(1 point) Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive. Σ(1 + )" 2n L = lim Van (Enter 'inf' for o.) 11-00 24 (1 + )" is: O A. convergent B. divergent C. The Root Test is inconclusive

The Greek mathematicians started using the symbol pi (π) for as long as 4000 years in mathematical world.

A Short History of Pi

Even if we counted the number of seconds in those 4000 years and round the value of pi (π) to so many places, we would still only be estimating the true value of pi. Pi has been known for over 4000 years. Below is a quick summary of the discovery of.

By multiplying the radius of a circle by three, the ancient Babylonians determined its area, yielding the number pi = three. About 1900–1680 BC Babylonian tablets show a value of 3.125 for, which is a more accurate estimate.

The Rhind Papyrus, which dates to around 1650 BC, sheds light on ancient Egyptian mathematics. The calculation used by the Egyptians to determine a circle's area yielded a result that was around 3.1605 for.

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Answer:

I'm pretty positive its (0, 0)

The values of w typically vary, on average, from the mean of the distribution about 3.46.

The degree of data dispersion from the mean is indicated by the standard deviation. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

For a geometric(p = 0.25) distribution, the variance is computed here as:

Var(X) = (1 - p)/ p2 = (1 - 0.25) / 0.252 = 12

Therefore, the standard deviation is computed as:

= ✓(12) = 3.46 observations.

This is the standard deviation of the given distribution here.

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We can write the absolute value equation in the form |x-0|=15, which simplifies to |x|=15.

To write the absolute value equation in the form |x-b|=c with the given solution sets, we need to remember that the absolute value of a number is its distance from zero on the number line. Therefore, the absolute value of (x-b) will be equal to c if and only if (x-b) is c units away from zero on the number line.

For the first solution set, x=2 and x=14, we can see that the midpoint between 2 and 14 is 8, and the distance from 8 to either endpoint is 6. Therefore, we can write two absolute value equations in the form |x-8|=6, one for each solution: |2-8|=6 and |14-8|=6.

For the second solution set, x=15, we can see that 15 is 15 units away from zero on the number line. Therefore, we can write the absolute value equation in the form |x-0|=15, which simplifies to |x|=15.    

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Answer:

The solution is (-4,-5)

Step-by-step explanation:

Answer:

First step - rewrite the equation to single out the variables.

Step-by-step explanation:

Write the equation again as 2x+3=-x-9

Solve for x and get  x = -4

Then, substitute x into the old equation as y = 2(-4)+3 and solve for y.

Solve for y and get y = -5

x = -4   y= -5

Since the distribution is symmetric, the mean and the median of the distribution are equal.

When a distribution is symmetric, the mean and the median are equal. From the dot plot in this problem, the distribution is uniform(as all outcomes are equally as likely, that is, they have the same frequency in the dot plot), and symmetric, hence the the mean and the median of the distribution are equal.

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The height of the cylinder is \(3 inch\)

Based on the attached figure,

Volume of the cylinder = 282.7 square inches

Radius of the cylinder =5 inches.

The height of the cylinder = ?

The volume of the cylinder  can be found with the formula as :

\(V=pi r^{2} h\)

\(h=\frac{V}{pi r^{2} } \\\\h = \frac{282.7}{3.142 * 5^{2} } \\\\=3 inch\)

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The yearly breakeven point for Umbridge Purses Unlimited is 20,000 units.

To determine the contribution margin per unit, we subtract the variable cost per unit from the sales price per unit.

In this case, the variable cost per unit is the cost to produce each purse, which is $20, and the sales price per unit is $35.

Therefore, the contribution margin per unit is $35 - $20 = $15.

Next, we divide the total fixed costs of $300,000 by the contribution margin per unit of $15 to find the yearly breakeven point in units.

Breakeven point in units = Total fixed costs / Contribution margin per unit

Breakeven point in units = $300,000 / $15 = 20,000 units.

Therefore, the yearly breakeven point for Umbridge Purses Unlimited is 20,000 units.

This means that the company needs to sell at least 20,000 units in a year to cover all its costs and reach the breakeven point without incurring any losses or making any profits.

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Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

To determine which planks Amanda should use to build the triangular-shaped kennel:

Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

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The variance of the probability distribution is 400

The Variables of X and their Probability Distribution.

To find Variance, first we should find out Mean and then Variance

The expected value of a discrete random variable X, symbolized as E(X), is often referred to as the long-term average or mean (symbolized as μ)

The variance of a probability distribution is symbolized as σ2. To find the variance σ2 of a discrete probability distribution, find each deviation from its expected value, square it, multiply it by its probability, and add the products.

Step – 1: Calculation of Mean                               Step – 2: Calculation of Standard Deviation= σ2=∑(x−μ)²P(x)

Mean = X * P(X)     Variance = Sum of (X – Mean)²*P(X)

X P(X) X*P(X)

-50 0.029 -1.45

-30 0.121 -3.63

-10 0.210 -2.1

10 0.485 4.85

30 0.145 4.35

50 0.010 0.5

Mean  2.52

X  P(X) X - Mean  (X – Mean)² (X – Mean)²*P(X)

-50 0.029 -52.52 2758.35                 79.99216

-30 0.121 -32.52 1057.55                 127.9636

-10 0.210 -12.52 156.7504         32.91758

10 0.485 7.48          55.950                  27.13594

30 0.145 27.48 755.1504         109.4968

50 0.019 47.48 2254.35                 22.5435

Variance=400.00

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The correct answer is a. H0: u≥2 hours and H1:u<2 hours. When testing a right-tailed hypothesis using a significance level of 0.025, a sample size of n=13, and with the population standard deviation unknown, the critical value is as follows:

To determine the critical value, we need to use the t-distribution since the population standard deviation is unknown.

Using a t-distribution table or calculator with 12 degrees of freedom (n-1), a one-tailed test, and a significance level of 0.025, the critical value is 2.1604.

If the test statistic is greater than or equal to this value, we can reject the null hypothesis in favor of the alternative hypothesis, which is a right-tailed hypothesis.

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Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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The steps to condensing the expressions
2loga(4)+3loga(X-4)loga(4)

Log(x+3)+log(x-3) is given below.

To condense the   expressions, we can apply the  properties of logarithms. Here are the condensed forms of the given expressions.

2loga (4) + 3loga(X - 4) - loga 4 )  

By using the product and quotient rules of logarithms, we can simplify this expression as follows

2 loga( 4) + 3 loga( X-4) - log a(4)

= loga(4 ²) + loga((X-4)³) -  loga (4) = loga (16 ) + loga((X-4)³) - loga (4)

Combining the logarithms  using the power rule and quotient rule we have

= loga(16(X-4)³/4)

log(x+3) + log (x-3)

By using the product rule of logarithms, we can combine these logarithms

log (x +3) +log (x - 3) = log ((x +3 )(x -3 ))

Simplifying further, we get

= log (x² - 9 )

So this means that the condensed forms of the given expressions are

2loga( 4) + 3loga(X -4) - loga (4) = loga(16 (X-4) ³/4)

log (x+ 3) + log(x- 3) = log(x² - 9)

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Answer:

24°

Step-by-step explanation:

134° - 110° = 24°

Answer:

Mark me as brain list plz for fun I need to get my expert rank

Step-by-step explanation:

There is no attachment to see any grams post then I will answer

If we will start by solving for y, it means that x is substituted in one of the equations.

If we clear the value of x from the first equation and replace it in the second equation, we would get:

Option A does not correspond to an equation of the system as it would be:

It is ignoring the coefficient -5 that multiplies x in the second equation.

Option B is exactly the result we have obtained from the substitution, so this is the equation.

Option C has the sign wrong as x=-3y+14.

Option D does not substitute x, so it won't be the step to solve for y.

Answer: Option B.

In simple feedback control systems, the location of poles is crucial and has significant implications. This question focuses on the significance of poles in systems where the plant contains a dead zone. The explanation will provide a step-by-step analysis of the topic.

In control systems, poles represent the roots of the characteristic equation, which determine the system's stability and response. When the plant contains a dead zone, it means there is a region of the input where the output remains constant. This non-linearity in the plant affects the location and significance of the poles.

To analyze the system, we consider the transfer function of the plant with a dead zone. The dead zone introduces non-linear behavior, leading to multiple poles in the system. The location of these poles determines the stability and performance of the control system.

The significance of the poles lies in their impact on system behavior. For stable systems, the poles should have negative real parts to ensure stability. If the poles have positive real parts, the system becomes unstable, leading to oscillations or divergent responses.

Furthermore, the location of poles affects the transient response, settling time, and frequency response of the system. Poles closer to the imaginary axis result in slower responses, while poles farther from the axis lead to faster responses.

By analyzing the pole locations and their significance, engineers can design appropriate control strategies to achieve desired system behavior and stability in simple feedback control systems with a dead zone in the plant.

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\(answer \\ = \frac{4}{25} \\ please \: see \: the \: attached \: picture \\ for \: full \: solution \\ hope \: it \: helps\)

Answer:

y=0.5x-3

Step-by-step explanation:

m=(-12+14)/(-18+22)=0.5

y+14=0.5(x+22)

y=0.5x-3

The answer to the question "Is the dependent variable continuous?" would be a. Yes, it is measured in interval form.

The question asks whether the dependent variable is continuous. In this context, a continuous variable is one that can take on any value within a certain range. The options provided are: (a) Yes, it is measured in interval form, (b) No, it is measured in variance form,

(c) Yes, it is measured, and (d) The error occurs when you reject the correct hypothesis during a hypothesis test. Among these options, the most appropriate answer is (a) Yes, it is measured in interval form.

This indicates that the dependent variable is continuous and can be measured on an interval scale, where the values can have a meaningful order and the differences between them are consistent.

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Hence, \(y=4+x\) is a proportional relationship.

What is the proportional?

Proportional or proportion meaning in math means equality between two ratios. In the mathematical equation \(\frac{a}{b}=\frac{c}{d}\), where \(a\) and \(b\) are in a similar proportion as \(c\) and \(d\).

A proportion is essentially established for solving a word problem in which one of its four quantities is unknown.

Here given that,

We have to check \(y=4+x\) is a proportional relationship or not.

So, the given equation is

\(y=4+x\)

Here, \(4\) is constant.

So, \(y=4+x\) is a proportional relationship.

Hence, \(y=4+x\) is a proportional relationship.

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67.50 + 12.50 = 80

80/100 = 0,8 x 3 = 2.4

so, the total bill was 80 + 2.4 = 82.4

hope it helps :)

Answer:

The x values are the same, so leave these be. They do not need to be factored. We need to find a way to factor y^4 and y^2

To do this, just factor using the formula for the difference between two squares

\(a^2-b^2 = (a+b)(a-b)\\\)

Substitute. A = y, b = 1

\(y^2(y+1)(y-1)\)

Since x^3 is the same, insert this before y^2

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

This is the factored form.

Step-by-step explanation:

Answer:

What is it love ?

Step-by-step explanation:

Answer:

See Below

Step-by-step explanation:

Ok, so in this problem you have some vertical angles. These are angles oppisites from each other. Therefore; d = 52, f = ?, and e = 77. All the angles added together will = 360. Let's add up the angles we know and subtract the whole from 360.

52 + 52 + 77 + 77 = ?

104 + 154 = 258

360 - 258 = 102

Since we know that f and the unlabeled angle are the same, we need to divide this total between the two of them.

102/2 = 51

Therefore;

d = 52

e = 77

f = 51

Answer:

quadrant 1

Step-by-step explanation:

b/c quadrant(+,+)

From the origin,

she is 22 units to the right and 1 unit upwards.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given:

Thalia is in the room located at (22,1).

From the origin to this point  (22,1).

In the first quadrant,

From the origin,

she is 22 units to the right and 1 unit upwards.

Therefore, she is 22 units to the right and 1 unit upwards.

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Answer:

Q6. 48     Q7. 49

Step-by-step explanation:

The green bar on question 6 is lined up to 48 units

The green bar on question 7 is lined up to 49 units