what is the explicit rule for the geometric sequence? 9,6,4,83,… enter your answer in the box.

Answers

Answer 1

The explicit rule for the geometric sequence 9,6,4,83,… is $a_n = 9(\frac{1}{3} )^{n-1}$.

How to calculate the nth term of a geometric sequence?

In Mathematics and Geometry, the nth term of a geometric sequence can be calculated by using this mathematical equation (formula):

aₙ = a₁rⁿ⁻¹

Where:

aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = 6/9

Common ratio, r = 2/3

For the explicit rule, we have:

aₙ = a₁rⁿ⁻¹

$a_n = 9(\frac{1}{3} )^{n-1}$

Read more on geometric sequence here: brainly.com/question/16423479

#SPJ1

Related Questions

studies that assign subjects to intervention groups on the basis of their extreme scores are vulnerable to regression toward the mean. True or False

Answers

True.

Studies that assign subjects to intervention groups based on their extreme scores are vulnerable to regression toward the mean. This phenomenon occurs because extreme scores are often due to measurement error, random fluctuations, or other factors that are not representative of the subject's true underlying ability or condition. When these subjects are retested, their scores tend to move closer to the mean, regardless of whether they receive an intervention or not. This can make it difficult to determine whether the intervention had any real effect, as any observed changes may simply be due to regression toward the mean.

To minimize the impact of regression toward the mean, researchers can use a variety of techniques such as random assignment, matching, or statistical adjustment. These methods help ensure that intervention and control groups are comparable at baseline, reducing the likelihood that differences in outcomes are due to chance or regression toward the mean.

Find the scale factor

Answers

Answer:

36/x =48/24

36/x =2

2x= 36

x= 36/2

x=18

Help me please this is due please help

Answers

Answer: 4/6 and 6/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 x 3 6

-------- = ---------

3 x 3 9

2 x 2 4

-------- = ----------

3 x 2 6

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places for the solution. 4) 3^(7x) = 3.3
5) e^(x+ 3) = 7 6) 7^x = 6^(x + 7)

Answers

Decimal approximation found is;

x ≈ 12.54

What is the best proccedure to calculate decimal approximation?

4) Applying the natural logarithm, we get:
$ln 3^{7x$ = ln(3.3)

Applying the property of logarithms that says ln($a^b$) = b ln(a).

7x ln(3) = ln(3.3)

Dividing both sides by ln(3), we get:

7x = ln(3.3)/ln(3)
Using a calculator, we get:

x ≈ 0.378

5) Applying natural logarithm, we get:
$ln(e^{x+3})$ = ln(7)

Applying property of logarithms that says ln($e^a$) = a.

x + 3 = ln(7)

Subtracting 3 from both sides, we get:

x = ln(7) - 3

Using a calculator, we get:

x ≈ 1.95

6) Applying the natural logarithm, we get:
$ln(7^x}) = ln(6^{x+7})$

Applying property of logarithms that says ln($a^b$) = b ln(a).
x ln(7) = (x+7) ln(6)

Expanding the right side using the distributive property, we get:

x ln(7) = x ln(6) + 7 ln(6)

Subtracting x ln(6) from both sides, we get:

x ln(7) - x ln(6) = 7 ln(6)

Factoring out x on the left side, we get:

x (ln(7) - ln(6)) = 7 ln(6)

Dividing both sides by ln(7) - ln(6), we get:

x = 7 ln(6)/(ln(7) - ln(6))

Using a calculator, we get:

x ≈ 12.54

Learn more about natural logarithm.

brainly.com/question/20785664

#SPJ11

I need help. It says select the expression that does not have the same value

Answers

Answer:

The answer is option C

Sorry that im late

Will give brainlist if correct.

Answers

Answer: $\frac{1}{16}$

Step-by-step explanation:

1. Original Equation: $4^4(4^-^7)(4)$

2.Simplify: $4^4(4^-^7)(4) ----> 4^4* 4^-^7 * 4\\$

3.Apply exponent rule: $4^4^-^7^+^1$

4. Simplify: $4^-^2\\$

5.Apply exponent rule: $\frac{1}{4^2}$

6.Simplify: $\frac{1}{16}$

for each diagram, determine whether angles 1 & 2 are adjacent angles, heeeelp please :(

Answers

Answer:

Diagram 5: Not adjacent angles

Diagram 6: Not adjacent angles

Diagram 7: Are adjacent angles

Diagram 8: Are adjacent angles

Step-by-step explanation:

In order for angles to be adjacent, they need to have all of three things:

1. Have a common vertex

2. Have a common side

3. Must not overlap

Diagram 5 does not have a common side between angles 1 and 2, so it is not adjacent.

Diagram 6 does not even have angles 1 and 2 connected in any way so it is not adjacent.

Diagrams 7 and 8 have all three conditions, so those diagrams are adjacent.

expand and simplify (3+√7)(1+√7)

Answers

Answer:

10 + 4√7

Step-by-step explanation:

Use the distributive property:

(A + B)(C + B) = (AC + AB) + (BC + B^2) = B^2 + AC + AB + BC

(3 + √7)(1 + √7)

= (√7)^2 + (3 * 1) + (3 * √7) + (√7 * 1)

and simplify.

= 7 + 3 + 3√7 + √7

= 10 + 4√7

help i’ll give Brain :(

Answers

Answer:

1, 4 and 5

Step-by-step explanation:

yup one, four, and five

Han earned $850 over the summer working odd jobs. He wants to put his money into a savings account for when he is ready to buy a car. His bank offers a simple interest account at 5%, how much interest will Han have earned after 2 years?

Answers

Answer:

$884.34

Step-by-step explanation:

$850.00*2%=$17.00

$850.00+$17.00=$867.00

$867.00*2%=$17.34

$867.00+$17.34=

$884.34

Answer: $850 x 2 = $1700.00

Step-by-step explanation: You just multiply 2 times $850 and you get your answer.

can someone do these? i'll give brainleist to whoever does them all

Answers

You have to multiply 6x6x6= 218

what are all the possible factors of the quadratic term for x2 10x − 24?

Answers

Answer:

The factors are,

x + 12 and x - 2

Step-by-step explanation:

x^2 + 10x - 24,

Here, we note that,

12 - 2 = 10,

and (12)(-2) = 24,

so, we can re-write 10x as 10x = 12x - 2x

so,

$x^2 + 12x - 2x - 24 = 0$

Taking x common from the 1st two terms (x^2 and 12x),

and taking -2 common from the last two tems (-2x and -24), we get,

$x^2 + 12x - 2x - 24 \\x(x+12)-2(x+12)\\taking \ (x+12) \ common,we \ get,\\(x+12)(x-2)$

So, The factors are,

x + 12 and x - 2

In isosceles ABC, AB=AC. if B=55,calculate A

Answers

Answer:

Two base angles of an isosceles triangles are equal.

55 + 55 + a = 180

110 + a = 180

a = 180-110

a = 70

answer with work and for brainliest

Answers

The solutions of the expressions are as below:

10. -9x - 2; x = -4 3411. 24 - 8x; x = -2.25 4212. 15x + 9; x = -1/10 7.5

13. (a, b) are points located on the first quadrant that is a is positive x axis and b is positive y axis

(-a, b) are points located on the second quadrant that is: a is negative x axis and positive y axis

(a, -b) are points located on the fourth quadrant that is: a is positive x axis and negative y axis

(-a, -b) are points located on the third quadrant that is: a is negative x axis and negative y axis

How to solve the given expressions

10. -9x - 2; x = -4

-9x - 2 for x = -4

= -9 * -4 - 2

= 36 - 2

= 34

11. 24 - 8x; x = -2.25

= 24 - 8 * - 2.25

= 24 + 18

= 42

12. 15x + 9; x = -1/10

= 15 * -1/10 + 9

= -1.5 + 9

= 7.5

13.

a are points in the x axis and b are points in the y axis

(a, b) are points located on the first quadrant that is a is positive x axis and b is positive y axis

(-a, b) are points located on the second quadrant that is: a is negative x axis and positive y axis

(a, -b) are points located on the fourth quadrant that is: a is positive x axis and negative y axis

(-a, -b) are points located on the third quadrant that is: a is negative x axis and negative y axis

Read more on graphs here: https://brainly.com/question/25020119

#SPJ1

Identifying a Point on Perpendicular Lines On a coordinate plane, line M N goes through points (2, 3) and (negative 3, 2). Point K is at (3, negative 3). Which point could be on the line that is perpendicular to Line M N and passes through point K? (0, −12) (2, 2) (4, 8) (5, 13)

Answers

To determine which point could be on the line that is perpendicular to Line MN and passes through point K, we need to analyze the slopes of the two lines.

First, let's find the slope of Line MN using the given points (2, 3) and (-3, 2):

Slope of Line MN = (2 - 3) / (-3 - 2) = -1 / -5 = 1/5

Since the lines are perpendicular, the slope of the perpendicular line will be the negative reciprocal of the slope of Line MN. Therefore, the slope of the perpendicular line is -5/1 = -5.

Now let's check the given points to see which one satisfies the condition of having a slope of -5 when passing through point K (3, -3):

For point (0, -12):

Slope = (-12 - (-3)) / (0 - 3) = -9 / -3 = 3 ≠ -5

For point (2, 2):

Slope = (2 - (-3)) / (2 - 3) = 5 / -1 = -5 (Matches the slope of the perpendicular line)

For point (4, 8):

Slope = (8 - (-3)) / (4 - 3) = 11 / 1 = 11 ≠ -5

For point (5, 13):

Slope = (13 - (-3)) / (5 - 3) = 16 / 2 = 8 ≠ -5

Therefore, the point (2, 2) could be on the line that is perpendicular to Line MN and passes through point K.

For such more question on reciprocal

https://brainly.com/question/29863935

#SPJ8

Please give answer to the problem.

Answers

y = x - 4 so if x = -3 then y = -3 - 4 = -7

Performance Matters
Question 17 of 24
Submit Test
- T-Math-GreReg-T5andTS-CBT
Question 1-17
Dana recorded the number of days her brother wore sneakers to school and the number of days he wore loafers to school The ratio of the number of days he wore sneakers
school to the number of days the wore loafers to school was 5 to 2
Dana observed and recorded her brother's choice of shoes for 49 days, how many times did the wear sneakers to school to the number of days her brother wore sneakers to the number of days he wore loafers to school was 5 to 2 if Dana observed and recorded her brothers choice of shoes for 49 days how many times did he wear sneakers

Answers

Dana's brother wore sneakers for 35 days out of the 49 days observed by Dana.

How to solve this

If the ratio of the number of days her brother wore sneakers to school to the number of days he wore loafers to school was 5 to 2, we can assume that he wore sneakers for 5x days and loafers for 2x days, for some positive integer x.

We know that the total number of days observed by Dana is 49, so we can set up the following equation to solve for x:

5x + 2x = 49

Simplifying the left side of the equation, we get:

7x = 49

Dividing both sides by 7, we get:

x = 7

Therefore, her brother wore sneakers for 5x = 5(7) = 35 days out of the 49 days observed by Dana.

Answers

The area enclosed in the figure of the graph of r² = sin(2θ) is

1 square units.

What is polar equation?

A polar equation of a curve is usually expressed in polar coordinates and written with {r} as a function of {θ}.

Given is a polar equation as follows -

r² = sin(2θ)

Area enclosed in the figure is equivalent to -

{A} = 2{∫1/2r²dθ}

{A} = ∫r²dθ

{A} = ∫sin(2θ) dθ

{A} = {- cos(2θ)/2} (integral limit -> 0 to π/2)

{A} = {- cos(π)/2 + cos(0)/2}

{A} = 1/2 + 1/2

{A} = 1

Therefore, the area enclosed in the figure of the graph of r² = sin(2θ) is

1 square units.

To solve more questions on area of the graphs, visit the link below -https://brainly.com/question/10283905

#SPJ12

1) Consider the quadratic function: f (x) = (x + 3)2 – 2 and a function, g(x), which is created by translating
f (x) three units to the right, two units up, and reflected vertically over the x-axis. Complete the following tasks:
a) 15 points: Graph f (x) on the axes below and label it. Graph g(x) on the axes below and label it.
b) 10 points: Write the vertex form equation for g(x) below.

Answers

The graph of both functions are in the image at the end, and the vertex of g(x) are (0, 0).

How to graph the function g(x)?

Here we know that the function f(x) is:

f(x)= (x + 3)² - 2

And g(x) is a translation of 3 units to the right, 2 units up, and reflected over the x-axis, then we have:

g(x) = -[ f(x - 3) + 2]

Replacing f(x) we get:

g(x) = -[ (x + 3 - 3)² -2 + 2]

g(x) = -x²

The graphs of both functions are the ones in the image at the end, there we can see that the vertex of g(x) is (0, 0).

Learn more about translations at:

https://brainly.com/question/24850937

#SPJ1

ou begin with a stick of length 1 and break it at point, chosen uniformly at random. you then take the left piece and break it once again at a uniformly random chosen point. what is the expectation and variance of the length of left piece after the breaking.

Answers

The expected length of shorter stick is 0.25 units.

What is variance?

The term variance refers to a applied mathematics measurement of the unfold between numbers in a very information set. additional specifically, variance measures however way every variety within the set is from the mean (average), and so from each different variety within the set.

Main body:

Stick length = 1 unit -

Let the stick break at the distance x.

Since expected length of the shorter stick is needed x € [0, 0.5]

For uniform distribution,

Probability density function = p(x) = 1/b-a =1/0.5-0 = 2

expected length = E(x)

E(x) = $\int\limits^a_0 {xp(x)} \, dx$ where a = 0.5

E(x) = $\int\limits^a_0 {2x(x)} \, dx$

= $2\frac{x^{2} }{2}$

now putting limits ,

= 2[0.25]^2

= 0.25

therefore ,the expected length of shorter stick is 0.25 units.

to know more about variance , click on the link below

https://brainly.com/question/25639778

#SPJ4

Solve for x given that the polygons are similar. Then find the scale factor of the smaller figure to the larger figure.

Answers

The given polygons are similar and the scale factor of dilation is 3 : 2

Given data ,

Let the scale factor of the dilation be represented as k

Now , the value of k is

The measure of the ratio of corresponding sides are given as

21 / 14 = 12 : 8

3 : 2 = 3 : 2

Therefore , the dilation factor is 3 : 2

And , the measure of x is given by

21 / 14 = x / 12

3 / 2 = x / 12

Multiply by 12 on both sides , we get

x = 18

Hence , the dilation of polygon is solved

To learn more about dilation click :

https://brainly.com/question/13176891

#SPJ1

The complete question is attached below :

Solve for x given that the polygons are similar. Then find the scale factor of the smaller figure to the larger figure

Here are the 16 values for Brett Favre.

18 19 33 38 39 35 31 22 20 32 27 32 30 20 18 28

Calculate and interpret the mean absolute deviation (MAD).

Answers

The mean absolute deviation (MAD) of the 16 values we had is 6.172. It means that the average absolute distance between each data value and the mean of the data set is 6.172.

The formula to calculate the mean absolute deviation (MAD) is

MAD = ∑(|x - x⁻|)/ n

where x⁻ is the mean of the data and

n is the total number of values in the data set

The mean is calculated by

x⁻ = (18 + 19 + 33 + 38 + 39 + 35 + 31 + 22 + 20 + 32 + 27 + 32 + 30 + 20 + 18 + 28)/ 16

x⁻ = 27.625

Now ∑(|x - x⁻|) = 9.625 + 8.625 + 5.375 + 10.375 + 11.375 + 7.375 + 3.375 + 5.625 + 7.625 + 4.375 + 0.625 + 4.375 + 2.375 + 7.625 + 9.625 + 0.375 = 98.75

Therefore, the mean absolute deviation is

MAD = ∑(|x - x⁻|)/ n

MAD = 98.75/ 16

MAD ≈ 6.172

To know more on mean absolute deviation

https://brainly.com/question/10528201

#SPJ4

Please help!
I really need it asap

Answers

I’m pretty sure your answer is E

Brianna started watching a movie at 2:45 p.m. If the movie is 2 hours and 32 minutes long, when will it be over?

Answers

Answer:

It will be over at 5:17 pm

Step-by-step explanation:

2:45 +32 would be 3:17, we add 2 hours it would be 5:17

Answer:

5:17 pm

Step-by-step explanation:

Since Brianna started watching a movie at 2:45 p.m and the movie is 2 hours and 32 minutes long

Thus,

2:45 + 2 and 32 Minutes

2 + 2 = 4

45 + 32 = 77 minutes

1 Hour = 60 Minutes

Thus, 77 - 60 =17

Hence, 4 + 1 = 5

Thus, the movie will be over at 5:17 Pm

~Lenvy~

f(x) = -424 x + 4Find f(-7)

Answers

$\begin{gathered} f(x)=-424x+4, \\ So,\text{ f}(-7)=-424\times(-7)+4 \\ \Rightarrow\text{f}(-7)=2968+4 \\ \Rightarrow\text{f}(-7)=2972 \end{gathered}$

Use the Pythagorean Theorem to find the measure of the space diagonal line in the box
picture if the length of the box "a" = 13 inches; width of the box "b" = 5 inches; and height
of the box "c"= 8 inches. * S
(10 Points)
Pythagorean Theorem Formula: a? + b2 = 2
256 inches
257 inches
258 inches
(259 inches

Answers

Answer:

14.42inches

Step-by-step explanation:

Given the following

b = 5 in

c = 8in

we are to find the measure of the space diagonal line

Using the pythagoras theoreml

l^2 = b^2 + c^2

l^2 = 13^2 - 5^2

l^2 = 169 -25

l^2 = 144

l = 12in

To get the measure of the space diagonal line in the box, we will use the pythagoras theorem;

s^2 = l^2 + c^2

s^2 = 144 + 8^2

s^2 = 144 + 64

s^2 = 208

s= 14.42inches

Hence the required length ix 14.42inches

A local jewelry store sells class rings, which it purchases for $60 each. The store engraves a name and date on the ring and sells it using a markup rate of 340%.

Answers

Class rings are sold by a nearby jewelry store, which buys them for $60 each. The amount of markup is y=204.

Given that,

Class rings are sold by a nearby jewelry store, which buys them for $60 each. The ring has a name and date engraved on it, and the retailer markup it up by 340% before selling it.

We have to find the equation that can be used to find the amount of markup y.

So,

We can write the equation as

Amount of markup=340% of the purchases amount

Taking amount of the markup as y and purchases amount is $60.

y=340%×60

y=340/100×(60)

y=34×6

y=204

Therefore, The amount of markup is y=204.

To learn more about amount visit: https://brainly.com/question/13024617

#SPJ9

Can you solve 17+4x<9

Answers

Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

↬ x < -2

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

$\bf{4x < 9-17}$

$\bf{4x < -8}$

Divide each side by 4:

$\bf{x < -2}$

Hence, x < -2

When tax is added to the cost of a lipstick,its price increases from $16.50 to $18.48.what is the rate at which tax is charged?

Answers

Answer:

1.98 is your tax rate of the lipstick

If C is the unit circle in the complex plane C, and f(2)= 2², show that (2) dz = 0 using two ways: (a) by a direct multivariable integration by writing = +iy and suitably parametrizing C, and (b) using a relevant theorem. 2

Answers

(a) To show that the integral of f(z) dz over the unit circle C is equal to 0, we can parametrize C as z(t) = e^(it), where t ranges from 0 to 2π. Substituting this parametrization into f(z) = z^2, we get f(z(t)) = (e^(it))^2 = e^(2it). Now, dz = i e^(it) dt. Plugging these values into the integral, we have ∫[C] f(z) dz = ∫[0 to 2π] e^(2it) (i e^(it)) dt = i ∫[0 to 2π] e^(3it) dt. Evaluating this integral gives [e^(3it)/3i] from 0 to 2π. Substituting the limits, we get [e^(6πi)/3i - e^(0i)/3i].

Since e^(6πi) = 1, the expression simplifies to 1/3i - 1/3i = 0. Therefore, the integral of f(z) dz over C is indeed 0.

(b) By using the Cauchy's Integral Theorem, we can show that the integral of f(z) dz over C is 0. The theorem states that if f(z) is analytic inside and on a simple closed curve C, then the integral of f(z) dz over C is 0. In this case, f(z) = z^2, which is an entire function (analytic everywhere). Since C is the unit circle, which is a simple closed curve, we can apply the theorem. Thus, the integral of f(z) dz over C is 0.

Both methods, direct multivariable integration and the application of Cauchy's Integral Theorem, confirm that the integral of f(z) dz over the unit circle C is equal to 0.

To learn more about Integral Theorem - brainly.com/question/30992206

#SPJ11

Other Questions

Why & Who is your model teacher in nursing teaching professional subject/s? Select the correct symbol to make 11 , 1 of 1.Select Choice 323 a true statement. A full bottle holds 1/4gallon of juice, If of3/5the juice has beenpored how muchjuice is left in the bottle? Boleslaw: How many yards for 8 uniforms? Karen's bathroom floor has an area of 2 2/3 square yard she made out of rug that has an area of 1 1/4 yard what area of the floor is not covered by the rug The elements lithium and oxygen react explosively to from lithium oxide (Li2O). How much lithium oxide will form if 4.45 mol of lithium react? Can someone please help??? I cant figure this out. Pleaseeee Mackenzie is making cookies her mom told her not to make a mess so instead of using two measuring cups she uses the 1/3 cup she needs to use the 1/3 cup 8 times how much flour does the recipe need? A proton and an electron are in a vacuum and are separated by 0.10 nanometers. Protons are approximately 2000 times more massive than an electron. Note that protons and electrons have the same charge, but with opposite signs (protons carry a positive charge and electrons carry a negative charge). Which answer best describes the forces exerted by the two particles? Find the area of the region enclosed by the curves y = x^2 + 12and y = x^4 . Include a carefully drawn sketch of this region. At the end of the current year, the accounts receivable account has a debit balance of $4,500,000 and sales for the year total $81,500,000. Using this information, complete # 4 and # 5 below. 4. The a Write an expression for the calculation double the product of 3 and 2 who do you think is the loneliest person in the book? write a quote from the book to help you explain your answer. Suppose that 30% of skateboards stolen in a community arerecovered. What is the probability that, at least one skateboardout of 7 randomly selected cases of stolen skateboards isrecovered? True or false all foreign language results should be rated fails to meet Club A has 25 members and club B has 57 members. If the total number of people is 75 and every people joined in at least one club, how many people belong to both clubs? the critical checkpoints that control the cell cycle are at the The process of measuring, analyzing, enhancing, and then controlling processes once they have been brought within the narrow six sigma quality tolerances or standards is referred to as the:______. What are the physical features of people with this disorder? What is the voltage of the following circuit?