TLT () 2n + 3 4n+1 Exercise 1. Decide whether the following real sequences are convergent or not. If they converge, calculate the limit of the sequence. A mere answer is not enough, a justification is also required. (1.1) an := 3n2+2 - Vn+2, (1.2) bn = (1.3) := sin 2n + 1 ories for convergence. For the geometric and expo- nough, a justification is also

Answer:

The ratio of the number to the total of students in the band is: 3 : 14

Step-by-step explanation:

To find the ratio of girls to total students, we have to find the total number of students. You can do this by adding the number of boys and girls together, for a total of 14 kids. The number of girls is 3 out of the total 14 kids. So the ratio is 3:14

The other root of the polynomial is 1 - √3.

The roots of a polynomial are the values of the independent variable at which the polynomial is zero.

If a polynomial has integral coefficients with 3 + i and 1 + √3  as roots, then what other roots must it have? To find the roots it has, we note that the root of a polynomial with a square root in the root also has the conjugate of the square root as a root.

So, since 1 + √3, the conjugate is also a root.

The conjugate is 1 - √3.

So, the other root is 1 - √3.

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The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer:

k =1

Step-by-step explanation:

3x + y = -7

      y = -3x - 7

m = -3

Parallel lines have same slope

\(Slope = -3\\\\\dfrac{8-[-1]}{-2-k}=-3\\\\\\\dfrac{8+1}{-2-k}=-3\\\\\dfrac{9}{-2-k} = -3\)

Cross multiply,

9 = -3(-2-k)

9 = 6 + 3k

9-6 = 3k

3 = 3k

3/3 = k

k = 1

To calculate the standard deviation of the number of people with the disease in samples of size 200, we can use the binomial distribution.

The binomial distribution has a mean (μ) equal to the product of the sample size (n) and the prevalence of the disease (p). In this case, μ = n * p = 200 * 0.102 = 20.4.

The standard deviation (σ) of the binomial distribution is given by the square root of the product of the sample size (n), the prevalence of the disease (p), and the complement of the prevalence (1 - p). Therefore, σ = √(n * p * (1 - p)).

Let's calculate the standard deviation:

σ = √(200 * 0.102 * (1 - 0.102)) ≈ √(20.4 * 0.898) ≈ √18.3504 ≈ 4.28 (rounded to 1 decimal place)

Therefore, the standard deviation of the number of people with the disease in samples of size 200 is approximately 4.3 (rounded to 1 decimal place).

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Answer:

the 30th term is 239

Step-by-step explanation:

The computation of the 30th term is as follows:

As we know that

a_n = a_1 + (n-1)d

where

a_1 is the first number is the sequence

n = the term

And, d = common difference

Now based on this, the 30th term is

= 152 + (30 - 1) × 3

= 152 + 29 × 3

= 152 + 87

= 239

Hence, the 30th term is 239

The equation ax + by = c has integer solutions if and only if (a,b) | c, as the presence of integer solutions implies the divisibility of the GCD, and the divisibility of the GCD guarantees the existence of integer solutions.

The equation ax + by = c represents a linear Diophantine equation, where a, b, c, x, and y are integers. The statement "(a,b) | c" denotes that the greatest common divisor (GCD) of a and b divides c.

To understand why ax + by = c has integer solutions if and only if (a,b) | c, we need to consider the properties of the GCD.

If (a,b) | c, it means that the GCD of a and b divides c without leaving a remainder. In other words, a and b are both divisible by the GCD, and thus any linear combination of a and b (represented by ax + by) will also be divisible by the GCD. Therefore, if (a,b) | c, it ensures that there exist integer solutions (x, y) that satisfy the equation ax + by = c.

Conversely, if ax + by = c has integer solutions, it implies that there exist integers x and y that satisfy the equation. By examining the coefficients a and b, we can see that any common divisor of a and b will also divide the left-hand side of the equation. Hence, if there are integer solutions to the equation, the GCD of a and b must divide c.

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Answer:

y= 1330

Step-by-step explanation:

it might be wrong but

-4x -7.5 = 3312.5

4x +4y = 2000      (x cancels out)

4y -7.5 = 5312.5

4y = 5320

y= 1330

Answer:

the answer is B

Step-by-step explanation:

x + x = 2x

y - y = 0

6 + 2 = 8

2x = 8

Answer:63

Step-by-step explanation:

The grade of a highway up a hill is 26%, therefore the amount of change in horizontal distance if the vertical height of the hill is 600 feet is 2307ft.

This is referred to as the numerical or occasionally qualitative measurement of how far apart objects or points are.

First, express the grade as a decimal.

26% → 0.26

Grade = (change in vertical height) / (change in horizontal distance)

0.26 = (600 ft) / x

x = (600 ft) / 0.26 = 2307 ft

That is the change in horizontal distance.

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Answer:

Step-by-step explanation:

Let the third interior angle be x

Since it's a triangle , all it's interior angles sum up to 180°

To find the third interior angle , add up the two of the equivalent angles that's 34 and subtract it from 180

We have

x + 34 + 34 = 180

x + 68 = 180

x = 180 - 68

We have the final answer as

Hope this helps you

Answer:

The Answer To This Question Would Be 116

Step-by-step explanation:

Step One. 34 + 34 = 68

Since Two Of The Angles Are Each 34 Degrees We Want To Add Them Both Up That Way We Get 68 Which Leads To Another Step To Find The Measure Of The Third Interior Angle.

Step Two. 180 - 68 = 116

We Got 180 Because Every Triangle No Matter What Type It Is It Will Always Equal To 180 Degrees.

With That Being Said, The Answer To This Is 116.

I Hoped I Helped You Today, Have A Amazing Day (:

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Answer:

439.6 cm²

Step-by-step explanation:

Surface area of the cylinder is the length of the rectangular strip that goes around, and the are of the two circles

Area circle = πr²

Area circle = 3.14 * 7²

Area circle = 3.14 * 49

Area circle = 153.86

The area of both circles is 153.86 x 2 = 307.72

The rectangular strip is the diameter by the height

Diameter = 2πr

Diameter = 14*3.14 = 43.96

The strip is 43.96 x 3 = 131.88

Total surface area is 307.72 + 131.88 = 439.6

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Answer:

The two numbers with the sum of 9 and difference of 1 is 5 and 4.

Step-by-step explanation:

Answer:

The answer is 4 and 5.

Step-by-step explanation:

4+5 = 9

5-4 = 1

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Answer:

\(6\sqrt{5}-4\sqrt{15}\)

Step-by-step explanation:

\(\sqrt{5} \times (6 - 4\sqrt{3} )\)

\(\sqrt{5}\times 6-\sqrt{5}\times4\sqrt{3}\)

\(6\sqrt{5}-4\sqrt{5}\sqrt{3}\)

\(6\sqrt{5}-4\sqrt{5 \times 3}\)

\(6\sqrt{5}-4\sqrt{15}\)

Answer:

6\(\sqrt{5}\) - 4 \(\sqrt{15}\)

Step-by-step explanation:

1. Multiply each term in the parentheses by \(\sqrt{5}\)

2. calculate the product

3. solution :)

The rate of change of h(x) with respect to x when x=2 is -3. To find d/dx, we need to take the derivative of the function h(x) and evaluate it at x=2.

h(2) tells us that when x=2, h(x)=4.

h'(2) tells us that the slope of the tangent line to the graph of h(x) at x=2 is -3.

So, we can use this information to find d/dx as follows:

h(x) = y

dy/dx = h'(x)

We know that when x=2, y=h(2)=4.

We also know that the slope of the tangent line to the graph of h(x) at x=2 is h'(2)=-3.

So, we can write the equation of the tangent line at x=2 as:

y - 4 = (-3)(x - 2)

y = -3x + 10

Now we can take the derivative of y with respect to x to find d/dx:

d/dx (y) = d/dx (-3x + 10)

d/dx (y) = -3

Therefore, d/dx = -3.

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Answer:

Step-by-step explanation:

it will be B because you have to divved

Answer:

5/7 x 14/20= 1/2 or 0.5

The length of the base of the parallelogram is 16 inches.

What is parallelogram?

A parallelogram is a four-sided plane figure with opposite sides parallel and congruent (having the same length). This means that the opposite sides of a parallelogram are parallel to each other and have the same length. Additionally, the opposite angles of a parallelogram are equal in measure, which means they have the same degree of rotation.

Let's use the information given in the problem to set up an equation and solve for the length of the base.

From the problem, we know that the height of the parallelogram is 5 inches.

h = 5

We also know that the base of the parallelogram is six more than twice the height. Let's use b to represent the length of the base:

b = 2h + 6

Now we can substitute the value we know for the height and solve for the base:

b = 2(5) + 6

b = 10 + 6

b = 16

Therefore, the length of the base of the parallelogram is 16 inches.

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we compute the dot product and integrate term by term:

\(\int F . dr2 = \int(0 to 1) [(t^2 / (2t^2), (1 - t)^2) . (dt, -dt)].\)

What do you mean by integrate?

When we integrate a function, we are essentially calculating the area under the curve represented by the function within a specific interval. Integration has various applications, such as determining displacement from velocity, finding the total accumulated value over time, calculating areas and volumes, and solving differential equations.

After calculating the integrals for both parts of the region, add the results to obtain the final value of the integral ∫ F · dr over the given region.

To evaluate the integral ∫ F · dr over the region bounded by the triangle with vertices at (1, 0), (0, 1), and (1, 0), oriented counterclockwise, where F = \((y^2 / (2r^2), y^2)\), we can divide the region into two parts and compute the integrals separately. Let's consider the two parts of the region.

Part 1: The line segment from (1, 0) to (0, 1)

To parameterize this line segment, we can use a parameter t that ranges from 0 to 1. Let's call the parameterized curve r1(t). We have:

r1(t) = (1 - t, t), for 0 ≤ t ≤ 1.

To compute ∫ F · dr over this line segment, we substitute the parameterized curve r1(t) into F and compute the dot product:

\(F(r1(t)) = (t^2 / (2(1 - t)^2), t^2).\)

dr1(t) = (-dt, dt).

Now, we can evaluate the integral:

\(\int F . dr1 = \int(0 to 1) [(t^2 / (2(1 - t)^2), t^2) . (-dt, dt)].\)

Simplifying the dot product and integrating term by term, we get:

\(\int F . dr1 = \int(0 to 1) [-(t^2 / (2(1 - t)^2)) dt + t^2 dt].\)

Evaluate each integral separately:

\(\int(-(t^2 / (2(1 - t)^2)) dt = -\int(0 to 1) (t^2 / (2(1 - t)^2)) dt.\\\\\int(t^2 dt) = \int(0 to 1) t^2 dt.\)

Evaluate these integrals and add the results.

Part 2: The line segment from (0, 1) to (1, 0)

Similarly, we can parameterize this line segment using a parameter t that ranges from 0 to 1. Let's call the parameterized curve r2(t). We have:

r2(t) = (t, 1 - t), for 0 ≤ t ≤ 1.

Following the same process as in Part 1, we compute the dot product and integrate term by term:

\(\int F . dr2 = \int(0 to 1) [(t^2 / (2t^2), (1 - t)^2) . (dt, -dt)]\).

Evaluate each integral separately.

After calculating the integrals for both parts of the region, add the results to obtain the final value of the integral ∫ F · dr over the given region.

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Answer:

The answer is below

Step-by-step explanation:

The question would not give a valid answer, the question should be in the form:

A Florida citrus grower estimates that if 30 orange trees are planted, each tree will produce 500 oranges. For each additional tree planted on the same acreage, the number of oranges each tree produces will decrease by 10 oranges. Find the maximum number of oranges the citrus grower can produce. How many trees will the citrus grower need to plant?

Solution:

Let x represent the number of orange trees above 30 to be planted on the acreage and let y be the number of oranges. Since for every additional tree there is a decrease of 10 oranges, hence:

y = (30 + x)(500 - 10x)

y = 15000 - 300x + 500x - 10x²

y = 15000 + 200x - 10x²

The number of oranges is maximum at y' = 0. Hence:

y' = 200 - 20x

200 - 20x = 0

20x = 200

x = 10

Second derivative test = y" = -20 (so this is maximal)

Therefore the number of trees needed = 30 + 10 = 40 trees

Maximum number of oranges = (30 + 10)(500 - 10(10)) = 40(400) = 16000 oranges

Answer:

Step-by-step explanation: this is 150 multiplied by 500

The slope of a plot of ln k versus 1/t equal to: −E_a/R

The Arrhenius equation is one that describes the relation between the rate of reaction and temperature for many physical and chemical reactions.

Arrhenius equation is expressed as:

k = \(Ae^{-E_{a}/RT }\)

Taking natural log on both sides,

ln k = ln \(Ae^{-E_{a}/RT }\)

In k = In A - E_a/RT

In k = In A - (E_a/R * (1/T))

This equation is in the form of y = mx + c

The plot of ln k vs 1/T gives a straight line with negative slope.

Slope = −E_a/R

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Answer:

44

Step-by-step explanation:

Step 1:

e - 13 = 31      Equation

Step 2:

e = 31 + 13     Add 13 on both sides

Answer:

e = 44      Add

Hope This Helps :)

Equilateral ΔD E F with sides 4 b units long has been plotted below.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

An equilateral triangle is a triangle whose all sides are the same.

The all interior angle of an equilateral triangle is 60 degrees.

The length of each side of the given equilateral ΔDEF is 4b.

Hence "Equilateral ΔD E F with sides 4 b units long has been plotted below".

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Answer:

3rd box and last box

Step-by-step explanation:

it's is thise because i had that same question and those where the answers

Answer:

5. 4 hour 17 minutes

Step-by-step explanation:

Lilith can complete work in 6 hours so every hour she will complete 1/6 of the work

Janice can complete work in “x” hours so every hour she will complete 1/x of the work.

so if they both work together in 2.5 hours

Lilith will complete 2.5(1/6) work

Janice will complete 2.5(1/x) work

so 2.5(1/6) + 2.5(1/x) = 1

=> 1/6 + 1/x = 0.4

=> 1/x = 0.4 - 1/6

=> 1/x = 2.4/6 - 1/6

=> 1/x = 1.4/6

=> 1(6) = 1.4(x)

=> x = 6/1.4 = 5.6/1.4 + 0.4/1.4 = 4 + 0.4/1.4 hours

since 0.4/14 hour = (0.4/14)60 = 17.1  or 17 minutes

so x = 4 hour + 17 minutes

I hope this will help to solve the other problems

The area of pyramid base with a dimension of x + 2 and x - 1 is given as x² + x - 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that the base of the pyramid has a dimension of x + 2 and x - 1, hence:

Area of pyramid base = (x + 2)(x - 1) = x² + x - 2

The area of pyramid base with a dimension of x + 2 and x - 1 is given as x² + x - 2

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Answer:

D)6 x squared StartRoot 3 EndRoot units2

Step-by-step explanation: on edge

Hey there!

f(x) = g(x) = h(x) = y

Since, you have the value of x (8), you can substitute it in the equation to make it easier to solve. We just have to find your f(x) value (also known as the y-value)

f(x) -0 -3 * x^2 - 2

f(x) = -3x^2 - 2

y = -3x^2 - 2

y = -3(8)^2 - 2

y = -3(8^2) - 2

y = -3(8 * 8) - 2

y = -3(64) - 2

y = -192 - 2

y = -194

Therefore, your answer should be:

f(x) = -194

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)