Help me out, please.​

An example of a convergent series (exn) and a divergent series (eyn) such that the product series e(xn * yn) is convergent.

EXPLANATION:

Let's consider the following two series:

1. Convergent series (exn): xn = 1/n^2
2. Divergent series (eyn): yn = n

Now, let's analyze the product series e(xn * yn):

e(xn * yn) = (1/n^2) * n = 1/n

The product series e(xn * yn) is a harmonic series, which is a convergent series.

In this example, the convergent series (exn) is the series of 1/n^2, the divergent series (eyn) is the series of n, and their product series e(xn * yn) is the harmonic series (1/n), which is convergent.

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The given polynimial exression is

(w^3-2w^2-2w+1)÷(w-1)

We wuld apply the long division method as shown below

The first step is todivide w^3 by w to give us w^2. w^2 is used to multiply w + 1 to give us w^3 + w^2 and this is subtracted from w^3 - 2w^2. The process continues until we cannot divide further. Thus, from the daigram above, the solution is

w^2 - 3w + 1

Therefore, the simplified expression is 15p^6r^5.

To simplify this expression, we can use the distributive property and combine like terms.
First, we multiply 3p^2r^4 by 5p^4r:
3p^2r^4 x 5p^4r = 15p^6r^5
So the simplified expression is 15p^6r^5.
To simplify the expression 3p^2r^4 x 5p^4r, we can use the distributive property and combine like terms. Multiplying 3p^2r^4 by 5p^4r gives us 15p^6r^5.

Therefore, the simplified expression is 15p^6r^5.

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The list with the smallest standard deviation is the following: 16, 12, 13, 16, 14, 15, 16, 14, 14, 13.

What is standard deviation?

Standard deviation is a statistical measure of the variability of a set of data values. It's a step-by-step process for determining how far each value is from the mean. It is important since it may reveal the amount of variability in a set of data. The formula for calculating standard deviation is as follows:

σ=√∑(x−μ)²nσ=√∑(x−μ)²n

In this equation, x represents the values in the data set, μ represents the mean of the data set, and n represents the number of values in the data set. Let us now compute the standard deviation of each of the given data sets, starting with the first one. We can utilize the formula given above to do so:

6, 19, 9, 18, 19, 9, 17, 18, 17, 15                        μ = 15.8,σ = 4.83 (rounded to two decimal places)

31, 30, 26, 28, 18, 28, 18, 21, 23, 32                μ = 25.5,σ = 5.93 (rounded to two decimal places)

20, 21, 20, 19, 25, 24, 19, 14, 21, 15                μ = 19.8,σ = 3.98 (rounded to two decimal places)

14, 20, 16, 14, 28, 13, 17, 21, 12, 22                μ = 17.7,σ = 4.96 (rounded to two decimal places)

16, 12, 13, 16, 14, 15, 16, 14, 14, 13                  μ = 14.3,σ = 1.96 (rounded to two decimal places)

The list with the smallest standard deviation is the following: 16, 12, 13, 16, 14, 15, 16, 14, 14, 13.

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The required general solution of the differential equation y" - 2y – 3y = e^(-t) + 1 is given by the expression,

y = A e^(3t) + B e^(-t) + C t e^(-t) + Ate^(-t) + B

We are required to find the general solution of the differential equation y" - 2y – 3y = e^(-t) + 1 using the Annihilator Method.

The given differential equation is, y" - 2y – 3y = e^(-t) + 1

The characteristic equation of the given differential equation is, r² - 2r - 3 = 0(r - 3)(r + 1) = 0r₁ = 3 and r₂ = -1

Now, we will consider the following cases:

Case I: When the right-hand side has a term of the form f(t) = e^(rt), then we take the annihilator as (D - r).

∴ The annihilator for e^(-t) is (D + 1).

Case II: When the right-hand side has a constant term, then we take the annihilator as D.

∴ The annihilator for 1 is D⁰.

Now, we will write the annihilators for the given differential equation. The annihilator for y" is (D - 3)(D + 1)

The annihilator for 2y is 2D⁰

The annihilator for 3y is 3D⁰

The annihilator for e^(-t) is (D + 1)

The annihilator for 1 is D⁰

Using the Annihilator Method, we have, (D - 3)(D + 1)(D + 1) [y"] + 2 [D⁰] y - 3 [D⁰] y = 0(D - 3)(D + 1) [D + 1] y" + 2 y = 3 y - e^(-t)

Now, we will solve the homogeneous equation, (D - 3)(D + 1) [D + 1] y" + 2 y = 3 y(D - 3)(D + 1) (r - 3) (r + 1) (r + 1) yh = A e^(3t) + B e^(-t) + C t e^(-t)

Now, we will find the particular integral, yₚ, for e^(-t) + 1. The particular integral for e^(-t) is, yp₁ = Ate^(-t)

And, the particular integral for 1 is, yp₂ = B

Therefore, the particular integral yₚ = yp₁ + yp₂ = Ate^(-t) + B

The general solution of the given differential equation is, y = yh + yₚ = A e^(3t) + B e^(-t) + C t e^(-t) + Ate^(-t) + B

Therefore, the required general solution of the differential equation y" - 2y – 3y = e^(-t) + 1 is given by the expression, y = A e^(3t) + B e^(-t) + C t e^(-t) + Ate^(-t) + B

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The graph that matches the given linear inequality is (B) .

In the question ,

it is given that

the linear inequality is y \(>\) -x + 4

on rewriting the inequality

we get

x + y \(>\) 4

to plot the inequality , we need points to plot .

So ,when x = 0 , we have y = 4

and when y = 0 , we have x = 4

so the two points are (0,4) and (4,0) .

For shading the inequality , we put x = 0 and y = 0 ,

and get 0+0 > 4

0>4 , the result is False , So , the shaded region will be away from the origin which is shown in option (b) .

Therefore , The graph that matches the given linear inequality is (B) .

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y equals x times 5 is the answer because 2 times 5 is 10 and so on and so forth hope this helps :D

The correct match of each dilation to its function is: j(x) = (1/2x)^2: vertical stretch, k(x) = 2x²: vertical compression, h(x) = (2x)²: horizontal compression, and g(x) = x²: no dilation, it is the parent function.

Each of the given functions is a dilation of the parent function f(x) = x^2, which means that they are obtained by stretching or compressing the graph of the parent function either vertically or horizontally.

- j(x) = (1/2x)^2: This function is a vertical stretch of the parent function, because the constant factor of 1/2 in front of the x causes the function to be stretched vertically by a factor of 2.

- k(x) = 2x²: This function is a vertical compression of the parent function, because the constant factor of 2 in front of the x^2 causes the function to be compressed vertically by a factor of 1/2.

- h(x) = (2x)²: This function is a horizontal compression of the parent function, because the constant factor of 2 inside the x^2 causes the function to be compressed horizontally by a factor of 1/2.

- g(x) = x²: This is the parent function, and it is not dilated in any way. Its graph is a parabola that opens upwards and has a vertex at the origin.

Thus, this is the correct match for the given scenario.

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The object will be 78.12 meters high after 2 seconds. To convert meters to feet, we can multiply by 3.28:
78.12 meters x 3.28 feet/meter = 256.14 feet

The equation given for the object's height at time t is s(t) = -4.97t2 + 19.6t + 58.8, where s is in meters. To find the height of the object after 2 seconds, we can substitute t = 2 into the equation and solve for s(2):

To find the height of the object after 2 seconds, we need to plug t = 2 into the given equation:

s(t) = -4.97t^2 + 19.6t + 58.8

First, replace t with 2:

s(2) = -4.97(2^2) + 19.6(2) + 58.8

Now, perform the calculations step by step:

1. Calculate 22:
2^2 = 4

2. Multiply the result by -4.97:
-4.97(4) = -19.88

3. Multiply 19.6 by 2:
19.6(2) = 39.2

s(2) = -4.97(2)^2 + 19.6(2) + 58.8
s(2) = -4.97(4) + 39.2 + 58.8
s(2) = -19.88 + 98
s(2) = 78.12

4. Add the results to 58.8:
-19.88 + 39.2 + 58.8 = 78.12

The height of the object after 2 seconds is approximately 78.12 meters. Now, convert this to feet (1 meter = 3.28084 feet):

78.12 meters * 3.28084 = 256.363 feet

The height of the object after 2 seconds is approximately 256.363 feet. However, this value does not match any of the options provided. Please double-check the options or the given equation to ensure accuracy.

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Using the graph method, Central Fabric should determine the most profitable numbers of bolts to purchase from mills A and B by considering profit calculations, supply and demand constraints, and plotting a profit graph.

To determine the most profitable numbers of bolts that Central Fabric should purchase from mills A and B using the graph method, we need to create a profit graph based on the given information.

Start by calculating the total available supply for each market channel:

Fabric Stores: (0.40 * Total Bolts from Mill A) + (0.20 * Total Bolts from Mill B)

Discount Stores: (0.10 * Total Bolts from Mill A) + (0.20 * Total Bolts from Mill B)

Direct Mail: (0.30 * Total Bolts from Mill A) + (0.40 * Total Bolts from Mill B)

Determine the maximum number of bolts that can be sold in each market channel:

Fabric Stores: 1,600 bolts

Discount Stores: 2,800 bolts

Direct Mail: 2,600 bolts

Calculate the profit for each combination of bolts purchased from mills A and B:

Profit from Mill A: (0.60 * Total Bolts from Mill A - 0.20 * Total Bolts from Mill A) * P8,000

Profit from Mill B: (0.80 * Total Bolts from Mill B - 0.20 * Total Bolts from Mill B) * P6,000

Plot the profit graph by considering different combinations of Total Bolts from Mill A and Total Bolts from Mill B, while taking into account the constraints of available supply and market demand.

Find the combination of Total Bolts from Mill A and Total Bolts from Mill B that maximizes the profit while satisfying the supply and demand constraints. This point on the graph represents the most profitable numbers of bolts to purchase from mills A and B.

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The probability that the rack ends up in alphabetical order is 1/9! or approximately 1.46 x 10⁻⁷.

The problem involves arranging 9 CDs out of 16 in alphabetical order in a CD rack. The total number of possible ways to arrange 9 CDs out of 16 is 16 choose 9, which equals 11440. Only one of these arrangements is in alphabetical order. Therefore, the probability of randomly selecting an alphabetical order is 1/11440, which is approximately 0.0000874 or 0.00874%. This is a very small probability, indicating that it is highly unlikely that the CDs will end up in alphabetical order by chance.

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The length of the curve drawn by f as t runs from 0 to 1, we can use the formula for arc length:
the length of the curve drawn by f as t runs from 0 to 1 is sqrt(3).
\(L = ∫a^b ||r'(t)|| dt\)

where r(t) is the vector function that describes the curve, a and b are the limits of integration, and ||r'(t)|| is the magnitude of the derivative of r(t).

In this case, we have

\(r(t) = ⟨t^2, t^2, t^2⟩, so r'(t) = ⟨2t, 2t, 2t⟩\)

. The magnitude of r'(t) is then

\(||r'(t)|| = sqrt((2t)^2 + (2t)^2 + (2t)^2) = 2sqrt(3)t.\)

Substituting these values into the arc length formula, we get:

\(L = ∫0^1 2sqrt(3)t dt = 2sqrt(3) * ∫0^1 t dt = 2sqrt(3) * [t^2/2]\)

from 0 to 1 = sqrt(3)
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Answer:

1/3

Step-by-step explanation:

10 to 10:30

10:30 to 11

11 to 11:30

3 periods of time

10 to 11 is 2/3 periods

3/3 - 2/3 = 1/3

The tick marks on the two sides mean those two lengths are the same, which also means the angles opposite them are the same measure.  (AKA It's an isosceles triangle.)

Since the two missing angles are equal, we can solve:

    28 + x + x = 180

to find that x = 76.

The two angles are 76 degrees.

And since LM = LN, we know LN = 18 in.

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

Answer:

LCM = 840

Explanation:

First, we need to find the prime factorization of every number. So 14, 21, and 40 are equal to the product of the following prime number:

14 = 2 x 7

21 = 3 x 7

40 = 2 x 2 x 2 x 5

Now, we need to identify all the prime numbers and the maximum number of times that every prime appears. So, the prime numbers are:

2 = Appears maximum 3 times

3 = Appears 1 time

5 = Appears 1 time

7 = Appears maximum 1 time

So, the LCM is the multiplication of the prime numbers as:

LCM = 2 x 2 x 2 x 3 x 5 x 7

LCM = 840

Therefore, the LCM is 840

The rate of change of the function that has a graph that passes

through the points (-1, 3) and (-2,-4) is slope and is equal to 7.

We have given two points  (-1, 3) and (-2,-4) .

Rate of change of graph is given by slope

Using slope formula , we get

      m = -4 - 3 / -2 - (-1)

      m = -7 / -2 + 1

      m = -7 / -1

       m = 7

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Answer:

..................

Step-by-step explanation:

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The coefficient of determination for the model r² is  1 - SSE/SSTO.

Here we have three terms that is

Total sum of squares i.e. SSTO

Regression sum of squares i.e. SSR and

Error sum of squares i.e. SSE

Now we know,

SSTO = SSR + SSE

which means,

SSR = SSTO - SSE

Since,

         r² = SSR/SSTO

So,

     r² = SSTO - SSE/SSTO

         = SSTO/SSTO - SSE/SSTO

         = 1 - SSE/SSTO

Therefore when the data is given this is the way to calculate the coefficient of determination for the model r².

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The above question is missing data.

Answer:

c = 49

Step-by-step explanation:

A perfect square trinomial is of the form (x + a)²

If we expand (x + a)² we get:

x² +  2ax + a²

Compare this to the specific equation given:
x² +   2ax + a²
x²  +   14x + c

Comparing like terms in both equations:
2ax = 14x ==> 2a = 14 ==> a = 14/2 = 7

Therefore a² = 7²

= 49
and this must be the value of c in the equation

Therefore c = 49

It is given that PG grading requirement is met if the values of S(t) are between -3.2 and +3.2. As all the calculated values of S(t) lie within this range, the asphalt meets PG grading requirement.

Given data: Bending rheometer: 0.4mm, 0.5mm, 0.65mm, 0.82mm, 0.98mm, and 1.3mm for t = 15s, 30s, 45s, 60s, 75s, and 90s.

We are supposed to calculate the values of S(t) and m to check if the asphalt meets PG grading requirement.

Calculation of m:

Mean wheel track rut depth = (0.4+0.5+0.65+0.82+0.98+1.3)/6

= 0.7933mm

Calculation of S(t)

S(t) = (x - m)/0.3

Where, x = 0.4mm, 0.5mm, 0.65mm, 0.82mm, 0.98mm, and 1.3mm

Given, m = 0.7933mm

Substituting these values into the formula above:

S(15s) = (0.4 - 0.7933)/0.3

= -1.311S(30s)

= (0.5 - 0.7933)/0.3

= -0.9777S(45s)

= (0.65 - 0.7933)/0.3

= -0.4777S(60s)

= (0.82 - 0.7933)/0.3

= 0.128S(75s)

= (0.98 - 0.7933)/0.3

= 0.62S(90s)

= (1.3 - 0.7933)/0.3

= 1.521

It is given that PG grading requirement is met if the values of S(t) are between -3.2 and +3.2. As all the calculated values of S(t) lie within this range, the asphalt meets PG grading requirement.

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The best-fitting line through a scatterplot is known as the linear regression line.

The linear regression line is a statistical method used to model the relationship between two variables by fitting a straight line that minimizes the overall distance between the observed data points and the line.

The linear regression line is often used to determine the strength and direction of the linear relationship between two variables. It provides an estimate of the average relationship between the independent variable (x) and the dependent variable (y) in the form of a linear equation (y = mx + b), where "m" represents the slope of the line and "b" represents the y-intercept.

The goal of the linear regression line is to find the line that best represents the pattern of the data points. It minimizes the sum of the squared differences between the observed y-values and the predicted y-values based on the line. By finding the best-fitting line, we can make predictions or infer the relationship between the variables beyond the observed data points.

Therefore, the best-fitting line through a scatterplot is known as the linear regression line.

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Answer:

The three integers are

11, 13, and 15.

Step-by-step explanation:

We shall consider the integers as

x, (x+2), and (x+4). The sum of these is 39, so we can write:

x+(x+2)+(x+4)=39

Open the brackets and simplify.

x+x+2+x+4=39 3x+6=39 Subtract 6 from each side.3x=33 Divide both sides by 3.x=11 Therefore: (x+2)=13and (x+4)=15

Answer:

The three integers are 11, 13, and 15 .

Step-by-step explanation:

We shall consider the integers as x, ( x + 2 ) , and ( x + 4 ) . The sum of these is 39, so we can write:

x + (x + 2) + (x + 4) = 39

Open the brackets and simplify.

x + x + 2 + x + 4 = 39

3x + 6 = 39

Subtract 6 from each side.

3x = 33

Divide both sides by 3.

x=11

Therefore: (x + 2) = 13 and (x + 4) = 15

Answer:

The table represents a function and the slope is -1/2

Step-by-step explanation:

Here, we want to know if the given table is a function

For a relation to be a function, no two y values have same x value

however, 2 x values can have same y value

Looking at the table, we can conclude that what we have is a function

To find the slope, we select any two points and apply the slope formula

m = (y2-y1)/(x2-x1)

(x1,y1) = (6,-2)

(x2,y2) = (-2,2)

m = (2 -(-2))/(-2-6) = 4/-8 = -1/2

The variables on the horizontal and vertical axes of a scatter plot are always continuous.Corresponding: When two sets of data are plotted on a scatter plot, each data point in the two sets has a corresponding point in the other set.

When you plot two sets of data on a scatter plot, you should use different colors or symbols for the data points from each set.The horizontal axis represents one variable while the vertical axis represents the other. Each point on the graph represents one set of data that corresponds to both variables, with the x-value and y-value corresponding to the respective data points being plotted.Scatterplot versus: A scatter plot has two axes that correspond to two variables. In a scatter plot, we can determine how one variable changes as the other variable changes. The variables on the horizontal and vertical axes of a scatter plot are always continuous.Corresponding: When two sets of data are plotted on a scatter plot, each data point in the two sets has a corresponding point in the other set. When you plot two sets of data on a scatter plot, you should use different colors or symbols for the data points from each set.

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The proper order of the designs, from the one with the least amount of control over variables to the most, is (b) one-group pretest posttest, quasi-experimental, pretest posttest control group, Solomon four-group.

The designs can be ordered based on the level of control they provide over variables. The one-group pretest posttest design (b) has the least amount of control as it lacks a control group. The quasi-experimental design (d) provides some control but still lacks random assignment. The pretest posttest control group design (c) includes a control group but lacks random assignment of participants. Finally, the Solomon four-group design (a) provides the highest level of control as it includes both a pretest posttest control group design and a quasi-experimental design, allowing for comparisons and additional control.

By considering the features of each design, we can determine the level of control they offer over variables. It's important to note that the proper order may vary depending on the specific research context and the researcher's goals.

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(3,-1)

it should shape like a square or rectangle when you plot it

hope it helps !

By using the table of values, we have the following:

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value or f(x)).

In this exercise, you're required to determine the value of each function based on the value of x shown in the table above. Therefore, you would identify the input variable (x-value) that corresponds to the value of the output variable (y-value or f(x)) in the given table and vice-versa.

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