a series is given by 131+232+333+434+535+.... francine correctly applies the ratio test to determine whether the series converges or diverges. which statement reflects francine's conclusion?

The Pythagorean theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

Therefore, for the given values of 3, 4, and 5, these lengths can indeed form a right triangle. Specifically, this triangle is a 3-4-5 triangle, which is a special type of right triangle whose sides have integral lengths and whose angles are all multiples of 30°.

Mathematically, this can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the two legs of the triangle and c is the length of the hypotenuse. The theorem is a fundamental result in geometry and has wide-ranging applications in mathematics, physics, engineering, and other fields.

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Answer:

[tex]4y^{2}[/tex]

Step-by-step explanation:

A = Area

w = width

l = length

[tex]A=lw[/tex]

in this equation the area is [tex]32xy^{3}[/tex] and the length is [tex]8xy[/tex].

To find the equation we simply have to divide the area ([tex]32xy^{3}[/tex]) by the length ([tex]8xy[/tex]).

[tex]32xy^{3} =(8xy)w[/tex]

When dividing, it's important to remember two things:

Using these two rules, we divide the common bases (number by number, x by x, y by y):

[tex]\frac{32}{8}=4[/tex]

[tex]\frac{x}{x}=1[/tex]

[tex]\frac{y^{3} }{y}=y^{2}[/tex]

Multiplying all of them together, we find that the width is:

[tex]4y^{2}[/tex]

Answer:

Step-by-step explanation:

The value of the given expression will be 4.

It is not appropriate to assume that the sampling distribution of the sample mean is approximately normal when the sample size is small and the population distribution is skewed to the right or to the left. So, the options C and D are not appropriate. A and B are appropriate as the sample size is large and the population is normally distributed. E is also appropriate as the sample size is large.

The central limit theorem states that if we have a large enough sample size (typically n >= 30) from any population with a well-defined mean and finite variance, then the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and variance equal to the population variance divided by the sample size.

However, if the population distribution is highly skewed, meaning it is not symmetric, then even a large sample size may not lead to a normal distribution of the sample mean.

In this case, it is not appropriate to assume that the sampling distribution of the sample mean is approximately normal. This is why options C and D are not appropriate as the sample size is large (10 and 75 respectively) but the population distribution is skewed to the right or to the left. On the other hand, options A and B are appropriate as the sample size is large and the population is normally distributed. Option E is also appropriate as the sample size is large, regardless of the shape of the population distribution.

The complete question is given below:

""

For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal?

A) A random sample of 8 taken from a normally distributed population.

B) A random sample of 50 taken from a normally distributed population.

C) A random sample of 10 taken from a population distribution that is skewed to the right.

D) A random sample of 75 taken from a population distribution that is skewed to the left.

E) A random sample of 100 taken from a population that is uniform.

"

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Answer:

= [tex]-\frac{5}{2}[/tex]

= m = -2.5

Step-by-step explanation:

Hope it helps on your assignment/quiz/test/homework

Answer:-5/2

Step-by-step explanation:

(3,-9) and (1,-4)

(x1,y1)       (x2,y2)

[tex]\frac{-4+9}{1-3\\}[/tex] = [tex]\frac{-5}{2}[/tex]

The experimenter cannot control the probability of a Type I error, but they can control the level of significance they set, and that will determine the probability of making this type of error.

The probability of committing a Type I error is determined by the level of significance (α, alpha) that one chooses. This is because the level of significance is the probability of rejecting the null hypothesis when it is actually true. In other words, the level of significance is the probability of making a Type I error (falsely rejecting the null hypothesis). For example, if the level of significance is set to 0.05, then the probability of making a Type I error is 0.05. This can be expressed mathematically as: P(Type I Error) = α. Therefore, the experimenter cannot control the probability of a Type I error, but they can control the level of significance they set, and that will  the probability of making this type of error.

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Answer: The statement "Stephen failed to avoid spoilers on the new Star Wars movie" contains a negative phrase "failed to avoid". When a sentence contains a negative phrase, it can sometimes be difficult to determine the meaning. However, in this case, the meaning of the sentence is that Stephen did see spoilers on the new Star Wars movie. The use of "failed to avoid" indicates that Stephen made an effort to avoid spoilers but was unsuccessful, which means that he saw them.

Step-by-step explanation:

The solution is Option C.

The measure of TR of triangle STR is TR = 30

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔPQR

Let the second triangle be represented as ΔSTR

The measure of PR = 35

The measure of SR = 25

The measure of QR = 42

The measure of QT = x

The measure of TR = 42 - x

Now , PQ is similar to ST

Now , the triangles PQR and STR are similar triangles

And , corresponding sides of similar triangles are in the same ratio

Substituting the values in the equation , we get

SR / PR = TR / QR

25 / 35 = ( 42 - x ) / 42

On simplifying the equation , we get

Multiply by 42 on both sides of the equation , we get

( 42 - x ) = ( 25 x 42 ) / 35

On further simplification , we get

42 - x = 30

Adding x on both sides of the equation , we get

x + 30 = 42

Subtracting 30 on both sides of the equation , we get

x = 12

Now , the measure of TR = 42 - x

Substitute the value of x in the equation , we get

The measure of TR = 42 - 12 = 30

Hence , the measure of TR of triangle is 30

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The area of the triangle is  2. 6 square units

The formula for calculating the area of a triangle is expressed as;

A = 1/2bh

Given that the parameters are;

using the trigonometric identity, sine, we have;

sin 60 = h/4

substitute the values

0. 8660 (4) = h

h = 3.5

substitute the value

Area = 1/ 2 × 3. 5 × 1. 5

multiply the values

Area = 2. 6 square units

Hence, the value is 2. 6 square units

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Answer:

true

Step-by-step explanation:

A unit rate is a price for one unit of anything. This is written as a ratio with a denominator of one.

Therefore , the solution of the given problem of volume comes out to be density  1.15625 g/ cm³.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two examples of cubic units are cm3 and in3. The amount of matter in a thing is measured by its mass, on the other hand. The weight of an object is typically converted into mass quantities like pounds and kilograms.

Here,
Given:

Density = mass /volume

mass = 370 gm

volume = 320  cm³

Density = 370/320

=>Density = 1.15625 g/ cm³

thus , density  1.15625 g/ cm³

Therefore , the solution of the given problem of volume comes out to be density  1.15625 g/ cm³.

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The sum of residuals (error) for any first order simple linear regression least squares line is zero (0).

To show that the sum of residuals (error) for any first order simple linear regression least squares line is zero (0), we can use the following equation:

Where b0 is the intercept and b1 is the slope of the line, and xi and yi are the x and y values of the ith data point. This equation can be expanded by substituting the least squares solution for b0 and b1 into the equation:

∑i = 1n (yi − (∑i = 1n yi)/n − (∑i = 1n xiyi − (∑i = 1n xi)(∑i = 1n yi))/(∑i = 1n xi2 − (∑i = 1n xi)2/n)) = 0

Simplifying both sides of the equation, we get:

∑i = 1n (yi − (∑i = 1n xiyi)/(∑i = 1n xi2)) = 0

Therefore, the sum of residuals (error) for any first order simple linear regression least squares line is zero (0).

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They are congruent by the by the Angle-Side-Angle (ASA) congruence criterion.

Angle-Side-Angle (ASA) congruence criterion states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent. In this case, the angles angle E = angle I and EG=FI (a non-included side), so the triangles ADEF and AHIG are congruent by ASA.

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The remaining length when 85 cm is cut from 1.3 meters is 0.45 meters.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

We know, 1.3 meters = 1.3×100 cm = 130 cm.

Now, 83 cm is cut from it.

Therefore, The remaining length is,

= (130 - 85) cm.

= 45 cm.

And 45 cm is equal to (45/100) meters.

= 0.45 meters.

Q. 83 cm is cut from 1.3 meters what would the remaining length in meters?

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The system shown consists of a rotational mass, a pinion, and a linear mass.

The equations of motion for this system can be formulated in terms of x, theta, and theta a in terms of rotational and linear acceleration.

The equation of motion for rotational acceleration is given by:

θ¨ = (1/J) * (T - (b*x¨))

Where J is the moment of inertia of the rotational mass, T is the torque applied to the pinion, and b is the coefficient of friction between the pinion and the linear mass.

The equation of motion for linear acceleration is given by:

x¨ = (1/m) * (T - (b*θ¨))

Where m is the mass of the linear mass, T is the torque applied to the pinion, and b is the coefficient of friction between the pinion and the linear mass.

The equations of motion for the system shown can be formulated in terms of rotational acceleration (θ¨) and linear acceleration (x¨) using the moment of inertia (J) and mass (m) of the rotational and linear masses, respectively, as well as the coefficient of friction (b) between the two.

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Answer:

26 inches, or 2 ft 2 in.

Step-by-step explanation:

1 ft = 12 in.

6 ft 8 in. = 6 ft + 8 in. =

= 6 ft × 12 ft / in. + 8 in.

= 72 in. + 8 in.

= 80 in.

He needs 80 inches.

80 - 54 = 26

Answer 26 inches or 2 ft 2 in.

Answer:

he needs 26 inches

Step-by-step explanation:

[tex]\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=6\\ r=8 \end{cases}\implies SA=2\pi (8)(6+8) \\\\\\ SA=16\pi (14)\implies SA=224\pi \implies SA\approx 703.72~units^2[/tex]

The area of each composite figure is 828.96 cm².

A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.

Given:

Surface area = SA of Cone + SA of Hemisphere

Cone:

radius = 8 cm

slant height = 17 cm

So, SA of Cone = πrl

                          = 3.14 x 8 x 17

                          = 427.04 cm²

Hemisphere:

radius = 8 cm

So, SA of Hemisphere = 2πr²

                                     = 2 x 3.14 x 8 x 8

                                     = 401.92 cm²

Thus, the SA of figure = 427.04 + 401.92 = 828.96 cm²

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Answer:

Step-by-step explanation:

you look it up, If that doesn't work, see if someone asked the same question on this, if not, I got nothing.

The statement “The relationship between the spring constant (k), the mass (m), and the period of oscillation (t) is given by the equation (19) this is not a linear equation, but it can be linearized using the same method used to linearize equation 10.” is true because equation 19 can indeed be linearized with the same method used to linearize equation 10.

Equation 10 is a non-linear equation and can be linearized by taking the natural logarithm of both sides. This will convert the equation into a linear form which can be used to calculate the parameters of the original equation.

Similarly, equation 19 can be linearized by taking the natural logarithm of both sides. The linearized form of equation 19 will also be useful in finding out the parameters of the original equation.

By linearizing the equations, it becomes easier to solve for the parameters of the equations. This is because linear equations are much simpler and can be solved using basic algebraic methods.

Linear equations can also be solved using matrix methods and can be used to solve for the parameters of the original equations more accurately.

Therefore, it is true that equation 19 can be linearized using the same method used to linearize equation 10. This will make it easier to solve for the parameters of the original equation.

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If each value is equally likely and the mean of x is 6, x = 24.

The arithmetic mean (arithmetic average or simply the mean or average) in statistics is the sum of a collection of numbers divided by the count of numbers in the collection, which is is often a set of results from an experiment, a survey, or observational study.

The arithmetic mean A is defined to be the formula: [tex]A = \frac{1}{n} \sum_{i=1}^{n} a_i=\frac{a_1+ ... +a_n}{n}[/tex].

We're given a set of {0, 1, 2, 3, x} where x is unknown and the mean of x is 6. In order to find the value of x, we can plug all the known values in the formula first and then we're going to simplify the equation:

[tex]A = \frac{a_1+...+a_n}{n}\\\\6 = \frac{0+1+2+3+x}{5}\\\\6 = \frac{6+x}{5}\\\\30 = 6 + x\\\\30 - 6 = x\\\\x = 30 - 6\\\\x = 24[/tex]

We've confirmed that x is indeed equal to 24.

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Angle B is equal to angle Y and angle A is equal to angle X. And AB is equal to side XY.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔABC is congruent to the triangle ΔXYZ.

In triangles ΔABC and ΔXYZ, then we have

∠B = ∠Y               (Corresponding angles)

∠A = ∠X              (Corresponding angles)

AB = XY               (Common side)

Angle B is equal to angle Y and angle A is equal to angle X. And AB is equal to side XY.

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Answer:

Class B

Step-by-step explanation:

duh

Answer:

b

Step-by-step explanation:

A 130

The red line meets the measuring tool at 155 and 25 therefore we get:

155-25 = 130

Answer: 3 times 5 minus a number x

Step-by-step explanation:

The value of the expression given as √2(2+6)​ is 4

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

√2(2+6)​

We start by evaluating the expression in the bracket

So, we have the following

√2(2+6)​ = √2(8)

Evaluate the products

This gives

√2(2+6)​ = √16

Lastly, we have

√2(2+6)​ = 4

Hence, the solution is 4

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Answer:

Step-by-step explanation:

9x - 7y > -7

-7y > -9x - 7

y < 9/7x + 1

The set of solutions for the linear system is x1 = 6, x2 = 3, and x3 = -4.

The linear system is given as follows:

x1 + x2 - x3 = 6

2x1 + x2 + 2x3 = 8

3x1 + 2x2 + 3x3 = 14

To solve this system, we will use the Gauss-Jordan elimination method. First, we will subtract twice the first equation from the second equation and three times the first equation from the third equation.

2x1 + x2 + 2x3 = 8

- 2(x1 + x2 - x3 = 6)

2x1 + x2 + 2x3 = 8

3x1 + 2x2 + 3x3 = 14

- 3(x1 + x2 - x3 = 6)

0x1 + 3x2 + 5x3 = 6

Next, we will subtract three times the second equation from the third equation.

3x1 + 2x2 + 3x3 = 14

- 3(0x1 + 3x2 + 5x3 = 6)

3x1 + 2x2 - 2x3 = 8

Finally, we will divide the first equation by 1, the second equation by 3, and the third equation by -2.

x1 + x2 - x3 = 6

/ 1

x1 + (1/3)x2 + (5/2)x3 = 3

(-1/2)x1 + x2 + x3 = -4

The set of solutions for the linear system is x1 = 6, x2 = 3, and x3 = -4.

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The average yearly salary of an individual with each of these final degrees is $22333 and $16666.6.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form

Ax + B = 0.

Given;

The average yearly salary of an individual whose final degree is a​ master's is ​$43000 less than twice that of an individual whose final degree is a​ bachelor's.

Combined, two people with each of these educational attainments earn ​$110 thousand.

Now, let the salary of bachelors be x

Then salary of masters= 2x-43000

x+2x-43000=110000

3x=67000

x=22333.33

2x-43000=16666.66

Therefore, by solving equations answer will be $22333 and $16666.6.

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