Is the sequence geometric if so identify the common ratio 1/3, 2/9, 4/27, 8/81

Answers

Answer 1

Answer:

It is a geometric sequence and the common scale factor is [tex]\frac{2}{3}[/tex].

Step-by-step explanation:

In an arithmetic sequence, the difference between consecutive terms is always the same.

[tex]a_n=a_1+(n-1)d[/tex]

where aₙ is the nth term, a₁ is the first term, n is the index, and d is the common difference.

In a geometric sequence, each consecutive term was multiplied by some factor over the last.

[tex]a_n=ax^n^-^1[/tex]

where aₙ is the nth term, n is the index, and x is the scale factor.

In the given sequence, there is no common difference so it is not an arithmetic sequence. There is, however, a common scale factor applied to each consecutive term. Each term is multiplied by [tex]\frac{2}{3}[/tex] over the last.

The formula for this sequence would be:

[tex]a_n=a\frac{2}{3} ^{n-1}[/tex]

Answer 2

Answer:

r = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

If the sequence is geometric then there will be a common ratio r between consecutive terms , that is

r = a₂ ÷ a₁ = a₃ ÷ a₂ = a₄ ÷ a₃

Then

a₂ ÷ a₁ = [tex]\frac{2}{9}[/tex] ÷ [tex]\frac{1}{3}[/tex] = [tex]\frac{2}{9}[/tex] × 3 = [tex]\frac{2}{3}[/tex]

a₃ ÷ a₂ = [tex]\frac{4}{27}[/tex] ÷ [tex]\frac{2}{9}[/tex] = [tex]\frac{4}{27}[/tex] × [tex]\frac{9}{2}[/tex] = [tex]\frac{2}{3}[/tex]

a₄ ÷ a₃ = [tex]\frac{8}{81}[/tex] ÷ [tex]\frac{4}{27}[/tex] = [tex]\frac{8}{81}[/tex] × [tex]\frac{27}{4}[/tex] = [tex]\frac{2}{3}[/tex]

Then sequence is geometric with common ratio r = [tex]\frac{2}{3}[/tex]


Related Questions

There are 10 pink cars, 12 blue cars and 8 yellow cars in the parking lot.


What is the ratio of yellow cars to the total number of cars in Erica’s toy box?
Show work
4: 15

15 : 4

5 : 4

2 : 3

Answers

Answer:

4 : 15

Step-by-step explanation:

total cars = 10 + 12 + 8 = 30 , then

yellow : total

= 8 : 30 ( divide both parts by 2 )

= 4 : 15 ( in simplest form )

Answer:

4 : 15 is the correct answer.

Step-by-step explanation:

10+12+8 is 30. 8 cards are yellow so 8/30 simplified is, 4 : 15.

Please show work
I just need long division, I got synthetic division done .

Answers

Answer:

(10x^4-50x^3-800)/(x-6)

Step-by-step explanation:

Images with work attached

Answer:

            10 • (x^4 - 5x^3 - 80)

 ————————————————————

                      x - 6  

Step-by-step explanation:

STEP 1:

Equation at the end of step 1

 

STEP 2:

Equation at the end of step  2

:

 

STEP 3:

                           10x4 - 50x3 - 800

Simplify   —————————————————

                                        x - 6      

STEP 4:

Pulling out like terms

     Pull out like factors :

  10x^4 - 50x^3 - 800  =   10 • (x^4 - 5x^3 - 80)  

Polynomial Roots Calculator :

    Find roots (zeroes) of :       F(x) = x^4 - 5x^3 - 80

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -80.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,4 ,5 ,8 ,10 ,16 ,20 ,40 ,80

 

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -74.00      

     -2       1        -2.00        -24.00      

     -4       1        -4.00        496.00      

     -5       1        -5.00        1170.00      

     -8       1        -8.00        6576.00      

 

Polynomial Roots Calculator found no rational roots

Polynomial Long Division :

   

Dividing :  x^4 - 5x^3 - 80  

                             ("Dividend")

By         :    x - 6    ("Divisor")

dividend     x^4  -  5x^3          -  80  

- divisor  * x^3     x^4  -  6x^3              

remainder         x^3          -  80  

- divisor  * x^2         x^3  -  6x^2          

remainder             6x^2      -  80  

- divisor  * 6x^1             6x^2  -  36x      

remainder                 36x  -  80  

- divisor  * 36x^0                 36x  -  216  

remainder                     136  

Quotient :  x^3 + x^2 + 6x + 36  

Remainder :  136

=               10 • (x^4 - 5x^3 - 80)

 ————————————————————

                           x - 6  

Hope this helps, have a nice day/night! :D

The answer is right, but I am not 100 percent sure.

Answers

Step-by-step explanation:

a bc it should be good anser

Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. He finds the mean is 14. His steps for finding the standard deviation are below. S = StartRoot StartFraction (12 minus 14) squared (14 minus 14) squared (9 minus 14) squared (21 minus 14) squared Over 4 EndFraction EndRoot. = StartRoot StartFraction negative 2 squared 0 squared negative 5 squared 7 squared Over 4 EndFraction EndRoot. = StartRoot StartFraction 4 0 25 49 Over 4 EndFraction EndRoot. = StartRoot StartFraction 78 Over 4 EndFraction EndRoot. = StartRoot 19. 5 EndRoot. What is the first error he made in computing the standard deviation? Yuri failed to find the difference between each data point and the mean. Yuri divided by n instead of n -1. Yuri did not subtract 9 - 14 correctly. Yuri failed to square -2 correctly.

Answers

Answer:

He divided by n instead of n-1.

It is sample data so we need to divide by n-1 not n.

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

The first truck carries 35 tons less rice than the second truck. The number of paddy in the first truck is 2/3 of the amount in the second truck. How many tons of paddy does each cart hold?

Answers

Answer:

First truck = x

Second truck = y

x + 35 = y

x = 2/3y

So

2/3y +35=y

1/3y = 35

y = 35*3

y = 105

And ,

x = 2/3y = 70

The first truck carry 70 tons while the second carry 105 tons

Let the amount the first truck can carry be x

Let the amount the second can carry be y

If the first truck carries 35 tons less rice than the second truck, then;

x = y - 35

If the number of paddy in the first truck is 2/3 of the amount in the second truck

x = 2/3 y

Equate both to have:

2/3 y = y - 35

2/3y - y = -35

-y/3 = -35

y = 105

Since x = 2/3 y

x = 2/3 * 105

x = 70

Hence the first truck carry 70 tons while the second carry 105 tons

Laern more on equations here: https://brainly.com/question/16863577

How would you best describe the angle pair <6 and <7

Answers

Answer:

Consecutive interior angles

Step-by-step explanation:

Multiplication:
(a) 7/3×2/9 (b) 3/7×5/11 (c) 15/8×6/25 (d) 21/20×15/14
Division:
(a) 3/4÷5/7 (b) 9/5÷6/11 (c) 15/8 ÷6 (d) 8/7÷12
Culcul constant des fractions:
(a) 3/7+15/7×3/2 (b) 9/5×(1/4-5/12) (c) (3/8+7/5)÷(9/4-5/3)​

Answers

Multiplication:-

a. 7/3 × 2/9 = 7x2/3x9 = 14/27.

b. 3/7 × 5/11 = 3×5/7×11 = 15/77.

c. 15/8 × 6/25 = 3×3/4×5 = 9/20.

d. 21/20 × 15/14 = 3×3/4×2 = 9/8.

Division:

a. 3/4 ÷ 5/7 = 3/4 x 7/5 = 21/12 = (3 x 7) / (3 x 4) = 7/4

b. 9/5 ÷ 6/11 = 9/5 x 11/6 = 99/30 = (3 x 33) / (3 x 10) = 33/10

c. 15/8 ÷ 6 = 15/8 x 1/6 = 15/48 = (3 x 15) / (3 x 16) = 15/16

d. 8/7 ÷ 12 = 8/7 x 1/12 = 8/84 = (4 x 2) / (4 x 21) = 2/21.

Culcul constant des fractions:

a. 3/7 + 15/7 x 3/2

= 3/7 + 45/14

= (3 x 2) / (7 x 2) + 45/14

= 6/14 + 45/14

= 51/14

b. 9/5 x (1/4 - 5/12)

= 9/5 x [(1 x 3) / (4 x 3) - 5/12]

= 9/5 x (3/12 - 5/12)

= 9/5 - 2/12

= (9 x 12) / (5 x 12) - (2 x 5) / (12 x 5)

= 108/60 - 10/60

= 98/60

= (2x 49) / (2 x 30)

= 49/30.

c. (3/8 + 7/5) ÷ (9/4 - 5/3)

= [(3 x 5) / (8 x 5) + (7 x 8) / (5 x 8)] ÷ [(9 x 3) / (4 x 3) - (5 x 4) / (3 x 4)]

= (15/40 + 56/40) ÷ (24/12 - 20/12)

= 71/40 ÷ 4/12

= 71/40 x 12/4

= 852/160

= (4 x 213) / (4 x 40)

= 213/40.

Hope this helps..

please help me asap

Answers

Answer:

No, it isn't linear because the graph is not a straight line.

Step-by-step explanation:

(see picture of graph)

Linear means a straight line, and these points do not form a line, so it is not linear. You can also calculate this by finding the slope between each point and the previous.

A 5-pound bag of apples cost $3.50. Use that rate, to complete the table to identify equivalent ratios, and then answer the questions.

Apples cost $ __ per pound.
brainliest 100pts

Answers

Answer:

Cost 0.70 per pound.

Step-by-step explanation:

If you see the cost and the weight you can get the price per pound, so if 5 pounds cost $3.50, you can evaluate doing a rule of three:

So if you clear X you´d get this:

So the cost per pound is $0.70.

Now that you have the cost per pound you can do the equivalent ratios:

Cost---------------Apples

0.70---------------1 pound

3.5--------------- 5 pounds

 7---------------  10 pounds

Brainliest me bro

Answer:

70 cents per pound

Step-by-step explanation:

$3.50/5lb= 70 cent

ABCD is a quadrilateral. Select all the criteria that are sufficient to prove that ABCD is a parallelogram.

Line segment AB is congruent to line segment DC and Line segment is congruent to line segment BC.
Line segment AB is parallel to line segment DC
X is the midpoint of line segment AC and line segment BD

Answers

A parallelogram is a shape which has opposite sides to be equal and parallel. Therefore, the required properties that are sufficient for the prove are:

A. Line segment AB is congruent to line segment DC and Line segment AD is congruent to line segment BC.

B. Line segment AB is parallel to line segment DC.

Quadrilaterals are four sided shapes. Examples are square, rectangle, parallelogram, trapezium etc. These have different or distinguishing properties.

A parallelogram is a figure that has its opposite sides to be equal in length and which are also parallel. This properties can be used to answer the given question.

Thus, the appropriate criteria that are sufficient to prove that ABCD is a parallelogram are:

A. Line segment AB is congruent to line segment DC and Line segment AD is congruent to line segment BC.

B. Line segment AB is parallel to line segment DC.

Visit: https://brainly.com/question/3100335


What are the values of m and n

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The required values are ~

[tex]m = 60 \degree[/tex]

[tex]n = 30 \degree[/tex]

Refer to attachment for solution ~

Jenny has three times as many new toys as she has favorite toys.

Answers

answer:

3x = y

step-by-step explanation:

૪・ i am inferring you have to create an equation?

・jenny have three times = 3x

・as her fav toys — 3x = y

・new toys = y

・fav toys = x

how many hours will it take me to get 777,777,777 cookies if i get 266,560 cookies per second

Answers

Answer:

approximately 43 - 44 minutes exact

Answer:

It would take you 2917 hours.

Step-by-step explanation:

Do 777,777,777 divided by 266,560.

2917 (with a a lot of other numbers).

I hope this helped at all.

Heyyyyyy , Can you please help me with this

Answers

Answer:

19 houses

Step-by-step explanation:

90*(2/5)=36

90-36=54

54*(2/3)=37

54-37=19

Please help!!!!!!!!!!!

Answers

Answer:

10. right triangle 11. obtuse triangle 12. right triangle 13. right triangle

Step-by-step explanation:

In rhombus WXYZ, if WX=15, find YZ.

Answers

Answer:

YZ=15

Step-by-step explanation:

All sides of a rhombus are equal so it would be the same length.

find the square root of 48​

Answers

The answer is 6.92820323028

[tex] \: \: \: \: \: [/tex]

6.92820323

step-by-step explanation

refer to the attachment

hope it helps

I will mark brainliest. Only REAL ANSWERS PLEASE!!!

Answers

Answer:

y > -4

Step-by-step explanation:

The line almost intercepts at the point -4, but it is slightly above it, meaning Y is bigger (>) than -4.

helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp i will put brailny

Answers

Answer:

fraction 1/4. decimal 0.25 percent 25%

Step-by-step explanation:

5:20=5/20=1/4

1/4 is 0.25

the percentage is 25% aftr multiplying the decimal by 100%

Does anybody have the answer to this???? Thank You

Answers

Answer:

Step-by-step explanation:

h(4)=2w+3

4=2w+3

Collect like terms (c. I. T)

4-3=2w

1=2w

Divide both sides by 2(d.b.s)

1/2=2w/2

0.5=w

h=0.5w

Find the slope of the line through each pair of points.
(-10,8), (5,-5)

Answers

Answer:

-0.86667

Step-by-step explanation:

m = -13 / 15 = -0.86667

does the right riemann sum underestimate or overestimate

Answers

That depends on the function in question.

If f(x) is integrable and non-decreasing, then the right Riemann sum overestimates the integral of f.

If f is non-increasing, the right Riemann sum underestimates the integral.

A company makes a profit of $y (in thousand dollars) when it produces x computers, where y is given by the formula = ( − 100)( − 200) for ≥ 0 If 120 computers are produced, the profit will be $3,200,000.
a) Find the value of a.
b) What is the maximum profit the company can make? At this profit, how many
computers should be produced?
(7 marks) c) If the company targets to make at least $4,800,000, what is the range of the
number of computers to be produced?

Answers

lol no

just give up in life

The function is used to model real life situation

The value of a is -2000 150 computers must be produced to maximize the profit of $5,000,000 A range of 140 to 160 computers would give the company at least $4,800,000  

 

(a) The value of a

The function is given as:

[tex]\mathbf{y = a(x - 100)(x - 200) }[/tex]

The profit on 120 computers is 3200000.

So, we have:

[tex]\mathbf{3200000 = a(120 - 100)(120 - 200) }[/tex]

[tex]\mathbf{3200000 = -1600a}[/tex]

Divide both side by -1600

[tex]\mathbf{a = -2000}[/tex]

Hence, the value of (a) is -2000

(b) The maximum profit

The function becomes

[tex]\mathbf{y = -2000(x - 100)(x - 200)}[/tex]

Expand

[tex]\mathbf{y = -2000(x\² - 200x - 100x + 20000)}[/tex]

[tex]\mathbf{y = -2000(x\² - 300x + 20000)}[/tex]

Expand

[tex]\mathbf{y = -2000x\² + 600000x - 40000000}[/tex]

Differentiate

[tex]\mathbf{y' = -4000x + 600000}[/tex]

Set to 0

[tex]\mathbf{-4000x + 600000 = 0}[/tex]

Collect like terms

[tex]\mathbf{4000x = 600000}[/tex]

Divide both sides by 4000

[tex]\mathbf{x = 150}[/tex]

Substitute 150 for x in [tex]\mathbf{y = -2000(x - 100)(x - 200)}[/tex]

[tex]\mathbf{y = -2000(150 - 100)(150 - 200)}[/tex]

[tex]\mathbf{y = 5000000}[/tex]

150 computers must be produced to maximize the profit of $5,000,000  

c) Range when the target is at least $4,800,000

This means that:

[tex]\mathbf{y \ge 4800000}[/tex]

So, we have:

[tex]\mathbf{-2000x\² + 600000x - 40000000 \ge 4800000}[/tex]

Collect like terms

[tex]\mathbf{-2000x\² + 600000x - 40000000 - 4800000 \ge 0}[/tex]

[tex]\mathbf{-2000x\² + 600000x - 44800000 \ge 0}[/tex]

Divide through by -2000

[tex]\mathbf{x\² - 300x +22400 \le 0}[/tex]

Factorize

[tex]\mathbf{(x - 140)(x - 160) \le 0}[/tex]

Express as inequality

[tex]\mathbf{140 \le x \le 160}[/tex]

A range of 140 to 160 computers would give the company at least $4,800,000

Read more at:

brainly.com/question/25471478

HELP PLZ You measured a floor tile as 12 inches by 10 inches. It is actually 10 inches by 10 inches. What is the percent error of the area?

Answers

Area of measured tile: 12 x 10 = 120 square inches

Area of actual tile = 10 x 10 = 100 square inches:

Percent error = 120-100 = 20/100 = 0.20 x 100 = 20%

Answer: 20%


need help for this question

Answers

The first one it's the first image, and the second one is the second image.

Iro drives 50 miles/hour for 0.6 hours. Kalini drives 65
miles/hour for 0.5 hours.
Who drove farther, and how far did that person drive?

Answers

Answer:

iro 50*.6 gives us 30 miles

andkalini drives 65 for .5 65*.5= 32.5 miles

so kalini drove further

Hector watched
1
4
of a movie in the morning, and he watched some more at night. By the end of the day, he still had
2
3
of the movie left to watch. How much of the movie did Hector watch at night?

Answers

Answer:

how watched 3/4 of the movie

Step-by-step explanation:

I know this because 2 is more then half of 3 and 3 is more then half of 4 so you can come to a conclusion that he watched a total of 3/4 and 2/4 at night.

P.S when ever using a fraction when typing like 1/4 instead of doing

1

4

do 1/4

Find the slope of the line for y = x - 6​

Answers

Answer:

Slope is equal to 1.

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slopeb - y-intercept

Step-by-step explanation:

Step 1: Define

Identify.

y = x - 6

Step 2: Find

Break equation, compare to slope-intercept general form.

Slope m = 1

y-intercept b = -6

I really need help with these geometry questions.

Answers

Hey there!

I'm going to go in order from images.

1. The angle measure 60 is linear to angle 6, this would make them supplementary.

Angle 6: 180 - 60 = 120

Angle 6 is vertical to angle 2, this makes them congruent. If angle 6 equals 120 measure 2 also equals 120.

2. Measure 6 is vertical from measure 2. We established in the last problem measure 2 equals 120.

If angle 2 equals 120 measure 6 also equals 120.

3. The 2 equations are alternate exterior angles.

2x+5=8x-7

    +7     +7

2x+12=8x

-2x     -2x

12=6x

12/6= 2

x=2

4. I cannot explain this one without showing it visually lol.

Measure 5 equals 30 degrees.

5. Measure 1 is verticle to the measure that reads 60. Vertical angles are congruent.

If measure 1 is congruent to the measure that reads 60. Measure 1 equals 60.

I hope this helps!!!

Tell 3 numbers that are less than 2 and greater than −1.

Answers

Answer:

0 and 1 and -2 and -3

Step-by-step explanation:

Do they have to be whole numbers?
If not, then 0, 1, and 1.75.
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