suppose the sequence {an} converges to a > 1. prove there exists an index n such that for all n > n , an > 1.

Answer:

for the first one, because its tan of D and also tan formula is opp/adj it should be tanD=80/18

for the second one, because sin(A) and cos(B) is the same thing, if one increases the other would increase as well

Step-by-step explanation:

One product/service that is currently in the decline stage is DVD rentals. The decline can be attributed to the rapid rise of digital streaming platforms and the decreasing popularity of physical media. Companies competing in a declining market have strategic options such as harvesting and divesting. Harvesting involves maximizing profits from the declining product/service by reducing costs and maintaining a loyal customer base, while divesting involves exiting the market and reallocating resources to more profitable ventures.

DVD rentals are in the decline stage of the product lifecycle due to several factors. The advent of digital streaming platforms like Netflix, Hulu, and Amazon Prime Video has revolutionized the way people consume media. The convenience and vast content libraries offered by these platforms have led to a significant decline in DVD rentals. Moreover, the proliferation of high-speed internet connections and the increasing availability of streaming devices have made it easier for consumers to access digital content.

In a declining market, companies have strategic options to consider. One option is harvesting, which involves maximizing profits from the declining product/service. Companies can achieve this by reducing costs associated with production, distribution, and marketing, as the demand for the product/service diminishes. They may also focus on retaining their loyal customer base by providing incentives, discounts, or exclusive offers. For example, DVD rental companies may lower rental fees, offer bundle deals, or introduce loyalty programs to retain their remaining customers.

Another strategic option is divesting, which involves exiting the declining market altogether. Companies may choose to reallocate their resources to more profitable ventures or invest in emerging technologies or industries. In the case of DVD rentals, companies could divest by shutting down physical rental stores and selling off their DVD inventory. They could then shift their focus to digital streaming services or invest in other areas with growth potential, such as content production or streaming device manufacturing.

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Answer:

a. y= 0.613x - 4.141

Step-by-step explanation:

y= ~ -4 when x= 0 so that will be our y-intercept.

so our option would be either A or D

if you look closely, the x goes up when y goes up, which means the slope is a positive

a. X and Y are jointly uniform, So, the joint PDF is constant. K =1

b. Marginal PDF of Y is given by

fY(y) = ∫f(x,y)dx

c.  X and Y are not independent.

Given, X and Y are two RVs with joint PDF f(x,y)= K for 0 ≤ y ≤x≤ 1, where X any Y are jointly uniform.

a. Find K:

To find K, we have to integrate the joint PDF f(x,y) over the range of 0 to 1 for x and y in terms of x.

That is,

K = ∫∫f(x,y)dydx

over the range of

0 ≤ y ≤ x ≤ 1

Given, X and Y are jointly uniform, So, the joint PDF is constant.

Therefore,

K = ∫∫f(x,y)dydx

= ∫∫Kdydx

= K ∫∫dydx

= K × 1

= 1

So, K = 1

b. Find the marginal PDFs:

Marginal PDF of X is given by

fX(x) = ∫f(x,y)dy integrating over all possible y

fX(x) = ∫0x1dy

fX(x) = x, where 0 ≤ x ≤ 1

Similarly, Marginal PDF of Y is given by

fY(y) = ∫f(x,y)dx

integrating over all possible x

fY(y) = ∫y11dx

fY(y) = 1-y,

where 0 ≤ y ≤ 1

c. Justify your answer:

X and Y are said to be independent if and only if their joint PDF is the product of their marginal PDFs.

So, let's check for the given case.

f(x,y) = 1 for 0 ≤ y ≤x≤ 1.

Also, marginal PDF of X,

fX(x) = x, and

marginal PDF of Y,

fY(y) = 1 - y.

Now, fX(x) × fY(y) = x(1 - y) ≠ f(x,y)

So, X and Y are not independent.

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Answer:

101.4 units²

Step-by-step explanation:

If  RT = 12  and TU = 5  then

⇒ RU = RT + TU

          = 12 + 5

          = 17 units

If RS is 7 more than RU then

⇒ RS = RU + 7

         = 17 + 2

         = 24 units

The ΔRSU is a right triangle with the right angle at ∠RUS.

Therefore, use Pythagoras' Theorem to find SU:

⇒ RU² + SU² = RS²

⇒ 17² + SU² = 24²

⇒ SU² = 24² - 17²

⇒ SU² = 287

⇒ SU = √287 units

Area of ΔRST = 1/2 × base × height

                       = 1/2 × 12 × √287

                       = 101.6464461... units²

(Please note: The answer quoted above is accurate. The answer given in the answer options uses the rounded value of SU to 1 decimal place).

The proportion that can be used to show that AC and CE has equal slope is: 2 - 0/3 - 0 = 4 - 2/6 - 3.

Using any two points on a given line, the formula to find the slope of the line is given as:

Slope (m) = change in y / change in x = rise/run or the line.

Given that triangles ABC and CDE are two similar right triangles, find the slope of AC and CE as explained below:

Point A is at (0, 0)

Point C is at (3, 2)

Point E is at (6, 4)

Slope of AC = change in y / change in x = 2 - 0/3 - 0 = 2/3

Slope of CE = 4 - 2/6 - 3 = 2/3

Thus, the proportion showing that the slope of AC and the slope of CE are the same would be expressed as:

2 - 0/3 - 0 = 4 - 2/6 - 3.

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For the given integer, the maximum starting population size that will eventually lead to extinction is 98, since any larger value will result in the population either stabilizing at a positive value or growing indefinitely.

The equation in question is:

dN/dt = -0.001N(N - 110)(N - 99)

Here, N represents the population size, and dN/dt represents the rate of change of the population with respect to time. The right-hand side of the equation tells us how the population size changes over time, and it's determined by the current population size N, as well as the two constants 110 and 99.

We can do this by setting dN/dt equal to zero and solving for N:

dN/dt = -0.001N(N - 110)(N - 99) = 0

=> N = 0, N = 99, N = 110

We can then plot the direction field (i.e., arrows indicating the direction of change) on each interval, and use this to determine the behavior of the solution curve. In this case, we can see that the direction of the arrows changes at each critical point, indicating that the population behavior switches between growing and declining as we move from one interval to the next.

Specifically, we can see that if the initial population size A is less than 99, the population will decline to extinction. If the initial population size is between 99 and 110, the population will initially decline but then grow and eventually stabilize at N = 110. If the initial population size is greater than 110, the population will grow exponentially and tend towards infinity.

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Answer:

400 divided by 10 Got it right in the assignment

Answer:400 divided by 10

Step-by-step explanation:

<3

Step-by-step explanation:

if it helps don't forget to like and Mark me

Answer: Water expands and becomes less dense when it freezes.

Step-by-step explanation:

When a solid is less dense than liquid that it is put in, it will float.

This is the case with icebergs. When water freezes, the molecules move away thereby expanding and increasing the volume of the water.

The larger the volume of an object, the smaller it's density.

The iceberg will therefore have a lower density that enables it to float.

Answer:

C: Water expands and becomes less dense when it freezes.

Step-by-step explanation:

I got it right on edge

Answer:

yes

Step-by-step explanation:

because the lines show that those two sides are congruent,  and because there are two congruent sides, then the third has to be the same to connect the triangles

Answer:

Yes.

Step-by-step explanation:

They have equal angles and line lengths

Answer:

The answer is B.

Step-by-step explanation:

x^2-5x = x + 5

(x^2-5x)( x + 5)

x^3 - 25x^2+25x^2-25x

x^3 - 25x

Gold costs less than platinum per ounce because the slope of the graph for gold is less than that of the chart for platinum. The slope of the graph tells you the unit rate in dollars per ounce.

In Mathematics, a slope is sometimes referred to as rate of change and it is typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.

Mathematically, the slope (rate of change) can be calculated by using this mathematical expression;

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the graph of the weight of gold and platinum, we can reasonably infer and logically deduce that the slope (unit rate) of the graph for gold is less than the slope (unit rate) of the graph for platinum.

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Complete Question:

Use the drop-down menus to complete the statements to match the information shown by the graph.

A graph has weight (ounces) on the x-axis, and cost (dollars) on the y-axis. A line labeled gold starts at (0, 0) and has a positive slope. A line marked platinum starts at (0, 0) and has a greater positive slope than gold.

Gold costs ---------------- platinum per ounce because the ----------- of the graph for gold is -------------that of the chart for platinum. The --------of the graph tells you the unit rate in _____.

Answer:

y = \(\frac{1}{2}\) x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = \(\frac{1}{2}\) so

y = \(\frac{1}{2}\) x + c ← is the partial equation

To find c substitute (4, 6) into the partial equation

6 = 2 + c ⇒ c = 6 - 2 = 4

y = \(\frac{1}{2}\) x + 4 ← equation of line

Answer:

See below.

Step-by-step explanation:

We have:

\(\frac{\sqrt3}{\sin(\theta)}=2\)

And we want to find two different angles between 0 and 180 that satisfy this equation.

First, let's get our sine out of the denominator. Notice that this is the same as:

\(\frac{\sqrt3}{\sin(\theta)}=\frac{2}{1}\)

Cross-multiply:

\(2\sin(\theta)=\sqrt{3}\)

Divide both sides by 2:

\(\sin(\theta)=\frac{\sqrt{3}}{2}\)

Here you go! I'll have the answer for you if you scroll down, so check it when you're ready!

#2 is correct. However, double check #3. The answer's down there too... :)

[Blank space...]

[More blank space...]

[And more...]

Answer for 1)

We have:

\(\sin(\theta)=\sqrt{3}/2\)

So, at what points between 0 and 180 does sine equal √3/2?

If we refer to the unit circle, we can see that this happens twice: at 60.

Thus, the second time it occurs will be at 180-60 or 120.

So:

\(\theta=60\textdegree\text{ or } 120\textdegree\)

Answer for 3)

So you are correct for the first three. So:

\(\sin(54)=t\)

However, sine stays positive. So, our angle must be between 0 and 180.

So, instead of 180+54, it should be 180-54, giving us:

\(\sin(54)=\sin(126)=t\)

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

<95141404393>

The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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Answer:

25%

Step-by-step explanation:

20 / 5 = 4

100 ÷ 4 = 25

= 25%

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

Answer: a= -3 and b=2.

Step-by-step explanation:

If a system of linear equations has infinitely many solutions, then

Ratio of coefficient of y= ratio of coefficient of x = ratio of constants.

Given system: \(y=2x+a\)

\(y=bx-3\)

It it has infinitely many solutions, then

\(\dfrac{1}{1}=\dfrac{2}{b}=\dfrac{a}{-3}\\\\\Rightarrow\ \dfrac{2}{b}=1\ \ \ \text{ and }\ \ \dfrac{a}{-3}=1\\\\\Rightarrow\ b=2\ \ \ \text{ and } \ \ a=-3\)

hence, a= -3 and b=2.

Answer:

12 + m

Step-by-step explanation:

it's 12 more, which would be +12 because it's adding 12

Answer:

it is going to have to be the 3rd one

Answer:

|x−10|=5

Step-by-step explanation:

just took the test

The following would need to be congruent to show that ΔABC ≅ ΔXYZ by AAS: A. ∠B ≅ ∠Y.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Furthermore, the lengths of three (3) pairs of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the angle, angle, side (AAS) similarity theorem, we can logically deduce that triangle ABC and triangle XYZ are both congruent due to the following reasons:

∠A ≅ ∠X.

∠B ≅ ∠Y.

AC ≅ XZ

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Answer:

The angle is 65°

Step-by-step explanation:

The angle is 65°

*See attachment for the diagram

Answer:

B. ∠EAB and ∠CAD;

D. ∠CAB and ∠DAE

Step-by-step explanation:

Vertical angles are two angles formed directly opposite each other when two straight lines crosses or intercepts each other. Vertical angles are of equal measure to each other.

Thus, from the diagram given,

<CAD is vertically opposite to <EAB, also,

<CAB is vertically opposite to <DAE.

Thus, the vertical angles are:

∠EAB and ∠CAD;

∠CAB and ∠DAE

Answer:

B and D

Step-by-step explanation:

Hope it helps ^w^

For part A, x equals 0.

Therefore (7²)⁰=7⁰=1

For part B, x could be any number because 0 multiplied by any number equals 0. eg. (7⁰)⁹=7⁰=1

Hope this helps!

Answer:

135

Step-by-step explanation:

Those are supplementary angles, you can tell because the bottom line is flat.

supplementary angles always equal 180 together

so 180-45=135

Answer:

Step-by-step explanation:

4mx+2m

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:w

Step-by-step explanation: