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The interval of convergence of the power series is (-10/7, 10/7).

What does Interval of convergence tell you?

A group of x-values on which a power series converges is known as the interval of convergence. In order to create a convergent series, you can plug in this interval of x-values.

The interval of convergence of a power series is the set of values of x for which the series converges. To find the interval of convergence of the given power series, we can use the ratio test.

The ratio test states that if the series [tex]∑ a_nx^n[/tex] has a positive radius of convergence R, then the series converges for |x| < R and diverges for |x| > R. The radius of convergence is given by the formula

                     [tex]R = 1/limsup|a_n+1/a_n|.[/tex]

In the given power series, the coefficient [tex]a_n[/tex] is given by  [tex]a_n = (7x)^n/(10n)!.[/tex]

We can rewrite this as [tex]a_n = x^n(7/10)^n/n!.[/tex]

Taking the limit of the ratio [tex]a_n+1/a_n[/tex] as n goes to infinity, we get:

             [tex]limsup|a_n+1/a_n| \\\\= limsup|x^(n+1)(7/10)^(n+1)/(n+1)!/(x^n(7/10)^n/n!)|\\\\= limsup|x(7/10)/(n+1)|\\\\= |x(7/10)|[/tex]

Therefore, the radius of convergence R is [tex]1/|x(7/10)|[/tex].

This means that the interval of convergence is  [tex]|x| < 1/|7x/10| = 10/7.[/tex]

We can check the endpoints of the interval to see if the series converges at these points. At x = 10/7, the series becomes [tex](7(10/7))^n/(10n)! = 1^n/(10n)!.[/tex]

This series is a geometric series with first term 1 and common ratio 1/10, and it converges because [tex]|1/10| < 1.[/tex]

At x = -10/7, the series becomes[tex](7(-10/7))^n/(10n)! = (-1)^n/(10n)![/tex]. This series is an alternating series with first term 1 and common ratio (-1/10), and it also converges because [tex]|-1/10| < 1.[/tex]

Therefore, The interval of convergence of the power series is (-10/7, 10/7).

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The inequality that represents the line in the figure will be y > - (2/3) x + 3.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

From the figure, the points of the line are (0, 3) and (3, 1). And the region above the line is a consideration. Then the equation of the line is given as,

(y - 3) > [(3 - 1) / (0 - 3)](x - 0)

Simplify the equation, then we have

(y - 3) > [(3 - 1) / (0 - 3)](x - 0)

(y - 3) > - (2/3)x

y > - (2/3) x + 3

The disparity that addresses the line in the figure will be y > - (2/3) x + 3.

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From the values that we have here, the statement that can be said to be true here would be that: There is no constant relationship between the number of video games collected by Cooper and Maria. Last option

A relationship with a fixed ratio between two quantities is referred to as proportionate. The graph will therefore be linear, or straight.

When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.

The values between these two does not show any constant relationship hence the last option

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Answer: part a

cooper- 35 45 55 65

maria 15 23 31 39

part B

there is no constant relationship between the number of video games collected by coopeer and maria

Step-by-step explanation:

Step-by-step explanation:

i hope this helps u get an idea how to solve the problems, sorry for the bad handwriting though

Good luck!!

1.  The average difference between the two values on the two stacks of cards is expected to be about 0 minutes best describes the outcome of the randomization test.

This randomization test was conducted to test whether the average difference of 32 minutes between the two groups could be attributed to chance. The test essentially involved shuffling the index cards containing the minutes slept by each subject and then dealing them into two equal-sized groups.

This process allows for a fair comparison between the two groups and ensures that any differences in the average minutes slept are due to chance. Since the cards are shuffled randomly, the average difference between the two stacks of cards is expected to be about 0 minutes.

If meditation is effective, then the difference between the values on the two stacks of cards would be expected to be more than 32 minutes.

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Answer:

since 12inches=1foot

x inches=34feet

34feet converted to inches =408inches

total inches=408+8

T=416inches

dividing 416 by 8 we have

52 inches left

converting back to feet we get

4ft 4in

w=9/2 =4,5

Step-by-step:

:)

The length of the birth in centimeters will be 58.42 centimeters.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

James was also measured 23 inches long.

We know that, in one inch, there are 2.54 centimeters.

The length of the birth in centimeters is calculated as,

⇒ 23 inches

⇒ 23 x 2.54 centimeters

⇒ 58.42 centimeters

The number of birth in centimeters will be 58.42 centimeters.

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The value of x in the inequality, -13x < 65, is simplified as, x > 5.

Any inequality given can be solved by find the value of the variable in the inequality, which will make it a true statement. To do this, isolate the given variable to make it stand alone on one side.

Given the inequality, -13x < 65, solve as shown below:

-13x < 65 [given]

Divide both sides by -13:

-13x/-13 < 65/-13

x > -65/13 {the sign changes from < to > because we divided both sides by a negative quantity]

x > 5

The value of x is simplified as x > 5.

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The following choices are binomial random variables: A. Take a random sample of 30 tours and let L = the number of tours that result in a sale. B. Take a random sample of 3 tours and let K = the number of tours that result in a sale.

Choice A is a binomial random variable because it represents the number of tours that result in a sale in a random sample of 30 tours. The trials are independent, as the results of one tour do not affect the results of other tours, and the probability of success (a sale) is constant at 5%.

Choice B is also a binomial random variable because it represents the number of tours that result in a sale in a random sample of 3 tours. The trials are independent and the probability of success is constant at 5%.

Choice C is not a binomial random variable because it represents the number of sales generated by a random sample of 3 tours, which is a continuous variable. Binomial random variables are always discrete, as they represent the number of successes in a sequence of trials.

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Answer:No

Step-by-step explanation:

When we substitute x=6 into the first equation we get

y=1/6 *6+5=6 so we get (6, 6)

When we substitute x=6 into the second equation we get

y=5/6*6+3=8  so we get (6, 8) . it works for the second equation but not the first. It must be true for both equations

Answer:

3/2 or 1.5 or 1 1/2 in mix number

The total area of the figure is equal to 192 square meters. The correct option is A.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Calculate the area of the rectangle by the formula written below,

Area of the rectangle = L x W

Area of the rectangle = 8 x 18

Area of the rectangle = 144 square meters

The area of the triangle will be calculated by the formula written as,

Area of triangle = 1/2 x B x H

Area of triangle = 1/2 x ( 18 - 6 ) x 8

Area of triangle = 1 / 2 x 12 x 8

Area of triangle = 48 square meters

Total area = 144 + 48

Total area = 192 square meters

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Answer:

C).    690

Step-by-step explanation:

When you see the word "sum" that means you add the numbers together

667 + 23 = 690

Answer:

OC. 690

Step-by-step explanation:

To find the sum of 667 and 23, you need to add the two numbers together. When you do this, you get 690 as the result. Therefore, the sum of 667 and 23 is 690.

This can be written as an equation: 667 + 23 = 690. The symbol "+" is used to represent the operation of addition, and the equals sign "=" is used to show that the value on the right side of the equation is the result of the operation on the left side.

In general, when you add two or more numbers together, you find their sum by combining their values and counting the total. For example, to find the sum of the numbers 3 and 4, you would add them together to get 7. To find the sum of the numbers 5, 6, and 7, you would add them together to get 18.

I hope this helps to clarify the concept of addition and the meaning of the term "sum." Let me know if you have any further questions.

Answer:

The inverse function of the exponential function f(x) = a^x is the logarithmic function with base a.

The inverse function of a function f is a function that "undoes" the original function, meaning that it reverses the transformation applied by the original function. In the case of the exponential function, the inverse function is the logarithmic function, which "undoes" the transformation applied by the exponential function.

For example, suppose we have the exponential function f(x) = 2^x. The inverse function of this function is the logarithmic function with base 2, which is written as y = log_2 x. If we apply the inverse function to 2^x, we get:

y = log_2 (2^x)

Solving for x gives:

x = 2^y

This means that the inverse function of the exponential function f(x) = a^x is the logarithmic function with base a, which is written as y = log_a x.

The other options (a. transcendental, c. rational, d. polynomial, e. algebraic) are not correct, since they do not describe the inverse function of the exponential function.

Answer:

b. logarithmic

Step-by-step explanation:

Given exponential function:

[tex]f(x)=a^x[/tex]

The inverse of the given function is the logarithmic function with base a.  

To find the inverse of a function, replace f(x) with y:

[tex]\implies y=a^x[/tex]

Swap the x and y:

[tex]\implies x=a^y[/tex]

Take logs with base a of both sides of the equation:

[tex]\implies \log_ax=\log_aa^y[/tex]

Apply the log power law:  logₐ xⁿ = n logₐ x

[tex]\implies \log_ax=y\log_aa[/tex]

Apply the log law:  logₐ a = 1

[tex]\implies \log_ax=y[/tex]

[tex]\implies y=\log_ax[/tex]

Replace y with f⁻¹(x):

[tex]\implies f^{-1}(x)=\log_ax[/tex]

Thus proving that the inverse of the exponential function f(x) = aˣ is the logarithmic function with base a.            

Answer:

Exact  answer 12 +  6[tex]\sqrt{2}[/tex]

Answer rounded to the nearest whole number 20

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the 6 trig functions of the angle -5π/6.

The angle is in the 3rd quadrant, so all trig functions are negative except the tangent and cotangent. The reference angle is -5π/6 +π = π/6.

Since you have memorized the values of the trig functions for multiples of π/6, you know ...

  sin(-5π/6) = -1/2

  cos(-5π/6) = -√3/2

  tan(-5π/6) = sin/cos = √3/3

  csc(-5π/6) = 1/sin = -2

  sec(-5π/6) = 1/cos = -2√3/3

  cot(-5π/6) = 1/tan = √3

Answer/Step-by-step explanation:

Use a Unit Circle, you may have access to (hopefully) or have been asked to memorize.

To find -5pi/6 count clockwise the sixths to 5. Or add:

-5pi/6 + 2pi

= -5pi/6 + 12pi/6

= 7pi/6

-5pi/6 is the same as 7pi/6 on the Unit Circle.

Use the coordinates at that spot

(-root3/2 , -1/2)

to find the six trig ratios.

The Unit Circle is a big, giant, Answer Key. It has all the trig answers on it all in one place. It looks like a scary math pizza, but really its all the answers all in one place.

Once you find your angle, the sine is the y-coordinate.

sin theta = -1/2

The cosine is the x-coordinate.

cos theta = -root3/2

Tangent theta is the sine over the cosine, sin/cos,

= y/x

= (-1/2) / (-rt3/2)

Use Keep-Change-Flip to simplify this.

see image.

= root3/3

Sec is cos flipped over. Csc is sin flipped over. Cot is tan flipped over (the math word is reciprocal)

Yes, just flip over sin to get csc:

sintheta = -1/2

csctheta = - 2/1 = -2

Flip over cos to get sec:

costheta = -rt3/2

sectheta = 2/-rt3

Then rationalize, see image.

= -2rt3/3

Flip over tan to get cot.

tantheta = 1/rt3

Use a form that's easy to flip.

cottheta = rt3/1 = rt3

see image.

Answer:

75.5

Step-by-step explanation:

B. Because the standard deviation is unaffected by a change in a single data value, it will remain unchanged.

A change in a single data value has no impact on the standard deviation, which measures the spread of a data collection. As a result, even if the single data value changes, the standard deviation won't.

The variability of a data set is measured by the standard deviation. It is calculated by taking the square root of the average of the sum of the squares of the differences between each value in a data set and the mean. When a single value in a data set is changed, the mean of the data set will change, but the standard deviation will not be affected. This is because the standard deviation is not calculated based on individual data points, but on the overall variability of the data set. Therefore, when a single data value is changed, the standard deviation of the data set will remain the same.

Let x be one of the students in the class

Mean = (76.9 + 82)/2 = 79.4

Standard Deviation = sqrt(((76.9 - 79.4)^2 + (82 - 79.4)^2)/2) = 3.2

The complete question is : There are 40 students in a college statistics class. After the first exam, their instructor told them that the class scores were normally distributed with a 10 points mean of 76.9 and a standard deviation of 3.2. However, one of the students pointed out that the instructor recorded 28 for his score when he actually earned 82. The class recalculates the mean and standard deviation The mean is now 78.1. Which of the following is true about the standard deviation? A. The standard deviation will increase because the value of an exam score increased. B. The standard deviation will stay the same because it is not affected by a change in a single data value C. The standard deviation will decrease because the change moved an exam score closer to the mean D. The standard deviation will increase because the change moved an exam score further from the mean

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The distance between these two points is given as follows:

[tex]d = 2\sqrt{1 - a}[/tex]

The equation of the parabola is given as follows:

y - k = a(x - h)².

Hence:

y = a(x - h)² + k.

The horizontal line one unit above the vertex has the equation given as follows:

y = k + 1.

(as k is the y-coordinate of the vertex).

Then the intersection of this line with the graph is obtained as follows:

k + 1 = a(x - h)² + k.

a(x - h)² = 1

(x - h)² = 1 - a

[tex]x - h = \pm \sqrt{1 - a}[/tex]

[tex]x = \pm \sqrt{1 - a} + h[/tex]

Then the points are given as follows:

The distance between these two points is of:

[tex]d = \sqrt{1 - a} + h - (-\sqrt{1 - a} + h)[/tex]

[tex]d = 2\sqrt{1 - a}[/tex]

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There are several reasons why researchers might not use the normal distribution to model real data which are due to assumptions of normal distribution.

First, the normal distribution assumes that the data is symmetric and is distributed around the mean. However, in some cases, the data may be skewed, making the normal distribution an inappropriate model.

Second, the normal distribution assumes that the data is homoscedastic, meaning that the variance is constant across the sample. However, in some cases, the variance may be heteroscedastic, meaning that the variance changes across the sample. This makes the normal distribution an inappropriate model for this type of data.

One situation in which researchers should not use the normal distribution approximation is when modeling financial data. Financial data often follows a power-law distribution, which is not normal. Therefore, researchers should use a power-law distribution to model this type of data.

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The equation of the line that is perpendicular to the line that passes through the points (-1, -4) and (4, 2): D. 5x + 6y = 27.

Perpendicular lines have slopes with a product of -1, or are negative reciprocals.

First find the slope of the line that passes through (-1, -4) and (4, 2):

Slope (m) = change in y / change in x = (2 -(-4)) / (4 -(-1))

m = 6/5

The negative reciprocal of 6/5 is -5/6. This means that the perpendicular line is, m = -5/6.

To write the equation of the line that is perpendicular to the given line, substitute m = -5/6 and (a, b) = (-3, 7) into y - b = m(x - a):

y - 7 = -5/6(x - (-3))

y - 7 = -5/6(x + 3)

6(y - 7) = -5(x + 3)

6y - 42 = -5x - 15

6y = -5x - 15 + 42

6y = -5x + 27

5x + 6y = 27

The answer is: D. 5x + 6y = 27.

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Answer:

3.8

Step-by-step explanation:

4 x 0.95 = 3.8

Answer:

  k = -7/2

Step-by-step explanation:

You want the k-value so that the point (1, -k) is on the line kx+3y=7.

The point will be on the line when its coordinates make the equation true. Using (x, y) = (1, -k), we have ...

  k(1) +3(-k) = 7

  -2k = 7 . . . . . . . . simplify

  k = -7/2 . . . . . . . divide by -2

The value of k = [tex]\frac{-7}{2}[/tex] so the point is on the line kx+3y=7

A line is an endlessly long object without breadth, depth, or curvature in geometry. Thus, despite the fact that they can exist in two, three, or higher dimensional environments, lines are one-dimensional things. The term "line" can also refer to a line segment that has two locations that serve as its ends in daily life.

given

the point of the line = ( 1 ,-k )

the line = kx + 3y = 7

the coordinates make the equation true when its points are on the line

so putting the values of x and y in equation of line

k( 1 ) + 3 ( -k ) = 7

k - 3k = 7

-2k = 7

k = [tex]\frac{-7}{2}[/tex]

The value of k = [tex]\frac{-7}{2}[/tex] so the point is on the line kx+3y=7

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Answer: 9/2

Step-by-step explanation:

To express 0.27 and 0.06 as fractions, we first need to convert them to fractions with denominators that are powers of 10. We can do this by multiplying 0.27 by 100 to get 27/100, and multiplying 0.06 by 100 to get 6/100. The ratio of 0.27 to 0.06 is then equal to the ratio of 27/100 to 6/100, which simplifies to 27/6. To express this ratio in simplest form, we can divide both the numerator and denominator by the greatest common factor of 27 and 6, which is 3. This gives us a simplified fraction of 27/6 = 9/2.

Answer:

p=8h

Step-by-step explanation:

P is the total pay, so it will be on one side of the equation. 8 represents the fact that Trey receives 8 dollars per hour. It's multiplied by h to represent the number of hours he works.

The coordinates of reflection image are (-1, -2).

What is point reflection?

A particular kind of Euclidean space isometry is known as a point reflection in geometry. A thing is said to have point symmetry if it is invariant under a point reflection; if it is invariant under a point reflection through its center, it is said to have central symmetry or to be centrally symmetric.

Given:

point Q is reflected across x = 1.

From graph the point Q is (3, -2).

We have to find the coordinates of its reflection image.

x = 1 is a vertical line passing through all points with an x- coordinate of 1.

(3, - 2) is 2 units to the right of x = 1 ( 3 - 1 ), thus

The reflection is 2 units to the left of x = 1 ( 1 - 2 = - 1 )

Q(3, - 2 ) → Q'(- 1, - 2 )

This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.

Hence, the coordinates of reflection image are (-1, -2).

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Answer:

-6/6 or -1

Step-by-step explanation:

To find the equation of the line (or the slope, assuming that's what equation means, ) we need to write the formula Y1-Y2/X1-X2

So, we need to fill in the numbers, which gives us the fraction -6-0/-2-(-8)

When we solve for the numerator (-6-0), we get -6.

When we solve for the denominator (-2 - {-8}), we get 6.

So, we have -6/6, which, when simplified, is -1.

(If the problem is not asking for slope when it says equation, then sorry!)

Two members of the maths competition team solve 13 problems in 1 hour.

Person=13

Time=1 hour

Then.

Rate=13/1 (person/time)

With the help of question,

Let us consider,

x team members are needed to solve in 1 hour 39 problems,

2M×1/13=1×xM/39

2M/13=x M/39

2M=x M/13

M=26

26 team members are needed to solve in 1 hour 39 problems,

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