Find the first four terms of the sequence given a1=18 and an+1=2+an2. A. 18, 10, 6, 5 B. 18, 10, 6, 9 C. 18, 14, 6, 9 D. 18, 10, 6, 4

Answers

Answer 1

The first four terms of the given sequence are 18, 10, 6, and 4 respectively.

What is a sequence?

A sequence is an ordered list object which related and connected by a common value.

There are many sequences. They are Arithmetic sequence, Geometric sequence, and so on.

Calculation:

It is given that,

The first term of the sequence is a1 = 18

And the terms of the sequence are related by,

a(n + 1) = (2 + an)/2

For n = 1;

a(1 + 1) = (2 + a1)/2

⇒ a2 = (2 + 18)/2 = 10

For n = 2;

a(2 + 1) = (2 + a2)/2

⇒ a3 = (2 + 10)/2 = 6

For n = 3;

a(3 + 1) = (2 + a3)/2

⇒ a4 = (2 + 6)/2 = 4

Thus, the first four terms of the given sequence are a1 = 18, a2 = 10, a3 = 6, and a4 = 4.

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Related Questions

i give u 5 star help me :))))))))))))

Answers

Answer:

parallel is 5x + 3y = 13

perpendicular is 6x - 10y = 7

Step-by-step explanation:

Find the marked angle P​

Answers

Answer:

the answer is (d) 57°

Step-by-step explanation:

since it's a straight angle it equals to 180°

you divide 180° from 123°

A 12 section game wheel has a 25% probability that the pointer will land on green. What is the likelihood that the pointer will land on green

Answers

Answer:

I’m not entirely sure what the question is asking but...

The spinner has a 1/4 chance of landing on green

with this, being a 12 section game wheel, it means that 3 of the sections are green.

what's 700.00divided by 120​

Answers

The answer is 3.5 because 120 can go into 700 three 1/2 times

Answer:

[tex]\Large \boxed{\frac{35}{6} }[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{700}{120}[/tex]

Reduce and simplify the fraction to lowest terms.

[tex]\displaystyle \frac{20(35)}{20(6)}[/tex]

[tex]\displaystyle \frac{35}{6}[/tex]

Give another name plane L

Answers

Answer:

Any one of these three works:

plane MOU

plane MNU

plane NOU

Step-by-step explanation:

A plane can be named by a single letter, such as L in this problem, or by any three non-collinear points that lie on the plane. Non-collinear points are points that do not all lie in a single line.

Points M, N, O, and U lie on plane L, so you can choose any 3 of the 4 points to name the plane with, but make sure all 3 points are non-collinear.

To name plane L with points, you cannot use points MNO together since they are collinear, but you can name it using point U plus any two of the points M, N, and O.

plane L can be named

plane MOU

plane MNU

plane NOU

Do not name it plane MNO

PLEASE help me with this question! No nonsense answers please. This is really urgent.

Answers

Answer:

15.6 ft²

Step-by-step explanation:

Given:

Radius (r) of circle = 5.7 ft

m<CBD = 55°

Required: Area of the shaded sector

SOLUTION:

Area of shaded sector = θ/360*πr²

Where,

θ = 55°

π = 3.14

r = 5.7 ft

Plug in your values

[tex] Area = \frac{55}{360}*3.14*5.7^2 [/tex]

[tex] Area = \frac{55}{360}*3.14*32.49 [/tex]

[tex] Area = 15.59 [/tex]

Area of shaded sector to nearest tenth = 15.6 ft²

Answer:

unij.,hsakj hdku ugkzsssssssjbfskjgfbskufjbghjbgfhjbghbfkjhbfsdf  mdftedtmtedemedeedttfgtubjcufttttttttgxdcgfvcdhfvvvvvdyuyuyuyfyfyfftftftftftyytftfftftffttyfjvhghfhgfghfgfghfhgfghfhgfghfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfhf

Step-by-step explanation:

u suck balls

1/3(12-6x)=4-2x I need help pls

Answers

Answer:

no solution

Step-by-step explanation:

1/3(12-6x)=4-2x

4-1.3x=4-2x

4=4-0.7x

0=0.7x

ns

PLEASE HELP
Arrange the functions for which the result is a non-infinite value and the limit exists in ascending order of their limit values as x tends to infinity.

Answers

Answer:

h,k,i,m,g,l

Step-by-step explanation:

I did all the work and i(x) limt should = -.25 and k(x) =0 but it said it was wrong.  f(x) and j(x) cant be used, so my guess is to switch i(x) and k(x)

The answer is given in the image below.

Do all functions have limits?

One of the fundamental standards of calculus is limits (limits of a function); it offers the fee of a function at a particular factor called limit. Limits are used to calculate the exact vital of the function. Not all functions include limits. A few functions no longer have any restrictions as the variable has a tendency to infinity.

What are examples of nonfunctions?

The equations y = ± x and x 2 + y 2 = 9 are examples of non-function due to the fact there is at least one -price with or greater -values.

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PLEEEEEEEASE HELLLP What is the midpoint of segment RT with endpoints at (-5,2) and (1, -3)?

Answers

Answer:

-2, -1/2

Step-by-step explanation:

Step-by-step explanation:

The midpoint of a line segment between two points is given by

[tex]M = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]

where ( x1 , y1) and ( x2 , y2) are the points

From the question

The midpoint of the line segment using points (-5,2) and (1, -3) is

[tex]M = ( \frac{ - 5 + 1}{2} , \frac{2 - 3}{2} )[/tex]

[tex]M = ( - \frac{ 4}{2} , - \frac{1}{2} )[/tex]

We have the final answer as

[tex]M = ( - 2, - \frac{1}{2} )[/tex]

Hope this helps you

Which is the simplified form of x-12?
Help

Answers

Answer:

1 / x^12

Hope this helped!!!

Answer: c)

Answer:

1 / x^12

Which of the following sets represents a function? {(1, 2), (3, 2), (5, 7)} {(3, 5), (-1, 7), (3, 9)} {(1, 2), (1, 4), (1, 6)}

Answers

Answer:

{(1, 2), (3, 2), (5, 7)}

Step-by-step explanation:

A function has a one to one correspondence

Each x can go to only 1 y value

{(1, 2), (3, 2), (5, 7)} function

{(3, 5), (-1, 7), (3, 9)} 3 goes to more than 1 y value

{(1, 2), (1, 4), (1, 6)} 1 goes to more than 1 y value

Answer:

[tex]\huge \boxed{ \{(1, 2), (3, 2), (5, 7)\} }[/tex]

Step-by-step explanation:

[tex]\sf A \ function \ is \ a \ relation \ if \ each \ x \ value \ is \ for \ each \ y \ value.[/tex]

[tex]\{(1, 2), (3, 2), (5, 7)\} \ \sf represents \ a \ function.[/tex]

[tex]\{(3, 5), (-1, 7), (3, 9)\} \ \sf does \ not \ represent \ a \ function.[/tex]

[tex]\{(1, 2), (1, 4), (1, 6)\} \ \sf does \ not \ represent \ a \ function.[/tex]

The sum of the cubes of 3 numbers which are in the ratio 1:2:3 is 7776. Find the numbers

Answers

the numbers - [tex]x,2x,3x[/tex]

[tex]x^3+(2x)^3+(3x)^3=7776\\x^3+8x^3+27x^3=7776\\36x^3=7776\\x^3=216\\x=6\\2x=12\\3x=18[/tex]

6,12,18

Write an equation for a parabola with a focus of (1,-2) and a directrix of y=6

Answers

Answer:

y = - [tex]\frac{1}{16}[/tex](x - 1)² + 2

Step-by-step explanation:

Any point (x, y) on the parabola is equidistant from the focus and the directrix.

Using the distance formula

[tex]\sqrt{(x-1)^2+(y+2)^2^}[/tex] = | y - 6 |

Square both sides

(x - 1)² + (y + 2)² = (y - 6)² ( expand the factors in y )

(x - 1)² + y² + 4y + 4 = y² - 12y + 36 ( subtract y² - 12y from both sides )

(x - 1)² + 16y + 4 = 36 ( subtract 4 from both sides )

(x - 1)² + 16y = 32 ← subtract (x - 1)² from both sides )

16y = - (x - 1)² + 32 ( divide all terms by 16 )

y = - [tex]\frac{1}{16}[/tex] (x - 1)² + 2

PLEASE HELP:

On a number​ line, suppose point E has a coordinate of 5​, and EG=4. What are the possible coordinates of point​ G?

The possible coordinates for G are ___
(Type integers or decimals. Use a comma to separate answers as​ needed.)

Answers

Answer:

G = 1, 9.

Step-by-step explanation:

There are two cases to this problem: G is either to the left or right of E. If G is to the left of E, then G = 5 - 4 = 1 and if G is to the right of E, then G = 5 + 4 = 9. Therefore, our answer is G = 1, 9.

if the area of the rectangle is 120, what is the area of triangle cpd

Answers

Answer:

Step-by-step explanation:

area of rectangle=120

find area of CPD

area=1/2  (area of the rectangle)

area =  1/2×120=60

The area of triangle CPD IS 30 square units.

If the area of the rectangle is 120, then the area of triangle CPD is 30.

The area of a rectangle is given by the formula:

Area = length × width

In this case, the length of the rectangle is 120/width.

The area of a triangle is given by the formula:

Area = (1/2) × base × height

The base of triangle CPD is the width of the rectangle, and the height of triangle CPD is half the length of the rectangle.

Therefore, the area of triangle CPD is:

(1/2) × width × (120/width) = 30

So the answer is 30.

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please help me as soon as you can please​

Answers

Answer:

f(x) = 5 * ( 8/5) ^x

Step-by-step explanation:

f(x) = a b^x

Let x = 0

5 = a * b^0

5 = a*1

a = 5

Let x = 1

8 = 5 * b^1

Divide each side by 5

8/5 = b

f(x) = 5 * ( 8/5) ^x

what do you think would happen to a person if mortor neuron from the grey matter of spinal cord is removed?​

Answers

Step-by-step explanation:

Introduction

Until World War II, a serious spinal cord injury (SCI) usually meant certain death. Anyone who survived such injury relied on a wheelchair for mobility in a world with few accommodations and faced an ongoing struggle to survive secondary complications such as breathing problems, blood clots, kidney failure, and pressure sores. By the middle of the twentieth century, new antibiotics and novel approaches to preventing and treating bed sores and urinary tract infections revolutionized care after spinal cord injury. This greatly expanded life expectancy and required new strategies to maintain the health of people living with chronic paralysis. New standards of care for treating spinal cord injuries were established: reposition the spine, fix the bones in place to prevent further damage, and rehabilitate disabilities with exercise.

Today, improved emergency care for people with spinal cord injuries, antibiotics to treat infections, and aggressive rehabilitation can minimize damage to the nervous system and restore function to varying degrees. Advances in research are giving doctors and people living with SCI hope that spinal cord injuries will eventually be repairable. With new surgical techniques and developments in spinal nerve regeneration, cell replacement, neuroprotection, and neurorehabilitation, the future for spinal cord injury survivors looks brighter than ever.

PLEASE FOR THE LOVE OF FOOD ANSWER MY QUESTION!

Given that a quadrilateral PQRS is a parallelogram, PQ and RS are opposite sides, PQ = 7x + 16, RS = 5x +28, and QR = 67 which of the following statements are correct? More than one answer may be correct.

Answers

Answer:

PQ = 58

Perimeter = 250

Opposite sides are congruent

Step-by-step explanation:

PQ = 58:

Because PQRS is a parallelogram, PQ equals RS.

1. Set up the equation and solve

7x + 16 = 5x + 28

2x = 12

x = 6

2. Plug in x into PQ

7(6) + 16 = 58

Perimeter = 250:

PQ = RS and QR = SP

1. Add the sides

58 + 58 + 67 + 67 = 250

Opposite sides are congruent:

definition of a parallelogram

hi i need help once again lol A company asked its employees how much time they spend reading and responding to email. The line plot displays the employees' responses. How many total hours do the employees spend using email?

Answers

Answer:

C

Step-by-step explanation:

you multiply each dot by the fraction of hours it is under. you add everything up and you should get 66/8 which is equivalent to 8 and 1/4

Answer:

Is c

Step-by-step explanation:

For plato Users

I NEED HELP PLEASE FIRST PERSON TO GET ANSWER RIGHT GETS 5 STARS !

Answers

Answer:9/5

Step-by-step explanation:

In the figure shown, what is the measure of angle x? (5 points) 115 degrees 130 degrees 145 degrees 150 degrees

Answers

Answer:

x=115

Step-by-step explanation:

180 - (115) =65(triangle)

65 + x = 180(on a line)

x=180-65

x = 115

Answer:

115 degrees

Step-by-step explanation:

the person above me is right, but there is an easier way.

Just add 50 and 65 degrees and boom you have your answer.

Two Fair six-sided dice are rolled and the face values are added. What is the probability of obtaining an even number less than 7?

Answers

Answer:

The probability is 1/4

Step-by-step explanation:

In this question, we are interested in calculating the probability of obtaining even numbers which are less than 7, when two fair six-sided dice are rolled.

Now, mathematically the probability will be;

number of even numbers less than 7/total number of outcomes

Firstly, the total number of outcomes is 36. Now to get the number of even numbers less than 7, we need to construct tables that could show our sample space.

Please check attachment for this.

Now from the constructed table, we can find the number of even numbers less than 7.

By counting, we can see that the we have 9 even numbers which are less than 7

Thus, the probability of selecting an even number which is less than 7 is;

9/36 = 1/4

Use linear regression to predict the length of a 40-month-old animal. The ages and lengths of several animals of the same species are recorded in the following table: (2 points)

Answers

Answer:

Aw what animal

Step-by-step explanation:

Srry I need pointse

Jasmine is having friends over to watch a football game. She has 2 1/2 hours until her guests arrive. She spends 2/5 of that time cleaning and the rest of the time preparing snacks. How much time does Jasmine spend preparing snacks?

Answers

Answer:

1 Hour and 30 Minutes

OR

1 1/2 Hours

Step-by-step explanation:

Convert 2 1/2 hours to minutes.

That is 150

Multiply 2/5 with 150.

Subtract that from 150.

It gives 120 minutes.

Convert that back to Hours.

You get 1 Hour and 30 Minutes or 1 1/2 Hours.

A fraction is a way to describe a part of a whole. The time that is spent by Jasmine to prepare for snacks is 2.1 hours or 2 1/10 hours.

What is a Fraction?

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

What is a Mixed Fraction?

A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator. A mixed fraction can be converted as,

2 1/2

= (2×2 + 1)/2

= 5/2

= 2.5

Given that Jasmine has 2 1/2 hours until her guests arrive. She spends 2/5 of that time cleaning and the rest of the time preparing snacks. Therefore, the time spent on preparing snacks is,

Time spent on preparing for snacks = 2 1/2 - 2/5

                                                            = 5/2 - 2/5

                                                            = 2.5 - 0.4

                                                            = 2.1 hours

                                                            = 2 1/10

Hence, the time that is spent by Jasmine to prepare for snacks is 2.1 hours or 2 1/10 hours.

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Solve the triangle. A = 51°, b = 14, c = 6 A. a ≈ 14.9, C ≈ 28.1, B ≈ 100.9 B. a ≈ 11.2, C ≈ 24.1, B ≈ 104.9 C. a ≈ 14.9, C ≈ 24.1, B ≈ 104.9

Answers

Answer:

(B) has the closest values.

Step-by-step explanation:

Solve the triangle: A = 51°, b = 14, c = 6

A. a ≈ 14.9, C ≈ 28.1, B ≈ 100.9

B. a ≈ 11.2, C ≈ 24.1, B ≈ 104.9

C. a ≈ 14.9, C ≈ 24.1, B ≈ 104.9

Using the cosine rule,

a^2 = b^2+c^2-2bc (cos(A))

= 196+36 - 2(14)(6)cos(51)

=  196+36 - 105.72

= 126.27

a = sqrt(126.27)

= 11.24

using sine rule,

sin(C)/sin(A) = 6/11.24

sin(C) = 6/11.24*sin(51)= 0.41495

C = arcsin(0.41495 = 24.5 degrees, reasonably close to the given value, probably due to the answer used the rounded value of a.

B = 180-51-24.5 =104.5

Out of the given options, only (B) has the correct value of a and C

Using a sample of 60 undergraduates, Dr. Hotchkins discovers a negative correlation between stress and emotional well-being. While looking at a scatterplot of the data, Dr. Hotchkins realizes there are 4 outliers in the data, all for individuals with extremely high scores on stress and extremely high scores on well-being. What is the effect of these outliers on the correlation

Answers

Answer and explanation:

A negative correlation means a relationship between two variables whereby each variable affects the other such that an increase in one variable means a decrease in the other and vice versa. This is the situation with the correlation graph/scatter plot of Dr. Hotchkins: An increase in stress would cause a decrease in emotional well being and vice versa

An Outlier is a data point on the scatter plot that does not fall into the pattern of the correlation graph. From the above, 4 points are outliers: extremely high points on stress and emotional well being. These points would affect (increase or decrease) the correlation coefficient depending on where they fall in the pattern. In this case there are 4 outliers out of 60 data points and we know that the more outliers there are the more effect they have on the correlation coefficient and vice versa(also depending on where the outlier is on the scatter plot)

3x is a ____ of 3x^2 - 6x^3.

Answers

Answer:

[tex]\boxed{factor}[/tex]

Step-by-step explanation:

Hey there!

3x * x = 3x^2

3x * 2x = 6x^3

So 3x is a factor of 3x^2 - 6x^3.

Hope this helps :)

Please help, 50 points! :)
PDF attached below

Answers

Answer:

See below

Step-by-step explanation:

Attachment 1 : (a) Remember that it mentions x is the years since 1900. That would mean that the table is a bit different. To create this " new table " simply subtract 1900 from the years provided, and substitute.

To create this equation we will need a regression calculator. The equation will be as follows.

y = 0.125873x - 7.11916 ( note that you can double check this equation be substituting points from the table in the attachment )

(b) 2025 - 1900 = 126 years,

y = 0.125873(125) - 7.11916 = $ 8.614965

Minimum Wage : $ 8.614965

Attachment 2 : The rest of the problems can be solved similarly...

(a) Quadratic Regression Equation : - 0.49311x² + 23.2798x + 996.029

(b) - 0.49311(20)² + 23.2798(20) + 996.029 = 1264.381 mg/cm³

Attachment 3 : (a) Exponential Regression : 9.08292(1.09965)ˣ

(b) 9.08292(1.09965)⁶⁰ = [tex]2713.27743\dots[/tex] ( About 2713 recommendations )

A factory costs $280,000. You forecast that it will produce cash inflows of $80,000 in year 1, $140,000 in year 2, and $220,000 in year 3. The discount rate is 12%. What is the value of the factory?

Answers

Answer:

=$339,627.36

Step-by-step explanation:

PV = FV/(1+R)^n

where

PV = Present Value

FV = Future Value

R = Rate

n = number of periods

PV

Year 1=$80,000

Year 2=$140,000

Year 3=$220,000

r=12%=0.12

Year 1:

PV=80,000 / (1+0.12)^1

=80,000 / 1.12

=$71,428.57

Year 2:

PV=140,000 / (1+0.12)^2

=140,000 / (1.12)^2

=140,000 / 1.2544

=$111,607.14

Year 3:

PV=220,000 / (1+0.12)^3

=220,000 / (1.12)^3

=220,000 / 1.404928

=$156,591.65

Value of the factory= 71,428.57 + 111,607.14 + 156,591.65

=$339,627.36

Find the measure Of PR

Answers

Answer:

18

Step-by-step explanation:

The formula for this is a x b = c x d where a is SR, b is FR, c is QR and d is PR. This will give us the equation 9(16) = 8(5x + 8); 144 = 40x + 64; 80 = 40x; x = 2. Now, plug this into PR which will be 5(2)+8 = 18. This is your answer.

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