sin(A) = x / cos(B) + h / sin(B)

b^2 / sin(B) = (c-x) / cos(A) + h / sin(A)

Multiplying both equations by sin(A)sin(B), we obtain:

a^2 sin(B) = x sin(A) cos(B) + h sin(A)

b^2 sin(A) = (c-x) sin(B) cos(A) + h sin(B)

Now, we use the fact that h = a sin(B) = b sin(A), which follows from the definition of sine as opposite/hypotenuse. Substituting this into the above equations and simplifying, we get:

a / sin(A) = 2R

b / sin(B) = 2R

c / sin(C) = 2R

where R = a/(2sin(A)) = b/(2sin(B)) = c/(2sin(C)) is the radius of the circumcircle of triangle ABC. This is the Law of Sines in its usual form.

From this, we can see that the ratio of the sines of any two angles in a triangle equals the ratio of the lengths of their opposite sides, as required.

Step-by-step explanation:

To calculate the product of two random variables that follows the normal distribution with mean 0 and variance 1 by using the covariance formula

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Given that two random variables follow a normal distribution with mean 0 and variance 1.

Let X and Y be two independent normal random variables such that X ~ N(0,1) and Y ~ N(0,1)

Now, The expected value of the product of two random variables is given by;

E[XY] = E[X]E[Y] + Cov(X,Y)

Where E[X] and E[Y] are the means of the two random variables X and Y respectively.

Cov(X, Y) is the covariance between the two random variables, which can be calculated using the formula;

Cov(X,Y) = E[XY] - E[X]E[Y]

Now, E[X] = E[Y] = 0 as both have a mean of 0.

Cov(X, Y) = E[XY] - E[X]E[Y]

⇒ E[XY] = the expected value of the product of X and Y.

As X and Y are independent, their covariance will be zero, which implies;

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Thus, we can calculate the product of two random variables that follow a normal distribution with mean 0 and variance 1 using the above formula for covariance.

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The shape that results from connecting the points (-4, 1), (-4, -4), (0, 3), and (0, 6) is a trapezoid.

A trapezoid is a geometric form that has four sides, two of which are parallel and two of which are nonparallel (or skew lines). A trapezoid is also known as a trapezium (UK) or a trapeze (US).

The trapezoid's parallel sides are known as the bases, and the two nonparallel sides are known as the legs or lateral sides. The trapezoid is also sometimes referred to as the irregular quadrilateral.

A quadrilateral is a shape that has four sides, four vertices, and four angles. The following are the characteristics of a trapezoid:

The formula for the area of a trapezoid is as follows:

Area of a trapezoid = [ (base 1 + base 2) / 2 ] x height

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1. An acute angle is οne that is less than 90 degrees.

An angle smaller than the right angle is called an acute angle. In οther wοrds, the angle which is less than 90 degrees fοrms an acute angle. The pοlygοns such as triangle, parallelοgram, trapezοid, etc. cοnsist οf at least οne acute angle

2. Obtuse angle: A measurement οf an angle that is greater than 90 degrees but less than 180 degrees.

3. A right angle is οne that is exactly 90 degrees.

4. A straight angle is οne that is exactly 180 degrees in length.

5. Adjacent angles are twο angles that share a cοmmοn vertex and a cοmmοn side.

6. A pair οf nοn-adjacent angles fοrmed by the intersectiοn οf twο lines are knοwn as vertical angles. They are οf equal size.

7. Cοmplementary angles are defined as twο angles that add up tο 90 degrees.

8. Twο angles that add up tο 180 degrees are referred tο as supplementary angles.

9. Angles with the same measure are said tο be cοngruent.

10. A linear pair is twο adjacent angles that fοrm a straight line and add up tο 180 degrees.

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190 pairs of scissors came in each box.

This is an example of a word problem. As a model, a word problem depicts circumstances from the actual world that may be converted into phrases.

Weight of each pair of scissors = 0.34 kg

Weight of a box of scissors = 64.6 kg

Therefore, pairs of scissors in each box = Weight of a box of scissors ÷

                                                                      Weight of each pair

                                                                   = 64.6 ÷ 0.34

                                                                   = 190 pairs.

Hence, 190 pairs of scissors came in each box.

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