What is the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2?

Answers

Answer 1

The answer to this question What is the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2 is (7/65/128)

Answer 2

Answer:

[tex]\frac{765}{128}[/tex]

Step-by-step explanation:

We have been given that 1st term of a geometric series is 3 and common difference is 1/2 . We are asked to find the sum of 1st 8 terms of the given series.

We will use geometric series formula to solve our given problem.

[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]

Upon substituting our given values in the above formula we will get,

[tex]S_8=\frac{3(1-(\frac{1}{2})^8)}{1-\frac{1}{2}}[/tex]

[tex]S_8=\frac{3(1-\frac{1^8}{2}^8)}{\frac{2-1}{2}}[/tex]

[tex]S_8=\frac{3(1-\frac{1}{256})}{\frac{1}{2}}[/tex]

[tex]S_8=\frac{3(\frac{256-1}{256})}{\frac{1}{2}}[/tex]

[tex]S_8=\frac{3(\frac{255}{256})}{\frac{1}{2}}[/tex]

[tex]S_8=3(\frac{255}{256}\times\frac{2}{1})[/tex]

[tex]S_8=3(\frac{255}{128})[/tex]

[tex]S_8=\frac{765}{128}[/tex]

Therefore, the sum of our given series is [tex]\frac{765}{128}[/tex].

Related Questions

Outlet malls sell goods _____

Answers

at a discounted price

1. at a discount

2. add all the items together at their sales cost then add salves tax

3. $26.75

4. $66.23

What value of x makes the equation below true?

6x - 9 = 39

A. 13

B. 5

C. 8

D. 24

Answers

The answer is C. eight

6x - 9 = 39
6x = 48
x = 8

hope this helps , give brainliest

Divide (67 gallons 2 quarts)÷3

A) 21 gallons 1 quart
B) 22 gallons 3 quart
C) 21 gallons 3 quart
D) 22 gallons 1 quart
E) NONE

Answers

the answer is e none of the above

E) None is correct.

To solve this problem, we need to divide the total volume of 67 gallons 2 quarts by 3.

Convert the total volume to only quarts since both gallons and quarts are involved in the problem. There are 4 quarts in a gallon.

67 gallons = 67 * 4 quarts = 268 quarts

Add the additional 2 quarts: 268 quarts + 2 quarts = 270 quarts

Divide the total quarts by 3 to find the result:

270 quarts ÷ 3 = 90 quarts

Convert the result back to gallons and quarts. Since there are 4 quarts in a gallon:

90 quarts ÷ 4 = 22 gallons with a remainder of 2 quarts

Which of the follow is NOT equivalent to -9-8
A. -9+-8
B. -8+-9
C. -17
D. -8-9

Answers

I think the answer is E) neither

A. -9+8=-1
B: -8-9=-17
C: -17
D. -8-9=-17
Answer is A, because -9+8=-1.

Complete each statement regarding an angle θ and its reference angle theta hat using radian measure. (Assume 0 ≤ θ < 2π. Give your answers in terms of θ.) (a) If θ is in QI, then theta hat = . (b) If θ is in QII, then theta hat = . (c) If θ is in QIII, then theta hat = . (d) If θ is in QIV, then theta hat = .

Answers

The reference angle is simply the acute angle between the terminal side and the x-axis

The terminal angles in the four quadrants are

[tex]\bar \theta = \theta[/tex].[tex]\bar \theta = \pi - \theta[/tex].[tex]\bar \theta = \theta - \pi[/tex].[tex]\bar \theta = 2\pi - \theta[/tex]

The given parameters are:

[tex]\theta \to[/tex] reference angle

[tex]\bar \theta \to[/tex] terminal angle

(a) If the reference angle is in the first quadrant

In the first quadrant, the x-axis is at [tex]0\ rad[/tex]

So, the terminal angle is:

[tex]\bar \theta = \theta - 0[/tex]

[tex]\bar \theta = \theta[/tex]

(b) If the reference angle is in the second quadrant

In the second quadrant, the x-axis is at [tex]\pi \ rad[/tex],

While the reference angle is between [tex]\frac{\pi}{2}[/tex] and [tex]\pi \ rad[/tex]

It means that, we have to subtract the reference angle from the x-axis

So, the terminal angle is:

[tex]\bar \theta = \pi - \theta[/tex]

Here, the x-axis is still at [tex]\pi \ rad[/tex],

But the reference angle is between [tex]\pi \ rad[/tex] and [tex]\frac{3}{2}\pi[/tex]

It means that, we have to subtract the x-axis from the reference angle.

So, the terminal angle is:

[tex]\bar \theta = \theta - \pi[/tex]

(d) If the reference angle is in the fourth quadrant

Here, the x-axis is at [tex]2\pi \ rad[/tex]

And the reference angle is between [tex]\frac{3}{2}\pi[/tex] and [tex]2\pi \ rad[/tex]

It means that, we have to subtract the reference angle from the x-axis.

So, the terminal angle is:

[tex]\bar \theta = 2\pi - \theta[/tex]

See attachment for illustration of terminal angles

Answers

https://brainly.com/question/6360856

The sine of the measure of an angle in a right triangle, is the ratio of the opposite side of that angle, to the hypotenuse.

The cosine of the measure of an angle in a right triangle, is the ratio of the adjacent side of that angle, to the hypotenuse.

According to these, we have:

[tex]\displaystyle{ \sin(x^{\circ})= \frac{6}{10} [/tex]

and

[tex]\displaystyle{ \sin(y^{\circ})= \frac{6}{10} [/tex].

Thus, the ratios of both are identical [tex]( \frac{6}{10} \ and \ \frac{6}{10} )[/tex]

The ratios of sin (x) and cos (y) are both identical [tex](\frac{6}{10}\; and\; \frac{6}{10})[/tex].

RIGHT TRIANGLE

A triangle is classified as a right triangle when it presents one of your angles equal to 90º. A math tool applied for finding angles or sides in a right triangle is trigonometric ratios.

The main trigonometric ratios are:

[tex]sin(\alpha )=\frac{opposite\;side}{hypotenuse} \\ \\ cos(\alpha )=\frac{adjacent\;side}{hypotenuse}\\ \\ tan(\alpha )=\frac{sin (\alpha )}{cos(\alpha } =\frac{opposite\;side}{adjacent\;side}[/tex]

The question asks the sin x and cos y, for solving this you should apply the trigonometric ratios. Therefore,

[tex]sin (x)=\frac{opposite\; side}{hypotenuse} =\frac{6}{10}[/tex]

and

[tex]cos (y)=\frac{adjacent\; side}{hypotenuse} =\frac{6}{10}[/tex]

Learn more about trigonometric ratios here:

brainly.com/question/11967894

#SPJ5

How many terms are in the arithmetic sequence 7, 0, −7, . . . , −175?

Answers

so hmmm 7, 0, -7.... what the dickens is going on? hmmm is really dropping each time by 7, so, 7-7, 0, and 0-7, -7 and so on.

so, the "common difference" is then -7, and our first term is 7, now, who's -175? let's check.

[tex]\bf a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ d=-7\\ a_1=7\\ a_n=-175 \end{cases} \\\\\\ -175=7+(n-1)(-7)\implies -175=7+7-7n \\\\\\ 7n=14+175\implies 7n=189\implies n=\cfrac{189}{7}\implies n=\stackrel{terms}{27}[/tex]

family drinks 1 3/4 gallons of milk every 4 1/2 days what is the unit rate of milk per day

Answers

[tex]\bf \cfrac{milk}{day}\qquad \cfrac{1\frac{3}{4}}{4\frac{1}{2}}\implies \cfrac{\frac{1\cdot 4+3}{4}}{\frac{4\cdot 2+1}2}\implies \cfrac{\quad \frac{7}{4}\quad }{\frac{9}{2}}\implies \cfrac{7}{\underline{4}}\cdot \cfrac{\underline{2}}{9}\implies \cfrac{7}{2}\cdot \cfrac{1}{9}\implies \cfrac{7}{18}[/tex]

which gives us a quotient of about 0.39 gallons of milk for one day.

A scuba diver swimming at the Deppe shown, and then swim 0.5 feet toward the surface every three seconds. What is the location of the scuba diver, relative to the surface, after 15 seconds?

Answers

For every 3 seconds, the scuba diver dives 0.5 feet
after 15 seconds = your answer

3 x 5 = 15
0.5 x 5 = your answer

your answer = 2.5

2.5 is your answer

hope this helps

5836197 to the nearest hundred

Answers

5836200 because it's rounded

The answer to the question is 5,836,200

45+5/6x=50
need to find x and math for x

Answers

45 + 5/6x = 50

5/6x = 50 - 45

5/6x = 5

5x = 5 * 6

5x = 30

x = 6

hope that helps, God bless!

The solution of expression is, x = 6

We have to give that,

An expression to simplify as,

⇒ 45 + 5/6x = 50

Now, Simplify the expression by combining like terms,

⇒ 45 + 5/6x = 50

Subtract 45 on both sides,

⇒ 45 + 5/6x - 45 = 50 - 45

⇒ 5/6x = 5

Multiply by 6 on both sides,

⇒ 5x = 5 × 6

⇒ 5x = 30

Divide by 5 on both sides,

⇒ x = 30/5

⇒ x = 6

So, The solution is, x = 6

To learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

Jenny drove 1,255 miles last week. She drove 187 miles on Monday. On Tuesday, she drove 53 more miles than on Monday, on Wednesday she dove 26 more miles than on Tuesday. How many more miles did Jenny drove on Monday and tuesday together than on Wednesday and Thursday together?

Answers

The answer should be 401

What percent is 6 out of 30? 2% 6% 20% 30%

Answers

6 is 20 percent of 30

The answer is 20%. Hope I helped

Tammy's take-home pay is $800 a month. She spends 7% of her take-home pay on her cell phone bill. How much is Tammy's monthly cell phone bill? A. $76 B. $69 C. $56 D. $109

Answers

56$ hope that helped also.......................

Answer:56

Step-by-step explanation:

anyone help me please!
A stereo listed for $350 is on sale for 20% off the list price. The sales tax is 6%. What total price does a customer pay for the stereo if she/he buys it on sale?
1 $324.00
2 $259.00
3 $262.20
4 $296.80
5 $301.00

Answers

The answer would be 296.80.Hope this helps!

20% subtracted from $350 leaves you with $280

then you need add 6% onto the price

Im not sure if youre supposed to calculate 6% of the original price or the price with 20% off

tax of normal price + discounted price= $301
tax of discounted price + discounted price= $296.60

Your answer should be E since $301 is an answer choice

"example 1: the radius of a circle is 3 inches. what is the area?"

Answers

= 28.26 in thats your answer

During strenuous exercise, an athlete can burn 12 calories per minute on a treadmill and 8.5 calories per minute on an elliptical machine. If an athlete uses both machines and burns 325 calories In a 30- minute workout, how many minutes does the athlete spend on each machine?

Answers

Hope it helps 10 mins on the elliptical and 12 on the treadmil

The athlete spends 20 minutes on the treadmill and 10 minutes on the elliptical machine. This is determined by setting up and solving a system of linear equations based on the calorie burn rate of each machine and the total calories burned during the workout.

To solve the problem of how many minutes an athlete spends on each machine during their workout, we must set up a system of linear equations. The athlete burns 12 calories per minute on a treadmill and 8.5 calories per minute on an elliptical machine. In a 30-minute workout, the athlete burns a total of 325 calories. Let's denote the time spent on the treadmill as t minutes and the time spent on the elliptical machine as e minutes.

The total time spent on both machines is 30 minutes: t + e = 30The total calories burned is 325: 12t + 8.5e = 325

We now have two equations and two unknowns, which can be solved simultaneously.

Subtract the second equation from 12 times the first equation to eliminate eSolve the resulting equation for t to find the number of minutes on the treadmillSubstitute the value of t in the first equation to find the number of minutes on the elliptical machine

Using these steps, we find that:

12t + 12e = 360 (by multiplying the first equation by 12)12t + 8.5e = 325 (second equation as is)Subtracting these equations, we get 3.5e = 35Solving for e, we find that e = 10 (the athlete spends 10 minutes on the elliptical machine)Plugging e = 10 into the first equation, we find that t = 20 (the athlete spends 20 minutes on the treadmill)

Therefore, the athlete spends 20 minutes on the treadmill and 10 minutes on the elliptical machine during their 30-minute workout.

What is the simplified expression for the expression below? 1/2(8x+4)+1/3(9-3x)

Answers

1/2(8x + 4) + 1/3(9 - 3x)

Simplify.

4x + 2 + 3 - x

Combine like terms.

(4x - x) + (2 + 3)

Simplify.

3x + 5

~Hope I helped!~

Answer:

3x + 5

Step-by-step explanation:

Caroline bought 20 shares of stock at 10 ½, and after 10 months the value of the stocks was 11 ¼. If Caroline were to sell all her shares of this stock, how much profit would she make? A. $210 B. $10 C. $15 D. $225

Answers

20 shares at 10 1/2 (or 10.5) = 20 * 10.5 = 210
20 shares at 11 1/4 (or 11.25) = 20 * 11.25 = 225

so the profit made would be : 225 - 210 = $ 15 <==

A section of a roller coaster track forms a parallelogram ABCD. If m∠ABC = 72°, what is m∠DAB? A) 72° B) 108° C) 144° D) 216°

Answers

check the picture below.

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

A section of a roller coaster track forms a parallelogram ABCD.

If m∠ABC = 72°

We need to find the m∠DAB,

Since ABCD is a parallelogram .

So, "Sum of interior angles on the same side is supplementary":

[tex]m\angle ABC+m\angle DAB=180\textdegree\\\\72\textdegree+m\angle DAB=180\textdegree\\\\m\angle DAB=180\textdegree-72\textdegree\\\\m\angle DAB=108\textdegree[/tex]

Hence, Option 'B' is correct.

What is 129,543 rounded to the nearest ten thousand

Answers

129,543 rounded to the nearest ten thousand is 130,000

hope this helps

129,543 rounded to the nearest ten thousand is 130,000. Hope this helps! Can u plz mark me as brainliest? I really need it !

How much greater is the area of a square with a side length of 9 inches than the area of a circle with a radius of 3 inches?

Answers

The area of the square is 81 sq in, and the area of the circule is (3.14)(3 in)^2, or approx 3.14(9) sq in, or approx 28.27 sq in.

Subtract: 81 sq in - 28.27 sq in = approx. 52.73 sq in.

The difference is 52.73 sq in; the square is larger, the circle smaller.

[tex] \frac{dx}{dt} = \frac{t^{2}+3tx+ x^{2} }{ t^{2} } [/tex]

Answers

[tex]\dfrac{\mathrm dx}{\mathrm dt}=\dfrac{t^2+3tx+x^2}{t^2}[/tex]
[tex]\dfrac{\mathrm dx}{\mathrm dt}=1+\dfrac{3x}t+\dfrac{x^2}{t^2}[/tex]

Let [tex]x(t)=ty(t)[/tex], so that [tex]\dfrac{\mathrm dx}{\mathrm dt}=t\dfrac{\mathrm dy}{\mathrm dt}+y[/tex].

[tex]t\dfrac{\mathrm dy}{\mathrm dt}+y=1+3y+y^2[/tex]
[tex]t\dfrac{\mathrm dy}{\mathrm dt}=1+2y+y^2=(1+y)^2[/tex]
[tex]\dfrac{\mathrm dy}{(1+y)^2}=\dfrac{\mathrm dt}t[/tex]
[tex]\implies-\dfrac1{1+y}=\ln|t|+C[/tex]
[tex]\implies y+1=-\dfrac1{\ln|t|+C}[/tex]
[tex]\implies yt=x=-t-\dfrac t{\ln|t|+C}[/tex]

Find the ratio and simplify. In this triangle, find the ratio of the shortest side to the longest. A triangle has three sides with lengths 15.2, 5.6, 14.1

Answers

well, the shortest will be 14.1 clearly, and the longest of all three is 15.2.

let's check the ratio from shortest to longest.

[tex]\bf 14.1\implies \cfrac{141}{10}\qquad \qquad\qquad 15.2\implies \cfrac{152}{10} \\\\\\ \cfrac{shortest}{longest}\qquad 14.1:15.2\qquad \cfrac{14.1}{15.2}\implies \cfrac{\quad \frac{141}{10}\quad }{\frac{152}{10}}\implies \cfrac{141}{10}\cdot \cfrac{10}{152} \\\\\\ \cfrac{141}{152}[/tex]

What is the product in simplest form?

−89⋅56

Answers

The product would be -4984.

The answer in siplest form is -

If x2 - 4 = 45, then x could be equal

Answers

Here is your answer: First write the equation: x2-4=45 Then add 4 on both sides: 45+4=49 x2=49 Then divide two on each side: 49/2=24.5 =24.5

The answer would be 24 I believe

a woman walks in and steals 100 from a register. 5 minutes later uses the same 100 to buy merchandise from that same store and buys 70 worth of merchandise with that same 100. he gives her 30 in change. how much did the store lose

Answers

she took 100, the store has - 100
she went back and bough
70 bucks in stuff, the store has - 70

yes, she took the $100 bill and gave it, got back $30, that means she only kept $30 from the original bill.

the store however, lost the original $100 bill plus the $70 in merchandise, so they have -$170.

3 divided by what equals 5

Answers

It’s 0.6 because temper three can’t equally go into five.

3 divided by what equals 5
1st step: Write this as an algebraic equation
3/x=5
2nd step: Multiply by x on both sides
3=5x
3rd step: Divide both sides by 5
3/5=x
So your answer is 3/5 or 0.6

A pro shop in a bowling center decreases the price of a urethane bowling ball by 22% to a sale price of $88.14. What is the former price

Answers

88.14/.78=$113 is you Answer

1x - .22x = 88.14
.78x = 88.14

divide by .78 x = 113

A grey squirrel population was introduced in a certain county of Great Britain 35 years ago. Biologists observe that the population doubles every 7 years, and now the population is 60,000.
(a) What was the initial size of the squirrel population?

Answers

if this occurred over a span of 35 years and the population doubles every 7 years, we can divide 35 by 7 to find how many times the population has doubled, which would be 5 times. If we divide 60,000 by 2 (or multiply by 1/2) 5 times, you would get the answer, which would be 1,875.

Final answer:

To find the initial size of the grey squirrel population, we used the exponential growth formula. After calculating, we determined that the initial population size was 1,875 squirrels.

Explanation:

The student asked how to find the initial size of a grey squirrel population that doubles every 7 years and now has a population of 60,000 after 35 years.

To calculate the initial population size, we'll use the formula for exponential growth: P(t) = P0 × (2t/T), where P(t) is the population at time t, P0 is the initial population size, 2 is the base because the population doubles, t is the number of years, and T is the time it takes for the population to double.

The problem gives us 35 years (t) and a doubling time (T) of 7 years. Plugging these into the equation, we have 60,000 = P0 × (235/7). Simplifying, we get 60,000 = P0 × 25 or 60,000 = P0 × 32. Dividing both sides by 32, we find the initial population size is 1,875 squirrels.

Thus, the initial size of the grey squirrel population was 1,875.

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