What is the sum of the infinite geometric series? −5+2−4/5+8/25−16/125...

Answers

Answer 1

Answer:

  -25/7

Step-by-step explanation:

The sum of an infinite series with first term 'a' and common ratio 'r' is ...

  S = a/(1 -r)

Your series has a=-5 and r=-2/5, so the sum is ...

  S = (-5)/(1 -(-2/5)) = -5/(7/5) = -25/7

The sum of the series is -25/7.


Related Questions

What is the lateral surface area of the triangular prism?



Round to the hundredths place.

Answers

Answer:

A triangular prism is a three-dimensional shape having two triangular bases and three rectangular sides.

8) A company sells small and large photo books. Each page of a small photo book costs
the same. The table below shows the relationship between the number of pages in a
small photo book and the total cost of the photo book.
Part A) What is the cost per page for a small photo book?
Small Photo Book
Number of Pages
Total Cost ($)
30
20
32
48
57

Answers

The cost per page is $1.5 and 38 pages of the book will cost $57

Proportions

Data;

number of page = 20cost = $30

To solve this question, we have to know the cost of one page of the book.

In the first scenario, 20 pages cost $30, let's find the cost of one page here.

[tex]20 page = \$30\\1 page = x\\x = \frac{30}{20}\\x = 1.5[/tex]

We can confirm our answer here by testing with the second scenario;

[tex]32 page = \$48\\1page = y\\y = \frac{48}{32} = 1.5[/tex]

Now can say that one page of the book cost $1.5, let's divide 57 by this to determine the number of pages

[tex]z = \frac{57}{1.5} \\z = 38[/tex]

From the calculations above, 38 pages of the book will cost $57.

Learn more on proportions here;

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Please Help i need a professional no scam answers that have been happening i need to get allot done bye friday

Answers

Answer:

39%

Step-by-step explanation:

21/125=.168

33/125=.264

.432-.044352=.387648*100=39%

The pie chart below indicates the eye colors of students
in a statistics class
Which of the following could be the percentage of
students with brown eyes?
Eye Colors
O 10%
15%
20%
O 35%
Blue
Brown
Green
Hazel
Gray

Answers

Answer:

15% could be for brown eyes

PLEASE HELP, I'M BEING TIMED ;----;

Find the volume of this triangular prism.
Be sure to include the correct unit in your answer.

Answers

Answer:

196 ft cubed

Step-by-step explanation:

formula = ((bxh)/2) x length

so

7 x 7 = 49

49 / 2 = 24.5

24.5 x 8 = 196

Hope this helps! If you need further help, let me know!

- profparis

A basketball player averaged 20 points a game over the course of six games. His
scores in five of those games were 23, 18, 16, 24, and 27. How many points did he score in the sixth game?

Answers

Hello There!!

Given,

Average Points= 20

No. of games = 6

Total points= 20×6=120

So, Sum of Score of five games= 23+18+16+24+27= 108

Therefore, Score in 6th game= 120-108= 12

Hope this helps

[tex]\sf\large \green{\underbrace{\red{Answer⋆}}}:[/tex]

To find :-

The sixth score of the game

Given :-

All five scores = 23, 18, 16, 24, and 27

The average of all six score = 20

Solution :-

We will use the average formula to find the sixth score.

[tex]average = \frac{total \: of \: all \: scores}{number \: of \: scores} [/tex]

And let the sixth score be x.

[tex]20 = \frac{23 + 18 + 16 + 24 + 27 + x}{6} [/tex]

Now we will cross multiply, the 6 which on L.H.S will come to R.H.S and multiply with 20.

[tex]20 \times 6 = 23 + 18 + 16 + 24 + 27 + x \\ 120 = 108 + x \\ 120 - 108 = x \\ 12 = x[/tex]

Result :-

The sixth score by the baseball player is 12.

If F(x) and f-1(x) are inverse functions of each other and f(x) = 2x+5, what is f-1( 8) ?


O -1
O 3/2
O 41/8
O23

Answers

Answer:

the answer is 3/2........

all of these are service industries except zoo bakery law firm or travel agency

Answers

Answer:

A zoo

Step-by-step explanation:

A zoo can't be consisdered a "service industry" compared to the other ones.

So

A.) Zoo

is your answer

PLEASE HELP FOR BRAINLIEST ;-;

Find the area of this parallelogram. Be sure to include the CORRECT UNIT in your answer.

Answers

Answer:

182ft^2

pls give brainlyist

Step-by-step explanation:

area of a parallelogram is base  * hight

13ft* 14ft

182ft^2

HELLLPPLPPPP MUDDLE SCHOOLLL!!!!

Answers

Answer:

D.

Thats what gauth.math said

Convert 1.5 kg to grams

Answers

Answer:

  1500 g

Step-by-step explanation:

The SI prefix "kilo-," abbreviated "k," means 1000. So, 1.5 kilograms is ...

  1.5×(1000 g) = 1500 g

Kerry participated in a fundraiser for the Children's Wish Foundation yesterday. She sold 115 pins for $3 each, 214 ribbons for $4 each, 85 coffee mugs for $7 each, and 347 baseball hats for $9 each. Calculate the average amount Kerry raised per item.

Answers

Answer:

  $6.46

Step-by-step explanation:

The average per item is the quotient of the total raised and the number of items. The total raised is the sum of the products from multiplying the number of items at a given price by that price.

__

A weighted average is computed easily using a spreadsheet or calculator.

Here, the average amount per item is computed by a calculator to be ...

  $6.46 per item, average

9)

What is the complete factorization of x2 + 4x-45?
OA (x + 15)(x-3)
OB. (x- 9)(x + 5)
OC. (x + 9)(x - 5)
OD. (x - 15)(x+3)​

Answers

Answer:

C

Step-by-step explanation:

x^2+4x-45

(x+9)(x-5)

since 4x is positive, the larger factor of 45 needs to be positive

that's why the 5 is negative

when solving problems like this, just find two factors of the last number that add up to the middle number

then throw them in parenthesis with an x

Hi,

x2 + 4x − 45 can be factorized to (x + 9)(x - 5).

the correct answer is C (x + 9)(x - 5).

I added a screenshot...

XD


Combined test scores were normally distributed with mean 1493 and standard deviation 342. Find the combined scores that correspond to these percentiles.
​a) 20th percentile
​b) 75th percentile
​c) 80th percentile

a) The combined scores that correspond to 20th percentile is about ___? ​(Round to the nearest integer as​ needed.)

​b) The combined scores that correspond to 75th percentile is about ___? ​(Round to the nearest integer as​ needed.)

​c) The combined scores that correspond to 80th percentile is about ___?​(Round to the nearest integer as​ needed.)

Answers

The combined scores that correspond to 20th percentile is about 1206.

The combined scores that correspond to 75th percentile is about 1724.

The combined scores that correspond to 80th percentile is about 1780.

What is z score?

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given the mean 1493 and standard deviation 342.

a) 20th percentile has a z score of -0.84, hence:

-0.84 = (x - 1493)/342

x = 1206

b) 75th percentile has a z score of 0.675, hence:

0.675 = (x - 1493)/342

x = 1724

c) 80th percentile has a z score of 0.84, hence:

0.84 = (x - 1493)/342

x = 1780

The combined scores that correspond to 20th percentile is about 1206.

The combined scores that correspond to 75th percentile is about 1724.

The combined scores that correspond to 80th percentile is about 1780.

Find out more on z score at: https://brainly.com/question/25638875

a how much will he have in 4. At the age of 30, Jasmine started a retirement account with $50,000 which compounded interest semi-annually with an APR of 4%. She made no further deposits. After 25 years, she decided to withdraw 50% of what had accumulated in the account so that she could con- tribute towards her grandchild's college education. She had to pay a 10% penalty on the early withdrawal. What was her penalty?​

Answers

Answer:

6795.70

Step-by-step explanation:

smart people

After paying 10% penalty on the early withdrawal, Jasmine's penalty for the early withdrawal was calculated to be $5,352.24.

What is the compound interest?

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

here, we have,

We can use the formula for compound interest in ordr to solve this problem.

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal (starting amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, we have the following values,

P = $50,000

r = 1.75% = 0.0175 (since it is compounded semi-annually, n = 2)

t = 25 years

So the final amount after 25 years can be calculated as under

A = 50000(1 + 0.0175/2)^(2×25) = $107,044.84

Jasmine has withdrawn  50% of this amount, which is:

$107,044.84 × 0.5 = $53,522.42

She had to pay a 10% penalty on the early withdrawal, so her penalty would be:

$53,522.42 × 0.1 = $5,352.24

Therefore, the penalty of Jasmine penalty for the early withdrawal was $5,352.24.

Learn more about compound interest :

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A system of equations is shown below.
Equation A: 4x - y = -5
Equation B: x + 2y = 1
Which method eliminates one of the variables?
1.
Multiply equation A by 2 and add the result to equation B.
2.
Multiply equation B by 4 and add the result to equation A.
3.
Multiply equation A by 2 and equation B by 4, and add the results toge
4.
Multiply equation B by 2 and equation A by 4, and add the results toge

Answers

Answer:

this one has to be answer 1

Step-by-step explanation:

4x - y = -5

x + 2y =1

8x - 2y = -10

x + 2y = 1

9x = -9

PLEASE HELP

A bank is offering 2.5% simple intrest on a savings account if 5,000 is deposited what is the balance in a year​?

Answers

Answer:

The principal amount is 5000 dollars = 3, 70,000 rupees (5000 dollars x 74 Rupees)

Rate = 2.5%

Time = 1 year

Now, on putting the values given in the formula

S.I.= 9,250 Rupees

Now we convert it into dollars by diving 9,250 rupees by 74 rupees.

We get,

9250/74 = 125 dollars

Step-by-step explanation:

125 dollars a year!!

Should be correct! :)

5x-2y=42
-3x+2y=-26
which of the following shows the results of the two equation added together?

Answers

Answer:

Step-by-step explanation:

When we add the two equaions, y will be cancelled becaue -2y + 2y = 0.

Thus we can find the value of x.

5x - 2y = 42 -----------(I)

-3x + 2y = -26   {Now add}

2x          = 16

         x = 16/2

        x = 8

Simplify this fraction to the lowest terms 14/12

Answers

Answer:

1 1/6 or 7/6

Step-by-step explanation:

Divide both 14 and 12 by 2

A woman bought some large frames for ​$18 each and some small frames for ​$8 each at a closeout sale. If she bought 21 frames for ​$​248, find how many of each type she bought.

Answers

Answer:

8 large frames and 13 small frames

Step-by-step explanation:

Given:
$18 each = large frames

$8 each = small frames

To Find:

⇒  Bought 21 frames for ​$​248, find how many of each type she bought

Solve:

1 Large frame costs = 18 $

Therefore, x large frames costs = 18x $

{where x is the number of large frames she bought}

1 Small frame costs = 8 $

Therefore, x Small frames costs = 8y $

{where y is the number of small frames she bought}

By the given condition :

18x + 8y = 248        {equation 1}

x + y = 21                 {equation 2}

Solve these equations simultaneously, from second equation we get :

x = 21- y

18⋅(21−y)+8y= 248

378 - 18y+8y = 248

-10y = -130

y = 13

Put y = 13 in eq x = 21- y

x = 21  - y

x = 21 - 13

x = 8

So the woman bought 8 large frames and 13 small frames.

~lenvy~

Currently, the lowest tax bracket in the United States is
Α. 0%
Β. 15%
C. 1%
D. 10%

Answers

Answer:

D 10%

Step-by-step explanation:

write the equation of line through (3,6) and (-4,-1)

Answers

Answer:

y=x+3

Step-by-step explanation:

The slope of a line passing through the two points P = (x1, y1)and Q = (x2, y2) is given by

m= (y2-y1)/(x2-x1)

We have that x1= 3, y1= 6, x2= - 4, y2= - 1

so m = 1

Now, the y-intercept is b=y1-mx1 (or b=y2-mx2, the result is the same).

b=6-(1)(3)

b=3

Finally, the equation of the line can be written in the form

y = mx+b

y=x+3

Help picture below problem 17

Answers

Answer:

b= 7

Step-by-step explanation:

Answer:

Missing Side = 7 feet

Step-by-step explanation:

by Pythagora

25² = P² + 24²

625 - 576 = P²

P² = 49

P = √49

P = 7 feet

A spinner is labelled with three colors: Red, Green and Blue Marcus spun the spinner once and tossed a coin once.
Construct a tree diagram for this situation. Determine how many outcomes are possible Complete your work in the
space provided or upload a file that can display math symbols if your work requires it. Include the tree diagram in yo
answer.

Answers

Answer:

there are three outcomes

Step-by-step explanation:

three colours= three outcomes

don't have a diagram

Triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3). The triangle translates 2 units up and 1 unit right. Which rule represents the translation? After the translation, what are the coordinates of vertex A'? Q: A: A) (x, y) → ( x + 1, y + 2); (−2, 6) B) (x, y) → ( x + 2, y + 1); (−1, 5) C) (x, y) → (x − 1, y + 2); (−4, 6) D) (x, y) → (x − 2, y − 1); A(−7, 3)

Answers

Answer:

a(-2.6) b(5, 0) c(9,5)

Step-by-step explanation:

the rule is x+1 y+2 for each of the vertices

I really need help now. 100 points plus brainly if correct. I GOT THINGS TO DO!!! Answer the question in the picture

Answers

Answer: 4,000

Step-by-step explanation:

The only logical choice there because of the rate of others

Answer: c is the answer

Step-by-step explanation:

I NEED HELP ASAP, I NEED BOTH QUESTIONS ANSWERED THIS IS WORTH 50 POINTS SO PLS HELP ASAP~~

Answers

that’s a lot of points ok gimme a second i’ll write the answer in the comments when I’m done

NO LINKS!! Explain your answer (show the support by showing the changes in x and y on your table). If the relationship is linear, inverse or exponential, write the equation. #9

Answers

Answer:

relationship: inverseequation: y = 25/x

Step-by-step explanation:

You are correct that the relationship is inverse, and that the product of x and y is a constant, 25.

__

The equation should be written so that y is a function of x:

  [tex]\boxed{y=\dfrac{25}{x}}[/tex]

The x in the denominator clearly shows that y is proportional to the inverse of x.

Answer:

Linear relationship: increasing or decreasing one variable will cause a corresponding increase or decrease in the other variable.

Inverse relationship:  the value of one variable decreases as the value of the other variable increases.

Exponential relationship: a constant change in the independent variable (x) gives the same proportional change in the dependent variable (y)

Question 5

As the x-value increases (by one unit), the y-value decreases.

Therefore, this is an inverse relationship.

The y-values can be calculated by dividing 25 by the x-value.

[tex]\sf y=\dfrac{25}{x}[/tex]

Ash buys 5 bunches of flowers. Each bunch contains 10 flowers. He gets 8 more flowers from his yard.

Let f represent the number of flowers Ash has in all.

Which equation could be used to find the value of f?


5+10−8=f

5 + 10 + 8 = f

5×10−8=f

5 × 10 + 8 = f

Answers

Answer:

5 x 10 + 8 = f

Step-by-step explanation:

The reason it is 5 x 10 + 8 = f, is because each bunch has 10 and Ash has five.

In order to find how many flowers he has in 5 bunches is to multiply by how many flowers each bunch has.

Then he gets 8 more flowers which is why it has +8 in the equation.

The equation to get the total number of flowers is the last one:

f = 5*10 + 8

Which equation could be used to find the value of f?

We know that Ash has 5 bunches of flowers, each one contains 10 flowers, so there we have:

5*10 = 50 flowers.

Then he adds 8 more flowers, then we can write the total number of flowers as:

f = 5*10 + 8.

So the equation that we need to use is the last one.

If you want to learn more about equations:

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At a concession stand, seven hot dog(s) and four hamburger(s) cost $21:25, four hot dog(s) and seven hamburger(s) cost $22.75 Find the cost of one hot dog and the cost of one hamburger

Answers

Step-by-step explanation:

If 4 hamburger = $21.25

1 hamburger = x

Cross multiply

4 x x = $21.25 x 1

4x = $21.25

Devide both side with the coefficient of x

4x/4 = $21.25/4

X = $5.3125

Therefore 1 hamburger cost $5.31

If 4 hotdogs = $22.75

1 hotdog = y

Cross multiply

4 x y = $22.75 x 1

4y = $22.75

Devide both sides with the coefficient of y

4y/4 = $22.75/4

Y = $5.6875

Therefore one hotdog cost $5.69

Answer:

See below ↓↓↓

Step-by-step explanation:

Given :

7 hot dogs + 4 hamburgers = $21.504 hot dogs + 7 hamburgers = $22.75

Let's set some variables.

hot dogs = xhamburgers = y

So, our equations are :

7x + 4y = 21.504x + 7y = 22.75

Mulitply equation #1 by 7 and equation #2 by 4.

49x + 28y = 150.50 (Equation 3)16x + 28y = 91.00 (Equation 4)

Subtract equation 4 from equation 3.

49x - 16x + 28y - 28y = 150.5 - 9125x = 59.5x = $2.38 [cost of one hot dog]

Substitute value of x in equation 4.

16(2.38) + 28y = 9138.08 + 28y = 9128y = 52.92y = $1.89 [cost of one hamburger]

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