The common ratio in a geometric series is 4 44 and the first term is 3 33. Find the sum of the first 8 88 terms in the series.

Therefore, the regression equation best fits the data set is yˆ=0.728x2−20.213x+179.246.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides, the left-hand side and the right-hand side, connected by an equal sign (=). The expressions on either side of the equal sign can be made up of numbers, variables, mathematical operations, and other mathematical symbols. Equations are used to represent various mathematical relationships and can be solved to find the value of one or more variables. Solving an equation involves manipulating the expressions on either side of the equal sign to isolate the variable being solved for. This is often done by applying a series of mathematical operations to both sides of the equation, with the goal of eventually isolating the variable on one side of the equal sign and obtaining a numerical value for it.

Here,

Using a graphing calculator, we can plot the data set of x and y values and use the regression feature to find the quadratic regression equation that best fits the data. Here's how we can do it:

Enter the x and y values into the calculator.

Plot the points on a scatter plot.

Choose the regression feature on the calculator.

Select the quadratic regression option.

The calculator will display the quadratic regression equation that best fits the data.

After performing these steps, we get the following quadratic regression equation:

yˆ=0.728x2−20.213x+179.246

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The height of the lighthouse is 48 feet.

To find the height of the lighthouse, we can use the concept of similar triangles. When two triangles are similar, it means that they have the same shape but different sizes. In this case, the two triangles are similar because they have the same angle to the sun. That is, the angle between the ground and the line from the top of the lighthouse to the sun is the same as the angle between the ground and the line from Zara to the sun.

This proportion is based on the fact that the two triangles are similar, so the corresponding sides are in proportion.

So, we have:

(height of lighthouse) / 36 feet = 4 feet / 3 feet

We can solve for the height of the lighthouse by cross-multiplying:

(height of lighthouse) = 36 feet × (4 feet / 3 feet)

Simplifying the expression, we get:

(height of lighthouse) = 48 feet

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The given question is incomplete, the complete question is

A lighthouse has a shadow that is 36 36 feet long. Zara is 4 4 feet tall, and has a shadow that is 3 3 feet long. The two triangles formed are similar because the angle to the sun is the same. Use this information to complete the statement about the lighthouse.

The height of the lighthouse is ___ feet .

Answer:

PQ is 35.6 units.

Step-by-step explanation:

From the problem, we can see that the smaller quatilateral is 4x smaller than the bigger one. We can multiply 8.9 by 4 to get 35.6 units.

Let w = x^3

Square both sides to find that w^2 = (x^3)^2 = x^(3*2) = x^6

In short: w^2 = x^6

The given expression 2+x^3-3x^6 turns into 2+w-3w^2 and rearranges into -3w^2+w+2

Set this equal to zero and use the quadratic formula. We'll plug in

So,

[tex]w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-1\pm\sqrt{(1)^2-4(-3)(2)}}{2(-3)}\\\\w = \frac{-1\pm\sqrt{25}}{-6}\\\\w = \frac{-1\pm5}{-6}\\\\w = \frac{-1+5}{-6} \ \text{ or } \ w = \frac{-1-5}{-6}\\\\w = \frac{4}{-6} \ \text{ or } \ w = \frac{-6}{-6}\\\\w = -\frac{2}{3} \ \text{ or } \ w = 1\\\\[/tex]

If w = -2/3, then that rearranges to the following

w = -2/3

3w = -2

3w+2 = 0

This makes (3w+2) a factor of -3w^2+w+2

If w = 1, then it rearranges to w-1 = 0.

This makes (w-1) a factor of -3w^2+w+2

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

To summarize the previous section, we found the factors of -3w^2+w+2 were:

It leads to (3w+2)(w-1)

We must stick a negative out front because the leading coefficient is negative.

Therefore, -3w^2+w+2 = -(3w+2)(w-1)

You can use the FOIL rule to confirm.

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

Recall we made w = x^3

Let's replace each w with x^3

-(3w+2)(w-1)

-(3x^3+2)(x^3-1)

This tells us that 2+x^3-3x^6 factors to -(3x^3+2)(x^3-1)

The next task is to factor x^3-1 using the difference of cubes factoring rule.

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

x^3 - 1^3 = (x-1)(x^2 + x*1 + 1^2)

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

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

So,

2+x^3-3x^6

-3x^6 + x^3 + 2

-(3x^3+2)(x^3-1)

-(3x^3+2)(x-1)(x^2 + x + 1)

-(2 + 3x^3)(-(1-x))(1 + x + x^2)

(2 + 3x^3)(1 - x)(1 + x + x^2)

Take careful notice that x-1 turned into -(1-x) in the 3rd step. The negative out front for -(1-x) cancels out with the original negative out front.

The domain of the function is (-∝, -3) ∪ (-3, +∝)

The range is (-∝, 3) ∪ (3, +∝) and the asymptotes are x = -3 and y = 3

From the question, we have the following parameters that can be used in our computation:

f(x) = 2/(x + 3) + 3

Set the denominator to not equal to 0

So, we have

x + 3 ≠ 0

So, we have

x ≠ -3

As an interval notation, we have

(-∝, -3) ∪ (-3, +∝)

Here, we have

f(x) = 2/(x + 3) + 3

When x = -3, we have

f(-3) = undefined + 3

This means that

f(x) ≠ -3

As an interval notation, we have

(-∝, 3) ∪ (3, +∝)

In (a), we have

x ≠ -3

This means that

Vertical asymptote: x = -3

In (b), we have

f(x) ≠ -3

This means that

Horizontal asymptote: y = 3

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Answer:

Step-by-step explanation: To expand the algebraic expression using the distributive property, we distribute the 3 to each term inside the parentheses:

3(3d + 2) = 33d + 32

Simplifying, we get:

3(3d + 2) = 9d + 6

Therefore, the expanded form of the expression 3(3d+2) is 9d + 6.

The solution to the inequality is any value of X that is less than or equal to -69.

What is Inequality?

An inequality is a relationship that compares two numbers or other mathematical expressions that are not equal. It is most commonly used to compare the sizes of two numbers on a number line.

The inequality X/(-3) ≥ 23 can be solved as follows:

We begin by multiplying both sides of the inequality by -3, which will reverse the direction of the inequality since we are multiplying by a negative number. This gives:

X ≤ -69

Therefore, the solution to the inequality is any value of X that is less than or equal to -69.

In interval notation, we can write the solution as:

(-∞, -69]

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According to the information, we can infer that the equation expressed by the parable symmetry axis is x = −b2a.

The symmetry axis of a parable is a term that refers to a vertical line that divides the parable into two congruent halves. The axis of symmetry always passes through the vertex of the parable.

To find the symmetry axis of this parable we must perform the following procedure taking into account the following information:

Additionally, we must compare the equation with y = ax2+bx+c to find the values of a, b, and c. Then these values would be like this:

According to the above, we can replace these values to solve the equation of axis of symmetry. then, the graph of a quadratic equation in the form Y = Ax2+Bx+C has ss its axis of symmetry the line X = −B2a.

Note: This Question is incomplete. Here is the complete information:

Attached Image

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The result of each length of the sides of a right triangle is as follows:

5, 12 and 13: Yes

12, 35 and 20√5: No

5, 10 and 5√5: Yes

8, 12 and 15: No

20, 99 and 101: Yes

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side (longest side) is equal to the sum of squares of the other two sides“.

For 5, 12 and 13:

13² = 5² + 13²

169 = 169 (This is true)

YES

For 12, 35 and 20√5 :

(20√5)² = 12² + 35²

2000 = 1369 (This is false)

NO

For 5, 10 and 5√5 :

(5√5)² = 5² + 10²

125 = 125 (This is true)

YES

For 8, 12 and 15:

15² = 12² + 15²

225 = 369 (This is false)

NO

For 20, 99 and 101:

101² = 20² + 99²

10201 = 10201 (This is true)

YES

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What is cartesian plane ?

A Cartesian plane (also known as a coordinate plane or rectangular coordinate system) is a two-dimensional plane formed by two perpendicular number lines, referred to as the x-axis and the y-axis, that intersect at a point called the origin. The x-axis is a horizontal line, and the y-axis is a vertical line.

Explanation:
To plot the following points in the Cartesian plane:

{(3,6),(-8,2),(-9,-4),(2,-8)}

First, we draw the x and y axes to form a Cartesian plane.

Then, for each point, we plot the x and y coordinates on the graph. The x coordinate indicates the horizontal position of the point on the x-axis, while the y coordinate indicates the vertical position of the point on the y-axis.

The point (3,6) is plotted as a dot on the Cartesian plane located 3 units to the right of the origin on the x-axis and 6 units above the origin on the y-axis.

The point (-8,2) is plotted as a dot located 8 units to the left of the origin on the x-axis and 2 units above the origin on the y-axis.

The point (-9,-4) is plotted as a dot located 9 units to the left of the origin on the x-axis and 4 units below the origin on the y-axis.

The point (2,-8) is plotted as a dot located 2 units to the right of the origin on the x-axis and 8 units below the origin on the y-axis.

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Answer: el enunciado cinco veces la diferencia de un numero y 3 es 17

Step-by-step explanation:

Answer:

ATQ, 5( x -3 ) = 17

5 x - 15 = 17

5x = 17 + 15

x = 32 /5

x = 6.4 ,

6 cups of dal may be used to make eight bowls of sambar.

The ratio can be defined as the number that can represent one quantity as a percentage of another. They can be compared only when the two numbers in a ratio have the same unit. Ratios are used to compare two objects.

Given, One bowl of sambar is made the use of 3/four cup dal.

If 1 bowl of sambar is made using 3/4 cup of dal, then the number of bowls of sambar that can be made from 6 cups of dal can be found by dividing 6 cups by 3/4 cup per bowl:

6 cups / (3/4 cup per bowl)

We can simplify by multiplying the numerator and denominator by the reciprocal of 3/4:

6 cups / (3/4 cup per bowl) * (4/3)

Simplifying, we get:

8 bowls

Therefore, 6 cups of dal can be used to make 8 bowls of sambar.

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The volume of the triangular prism is 137.2 units cube.

The triangular prism has a height of 8 units. The base of the prism is shown in the image. The volume of the prism can be represented as follows:

volume of a triangular prism = BH

where

Therefore, let's find the base area

B = 1 / 2 b h

let's find b

Hence,

tan 65 = b / 4

cross multiply

b = 4 tan 65

b = 8.57802768204

b = 8.58 units

Therefore,

B = 1 / 2  × 4 × 8.58

B = 17.1560553641

Therefore,

volume of a triangular prism = 17.156 × 8

volume of a triangular prism = 137.248442913

Hence,

volume of a triangular prism = 137.2 units cube

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We do not have information about whether the two events are mutually exclusive or not, we cannot determine whether P(full-time college student and 65 or older) is nonzero.

Probability is a method for assessing how likely something is to happen. Many occurrences cannot be foreseen with 100% accuracy. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

We cannot determine whether the probability of an adult being a full-time college student and 65 or older is nonzero based on the given information alone.

To see why, consider the following two scenarios:

Scenario 1: The proportion of adults who are both full-time college students and 65 or older is 0%.

In this case, the events "full-time college student" and "65 or older" are mutually exclusive. That is, no adult can be both a full-time college student and 65 or older. Therefore, P(full-time college student and 65 or older) = 0%.

Scenario 2: The proportion of adults who are both full-time college students and 65 or older is greater than 0%.

In this case, the events "full-time college student" and "65 or older" are not mutually exclusive. That is, there may be some adults who are both full-time college students and 65 or older. Therefore, P(full-time college student and 65 or older) is greater than 0%.

Since we do not have information about whether the two events are mutually exclusive or not, we cannot determine whether P(full-time college student and 65 or older) is nonzero.

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Answer:

x = 40° , y = 43° , z = 97°

Step-by-step explanation:

∠ DAC = y = ∠ ACB = 43°

• opposite angles in a parallelogram are congruent , then

z = ∠ D = 97°

the sum of the 3 angles in Δ ACD = 180° , that is

x + y + 97° = 180°

x + 43° + 97° = 180°

x + 140° = 180° ( subtract 140° from both sides )

x = 40°

then

x = 40° , y = 43° , z = 97°

The ratio of people waiting in line for the slingshot is 2:21

A ratio is a relationship between two quantities that expresses how many times one quantity is contained in the other. It can be expressed in different ways, such as with the use of a colon (:), a fraction (/), or the word "to.

From the question, the total number of people is 15 + 4 + 12 + 11 = 42

The number of people waiting for slingshot is = 4

The ratio of slingshot waiting in line = 4/42

The ratio = 2:21

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The key features of this rational function include the following:

Domain: (-∞, 2) ∪ (2, ∞)

Range: (-∞, -2) ∪ (-2, ∞)

Y-intercept: -7/2.

X-intercept: 7/2.

Vertical asymptote: x = 2.

Horizontal asymptote​: y = -2.

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

Additionally, the horizontal extent of any graph of a rational function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.

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A. The height of the cuboid is 2.5 cm.

B. The suggested dimensions of the cuboid is 25 x 5 x 1.

The volume of a given three dimensional figure is the total quantity of matter that it can contained. Thus various figures has different methods of determining their volume.

volume of a cube = length x length x length

                             = (length)^3

volume of a cuboid = length x width x height

Considering the given question, since the volumes of the cube and cuboid are the same, then we have:

volume of a cube = volume of a cuboid

(length)^3 = length x width x height

5^3 = 10 x 5 x height

125 = 50 x height

height = 125/ 50

           = 2.5

The height of the cuboid is 2.5 cm.

B. volume of the cuboid = length x width x height

                          = 10 x 5 x 2.5

                          = 125 cm^3

Thus possible dimensions for the cuboid 25 x 5 x 1.

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Answer:based on the student's work?A Each side of the equation, in one variable, can be found by isolating the x-variable of each equationin the s

Step-by-step explanation:

Chart that arranges all of the known elements in a particular order.

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

Rearrange unknown terms to the left side of the equation: [tex]x-2x = -4 - 3[/tex]

Combine like terms: [tex]-x = -4-3[/tex]

Calculate the sum or difference: [tex]-x = -7[/tex]

Divide both sides of the equation by the coefficient of variable: [tex]x = 7[/tex]

Answer:Mike has $100. He wants to buy a bike that costs $75 and three speakers that cost $30 each. trade of is example of Opportunity cost

Step-by-step explanation:

The average from 1986 to 2000 was 46.250 million and circulation was closest to 46.250 in 1994.

What is the definition of average?

An average of a list of data is a mathematical expression for the centre value of a set of data. It is defined mathematically as the ratio of the sum of all the data to the number of units in the list. The average of 2, 3, and 4 equals (2+3+4)/3 = 9/3 = 3.

Average = Sum of Values divided by Number of Values

Now,

As  The newspaper circulation between 1986 and 2000 can be modeled as:

n(x)=0.00692x³-0.42x²+3.557x+51.588 million newspaper, where x is the number of years since 1980.

1. We will determine the circulation by finding x (subtracting 1980 from the said year) and substitute it in the formula.

n(6)=59.305, n(7)=59.281, n(8)=58.707, n(9)=57.626, n(10)=56.078, n(11)=54.106, n(12)=51.750, n(13)=49.052, n(14)=46.054, n(15)=42.798, n(16)=39.324, n(17)=35.675, n(18)=31.891, n(19)=28.015, n(20)=24.088

2. We will add the values: Sum of n=693.750

3. Average newspaper circulation=Sum of circulation each year/No of years

   Average=693.750/15=46.250

4. Compare each year circulation to the average.

   The circulation in 1994 i.e.,46.054 was closest to the average i.e.,46.250

As a result, the average newspaper circulation from 1986 to 2000 was 46.25 million. Additionally, the year with the closest average circulation from 1986 to 2000 was 1994.

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Answer:

Let's start by figuring out how many blue beads Ann had initially.

If Ann had a total of 285 red and blue beads, and she used 45 red beads, then she had 240 blue beads remaining.

If Ann used 40% of the blue beads, then she used:

0.40 x 240 = 96 blue beads

After using 45 red beads and 96 blue beads, Ann had the following number of red and blue beads remaining:

Red beads = 285 - 45 = 240

Blue beads = 240 - 96 = 144

At this point, the ratio of red beads to blue beads is:

Red beads : Blue beads = 240 : 144 = 5 : 3

However, we want the ratio to be 1 : 3. To achieve this ratio, we need to divide both the red beads and blue beads by 5. This gives us:

Red beads = 240 / 5 = 48

Blue beads = 144 / 5 = 28.8

Since we can't have a fraction of a bead, we need to round up the number of blue beads to the nearest whole number. This gives us:

Red beads = 48

Blue beads = 29

Therefore, Ann initially had 285 - 48 - 29 = 208 beads, with 48 red beads and 29 blue beads.

Step-by-step explanation:

Simplifying this expression, we get: E[X] = n * (1 + (1-pm)/(n-1)) * H_{n-1} where H_{n-1} is the (n-1)th harmonic number.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

In the first scenario where we have imperfect throwers, the probability that a ball lands in a particular bin is (1-pm)/n, where pm is the probability that the ball misses all the bins. The probability that a ball does not land in a particular bin after k throws is (1- (1-pm)/n)^k.

Let X_i be a random variable representing the number of throws required to fill the ith bin for the first time. We know that X_i follows a geometric distribution with probability of success p_i = (1-pm)/n.

The expected value of X_i is given by:

E[X_i] = 1/p_i = n/(n - (1-pm))

Now, let X be the random variable representing the number of throws required to fill all n bins for the first time. We want to find the expected value of X, denoted as E[X].

Since each bin is being filled independently, the number of throws required to fill all n bins is given by the maximum of the X_i. Therefore, we have:

X = max(X_1, X_2, ..., X_n)

Using the formula for the expected value of the maximum of n independent and identically distributed random variables, we can write:

E[X] = n * E[X_i] - (n-1) * E[X_i, X_j]

where E[X_i, X_j] is the expected value of the minimum of X_i and X_j.

Since the X_i are identically distributed, we have E[X_i, X_j] = E[X_i]^2.

Substituting the value of E[X_i] in the above equation, we get:

E[X] = n * (n / (n - (1-pm))) - (n-1) * (n / (n - (1-pm)))^2

This is the expected number of throws required to fill each bin at least once, accounting for the probability that the balls may miss all bins with probability pm.

Therefore, Simplifying this expression, we get: E[X] = n * (1 + (1-pm)/(n-1)) * H_{n-1} where H_{n-1} is the (n-1)th harmonic number.

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The equation and solution to find the length of mis teak wood piece is x=3*8 and 24.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The length of oak wood=8inches

Teak wood= 3* oak wood

Now,

Let the length of teak wood be x

Then,

x=3*8

x=24

Therefore, by algebra the answer will be 24.

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Answer: it

Step-by-step explanation:

The Pseudocode is discussed below.

Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible.

Given is to write a Pseudo code.

Therefore, the Pseudocode is discussed above.

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Answer:

a) {0,1,3,5,8}

b) -

Step-by-step explanation:

the composition cannot be performed cos 3 is mapped to 2 by g, but 2 is not in the domain of f

The values for this problem are given as follows:

a) lim x -> 2^- f(x) = 3.

b) lim x -> 2^+ f(x) = 1.

c) lim x -> 2 f(x) is not defined.

d) f(2) = 3.

e) lim x -> 4 f(x) = 4.

f) f(4) is not defined.

To the left of x = 2, the graph of f(x) approaches x = 2 at y = 3, hence:

lim x -> 2^- f(x) = 3.

To the right of x = 2, the graph of f(x) approaches x = 2 at y = 1, hence:

lim x -> 2^+ f(x) = 1.

As the lateral limits are different, the limit of f(x) as x -> 2 is not defined.

Due to the closed circle, at x = 2, the function has a numeric value of f(2) = 3.

At x = 4, the graph of the function approaches x = 4 both left and right at y = 4, hence:

lim x -> 4 f(x) = 4.

Due to the open circle at x = 4, we have that f(4) is not defined.

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Answer:

length =7 breadth =2

Step-by-step explanation:

l x b = 14, so l= 14/b

2(l+b) =18 , l+b =9

14/b+b=9

[tex]b^ {2}[/tex] -9b+14=0

[tex]b^ {2}[/tex] -7b-2b+14=0

(b-7)(b-2) =0

b= 7 or 2