can someone please help me with Arithmetic Sequences

Can Someone Please Help Me With Arithmetic Sequences

Answers

Answer 1

Answer:

287

Step-by-step explanation:

Sum of A Finite Arithmetic Sequnece is

[tex] \frac{a _{1} + a _{n} }{2} n[/tex]

Where a1 is first term

an is final term

N is the number of terms.

We know a1 is 1

An is 40 but we don't know n.

To find n, we use the definition of a Arithmetic Sequence

[tex]a _{n} = a + (n - 1)d[/tex]

where d is the common difference. Let use the final term, 40 as a example.

Here the common difference is 3 so we have

[tex]40= 1 + (n - 1)3[/tex]

[tex]39 = 3(n - 1)[/tex]

[tex]13 = n - 1[/tex]

[tex]14 = n[/tex]

So we have 14 terms in this finite series.

Now we compute

[tex] \frac{1 + 40 }{2}(14) = \frac{41}{2} (14) = 41 \times 7 = 287[/tex]

So the answer is 287


Related Questions

Is the equality below true or false? Explain your answer.

Answers

Answer:

False. Sin is not a linear function. Thus, two smaller sin funstions will not equal a larger.

Step-by-step explanation:

What is 1.75 in standard form?

Answers

Answer:

1 3/4 I think.

Hope this helps

Necesito la respuesta con explicación de:
(6+5)-16

Answers

PEMDAS is the way to solve these types of equations

  [tex](6+5)-16=(11)-16 = 11 - 16 = -5[/tex]

Hope that helps!

The answer is -5 I hope this helps you

How many solutions does the system of equations below have?
5x + y = 8
15x + 15y = 14
no solution
one solution
infinitely many solutions

Answers

Answer:

One solution                    

Step-by-step explanation:

5x + y = 8

15x + 15y = 14

Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form

So we solve for "y" in the equation "5x + y = 8"

5x + y = 8

Step 1: Subtract 5x from both sides.

5x + y − 5x = 8 − 5x

Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped

y = −5x + 8

Now we can solve using substitution:

We substitute "-5x + 8" into the equation "15x + 15y = 14" for y

So it would look like this:

15x + 15(-5x + 8) = 14

Now we just solve for x

15x + (15)(−5x) + (15)(8) = 14(Distribute)

15x − 75x + 120 = 14

(15x − 75x) + (120) = 14(Combine Like Terms)

−60x + 120 = 14

Step 2: Subtract 120 from both sides.

−60x + 120 − 120 = 14 − 120

−60x = −106

Divide both sides by -60

[tex]\dfrac{ -60x }{ -60 } = \dfrac{ -106 }{ -60 }[/tex]

Simplify

[tex]x = \dfrac{ 53 }{ 30 }[/tex]

Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"

[tex]\mathrm{So\:it\:would\:look\:like\:this:\ y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}[/tex]

[tex]\mathrm{Now\:lets\:solve\:for\:"y"\:then}[/tex]

[tex]y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}[/tex]

[tex]\mathrm{Express\: -5 \times \dfrac{ 53 }{ 30 }\:as\:a\:single\:fraction}[/tex]

[tex]y = \dfrac{ -5 \times 53 }{ 30 } +8[/tex]

[tex]\mathrm{Multiply\:-5 \:and\:53\:to\:get\:-265 }[/tex]

[tex]y = \dfrac{ -265 }{ 30 } +8[/tex]

[tex]\mathrm{Simplify\: \dfrac{ -265 }{ 30 } \:,by\:dividing\:both\:-265\:and\:30\:by\:5} }[/tex]

[tex]y = \dfrac{ -265 \div 5 }{ 30 \div 5 } +8[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]y = - \dfrac{ 53 }{ 6 } +8[/tex]

[tex]\mathrm{Turn\:8\:into\:a\:fraction\:that\:has\:the\:same\:denominator\:as\: - \dfrac{ 53 }{ 6 }}[/tex]

[tex]\mathrm{Multiples\:of\:1: \:1,2,3,4,5,6}[/tex]

[tex]\mathrm{Multiples\:of\:6: \:6,12,18,24,30,36,42,48}[/tex]

[tex]\mathrm{Convert\:8\:to\:fraction\:\dfrac{ 48 }{ 6 }}[/tex]

[tex]y = - \dfrac{ 53 }{ 6 } + \dfrac{ 48 }{ 6 }[/tex]

[tex]\mathrm{Since\: - \dfrac{ 53 }{ 6 }\:have\:the\:same\:denominator\:,\:add\:them\:by\:adding\:their\:numerators}[/tex]

[tex]y = \dfrac{ -53+48 }{ 6 }[/tex]

[tex]\mathrm{Add\: -53 \: and\: 48\: to\: get\: -5}[/tex]

[tex]y = - \dfrac{ 5 }{ 6 }[/tex]

[tex]\mathrm{The\:solution\:is\:the\:ordered\:pair\:(\dfrac{ 53 }{ 30 }, - \dfrac{ 5 }{ 6 })}[/tex]

So there is only one solution to the equation.

i need it in 5 mins please

Answers

Answer:

hope u understand

180°-142°=38°

x=38°

here is your answer

mark as brilliant and follow pls

Answer:

142

Step-by-step explanation:

because it is an obtuse angle and it is equvilent to an exteroir angle which is also 142 degrees

pls mark brainliest

In New York, state sales tax is 8. 5%. If a book cost 12. 99 what is the total cost Simon will pay for a book

Answers

Answer:

14.09415

Step-by-step explanation:

Given the graphs of f(x) = 2x + 1 and g(x) = 5x – 2, what is the solution to the equation f(x) = g(x)?A)0B)1C)3D)–2

Answers

Answer:

x=1

Step-by-step explanation:

f(x) = 2x + 1

g(x) = 5x – 2

f(x) = g(x)

2x+1 = 5x-2

Subtract 2x from each side

2x+1 = 5x-2-2x

1 = 3x-2

Add 2 to each side

1+2 =3x-2+2

3 = 3x

Divide by 3

3/3 =3x/3

1 =x

Brainliest!


Adam dove 512 miles in 8 hours. The average speed for his trip is 512= x8


Using the formula d= rt, solve for x

Answers

Answer: 64 mph

Step-by-step explanation:

d = rt

512 = 8x

x = 512/8 = 64 mph

solve for x using logarithm:
25^x-3(5^x)=0​

Answers

Answer:

[tex]x = 0.68[/tex]

Step-by-step explanation:

We would like to find out the value of x using logarithms of the given equation .The equation is ,

[tex]\longrightarrow 25^x - 3(5^x)=0\\[/tex]

Add [tex]3(5^x)[/tex] on both sides,

[tex]\longrightarrow 25^x = 3(5^x) [/tex]

Using log to the base 10 on both sides, we have;

[tex]\longrightarrow log_{10}(25^x) = log_{10}\{3(5^x)\}[/tex]

Recall that [tex] log(ab ) = log\ a + log\ b [/tex] .

[tex]\longrightarrow log_{10}(25^x)=log_{10}3 + log_{10}5^x [/tex]

Recall the properties of logarithm as [tex] log\ a^b = b\ log\ a [/tex] .

[tex]\longrightarrow xlog25 = log_{10}3 + xlog_{10}5 [/tex]

Again we can rewrite it as ,

[tex]\longrightarrow xlog(5^2)=log_{10}3+xlog_{10}5\\ [/tex]

[tex]\longrightarrow 2x\ log_{10}5 = log_{10}3+xlog_{10}5 \\ [/tex]

[tex]\longrightarrow 2x\ log_{10}5-x\ log_{10}5 = log_{10}5 [/tex]

Simplify,

[tex]\longrightarrow x\ log_{10}5=log_{10}3 [/tex]

Divide both sides by log5 ,

[tex]\longrightarrow x =\dfrac{log_{10}3}{log_{10}5} [/tex]

Put on the values of log 3 and log5 ,

[tex]\longrightarrow x =\dfrac{0.47}{0.69} [/tex]

Simplify,

[tex]\longrightarrow \underline{{\underline{\boldsymbol{ x = 0.68}}}}[/tex]

And we are done!

Please Help 20 Points

Answers

Answer:

2nd one

Step-by-step explanation:

Just the 2nd one

Answer:

B Is the answer.

Step-by-step explanation:

The given curve will not pass through the even power. So when x=2, it will touch the x- axis at x=2, but not pass through it.

Hope this helps

At a local high school,the probability that the student speaks kankanaey and ilocano is 40%.The probability that a student speaks kankanaey is 70%.What is the probability that the student speaks ilocano given that he speaks kankanaey?​

Answers

Using conditional probability, it is found that there is a 0.5714 = 57.14% probability that the student speaks ilocano given that he speaks kankanaey.

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.

In this problem, the events are given as follows:

Event A: Student speaks kankanaey.Event B: Student speaks ilocano.

Hence, the parameters are given as follows:

[tex]P(A \cap B) = 0.4, P(A) = 0.7[/tex]

Then, the probability that the student speaks ilocano given that he speaks kankanaey is given by:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.7} = 0.5714[/tex]

More can be learned about conditional probability at https://brainly.com/question/14398287

The lengths of the sides of a triangle are in the extended ratio 5: 8:10. The perimeter of the triangle is 115 cm. What are the lengths of the sides?
The lengths of the sides in cm are ____

Answers

Given :

The length of the sides of the triangle are in the ratio 5:8:10 .The Perimeter of the Triangle is 115 cm.

To Find :

The length of the sides of the triangle.

Solution :

Let us assume the sides be 5x cm, 8x cm and 10x cm.

We know,

[tex]\qquad{ \bold{ \pmb{Sum \: of \: all \: sides \: of \: the \: triangle = Perimeter_{(Triangle)}}}}[/tex]

So, Substituting the values :

[tex]\qquad { \dashrightarrow{ \sf{5x + 8x + 10x = 115}}}[/tex]

[tex]\qquad { \dashrightarrow{ \sf{23x= 115}}}[/tex]

[tex]\qquad { \dashrightarrow{ \sf{ \dfrac{23x}{23} = \dfrac{115}{23} }}}[/tex]

[tex]\qquad { \dashrightarrow{ \bf{ x = 5 }}}[/tex]

Therefore,

The length of the sides of the triangle are :

[tex]\qquad { \dashrightarrow{ \sf{ 5x \: cm= 5 \times 5 \: cm = \bf \: 25\: cm }}}[/tex]

[tex]\qquad { \dashrightarrow{ \sf{ 8x \: cm= 8 \times 5 \: cm = \bf \: 40 \: cm }}}[/tex]

[tex]\qquad { \dashrightarrow{ \sf{ 10x \: cm= 10 \times 5 \: cm = \bf \: 50 \: cm }}}[/tex]

Step-by-step explanation:

Given:-

Ratio of sides of triangle is 5:8:10 , with perimeter of 115cm.

To Find :-

Measurement of each side

Solution :-

let the each side be 5x , 8x , 10x respectively

we know that ,

perimeter of triangle = sum of all sides

putting the known values ,

115cm = 5x + 8x + 10x

115/23 = x

5 = x

putting the value of x we get ,

each side is 25cm , 40cm , 50cm

13<2x<24 I need help in this questions pls help me asap

Answers

Answer:

13/2<x<12

or  (13/2, 12)

Step-by-step explanation:

break the promblem into two seperate equations and solve.

The graph of a function f is shown below find f(0). i don’t really understand these but I have to get this lesson done for class.

Answers

Answer:  4

Explanation:

Locate x = 0 on the x axis number line.

Then move up or down until you reach the blue curve. In this case we move upward.

You should arrive at y = 4

This means (x,y) = (0,4) is a point on the blue cubic curve, and that f(0) = 4.

6. James delivers 435 circulars in 3 hours. At this rate, how many circulars can he deliver in 4 5 hours?​

Answers

Answer:

580 circulars

Step-by-step explanation:

Formula: Number of circulars divide by Hours

435 circulars / 3 hours = x circulars / 4.5 hours

145 circulars / 1 hour = x circulars / 4 hours

(145 circulars / 1 hour) * 4 hours = x circulars

580 circulars = x circulars

x = 580 circulars, delivered in 4 hours

Hence, at this rate James will delivers 580 circulars in 4 hours.

[RevyBreeze]

James will be able to deliver 600 circulars in 4 hrs

Which expression is equivalent to 16w² + 24w + 9

Answers

Not sure what you want to me to do with the expression. I do not see an attachment.
You cannot simplify the expression anymore.

You can factor it though.

Answer:
(4w + 3)^2

The expression 16w² + 24w + 9 can be written in form as (4w+3)².

What is the expression?

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given as:

⇒ 16w² + 24w + 9

To factor this expression, we can use the following steps:

Find two numbers that multiply to 16w² and add to 24w. The two numbers are 4w and 6w.

Create two binomials with the two numbers found in step 1. The binomials are 4w+3 and  (4w+3).

Multiply the two binomials together to get the factored form of the expression. The factored form is  (4w+3)².

Therefore, the equivalent expression to 16w² + 24w + 9 is (4w+3)².

Learn more about Expressions here :

brainly.com/question/21751419

#SPJ2

Which statement about the possible designs is true, given the owner’s requirements? three circular displays can be placed in one row, exactly as shown on the given grid. two circular displays can be placed so they are each the same distance from the cashier’s station. the maximum number of circular displays that can be used is 4. the maximum number of circular displays that can be used is 5.

Answers

Answer:

The maximum number of circular displays that can be used is 4.

Or C on edge

Step-by-step explanation:

I need help can u pleas help me thank have a blessed day.

Answers

Answer:

I believe the answer is A

I NEED HELP!! also please be sure its the right answer!!

Answers

See the attached picture with the solution.

please help with this!

Answers

Answer:

See below.

Step-by-step explanation:

The y-intercept is the point in which the line intersects on the y-axis.

In this case, the y-intercept is (0,4), or 4.

-hope it helps

Samara runs 4 miles in 38 minutes. If she continues running at the same pace, how many minutes will it take her to run 12 miles?

Enter the correct answer in the box.

Answers

Answer:

114 minutes

Step-by-step explanation:

samara runs 4 miles in 38 minutes

---------------------------------------------------

time taken to cover a distance of 12 miles:

4 miles in 38 minute12 ÷ 4 = 33 × 38 minutes114 minutes

many minutes will it take her to run 12 miles is 114 minutes

Suppose you deposit $4000 in a savings account that pays interest at an annual rate of 3.1% compounded continuously How many years will it take for the balance in your savings account to reach $5625.41?

15 Minutes Remaining

Answers

The number of years it takes for the balance in your savings account to reach $5625.41 is 11 years

How to calculate compound interest

The formula for calculating compound interest is expressed as;

A =P(1+r)^t

Given the following

A =  $5625.41

P = $4000

r = 0.031

Substitute the given parameters into the formula to have:

$5625.41 = 4000(1.031)^t
1.4063525 = (1.031)^t
t = ln(1.4063525)/ln(1.031)

t = 0.34074/0.03052

t = 11 years

Hence the number of years it takes for the balance in your savings account to reach $5625.41 is 11 years

Learn more on compound interest here: https://brainly.com/question/24924853

good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Answers

Answer:

B. 1, 4, 16, 64...

D. 2, 8, 32, 128...

To find a common ratio, you divide each term by the previous term.

So, let's do it for each sequence.

A.

6 / 2 = 3

10 / 6 = 1.6667

It is incorrect because we did not get 4.

B.

4 / 1 = 4

16 / 4 = 4

It is correct because we got 4.

C.

400 / 1600 = 1/4

100 / 400 = 1/4

It is incorrect. The common ratio is 1/4.

D.

8 / 2 = 4

32 / 8 = 4

It does have a common ratio of 4. It is correct.

E.

12 / 16 = 0.75

8 / 12 = 0.6667

It does not have a common ratio of 4.

F.

1/8 / 1/2 = 1/4

1/32 / 1/8 = 1/4

It does not have a common ratio of 4. It has a common ratio of 1/4.

#B

Check ratio

4/1=416/4=4

Common ratio=r=4

#C

8/2=432/8=4

Common ratio=r=4

Option B and C are correct

you pack sandwiches for a mountain hike with your friends. Each sandwich takes 2 slices of bread, and each hiker eats one sandwich.
How many slices of bread are used for n hikers?

Answers

[tex][Hello,BrainlyUser][/tex]

Answer:

2n

Step-by-step explanation:

You pack sandwiches for a mountain hike with your friends.

Each [ meaning 1]  sandwich takes 2 slices of bread.

If each hiker eats one sandwich, and there are 'n' hikers

Thus, to find the number of breads used for 'n' hikers, we multiplied 2 by n

Hence, the expression will be 2n

[CloudBreeze]

1. What is the side length of Cube B?

2. What is the volume of Cube A?

3. What is the volume of Cube B?

Answers

Answer:

1. 8 cm

2. 64 cm

3. 512 cm

Step-by-step explanation:

The side lengths of cube are 8

The formula for volume is the length*width*height

A-4*4*4

4*4*4=64 cm

B-8*8*8=512 cm

Answer:1. 8 cm2. 64 cm3. 512 cmStep-by-step explanation:The side lengths of cube are 8The formula for volume is the length*width*heightA-4*4*44*4*4=64 cmB-8*8*8=512 cm

PLEASE HELP ME ASAP! Math 7th grade. Worth 38 points.

Answers

Answer:

Part A. x = 45°

Part B. Acute triangle

Step-by-step explanation:

Hope this help you.

Uh...I need help about my speaking.

Can you give me some tips and important things about "Myself" speaking?

Step-by-step explanation:

85+50+x=180

135+x=180

x=180-135

x=45

A) 45 degrees

B) 45 degree is a acute angle.

Find the volume of the following cylinder. Use π=3.14
V=

Answers

Answer:

it would be approx. 3015.93cm3

Step-by-step explanation:

Hope it helps!!!!

Show that the equation x3 + 4x = 1 has a solution between x = 0 and x = 1

Answers

Intermediate Value Theorem: Suppose that  f(x)  is an arbitrary, continuous function on an interval  [a,b] . If there exists a value  L  between  f(a)  and  f(b) , then there exists a corresponding value  c∈(a,b) , such that  f(c)=L

f(x)=x3+4x−1

f(0)=−1f(1)=4

Since the function changes sign in the interval  (0,1) , hence there exists a  c∈(0,1)  such that  f(c)=0

How much money will be in an account at the end of 8 years if $4,000 is deposited at 4% interest compounded 2 times per year? Assume no deposits or withdrawals are
made.
There will be about in the account at the end of 8 years.
(Round to the nearest dollar as needed.)

Answers

Answer:

$6560

Step-by-step explanation:

interest per year =4+4%=8%

interest in 8 years = 8×8% =64%

Money in account after 8 years= 100%+64%=164% of deposit

=164/100×4000

=$6560

Please mark my answer the brainliest and rate me 5.0*

400 people are asked if they drink tea. 7/10 say yes and 20% of the people who say yes drink at least 3 cups each day. Complete the frequency tree

Answers

Answer:

The problem is not shown:

7 / 10 = 70 %

70% of 400 = 280       drink tea

20% of 400 = 80     drink at least 3 cups / day

(70 - 20)% of 400 = 200 drink tea but not as much as 3 cups / day

30% of 400 = 120  do not drink tea

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