If P(n) and Q(n) are polynomials of degree j and k, respectively, then the series
Infinite
Σ P(n)/Q(n)
n=1
converges if j < k − 1 and diverges if j ≥ k – 1.
Use the polynomial test given above to determine whether the series converges or diverges.
Infinite
Σ 1/(n)^8 +7
n=1
O converges
Odiverges

Answers

Answer 1

Answer:

converges

Step-by-step explanation:

well the two polynomials in the series are 1 and n^8 (I'm assuming the +7 is not in the decimal but it seems to not matter). The degree of the polynomial 1 is 0 which can be represented by 1x^0. The second polynomial in the denominator has a degree of 8. So j = 0  and k = 8. Since 0 < (8-1)

0 < 7 the series converges


Related Questions

Rationalize the denominator. [tex]\frac{9}{\sqrt{x+3} }[/tex] Simplest form

Answers

The result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].

What is Rationalization?

Rationalization can be considered as the process used to eliminate a radical or an imaginary number from the denominator of an algebraic fraction.

Here, given fraction

 [tex]\frac{9}{\sqrt{x+3} }[/tex]

Multiply and divide by [tex]\sqrt{x+3}[/tex], we get

[tex]\frac{9}{\sqrt{x+3} } \frac{\sqrt{x+3} }{\sqrt{x+3} }[/tex]  =  [tex]\frac{9\sqrt{x+3} }{x+3}[/tex]

Thus, the result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].

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can someone please help me solve this question step by step not just give me the answer I want to learn lol

find f(x)•g(x)
if f(x)=8x+1 and g(x)=-5+9.

Answers

Answer: 32x+4

Step-by-step explanation:

[tex]f(x) \cdot g(x)=(8x+1)(-5+9)=4(8x+1)=\boxed{32x+4}[/tex]

Determine whether each set of data can be modeled by an exponential function. If so, find the exponential
function that fits the data.

Answers

It can be modeled by an exponential function, f(x) is divided by 3 each time x increases by 1.

This means that the base of the exponential function is 1/3, and since the value of f(x) when x=0 is 81, [tex]f(x)=81\left(\frac{1}{3} \right)^{x}[/tex]

Find the next number in the sequence: 2, 2, 5, 12, 62, 749, 46450,

Answers

Answer:

34791112

Step-by-step explanation:

Please check the attached for the explanation.

The next number for given sequence is 34791112.

The given sequence is 2,2,5,12,62,749,46450,......

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.

Each number in the sequence is of the form Number3 × Number2 + Number1 = Number4

5×2+2=12

12×5+2=62

62×12+5=749

749×62+12=46450

So, the required number is

46450×749+62=34791112

Therefore, the next number for given sequence is 34791112.

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Pleas hurry!!!!! Which line is perpendicular to a line that has a slope of -5/6
line JK
line LM
line NO
line PQ

Answers

Answer:

LM

Step-by-step explanation:

Perpendicular slope would be   - 1 / m   =   - 1/(-5/6)   = 6/5

slope m = rise / run       line   LM   rises 6    for a run of 5      

i need help with this geometry question

Answers

Answer:

radius ≈ 15.5

Step-by-step explanation:

the radius is RS

the angle between a tangent and the radius at the point of contact is 90°

then Δ RST is a right triangle

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

RS² + ST² = RT² ( substitute values )

RS² + 7² = 17²

RS² + 49 = 289 ( subtract 49 from both sides )

RS² = 240 ( take square root of both sides )

RS = [tex]\sqrt{240}[/tex] ≈ 15.5 ( to 1 dec. place )

How can I find the three iterations of 3^(x)= 2^(-x)+4

Answers

After factorizing the given equation, we can find the three iterations by putting the consecutive values of x.

The given equation is 3∧x = 2∧(-x) + 4. We can modify it as shown below:

Take logarithm on both the sides

log(3∧x) = log[2∧(-x) + 4]

xlog3 = log[2∧(-x) + 4]

x = log[2∧(-x) + 4] / log3

For the first iteration, put x = 1

x = log[2∧(-1) + 4] / log3

x = log4.5 / log3

x = 0.477

For the second iteration, put x = 2

x = log[2∧(-2) + 4] / log3

x = log4.25 / log3

x = 0.477

For the third iteration, put x = 3

x = log[2∧(-3) + 4] / log3

x = log4.125 / log3

x = 0.477

So, this is how we can find three iterations.

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Graph the line with slope 1/4 and y-intercept -8

Answers

Solution: Below! ^^

Detailed explanation:

Hii! I'm sorry, I can't graph the line for you, but I'll try to give you the best possible explanation.

First, note that the question provides us with the info that the y intercept is -8. This is a very valuable piece of information!

This means that the line crosses the y axis (since it's the y intercept) at the point (0,-8). Plot it on the co-ordinate plane.

Next, this question also provides us with the fact that the slope of the line is 1/4. This is yet another valuable piece of information!

What this tells us is: from that point (0,-8), you need to go up 1 unit, then over 4, and so forth, until you obtain a line.

_________

Hope I helped, best wishes & happy studies!

Please reach out to me if any queries arise.

_________

Answer:

Image attached below

Step-by-step explanation:

The line should cross y axis as -8 and should have a point of (0,-8)

The line should have a gradient / slope of 1/4

Evaluate using the trigonometric ratios Tan 60° + Cos 30° sin 60° + Cot 30° /CSC 30° Sec 30°

Answers

Answer:

(24 + 3√3) / 16.

Step-by-step explanation:

Tan 60° + Cos 30° sin 60° + Cot 30 /  csc 30 sec 30

= √3 + √3/2 * √3/2 + √3 /   2 * 2/√3

= 2√3 + 3/4 / 4/√3

= (8√3 + 3)/ 4 / √3

= 24 + 3√3 / 16

6x+2y=20 2x-3y=3 solve by substitution

Answers

I’m from Poland and i don’t know if we solve problems in the same way but i hope that i helped ;D

The solution of the system of linear equation by substitution method is (3,1).

What is the method of substitution?

The method of substitution is the method for solving the linear equation where the value of one variable of one equation is placed in the place of that variable in another equation.

Given here the linear equations are

Equation 1: 6x+2y=20

Equation 2: 2x-3y=3

in equation 1 the value of y will be

6x+2y=20

⇒2y=20-6x

⇒y=(20-6x)/2

⇒y=10-3x

substituting the value of y in the equation 2, we will get

2x-3y=3

⇒2x-3(10-3x)=3

⇒2x-30+9x=3

⇒11x-30=3

⇒11x=30+3

⇒11x=33

⇒x=33/11

⇒x=3

putting the value of x in value of y in equation 1

y=10-3x

⇒y=10-3(3)

⇒y=10-9

⇒y=1

The solution of the system of linear equation by substitution method is (3,1).

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Richards Corporation uses the FIFO method of process costing. The following
information is available for October in its Fabricating Department:
Units:
Beginning Inventory: 80,000 units, 60% complete as to materials and 20%
complete as to conversion.
Units started and completed: 250,000.
Units completed and transferred out: 330,000.
Ending Inventory: 30,000 units, 40% complete as to materials and 10%
complete as to conversion.
Costs:
Costs in beginning Work in Process - Direct Materials: $37,200.
Costs in beginning Work in Process - Conversion: $79,700.
Costs incurred in October - Direct Materials: $646,800.
Costs incurred in October - Conversion: $919,300.
Calculate the equivalent units of materials.

Answers

If Richards Corporation uses the FIFO method of process costing. The  equivalent units of materials is 294,000.

Equivalent unit of material (FIFO)

Using this formula

Equivalent unit of material (FIFO) =[(Beginning inventory×Percentage complete)+Units started and complete+ (Ending inventory× Percentage complete as to materials)]

Let plug in the formula

Equivalent unit of material (FIFO) = [80,000×40%+250,000+30,000×40%]

Equivalent unit of material (FIFO) = 32,000+250,000+12,000

Equivalent unit of material (FIFO) = 294,000

Therefore the equivalent units of materials is 294,000.

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solve the following inequality:
ALGEBRA 1

Answers

Answer:

[tex]m \leqslant 10 \: or \: m > 4[/tex]

Step-by-step explanation:

[tex] \frac{m - 2}{3} \leqslant - 4 \\ \frac{m - 2}{3} \times 3 \leqslant - 4 \times 3 \\ m - 2 \leqslant - 12 \\ m - 2 + 2 \leqslant - 12 + 2 \\ m \leqslant 10[/tex]

OR

[tex]3m - 8 > 4 \\ 3m - 8 + 8 > 4 + 8 \\ 3m > 12 \\ \frac{3m}{3} > \frac{12}{3} \\ m > 4 [/tex]

A man wants to cut down a tree in his yard. To ensure that the tree doesn’t hit anything, he needs to know the height of the tree. He measures his distance from the tree at 13 meters and the angle of elevation to the tree at 53°. What is the height of the tree to the nearest tenth of a meter

Answers

The height of the tree to the nearest tenth of a meter is 73.7m

What is angle of elevation?

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

Given:

base = 13 m

angle of elevation = 53

Using trigonometry

tan 53 = P/B

5.671 = P/ 13

P= 5.671 * 13

P= 73.723

Hence, the height of the tree is 73.7 m.

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Which graph represents the function f(x)=2·4^x?

Answers

Answer:

A (top left)

Step-by-step explanation:

Assuming that the dot is multiplying the numbers, we get the function:

[tex]f(x) = 8^{x}[/tex]

First, lets knock off the obviously wrong answers.

Substitute 0 into the x spot, as anything to the power of zero is one.

[tex]f(0) = 8^{0}=1[/tex]

Automatically, the two answers on the right are incorrect, as y is not equal to 1 when x is 0.

Next, lets substitute 1 into the x spot, as anything to the power of one is itself.

[tex]f(1) = 8^{1} = 8[/tex]

As a result, the top left graph is correct, as y is equal to 8 when x is 1, unlike the bottom left graph.

!!WILL GIVE BRAINLIES PLS HELP!!!
Which inequality in vertex form represents the region less than or equal to the quadratic function with vertex (-6,
12) and includes the point (-9, 15) on the boundary?

Answers

Answer:

is B

Step-by-step explanation:

this is the best possible answer

urgent help needed algebra 2

Answers

Answer:

it's 5 degrees celsius I think you must have entered a 4-32 instead of a 41-32 is what threw you off

Step-by-step explanation:

Which equation represents an exponential function with the initial value of 500?

Answers

Answer:

A exponential equation is usually of the form f(x)=a (1±r)ˣ.

Our limitation: Initial Vale is 500.

Let's look at our options:

#1- Initial Value of 1000  --- WRONG!

#2- Initial Value of 1000  --- WRONG!

#3- Initial Value of 500 ---- Maybe

#4- Initial Value of 500 ---- Maybe

Let's look at 3 and 4:

#3- Fits Our Form of f(x)=a (1±r)ˣ ---- CORRECT!

#4- Does not fit Our Form of f(x)=a (1±r)ˣ, It's to the 2nd power, not the x power! ---- WRONG!

Hence, #3 Is correct!

Step-by-step explanation:

Well, I hope you understood, and I'd gladly explain anything that didn't make sense. A brainliest would be appreciated, thank you!

-Zylynn Jade Ardenne

Rewrite the expression as a fraction.

Answers

8/17 put the 8 over the 17 because it’s being divided by the number 17

I don't even know Brian tanks

Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are spades, your friend will pay you $39 $ ⁢ 39 . Otherwise, you have to pay your friend $5 $ ⁢ 5 . Step 2 of 2 : If this same bet is made 623 623 times, how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.

Answers

The amount of winning is more than amount of loosing. Then the amount of winning will be $3738.

How to find that a given condition can be modelled by binomial distribution?

Binomial distributions consist of n independent Bernoulli trials.

The expected value will be

E(X) = np

Suppose that you and a friend are playing cards, and you decide to make a friendly wager.

The bet is that you will draw two cards without replacement from a standard deck.

If both cards are spades, your friend will pay you $39.

Otherwise, you have to pay your friend $5.

If this same bet is made 623 times.

The maximum amount of winning will be

E(win) = np

We have

p = 0.25

n = 623

Then we have

E(win) = 0.25 × 623

E(win) = 155.75

Then the winning amount will be

WA = 155.75 × 39

WA = $6074.25

The maximum amount of loosing will be

E(loose) = np

We have

p = 0.75

n = 623

Then we have

E(loose) = 0.75 × 623

E(loose) = 467.25

Then the loosing amount will be

LA = 467.25 × 5

LA = $2336.25

Then the amount of winning will be

⇒ $ 6074.25 - $ 2336.25

⇒ $ 3738

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DJ Erin is making a playlist for work; he is trying to decide what 10 songs to play and in what order they should be played.

Step 2 of 2 : If he has his choices narrowed down to 3 country, 6 pop, 7 disco, and 3 hip-hop songs, and he wants to play all 7 disco songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Answers

Using the combination and the arrangements formula, it is found that the number of possible playlists is given by:

[tex]7.98 \times 10^8[/tex]

What is the combination formula?

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, we have that:

7 disco songs are taken from a set of 7.3 remaining songs are taken from a set of 3 + 6 + 3 = 12 songs.

Hence, without considering the order, the number of playlists is given by:

[tex]C_{7,7}C_{12,3} = \frac{7!}{7!0!} \times \frac{12!}{3!9!} = 220[/tex]

What is the arrangements formula?

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, the 10 musics are arranged, hence the number of playlists, considering the order, is given by:

[tex]n = 10! \times 220 = 798336000 = 7.98 \times 10^8[/tex]

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The y-intercept of the line whose equation is 2x - 3y = 6 is
-2
3
6

Answers

Answer:

y = -2

(first option listed)

Step-by-step explanation:

a y-intercept is a point where the line crosses over the y-axis, which happens when x = 0.

So, the y-intercept is actually pretty each to find.

this is the easier way to find it:    {plug directly into equation given}

2x - 3y = 6

(set x equal to 0)

[0] - 3y = 6

(divide both sides by -3)

y = -2

but you might have seen/ learned to solve the equation like this {to actually find the equation of the line and solve from that}

[this method is helpful to know/practice for when equations for functions get more complex]

  2x - 3y = 6

      + 3y      + 3y           {add 3y to both sides}

 

  2x = 3y + 6

   -6          -6                {subtract 6 from both sides}

  2x - 6 = 3y

    ÷3      ÷3            {divide both sides by 3 to isolate y}

  [tex]\frac{2}{3}x[/tex] [tex]- 2 = y[/tex]                [flip sides of the equation]

 [tex]y=\frac{2}{3}x-2[/tex]  

set x equal to 0 (x = 0)

y = [tex]\frac{2}{3} (0)[/tex] - 2

y = 0 - 2

y = -2

So, the y-intercept is -2.

Compute the projection of u on v.

Answers

Answer:

[tex]\frac{3}{7}.v[/tex]    option (C) is correct

Step-by-step explanation:

projection of vectors: The vector projection of one vector over another vector is the length of the shadow of the given vector over another vector.

projection of vector u on v is given by :

[tex](\frac{u.v}{v.v}).v[/tex]

Given,

vector u = <5, 7, 1>

vector v = <2, -1, 3>

substituting these values in the above formula

[tex][\frac{(2,-1,3)(5,7,1)}{(2,-1,3).(2,-1,3)} ].v[/tex]  =  [tex]\frac{6}{14}.v= \frac{3}{7}.v[/tex]

thus the correct answer is option (C)

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9. What is the exact circumference of a circle that has a radius of 5 cm?
25ncm
5псм
10Kcm
100псм

Answers

Answer:

10π cm

Step-by-step explanation:

c = 2πr

c = (2*5) * π

c = 10π

A triangle with side lengths a, b, and c is shown below.



Which statement about the side lengths must be true?

A a+b>c
B b+c C a+b D a+c

Answers

The statement about the sides must respect to represent a triangle is given as follows:

A. a + b > c.

What is the condition for 3 lengths to represent a triangle?

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

The smaller sides for the triangle are given as follows:

a and b.

Hence the statement is:

a + b > c.

(as the sum of the lengths of the smaller sides a and b must be greater than the length of the larger side, which is of c).

Hence the correct statement is given by option A.

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Find the length of the side labeled . Round intermediate values
to the nearest tenth. Use the rounded values to calculate the next
value. Round your final answer to the nearest tenth.

Answers

Step-by-step explanation:

ATTACHED IS THE SOLUTION!!PLEASE DON'T HESITATE TO ASK WHERE YOU DON'T UNDERSTAND.

The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute.

A 2-row table with 10 columns. The first row is labeled time (minutes) with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4, 4.5. The second row is labeled temperature (degrees Celsius) with entries 75, 79, 83, 86, 89, 91, 93, 94, 95, 95.5.

According to the line of best fit, at what time will the temperature reach 100°C, the boiling point of water?

5
5.5
6
6.5.

Answers

According to the given table the line of best fit is

f(x)=4.54x+77.84

The term "line of best fit" describes a line that passes across a scatter plot of data points and best captures their connection. Statisticians often utilise regression analysis software or manual computations to arrive at the geometric equation for the line using the least squares approach. A straightforward linear regression study of two or more independent variables will provide a straight line

Hence, as asked by the question we need to find the time at which the tempurature will become 100°C.

To find that let us put f(x)=100 and find out the value of x for which it is satisfied.

4.54x+77.84=100

⇒[tex]x=\frac{100-77.84}{4.54}=4.88[/tex]

⇒x≈5

Therefore the time at which the tempurature is 100°C is 5 minutes.

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What is the solution to the equation 7(a-10)=13-2(2a+3)?
26
O a=11
O a=7
89
O a = 11
O a=621

Answers

Answer:

[tex]a = 7[/tex]

Step-by-step explanation:

[tex]1. \: 7a - 70 = 13 - 4a - 6 \\ 2. \: 7a - 70 = - 4a + 7 \\ 3. \: 7a = - 4a + 7 + 70 \\ 4. \: 7a = - 4a + 77 \\ 5. \: 7a + 4a = 77 \\ 6. \: 11a = 77 \\ 7. \: a = \frac{77}{11} \\ 8. \: a = 7[/tex]

Find the area of the triangle.

Answers

Answer:

take 1/2 multiply by sin 91°×2×8

What is the density of the oak board

Answers

We need more info or a pic

Step-by-step explanation:

easy how thick it is we need a picture

How many kilometers are in 462 meters? How many kilometers are in 462 meters ?​

Answers

Answer:

0.462

Step-by-step explanation:

1km=1000m

so to get from metres to kilometres you divide by 1000

so 462÷1000=0.462

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