4. Use the formula to evaluate the series 3 + 6 + 12 + 24 +48 +96. Sn a₁(1 - r^) 1-r​

Answers

Answer 1

Answer:

[tex]S_6=189[/tex]

Step-by-step explanation:

This is a geometric series with [tex]a_1=3[/tex] and common ratio [tex]r=2[/tex]. Using the formula [tex]\displaystyle S_n=\frac{a_1(1-r^n)}{1-r}[/tex] to find the sum of the first [tex]n=6[/tex] terms, we have:

[tex]\displaystyle S_n=\frac{a_1(1-r^n)}{1-r}\\\\S_6=\frac{3(1-2^6)}{1-2}\\\\S_6=\frac{3(1-64)}{-1}\\\\S_6=\frac{3(-63)}{-1}\\\\S_6=\frac{-189}{-1}\\\\S_6=189[/tex]

So, the given series works out to be [tex]S_6=189[/tex].


Related Questions

Jade thinks the area m•6+m•8. Arianna thinks the area is m(6+8). How can they both be correct?

HELP PLEASE HELP ME!!!

Answers

Answer:

6m=8m−40+6mNow simplify:=8− m−40+6− m=14m−40

Step-by-step explanation:

6m=8m−40+6mNow simplify:=8− m−40+6− m=14m−40

I need a bit of help with this question so please if you could answer:

To the nearest hundredth, what is the value of x?
Use a trigonometric ratio to compute a distance


59.72


56.35


35.94


27.08

Answers

the answer is 35.94

Check the picture below.

Make sure your calculator is in Degree mode.

help me please :( i need help

Answers

Answer:

B

Step-by-step explanation:

Use the expression PEMDAS

It helps to know what do to first

Parenthesis Exponent Multiply Divide Add Subtract

What is the 16th term in the following geometric sequence?
5, −10, 20, −40, 80,...

Answers

-163840

Explanation:

The formula to find the nth term for a geometric sequence is

(a1)(r)^n-1

So by plugging in the terms you get

(5)(-2)^16-1 = -163840
Answer: -163840

Step-by-Step Explanation:

As we can see, starting from the first term, every term is repeatedly multiplied by (-2) in order to form this sequence.

1) 5
2) 5 * -2 = -10
3) -10 * -2 = 20
4) 20 * -2 = -40
5) -40 * -2 = 80
6) 80 * -2 = -160
7) -160 * -2 = 320
8) 320 * -2 = -640
9) -640 * -2 = 1280
10) 1280 * -2 = -2560
11) -2560 * -2 = 5120
12) 5120 * -2 = -10240
13) -10240 * -2 = 20480
14) 20480 * -2 = -40960
15) -40960 * -2 = 81920
16) 81920 * -2 = -163840
17) -163840 * -2 =327680

Therefore, 16th Term = -163840

PLEASE HELP ME WITH THIS!! I NEED HELP

Answers

Answer:

It would be d

Step-by-step explanation:

Its d because its in a staright line

Answer:

D.

Step-by-step explanation: the rest are either non-linear , have no correlation, have a curvilinear relationship, or have no association.

How do you solve for x?

Answers

..........................

Polygon with exactly one line of symmetry label the line of symmetry

Answers

Answer:

Kite

Step-by-step explanation:

Kite. A kite has one line of symmetry

9x-3-8x=7-x solve for x

Answers

Answer:

x = 5

Step-by-step explanation:

Simplify both sides :

9x - 3 - 8x = 7 - xx - 3 = 7 - x

Add 3 to each side :

x - 3 + 3 = 7 - x + 3x = 10 - x

Add x to each side :

x + x = 10 - x + x2x = 10

Divide by 2 on each side :

2x/2 = 10/2x = 5

Answer:

x = 5

Step-by-step explanation:

9x-3-8x=7-x solve for x

9x - 3 - 8 x = 7 - x

x - 3 = 7 - x

2x = 10

x = 10 : 2

x = 5

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

check

9 * 5 - 3 - 8 * 5 = 7 - 5

2 = 2

the answer is good

2. Mary has saved $160 of the $250 she needs for rent.
She takes home $6 an hour from her part-time job.
Mary works the same number of hours each day for 3
days. How many hours does Mary have to work each
day to take home enough money to pay the balance
of her rent?
F. 3 hours
G.
4 hours
H.
5 hours
J.
6 hours
K
7 hours

Answers

Answer:

H - 5 hours

Step-by-step explanation:

We can setup an equation to solve the question.

Let [tex]h[/tex] be the number of hours Mary must work.

[tex]250 = 160 + 3(6h)[/tex]

250 - the amount of money Mary needs

160 - the amount of money Mary has saved already

3 - How many days she works

6h - How much she gets paid per day

[tex]250 = 160 + 3(6h)\\90 = 3(6h)\\90=18h\\5=h[/tex]

This means Mary must work 5 hours each day to pay her rent.

Brad weighs 125 pounds. How could you change 125 pounds
to tons

Answers

Divide mass value by 2000
125 pounds= 0.0625 tons
Divide 125 by 2000 = .0625

In Autobiography by Abraham Lincoln and the Life of Abraham Lincoln by John Hugh Bowers, each author tells the same story about Lincoln's life, but they provide different_________.
A settings
B. dialogue
C. facts

Answers

The answer is c :).

A baker is making cakes for a big party. She uses 1/4 cup of oil for each cake. How many cakes can she make if she has a bottle of oil that has 6 cups in it? PRITTY PLEASE HELP!!! NOW (ASAP)

Answers

Answer:

24 Cups

Step-by-step explanation:

you just need to divide 6 by 1/4, whihc equals 24/1

A car salesman has determined the probability of a person purchasing a car with cash is p = 0.08. Which term best describes the probability of this event?

Answers

Correct answer is B. Very Unlikely

Hope this helps :P

What is the solution to the system of equations? (You can either do the substitution or elimination method) x - 2y = 19 x + 3y = 14 (1.-17) (-1, 17) (-17, 1) (17,-1)​

Answers

Answer:

D. (17,-1)

Step-by-step explanation:

We'll start by canceling out x. To do so, multiple the first equation by -1

-1( x - 2y)=( 19 )(-1)

This gives us:

-x +2y = -19

x + 3y = 14

Add the equations together:

→ 5y = -15

→ y = -1

Plug in y = -1 into an equation:

→ x + 3(-1) = 14

→ x - 3 = 14

→ x = 17

(17,-1)

Hope this helps!

What equation describes the graph?

Answers

Answer:

C. y = 3x -2

Step-by-step explanation:

y = mx + b

start with b, the y-intercept, which is -2.

Next find m, the slope. From -2 on the y-axis you are going to find the slope by doing rise/run. You will rise 3 units and run 1 unit to get to the next point on the line.

The equation is y = 3x -2

Kara’s car used 1/16 gallons of gas to drive 1/8 of a mile at this rate how many miles can Kara’s car drive using one gallon of gas

Answers

Answer is 2 miles
Hope this helps

The answer in the calculation for this answer is incorrect.
120 = 12x
x=12 is not accurate -- it should be 10

Answers

Answer:

10

Step-by-step explanation:

it is 10 I jus did it 120 =12 x x =12 10

In the equation 120 = 12x, x = 10.

Explanation:

Ten is its own power, so we can just move 12 one shift to the left, which would result in 120. If x = 12, then the output would have to be 144.

Guys, I have a question.
Will I still pass if I got a C+ in terms 1, 2, and 3?
Because I got C+ in terms 1 and 2 and I'm scared to fail so can anyone tell me if I will fail or pass if I got a C+ in term 3, and motivate me and make me confident?

Answers

C+

if you get a C+ in term three and four then I don't think you will pass if you get a C+ in term three but get your grade up to B+ A- or A+ i term four you will and if you get in the B range for term 3 at least and keep it up in term four you will pass you just have to study and pay attention in class i believe in you. you can do it

Which statements describe the graph of 2 and StartFraction 8 over 9 EndFraction greater-than-or-equal-to x on a number line? Select three options. There is an open circle on 2 and StartFraction 8 over 9 EndFraction. The graph contains the point 0 There is a closed circle on 2 and StartFraction 8 over 9 EndFraction. The arrow points to the left. The arrow points to the right.

Answers

Inequalities help us to compare two unequal expressions. The options that are correct about the given statement are B, C, and D.

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The points that are correct about the given inequality 2(8/9)≥x are:

The graph contains the point 0There is a closed circle on 2 and StartFraction 8 over 9 EndFraction.The arrow points to the left.

Hence, the options that are correct about the given statement are B, C, and D.

Learn more about Inequality:

https://brainly.com/question/19491153

#SPJ1

Solve x + 8 > 13, x + 18 > 23, x + 28 > 33. Complete the description of a pattern. Then use the pattern to predict the solution of x + 5,558 > 5,563.



For each inequality, x > ?
, and the number added to x is ?
less than the number on the right side of each inequality. So, x > ?
is the solution of x + 5,558 > 5,563.

Answers

Answer:

For each inequality, x > 5

, and the number added to x is 5

less than the number on the right side of each inequality. So, x > 5

is the solution of x + 5,558 > 5,563.

Step-by-step explanation:

13-8=5

A survey was given to 90 high school students. They were asked if they preferred fiction or non-fiction and if they preferred indoor or outdoor activities. Partial survey results are shown in the table.

What percent of students in the survey, to the nearest whole number, prefer outdoor activities given they prefer non-fiction?

Enter a number in the box.
P(outdoor | non−fiction)= _%

Answers

Answer:

11% of people preferred outside and non-fiction

Step-by-step explanation:

Table attached,
10/90 = 0.11

0.11 = 11% 

The percent of students in the survey that prefer outdoor activities given they prefer non-fiction is 11%.

What is the percent?

The first step is to determine the total number of people that like fiction: 24 + 30 = 54

Now, determine the total number of people that like non-fiction: 90 - 54 = 36

The third step is to determine the total number of people that like indoor activities and non-fiction: 50 - 24 = 26

The fourth step is to determine the total number of people that like outdoor activities given they prefer non-fiction: 36 - 26 = 10

Percentage of people that prefer outdoor activities given they prefer non-fiction = (10 / 90) x 100 = 11%

To learn more about percentages, please check: https://brainly.com/question/25764815

#SPJ2

If tan theta=8÷15 find sin theta+cos theta÷cos theta (1- cos theta)​

Answers

Answer: 371/30

Step-by-step explanation:  

A 24-foot ladder leans against a wall the base of the ladder is 9 feet from where the wall meets the ground how far up the wall does the ladder reach ?

Answers

Answer

24*9= the answer

Step-by-step explanation:

What is the value of x?
Enter your answer in the box.
X =

Answers

Answer:

26°

Step-by-step explanation:

x + 64° = 90° ( being complementary angles)

x = (90 - 64)°

x = 26°

Answer:

x = 26°

Step-by-step explanation:

x + 64° = 90° [right angle]

x = 90° - 64°

x = 26°

Find the domain and range of the given relation (6,3), (-7,-3), (-4,1), (1,-4)

Answers

Answer:

Step-by-step explanation:

The domain are all the x values

(-7,-3), (-4,1), (1,-4), (6,3)

x here is from -7 to 6

domain ∈ [-7, 6]

The range are all the y values

(1,-4), (-7,-3), (-4,1), (6,3)

y here is from -4 to 3

range ∈ [-4, 3]

what are the domain and range of the function represented by the set of ordered pairs?. ​

Answers

A is the right answer. Ask anything if you have more questions.

Answer:

a

Step-by-step explanation:

domain is based on x values in the front

range is based on y values in the back

Which represents the complete factorization of 3v2 + 9v ?

Answers

Answer:

3v2 + 9v = 3v(v + 3)

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

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

        What is the complete factorization of 3v²+9v?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to solve:-}}}}\diamond[/tex]

First we need to find the GCF of this polynomial; when we find it, we should factor it out, or divide all the terms by it.

Since the greatest common factor (GCF) of this polynomial is 3v, we divide both terms by 3v:-

3v(v+3)

Good luck.

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

Need answers quick pleaseeee!!

Answers

Answer:

The measure of its complementary angle is 3.

Step-by-step explanation:

Evaluate the following when n = 7: 5(n - 5)

Answers

Hey! there

Answer:

10 is the answer

Step-by-step explanation:

In this question we are given value of n as 7 and an expression that is 5 ( n - 5 ) .

And we are asked to evaluate the expression .

SOLUTION : -

Expression :

[tex] \quad \longmapsto \qquad \: 5(n - 5)[/tex]

We are substituting value of n as 7 :

[tex] \quad \longmapsto \qquad \:5( \bold{7} - 5) [/tex]

Solving parenthesis that is subtracting 5 from 7 :

[tex] \quad \longmapsto \qquad \:5(2)[/tex]

Now we are multiplying 5 with 2 and We get :

[tex] \quad \longmapsto \qquad \: \underline{\boxed{ \frak{{10}}}} \quad \bigstar[/tex]

Henceforth , value of expression when n is equal to 7 is 10

#Keep Learning

Step-by-step explanation:

Answer:

10 is the answer

Step-by-step explanation:

In this question we are given value of n as 7 and an expression that is 5 ( n - 5 ) .

And we are asked to evaluate the expression .

SOLUTION : -

Expression :

[tex] \quad \longmapsto \qquad \: 5(n - 5)[/tex]

We are substituting value of n as 7 :

[tex] \quad \longmapsto \qquad \:5( \bold{7} - 5) [/tex]

Solving parenthesis that is subtracting 5 from 7 :

[tex] \quad \longmapsto \qquad \:5(2)[/tex]

Now we are multiplying 5 with 2 and We get :

[tex] \quad \longmapsto \qquad \: \underline{\boxed{ \frak{{10}}}} \quad \bigstar[/tex]

Henceforth , value of expression when n is equal to 7 is 10

2.5 divided by 0.5 what would that be

Answers

Answer:

1.25

Step-by-step explanation:

1/2 of 2.5 is 1.25

Think of it as the following

250 divided by 2 is 125 because 125+125=250

Answer:

5

Step-by-step explanation:

2.5 divided by 0.5 would = 5

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