Which geometric series converges? StartFraction 1 Over 81 EndFraction StartFraction 1 Over 27 EndFraction one-ninth one-third ellipsis 1 one-half one-fourth one-eighth ellipsis Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 7 (negative 4) Superscript n minus 1 Sigma-Summation Underscript n = 1 Overscript infinity EndScripts one-fifth (2) Superscript n minus 1.

Answers

Answer 1

The geometric series that converges from the listed option is [tex]1+\frac{1}{2} + \frac{1}{4} +\frac{1}{8} ,...[/tex] Option B is correct.

The nth term of a geometric sequence is expressed as;

[tex]a_n=ar^{n-1}[/tex]

a is the first term of the sequencer is the common ration is the number of terms.

For a geometric sequence to converge, the modulus of its common ratio must be less than 1 (|r| < 1), otherwise, it diverges.

For the first series given as [tex]\frac{1}{81} + \frac{1}{27} +\frac{1}{9} +\frac{1}{3}+ ,...[/tex]

[tex]r = \frac{1}{27} \div \frac{1}{81}\\r=\frac{1}{27} \times 81\\r=\frac{81}{27} \\r=3 > 1[/tex]

Since the common ratio of the sequence is greater than 1, hence the series diverges.

For the series [tex]1+\frac{1}{2} + \frac{1}{4} +\frac{1}{8} ,...[/tex]

[tex]r=\frac{1/2}{1} =\frac{1/4}{1/2} = \frac{1}{2}[/tex]

Since the common ratio of the sequence is less than 1, hence the series converges.

Learn more on convergence of series here: https://brainly.com/question/14294471

Which Geometric Series Converges? StartFraction 1 Over 81 EndFraction StartFraction 1 Over 27 EndFraction

Related Questions

Each time Bobby rides the JUTC bus, money will be deducted from the value of his card. He rode the bus 5 times and his card was charged $100. What integer best represents the the amount by which the balance of the card changed each time it was used?

Possible Answers

A. -$500
B. $20
C. -$20
D. $500

Answers

Answer:

Step-by-step explanation:

100/5= 20

he was charhed 20

i really dont know this

Answers

Answer:

your answer is b 8/10 - 5/10

Step-by-step explanation:

Find the area of the figure and type your result in the empty box

Answers

Answer:

where is the question ⁉️

The solution of the equation 3 + 5 (t-1) = 33 is ________.

Answers

Answer:

the solution is = 7

[tex]3 + 5(t - 1) = 33 \\ = > 3 + 5t - 5 = 33 \\ = > 5t = 33 - 3 + 5 \\ = > 5t = 30 + 5 \\ = > 5t = 35 \\ = > t = \frac{35}{5} \\ = > t = 7[/tex]

Answer:

Hope you could get an idea from here.

Doubt clarification - use comment section.

Which list below shows a way in which a 13-foot piece of pipe can be cut, to create 3 pieces that will form a triangle?

1 ft, 3 ft, 9 ft

3 ft, 3 ft, 7 ft

2 ft, 3 ft, 8 ft

2 ft, 5 ft, 6 ft

Answers

Answer:

2 5 and 6

Step-by-step explanation:

Any 2 sides have to add to more than the 3rd side.

What is the correct answer for this?

Answers

Answer:

Tan (X) = 72/65. = 1.1

Step-by-step explanation:

tan x = (opposite side) / (adjacent side)

From angle X the adjancent is the closest leg which has the value of 65 and the opposite is the furthest leg with a value of 72. (the line that is connecting the legs which is the biggest line is the hypotenuse and has a value of 97). You will not need the hypotenuse I just gave you extra information for future purposes.

so, since tan x = (opposite side) / (adjacent side):

Tan (X) = 72/65.

6. You are planning a camping trip. The campsite you want to rent charges a $15 fee
to reserve the site, plus an extra $3 per day.
Part I: Define your variables and write a linear equation in slope-intercept form to
represent the cost of the campsite. (4 points)
Part II: Find the y-intercept and interpret it. (2 points)
Part III: Graph the equation for the cost of renting the campsite. Label three
points on your graph and indicate the slope. (4 points) Place the given line on the
graph to represent your equation.

Answers

Answer:

y=3d+15

y intercept is 15

slope is 3

Step-by-step explanation:

to graph start at 15 on the y axis. then go up 3 points and over one point. keep doing this until you have a straight line.

The difference between total surface area and curved surface area of a hemisphere is 154 cm^2, find it's volume.

Answers

Answer:

Surface area of a sphere=4πr

=154cm

⇒4×

=154cm

⇒r

154

⇒r

⇒r=

∴r=

=3.5cm

Volume of the sphere=

πr

×(3.5)

×42.875‬=179.67cm

Each small square on this scale weighs 1 unit. Each larger square weighs 10 units. The weight of the triangle x is unknown. The scale is balanced. Look at the image. A balanced scale. On one side there are four small squares and three large squares each labeled ten. On the other side there are two small squares, two large squares each labeled ten, and a triangle labeled x. Question 1 Part A Write an equation to represent relationship of the weights shown on the scale. Enter the correct answer in the box.

Answers

The equation to represent the relationship of the weights shown on the scale s [tex]22 + x = 34[/tex]

The weights are given as:

[tex]Small\ Square = 1[/tex]

[tex]Larger\ Square = 10[/tex]

The total weight on one side, where there are 4 small squares and 3 large squares is:

[tex]Total =4\times Small\ Square + 3 \times Larger\ Square[/tex]

[tex]Total =4\times 1 + 3 \times 10[/tex]

[tex]Total =34[/tex]

The total weight on the other side, where there are 2 small squares, 2 large squares and 1 triangle is:

[tex]Total =2\times Small\ Square + 2 \times Larger\ Square + 1\times triangle[/tex]

[tex]Total =2\times 1+ 2 \times 10+ 1\times triangle[/tex]

[tex]Total =2+ 20+ 1\times triangle[/tex]

[tex]Total =22+ 1\times triangle[/tex]

[tex]Total =22+ triangle[/tex]

The weight of the triangle is x.

So, we have:

[tex]Total =22+ x[/tex]

The weights on both sides are equal, because the scale is balanced.

So, we have:

[tex]22 + x = 34[/tex]

Hence, the equation is [tex]22 + x = 34[/tex]

Answers

Answer:

slope=100

$100 per deposit

Step-by-step explanation:

A storage container leaks water at a rate of 15 gallons every 30 days.

What is the unit rate in gallons per week?

Enter your answer as a mixed number in simplest form in the box.

Answers

Answer:

i think 3.5 gallons per week

[tex]3 \frac{1}{2} [/tex]

Step-by-step explanation:

15 gallons every 30 days

x gallons per weeks (7 days)

15×7 = 30x

105 = 30x

105/30 = x

3.5 = x

answer as a mixed number in simplest form = 3 1/2

Answer: The answer is 3 1/2

Step-by-step explanation:

I took the quiz and did 100% :)

I’ll give 5 stars but you have to explain how you got 4.

Answers

Answer:

Step-by-step explanation:

I used the division, 36/9, which has the same end result. It is a similar equation, because of the numbers.

Answer:

Step-by-step explanation:

[tex]\frac{0.36}{0.09}[/tex]

Expand [tex]\frac{0.36}{0.09}[/tex] by multiplying both numerator and the denominator by 100.

= [tex]\frac{36}{9}[/tex]

Divide 36 by 9 to get 4.

[tex]4[/tex]

I hope this helps :)

please help me with this also jjodlask

Answers

Answer:

1. 15, 2. -23, 3. 220, 4. 4x-5

Step-by-step explanation:

f(x) = 4x + 3 g(x) = x - 2

1. f(g(5)): Put 5 in as x in g(x) 5 - 2 = 3. Now put the 3 as x into f(x) and solve. 4(3) + 3 = 15

2. g(f(-6)) 4(-6) + 3 = -21. -21 - 2 = -23

3. (f(f(7)) 4(7) + 3 = 31, 31(7) + 3 = 220

4. g(f(x)) 4(x-2) + 3 = 4x - 8 + 3 = 4x - 5

Composite functions

When a function is substituted into another function it is known as a composite function.

Given the following functions:

f(x) = 4x + 3

g(x) = x - 2

Determine [tex]f(g(x)) \ and \ g(f(x))[/tex]

[tex]f(g(x)) = f(x-2)\\ f(x-2) = 4(x-2)+3\\ f(x-2)=4x-8+3\\ f(x-2) = 4x - 5\\ f(g(x)) = 4x - 4 [/tex]

1) Determine the value of [tex]f(g(5))[/tex]

[tex]f(g(5))=4(5) - 4\\ f(g(5))=20-4\\ f(g(5))=16[/tex]

2) For the function [tex]g(f(-6))[/tex]

[tex]g(f(-6))=4(-6) + 1\\ g(f(-6))=-24+1\\ g(f(-6))=-23[/tex]

3) For the value [tex]f(f(7)), [/tex]we need to determine [tex] f(f(x))[/tex]

[tex]f(f(x)) = f(4x+3)\\ f(f(x))= 4(4x+3)+3\\ f(f(x))=16x+12+3\\ f(f(x))=16x+15\\ f(f(7)) = 16(7) + 15\\ f(f(7)) = 127[/tex]

4) For the function [tex]g(f(x));[/tex]

[tex]g(f(x))=(4x+3)-2\\ g(f(x))=4x+3-2\\ g(f(x))=4x+1[/tex]

learn more on composite functions here: https://brainly.com/question/10687170

How to graph a linear function from slope-intercept form

Answers

Answer:

Use the coefficient of x as the slope and constant as the y-intercept

Step-by-step explanation:

Start by going to your graph and plotting your y-intercept. For example, if the y- intercept is -2, plot the point (0, -2). Then from there, you need to plot the slope (let's pretend that the slope is 2/3). From the intercept, you will go up two and right one. Then starting from that point, continue using the rise over run to plot your points and then draw your line.

Find the midpoint of the segment with the following endpoints. (2, -9) and (-4,-4)

Answers

Answer:

(-1,-6.5)

Step-by-step explanation:

midpoint formula: (x_m, y_m) = (x1+x2)/2),(y1+y2)/2)

(2-4)/2=-1, -9-4=-13/2=-6.5

=(-1,-6.5)

Can someone plz help me?

Answers

Answer:

Step-by-step explanation:

I got it right on my quiz

what is the right answer
giving out brainliest

Answers

The answer is QT bisects VS

because according to the image you can see by the markings that both sides of VS are congruent being divide by QT

Hope this helps!
Brain is much appreciated!

What is the surface area of the cylinder with height 2 in and radius 8 in? Round your
answer to the nearest thousandth.

Answers

rounded to the nearest thousands will be 301.593 cm

Answer:

502.655

Step-by-step explanation:

The actual answer was 502.655

Two similar triangles are shown on the coordinate grid:

A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair negative 2, negative 1, vertex B on ordered pair 0, 0, and vertex C on ordered pair 1, negative 3. A triangle A prime B prime C prime is also shown with vertex A prime on ordered pair negative 4, 2 , vertex B prime on ordered pair 0, 0 and vertex C prime on ordered pair 2, 6.
Which set of transformations has been performed on triangle ABC to form triangle A′B′C′? (5 points)

Dilation by a scale factor of 4 followed by reflection about the x-axis
Dilation by a scale factor of 2 followed by reflection about the x-axis
Dilation by a scale factor of 4 followed by reflection about the y-axis
Dilation by a scale factor of 2 followed by reflection about the y-axis

Answers

The set of transformation is: (b) dilation by a scale factor of 2 followed by reflection about the x-axis

The coordinates of the triangles are given as:

Triangle ABC

[tex]A =(-2, -1)\\[/tex]

[tex]B =(0, 0)[/tex]

[tex]C =(1, -3)[/tex]

Triangle A'B'C'

[tex]A' = (-4, 2)[/tex]

[tex]B '=(0, 0)[/tex]

[tex]C '=(2, 6)[/tex]

Start by dilating triangle ABC by a scale factor of 2.

The rule of this transformation is [tex](x,y) \to (2x,2y)[/tex]

So, we have:

[tex]A' =(-4,-2)[/tex]

[tex]B' =(0,0)[/tex]

[tex]C' = (2,-6)[/tex]

Next, we reflect the triangle across the x-axis.

The rule of this transformation is [tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex]A' = (-4, 2)[/tex]

[tex]B '=(0, 0)[/tex]

[tex]C '=(2, 6)[/tex]

Hence, the set of transformation is: (b) dilation by a scale factor of 2 followed by reflection about the x-axis

Answers

The answer should b C

??????????????????????????

Answers

Answer:

Top left and bottom one

Step-by-step explanation:

What is the measure of angle B?

Answers

Answer:

m∡B = 120°

Step-by-step explanation:

base angles are equal

adjacent angles are supplementary so:

4x+20 + 3x-15 = 180

7x + 5 = 180

7x = 175

x = 25

∡B = 4(25) + 20

∡B = 120°

Answer:

39.6

Step-by-step explanation:

(3x-15)+(4x+20)+2x=360

9x+5=360

9x=355

*Divide each side by 9*

X=39.4

*SUBSTITUTE X*

3(39.4)-15=103.2

4(39.4)+20=177.6

*ADD THE TOTALS FROM ABOVE*

103.2+177.6= 280.8

360-280.8=79.2

*DIVIDE THE TOTAL BY 2*

79.2/2=39.6

*CHECK*

3(39.4)-15=103.2

4(39.4)+20=177.6

103.2+177.6+39.6+39.6=360 IS CORRECT.

Hope this helps! :)

The area of a rectangular patio is 21
1
8
square meters. The width of the patio is 3
1
4
meters. What is the length? Enter your answer as a mixed number in simplest form.

The length of the patio is meters.

Answers

Answer:

6 1/2

Step-by-step explanation:

21 1/8 divided by 3 1/4

Put into improper fractions

169 / 8 divided by 13 / 4

Multiply by the reciprocal

169 / 8 x 4 / 13

= 6 1/2

A sector of a circle makes a 127° angle at its centre. If the arc of the sector has length 36 mm, find
the perimeter of the sector.

Answers

Answer:

Approximately [tex]68.5\; \rm mm[/tex].

Step-by-step explanation:

Convert the angle of this sector to radians:

[tex]\begin{aligned}\theta &= 127^{\circ} \\ &= 127^{\circ} \times \frac{2\pi}{360^{\circ}} \\ &\approx 2.22\end{aligned}[/tex].

The formula [tex]s = r\, \theta[/tex] relates the arc length [tex]s[/tex] of a sector of angle [tex]\theta[/tex] (in radians) to the radius [tex]r[/tex] of this sector.

In this question, it is given that the arc length of this sector is [tex]s = 36\; \rm mm[/tex]. It was found that [tex]\theta = 2.22[/tex] radians. Rearrange the equation [tex]s = r\, \theta[/tex] to find the radius [tex]r[/tex] of this sector:

[tex]\begin{aligned} r&= \frac{s}{\theta} \\ &\approx \frac{36\; \rm mm}{2.22} \\ &\approx 16.2\; \rm mm\end{aligned}[/tex].

The perimeter of this sector would be:

[tex]\begin{aligned}& 2\, r + s \\ =\; & 2 \times 16.2\; {\rm mm} + 36\; {\rm mm} \\ =\; & 68.5\; \rm mm\end{aligned}[/tex].

what is the ratio of 9 boys and 6 girls in a class of 15 students

Answers

Answer:

3:2 i believe

Step-by-step explanation:

9:6

divide by 3

3:2

how to find the nth term

Answers

Answer:

Write full question

I cannot understand

Step-by-step explanation:

The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.

I need help?????????

Answers

Answer:

Step-by-step explanation:

Which expression is equivalent to -16 - 7?

A. -16 + 7
B. -16 + (-7)
C. 16 + (-7)
D. 16 + 7

Answers

Step-by-step explanation:

B. -16 + (-7) ...this is the same as -16-7

SOCCER Four soccer players are practicing a drill. Goalie A is facing Player B
to receive the ball. Goalie Athen turns tº to face Player A to pass her the ball. If
Goalie B is facing Player A to receive the ball, then through what angle
measure should Goalie B turn to pass the ball to Player B?

Answers

Answer:

Step-by-step explanation:

In a parallelogram opposite angles are equal, so if Goalie A angle is x, also Goalie B's will be x

The angle measure for Goalie B turn to pass the ball to Player B is given by the parallelogram and the angle is B = x°

What is a Parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , the measure of Goalie A = x°

And , for a parallelogram

Opposite angles are congruent

So , the angle of Goalie B = angle of Goalie A

Substituting the values in the equation , we get

The angle for Goalie B = x°

Therefore , the value of B = x°

Hence , the opposite angle of parallelogram is x°

To learn more about parallelogram click :

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Kyle is setting out Japanese food for a party he is having. He has 9 avocado rolls and 18 cucumber rolls. If he wants each plate to be identical, with no rolls left over, what is the greatest number of platters Kyle can create? GCF and LCM: word problems no links pls

Answers

Answer:

9 plates

Step-by-step explanation:

The number of plates Kyle can make is the GCF of 9 and 18. Since 9 is a factor of 18, that GCF is 9.

Kyle can make 9 plates, each containing 1 avocado roll and 2 cucumber rolls.

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