Find the 8th term of the geometric sequence whose common ratio is 3/2
and whose first term is 2.

Answers

Answer 1

Answer:

2187/64

Step-by-step explanation:

first term (a) = 2

common ratio (r) = 3/2

8th term (t8) = ?

We know

Tn = ar^ n - 1

t8 = 2 * (3/2)^ 8 - 1

= 2 * 2187/128

= 2187/64

Answer 2

A geometric sequence with a common ratio of 3/2 and a first term of 2 has an eighth term that is around 35.15625.

What is a geometric sequence?

The common ratio is a fixed constant that is multiplied by the preceding phrase to find each term in a geometric sequence (r). To put it another way, every term is a constant multiple of the term before it.

Use the formula for the nth term of a geometric series to determine the 8th term of the sequence with a common ratio of 3/2 and a first term of 2:

[tex]a_n = a_1 \times r^{n-1}[/tex]

If n is the term number we're looking for, r is the common ratio, and a₁ is the first term.

In this case, a₁ = 2 and r = 3/2, so we have:

[tex]a_8 = 2 \times \dfrac{3}{2}^{(8-1)}[/tex]

[tex]= 2 \times (\dfrac{3}{2})^7[/tex]

[tex]= 2 \times (\dfrac{2187}{128})[/tex]

= 35.15625

Therefore, the 8th term of the geometric sequence with a common ratio of 3/2 and a first term of 2 is approximately 35.15625.

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Related Questions

1/3 of 9
1/3 of 3
1/3 of 18
1/3 of 300
1/3 of 24

Answers

Step-by-step explanation:

3

1

6

100

8

They are the answers

Answer:

I will 2 of the problems and you can do the 3. If you need help then I am here, but try some on your own too. I will do :-

1/3 of 9

1/3 of 24

Hope this helps, thank you :) !!

help click the down load

Answers

Answer:

what is that i dont know what that is it looks horrible

Step-by-step explanation:

Answer:

we can't download

Step-by-step explanation:

PLEASE HELP MEEEEEEEEEEEEEEEE

Answers

Answer:

89

Step-by-step explanation:

Answer: 89 metres squared

Step-by-step explanation:

large area = 13 x 8 = 104

small area = 5 x 3 = 15

104 - 15 = 89

An athlete runs 6 miles in 1 hour on a treadmill. At this rate, how long will it
take the athlete to run 15 miles?

Answers

Answer:

150 minutes

Step-by-step explanation:

Answer:

2 hours and 30 minutes

Step-by-step explanation:

So if he runs for 2 hours it'll be 12 hours out of the 15, and if he only needs 3 more hours instead of 6, he'd have to only run half of the 6 hours, which would be 30 minutes

Which statement best justifies whether (x – 3) is a factor of the polynomial p(x) = x - 3x? - 2x - 6?

Answers

Answer:

It is not a factor

Step-by-step explanation:

It is because p(x)=-12 at x=3

twice the difference of a number and 8 is equal to three times the sum of the number and 8. find the number

Answers

Answer:

-24

Step-by-step explanation:

2(x-8)=3x+3

2x-16+16=3x+8+16

2x=3x+24

2x-3x=3x+24-3x

-x=24

x=-24

The above answer is incorrect. The correct answer and equation is below:
2(x-8) = 3(x+8)
2x - 16 = 3x + 24
_____ ______
-24 -24
______________
2x - 40 = 3x
_____________
-2x. -2x
____________
-40 = 1x

So x = -40
______________

plz help me out :( I really can't fail this

Answers

Answer:

99.37

Step-by-step explanation:

Brief Math lesson:

If you, for example, pay 10% of your income of $100 to charity and 5% of it goes to taxes,

The amount that goes to charity can be found by using:

10% * 100 = 0.1 * 100 = 10

And the amount for taxes is

5% * 100 = 0.05 * 100 = 5

So the total is 15 dollars. And then, subtract that from your salary, so you would earn 85 dollars

We can also just find it by finding how much of a total percentage is being taken and subtract that by 100. (because you would keep the rest of the money)

(100% - (10% + 5%)) * 100 = 85% * 100 = 85

Now, let's apply this information.

First, figure out how much you need to pay in taxes, social security, etc.

15% + 6.44% + 6.2% + 1.45% = 29.09% of your money is given away. So, you would keep 100% - 29.09%, which is 70.91% kept

10.01 dollars an hour at 14 hours is 10.01*14 = 140.14 dollars

Now, multiply the percent of salary you keep by your salary.

140.14 * 70.91% = 140.14 * 0.7091 = 99.373274

This is, rounded,

99.37

Hope this helps! Feel free to ask any questions!

Can someone please help with this question

Answers

Answer:

Domain: [-4,2]

Range: [2,4]

Step-by-step explanation:

Domain: [-4,2]

Range: [2,4]

What is the surface area? I got 562 inches squared

Answers

Answer:

Yep, it’s 562 in²

Step-by-step explanation:

15x8=120 (two of them)

15x7=105 (two of them)

8x7=56 (two of them)

120+120+105+105+56+56=562 in²

Find all solutions of cos x -sqrt = 0.

Answers

Answer:

Option A

Step-by-step explanation:

Good question!

We assume that x lies on the interval 0<=x<=360. We can therefore identify the solution in degrees:

[tex]\cos \left(x\right)-\sqrt{1-3\cos ^2\left(x\right)}=0,\:0\le \:x\le \:360^{\circ \:}[/tex]

Now we can solve by substitution, and when simplified we get cos(x) = 1/2.

Take the inverse: x = cos^-1(1/2) = π/3 <--- angle in first quadrant

                             x = (2π-π/3) = 5π/3 <----- angle in fourth quadrant

As you know π/3 in degrees is 60, and 5π/3 = 360-60 = 300

Therefore your solution is the first option, x = 60+n360 and x = 300 + n360

The sum of two numbers is 107, the difference is 51. Find the numbers.
Answer : The numbers are

Answers

Answer:

The answer is 56.

Others are 50 + 57 = 107, 44 + 63 = 107, and 39,68

Step-by-step explanation:

107-51 = 56

5x/8x^2+5x

Find the restricted values of x for the following rational expression. If there are no restricted values of x, indicate "No Restrictions".

Answers

Answer:

[tex]x\neq 0[/tex]

Step-by-step explanation:

Dividing by 0 is undefined, hence not allowed.

The denominator of the first term contains x^2.

Hence 0 is not allowed.

A triangle has a perimeter of 112 cm. Each of the two longer sides of the triangle is three times as long as the shortest side. Find the length of each side of the triangle.

Answers

Answer:

Two sides have a measure of 48 cm and the shortest side is 16 cm.

Step-by-step explanation:

this is an isosceles triangle

let x = length of shortest side

let 3x = length of other two sides

find x:

3x + 3x + x = 112

7x = 112

x = 16

3x = 48

HEY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

a) = 14, because we solve the absolute value first, making it 9 + 5.

b) = 4, because we solve -9 + 5 first, which equals -4, then we solve the absolute value which is 4.

Answer:

a

b

Step-by-step explanation:

Mhanifa please help me with this! I will mark brainliest! Please hurry before I get a bunch of random answers! I would really appreciate it! Random answers will be reported

Answers

Answer:

1. C. Reflexive property, SSS2. A. ASA postulate

Step-by-step explanation:

Question 1Blank 3 = Reflexive propertyBlank 4 = SSS

Correct choice is C

Question 2Blank 6 = ASA

Correct choice is A

What is 56 divided by 14.5

Answers

Answer:

3.86( rounded)

Step-by-step explanation:

Solve the problem. Check answers to be sure they are reasonable.
A​ 10-gal aquarium is 4 in. higher than it is wide. Its length is 17 ​in., and its volume is 4284 in.^3. What are the height and width of the​ aquarium?

Answers

Answer:

[tex]W = 18[/tex] -- Width

[tex]H = 14[/tex] --- Height

Step-by-step explanation:

Given

[tex]V = 4284[/tex] -- Volume

[tex]L = 17[/tex] -- Length

[tex]H = ??[/tex] -- Height

[tex]W = 4 + H[/tex] -- Width

Required:

Find the height and the width

Volume is calculated as:

[tex]V = LWH[/tex]

This gives:

[tex]4284 = 17 * (4+H) * H[/tex]

[tex]4284 = 17 * (4H+H^2)[/tex]

Open bracket

[tex]4284 = 17 * 4H+17*H^2[/tex]

[tex]4284 = 68H+17H^2[/tex]

Divide through by 17

[tex]252 = 4H+H^2[/tex]

Write as a quadratic expression

[tex]H^2 + 4H - 252 = 0[/tex]

Expand

[tex]H^2 + 18H - 14H - 252 = 0[/tex]

Factorize:

[tex]H(H + 18) - 14(H + 18) = 0[/tex]

Factor out H + 18

[tex](H - 14)(H + 18) = 0[/tex]

[tex]H -14 = 0[/tex] or [tex]H + 18 = 0[/tex]

[tex]H = 14[/tex] or [tex]H = -18[/tex]

But Height can not be negative. So:

[tex]H = 14[/tex]

Recall that:

[tex]W = 4 + H[/tex]

[tex]W = 4 + 14[/tex]

[tex]W = 18[/tex]

(a) An angle measures 51°. What is the measure of its complement?
(b) An angle measures 37°. What is the measure of its supplement?
measure of the complement:
°
X 5
?
measure of the supplement:

Answers

Answer:

a. 39 b.143

Step-by-step explanation:

90-51= 39

180-37=143

I need this please help

Answers

Function A has a rate of change of 0.75 while Function B has a rate of change of 0.25 so Function A has a greater rate of change.

Use 3.14 for Pi. *Answer choices may be rounded.* 5 points 1. 15 cm 7.5 cm 176.6 706.5 1324.7 5298.8​

Answers

Answer:

C. 1324.7 cm³

Step-by-step explanation:

Volume of cylinder = πr²h

π = 3.14

radius (r) = ½ of 15 = 7.5 cm

Height (h) = 7.5 cm

Plug in the values

Volume = 3.14*7.5²*7.5 = 1324.7 cm³

If Mrs. Maiers buys 24 stickers, is the cost of each sticker more then or less then 0.50

Answers

0.50 24 times is the answer just multiply them


Jennifer earns $9 per hour babysitting. Use this information to answer problems 18-20.
20. Is the function increasing or decreasing?
a. Increasing
b. Decreasing

Answers

Answer:

A

Step-by-step explanation:

Answer:

Increasing

Step-by-step explanation:

We know that Jennifer earns $9 dollars per hour babysitting, this is the only information provided. Meaning that the monetary value is constantly increasing, with no fees or anything being mentioned, this means that the function is increasing. Due to the situation, the line on the graph will always go up.

Jennifer's equation could be represented as 9x.

Solve help? That's it really.

Answers

Answer:

1).00390625

2).216

3).0231481481481

Step-by-step explanation:

Select the equivalent expression . (2^ -4 * z^ -3 )^ 5 =?

Answers

Step-by-step explanation:

The option is C

= 1/ 2^20 • z^15

Hope it will help :)

The equivalent expression of [tex](2^ {-4} * z^ {-3} )^ 5[/tex] will be [tex]\frac{1}{(2^ {20} * z^ {15} )}[/tex], i.e. option C is the correct answer.

What is an expression?

Expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An expression is a combination of numbers, variables, or a combination of numbers and variables, and symbols and it is connected by the sign of equal.

We have,

(2⁻⁴ × z⁻³)⁵ = ?

Now,

Using the exponent rule,

i.e.

(aⁿ)ᵇ = aⁿ ˣ ᵇ = aⁿᵇ

So,

(2⁻⁴ × z⁻³)⁵

i.e.

On solving,

We get,

(2⁻²⁰ × z⁻¹⁵)

Now,

Rewrite the above expression,

Using the exponent rule,

i.e.

[tex]\frac{1}{(2^ {20} * z^ {15} )}[/tex]

So,

(2⁻⁴ × z⁻³)⁵ = [tex]\frac{1}{(2^ {20} * z^ {15} )}[/tex]

I.e.

Option C is the correct answer for the expression (2⁻⁴ × z⁻³)⁵.

Hence, we can say that the equivalent expression of [tex](2^ {-4} * z^ {-3} )^ 5[/tex] will be [tex]\frac{1}{(2^ {20} * z^ {15} )}[/tex], i.e. option C is the correct answer.

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Westley and Buttercup are each saving money. Westley starts with $85 in in his savings and add $5 per week (y=85+5x)

Buttercup starts with $10 in her savings account and adds $20 per week (y=10+20x)

After how many weeks will they have the same amount of money?

Answers

Answer:

After 5 weeks.

Step-by-step explanation:

Westley starts with $85 and saves $5 per week. So:

[tex]y=85+5x[/tex]

Buttercup starts with $10 and saves $20 per week. So:

[tex]y=10+20x[/tex]

When they have the same amount of money, the two equations will be equal to each other. Therefore:

[tex]85+5x=10+20x[/tex]

Solve for x. Subtract 10 from both sides:

[tex]75+5x=20x[/tex]

Subtract 5x from both sides:

[tex]75=15x[/tex]

Divide both sides by 15:

[tex]x=5[/tex]

Westley and Buttercup will have the same amount of money after 5 weeks.

70 POINTS HELP PLEASE ON THIS

Answers

Answer:

no answer cuz it says 35 points instead of 70

Step-by-step explanation:

there is no answer it’s 35 and should be 70

please help me thank you

Answers

Answer:

Step-by-step explanation:

11/77=x/21

x=3

need help please Choose the best graph that represents the linear equation: -X = 2y + 1 Graph A

Answers

Answer:

Please refer to the attachment

Hope it helps

Please mark me as the brainliest

Thank you

Answer:

yes a is correct on edge!

Step-by-step explanation:

Question
Casey charges his neighbors $25 to mow their lawns. How many lawns must he mow next summer if his goal is to earn at
least $1,000?
Provide your answer below:
lawns
D FEEDBACK
MORE INSTRUCTION
SUBMIT
SUBMIT
Content attribution

Answers

Answer:

He must mow 40 lawns next summer to reach $1000.

Step-by-step explanation:

1000/25=40

what is 2+6x=28 pleas i need urgent help

Answers

Answer:

x=4.3

Step-by-step explanation:

2+6x=28

-2

6x=26/6

X= 13/3=4.333
Yeah ....
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