The value of a motorcycle each year follows the sequence $12,000 $9,600, $7,680, $6,144

Which formula represents the recursive definition of the sequence where n represents the number of years?



The Value Of A Motorcycle Each Year Follows The Sequence $12,000 $9,600, $7,680, $6,144Which Formula

Answers

Answer 1

The recursive definition of the geometric sequence is given by:

A. [tex]a_n = (0.8)a_{n-1}[/tex]

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The basic recursive relation is given as follows:

[tex]a_n = qa_{n-1}[/tex]

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, considering the given sequence, the common ratio is given by:

[tex]q = \frac{6144}{7680} = \frac{7680}{9600} = \frac{9600}{12000} = 0.8[/tex]

Hence option A is correct.

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Answer 2

The values of the motorcycle follows a geometric sequence

The recursive definition of the sequence is (a) [tex]a_{n} = 0.8a_{n-1[/tex]

How to determine the recursive definition?

The values are given as:

$12,000 $9,600, $7,680, $6,144

Calculate the common ratio using:

r = a2/a1

So, we have:

r = 9600/12000

Divide

r = 0.8

Recall that:

r = a2/a1

So, we have:

a2/a1 = 0.8

Multiply both sides by a1

a2 = 0.8a1

Rewrite as:

[tex]a_{2} = 0.8a_{2-1[/tex]

Substitute n for 2

[tex]a_{n} = 0.8a_{n-1[/tex]

Hence, the recursive definition of the sequence is (a) [tex]a_{n} = 0.8a_{n-1[/tex]

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Related Questions

Need help! i have no idea how to do domain and range!!!://

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Step-by-step explanation:

Dude THE Values for graph are given or not

Find the perimeter of the composite figure

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7+7+5+5=24

So therefore the permeter is 24

An angle measures 88° more than the measure of its complementary angle. What is the measure of each angle?

Could you guys help me with this?

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Answer:

It might be a two degree angle! :)

Step-by-step explanation:

A company claims that its tablet computers have an average recharge time of 3 hours. Using a random sample of 50 company tablet computers, a consumer group determines a mean recharge time of 2.5 hours with a standard deviation of 0.3 hours.

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Answer:

The correct answer is 1.65

Step-by-step explanation:

~Hope this helps! :)

find the LCM of denominator 3/8 and 3/4​

Answers

Answer:

Step-by-step explanation:

Actually, it is 8.

3/8: nothing need be done.

3/4: Multiply top and bottom of the fraction by 2.

3*2 / 4*2 = 6/8

So the lowest common multiple is 8.

The factions become 3/8 and 6/8

Enlarge the house using a scale factor of 1 : 2.

Answers

Answer:

See picture & explanation below.

Step-by-step explanation:

The scale is 1:2, so everything is doubled in size.

Count the number of squares each segment is in length and multiply it by 2. Then draw all new segments that are twice as long as the original ones to create a house that is twice as large as the original house.

See the picture below.

Fiona is studying how income taxes impact various families and their finances .she creates a table with various amounts of taxes owed and estimates that this represents 9%of each familys gross income

Answers

Income tax is the tax that is imposed by the government on the income that is generated by individuals and businesses.

What is a tax?

Your information is incomplete. Therefore, an overview of a tax will be given. It should be noted that a tax is a compulsory levy that is paid by individuals and businesses.

Also, income tax is the tax that is imposed by the government on the income that is generated by individuals and businesses. This is important to generate revenue for the government.

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The length of a rectangle is three times its width.
If the perimeter of the rectangle is 64 cm, find its length and width.

Answers

Answer:

Length: 24 cm

Width: 8 cm

Explanation:

Let Width be "w"

Then Length is "3w"

=================

Perimeter of rectangle = 2(length+width)

===================================

2(3w+w) = 64(4w) = 32w = 8

So, width is 8 cm

Length: 3w ⇒ 3(8) ⇒ 24 cm

Answer:

Length = 24 cmWidth = 8 cm

Step-by-step explanation:

Given

Length = 3 x Width Perimeter = 64 cm

Solving

Perimeter = 2(Length) + 2(Width)Perimeter = 2(Length + Width)Perimeter = 2(3 x Width + Width)Perimeter = 2(4 x Width)Perimeter = 8 x Width64 = 8 x WidthWidth = 64/8 = 8 cmLength = Width x 3 = 8 x 3 = 24 cm

Help, please! It's all in the screenshot

Answers

Answer:

cube root of 9. the third option

Step-by-step explanation:

x^3 = 9

we take the cube root of both sides.

so x = cube root of 9

please help I don't know the median give an answer and explanation

Answers

Answer:

Median is the middle of the data set. For example this data set is 4, 6, 7, 9, 10. First you take out 4 and 10. The you take out 6 and 9 to get a median of 7. But if there is an even amount of numbers like in this data set, 1, 2, 4, 5. Then you take out 1 and 5 and then find the middle point in between 2 and 4 which is 3.

HELP ASAP
Linear equations

Answers

The answer is that each dinner cost $20 each

What is the equation of this trend line?

Enter your answers by filling in the boxes.


please help me get into my dream school!

Answers

Answer:

Step-by-step explanation:

The line rises to the left so the slope is negative.

The slope m = -24/12 = -2.

Using the point-slope formula and taking the point (12, 0) on the line:

y - y1 = m(x - x1)   where m = -1, x1 = 12 and y = 0:

y - 0 = -2(x - 12)

y = -2x + 24   <------- this is the required equation.

Answer:

Blank 1 : -2

Blank 2 : 24

Step-by-step explanation:

The first blank denotes the rate of change, or the slope of the graph.

Slope = y₂ - y₁ / x₂ - x₁

m = 16 - 24 / 4 - 0m = -8/4m = -2Blank 1 : -2

The second blank denotes the value of variable K when the value of variable J is 0, or rather the y-intercept of the graph.

The y-intercept is clearly (0, 24)

Blank 2 : 24

this is hard i need help. Please this is due today.

Answers

Answer:

140

Step-by-step explanation: all you have to do is add all the numbers then multiply those by 4 then you will get 140

Which of the following proves these triangles are congruent

Answers

Answer:

ASA

Step-by-step explanation:

ASA rule states that: If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

The image below shows the answer/explanation⬇️

Solve log x = 4. plese help

Answers

Answer:

x = 10^4 =  10000

Step-by-step explanation:

log(x) = 4

x = 10^4

PLS HELP, EXPLANATION IS GREATLY APPRECIATED!!!!!

Answers

Answer:

a = alpha

(sin a)^2

Step-by-step explanation:

(tan a)^2=(sin a)^2/(cos a)^2

(sec a)^2 = 1/(cos a)^2

if we combine we get ((sin a)^2 * (cos a)^2)/(cos a)^2

simplafy

HOPE THIS HELPSSSS<3

3 L of water are shared equally among 5 friends. What fraction of a liter did each friend get?

Answers

Answer:  3/5 of a liter

Explanation: Simply divide 3 over 5. We cannot do much with the fraction since 3/5 can't be reduced. So we leave it as is.

3/5 in decimal form is exactly 0.6 and that converts to 60%, meaning each person gets 60% of a full liter.

Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof to prove that they are. N A B M​

Answers

Answer:

Step-by-step explanation:

Please help. this is beyond confusing. it’s stressing me out.

Answers

Answer:

D = 1120

Step-by-step explanation:

Given:

W = 70T = 4

Substitute the values into the equation:

⇒ D = WT²

[tex]\text{D = WT}^{2} \ \text{can also be written as D = (W)(T)(T)}[/tex]

⇒ D = (W)(T)(T)

⇒ D = (70)(4)(4)

Simplify the RHS:

⇒ D = 280(4)

D = 1120

Question 7 of 10
Which situation involves a conditional probability?
O A. The probability that you make a second free throw given that you
made the first free throw
B. The probability that you are given a book for your birthday
O C. The probability that you make two free throws in basketball
D. The probability that you roll a 6 on a number cube
SUBMIT

Answers

A) The probability that you make a second free throw given that you made the first free throw

The surface area of a cylinder is 432 pi yd2. The height of the cylinder is five times the radius. What is the diameter of the cylinder?

Answers

Since the surface area of this cylinder is [tex]432\pi \;yd^2[/tex], its diameter is equal to 12 yards.

How to calculate surface area.

Mathematically, the surface area (SA) of a cylinder is given by this formula:

[tex]S.A = 2\pi rh + 2\pi r^2[/tex]

Where:

h is the height.r is the radius.

Given the following data:

Surface area of cylinder = [tex]432\pi \;yd^2[/tex]Height = 5r.

Substituting the given parameters into the formula, we have;

[tex]432\pi = 2\pi r(5r) + 2\pi r^2\\\\432\pi = 2\pi 5r^2 + 2\pi r^2\\\\216=5r^2+r^2\\\\216=6r^2\\\\r^2=36\\\\r=\sqrt{36}[/tex]

r = 6 yards.

For the diameter:

Diamter = 2 x radius

Diamter = 2 x 6

Diameter = 12 yards.

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The distance from earth to the moon is about 3.84 times 10^6 meters. what is one fourth of this distance

Answers

3.84 x 10^6 = 3,840,000

3,840,000 / 4 = 960,000

If the distance from the earth to the moon is about 3.84 x 10⁶.One-fourth of this distance will be 960,000

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, the distance from the earth to the moon is about 3.84 x 10⁶.

One-fourth of this distance is found by dividing the total distance by 4.

We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.

Suppose the one-fourth of this distance will be x,

(1/4)× 3.84 x 10⁶ =x

x=(3.84 x 10⁶)/4

x=960,000

Thus, if the distance from the earth to the moon is about 3.84 x 10⁶. One-fourth of this distance will be 960,000

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#SPJ5

(05.01) A scale drawing of a kitchen is shown below. The scale is 1 : 20.
5 inches
4 inches
Show your work to determine the area of the room in square feet.

Answers

Answer:

500/9 or 55.56 ft²

Step-by-step explanation:

Find the dimensions of the kitchen, convert to feet

5 in * 20 = 100 in = 100/12 ft = 25/3 ft4 in * 20 = 80 in = 80/12 ft = 20/3 ft

The area is

25/3 * 20/3 = 500/9 = 55.56 ft² (rounded)

Answer:

5.56 ft² (nearest hundredth)

Step-by-step explanation:

Given:

width = 4 inlength = 5 in

If the scale is 1 : 20, then to scale up, multiply the width and length by 20:

⇒ width = 4 × 20 = 80 in

⇒ length = 5 × 20 = 100 in

Area = width × length

        = 80 × 100

        = 800 in²

1 ft = 12 in

⇒ 1 ft² = 12² in² = 144 in²

Therefore, to find the area of the room in square feet, divide the area in inches by 144:

⇒ area = 800 ÷ 144

            = 5.56 ft² (nearest hundredth)

help me, Sofia practices swimming and has every day for three weeks. the first day she trains 15 minutes and each day she trains 5 minutes more than the day before She constructs the sequence for the first week of training and determines the elements of the sequence and the type.

Answers

Answer:

20

Step-by-step explanation:

you add 15 and 5

In Texas, the average number of tornadoes in May was about 154% of the average number of tornadoes in April. Write and solve a proportion to find the average number of tornadoes that occurred in April.

Answers

The table of the average number of tornadoes is an illustration of proportions

The average number of tornadoes in April is 28

How to determine the average number of tornadoes in April?

From the table, we have:

Average number of tornadoes in May in Texas = 43

From the question, we have:

May = 154% * April

This gives

43 = 154% * April

Express as decimal

43 = 1.54 * April

Divide both sides by 1.54

April = 27.9

Approximate

April = 28

Hence, the average number of tornadoes in April is 28

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Finn removes the plug from a trough to drain the water. the volume, in gallons, in the trough after it has been unplugged can be modeled by the expression 12x2 −13x 3, where x is the time in minutes. choose the appropriate form of the expression that would reveal the time in minutes when the trough is empty. 12(0)2 − 13(0) 3 (3x − 1)(4x − 3) 12(x − 3)2 − 1 12(x − 1)2 − 3

Answers

The given expression [tex]\rm 12x^2-13x+3[/tex]equivalent to (3x - 1)(4x - 3) option second is correct.

What is a quadratic expression?

A quadratic expression is a second-degree algebraic expression represented by the:

[tex]\rm f(x)=ax^2+bx+c[/tex] ........(1)

Where a, b, and c are the constants and  

We have the quadratic expression:

[tex]\rm f(x)=12x^2-13x+3[/tex]

[tex]\rm f(x)=12x^2-9x-4x+3[/tex]  (we can write -13x as a sum of -9x and -4x)

After taking common term, we get:

[tex]\rm f(x)=3x(4x-3)-(4x-3)[/tex]

[tex]\rm f(x)=(4x-3)(3x-1)[/tex]  or

[tex]\rm f(x)=(3x-1)(4x-3)[/tex]

Thus, the given expression [tex]\rm 12x^2-13x+3[/tex]  is equivalent to (3x - 1)(4x - 3).

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What do a rectangle and a kite have in common?

Answers

Answer:

- Both are quadrilaterals.

- Both have two pairs of side of equal length.

I hope my answer helps you.

Answer: 2 pairs of congruent sides

Hope this helps!

have a nice day!

Fill in the blank to make the fractions equivalent. 10/16 and /8 ?

Answers

Answer:

5 or 5/8

Step-by-step explanation:

To go from 10/16 to a bottom number/denominator of 8, you have to divide by 2.

Whatever you do to the top, you also do to the bottom, so you would divide 10, the numberator, by 2 to find the missing value.

10/2 is 5.

There is your answer.

Analyze the diagram below and answer the question that follows.

What is the value of cosA in the triangle above?

A. cosA = 0.5
B. cosA = 1
C. cosA ≈ 0.707
D. cannot be determined without side lengths

Answers

Answer:

C

Step-by-step explanation:

the cos of an angle of 45° is equal to √2/2~=0,7071

Do you want the full explanation?

I need more help!....

Answers

Answer:

1) Factored Form: y = (x - 3)(x + 1)

  X intercepts: (-1, 0), (3, 0)

  Axis of Symetry: x = 1

  Vertex: (1, -4)

  Domain: All real numbers -  (-∞, ∞)

  Range: y ≥ 4

2) Facotred Form: y = (x - 8)(x + 1)

   X intercepts: (-1, 0), (8, 0)

   Axis of symetry: x = 3.5

   Vertex: (3.5, -20.25)

   Domain: All real numbers - (-∞, ∞)

   Range: y ≥ -20.25

Step-by-step explanation:

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