Find the sum of the following series. Round to the nearest hundredth if necessary,
3 + 6 + 12+ ... +49152
Sum of a finite geometric series:
Q] - a
Sn =
1-T

Answers

Answer 1

Answer:

[tex]sum = \frac{a( {r}^{n - 1} )}{r - 1} \\ : but \: l = a( {r}^{n - 1} ) \\ 49152 = 3( {2}^{n - 1} ) \\ 16384 = {2}^{n - 1} \\ {2}^{n} = 32768 \\ {2}^{n} = {2}^{15} \\ n = 15 \\ \therefore \: sum = \frac{3(2 {}^{15 - 1}) }{15 - 1} \\ = \frac{49152}{14} \\ = 3510.9[/tex]


Related Questions

Identify the transformations of the
function f(x) = x^2 to g(x)=(x-7)^2+4

Answers

We will take the opposite of what is in the bracket, so if we see -7 in the bracket, that means it moves 7 units to the right and 4 units up.

Find the circumference of each circle from the given radius or diameter

Please help

Answers

Answer: 1) 113.20 yds 2) 75.40 yds 3) 44 yds

*These answers were calculated using the true value of pi, not 3.14*


Hope this helps シ

What is an equivalent expression for 6v + -1 ?

Answers

Answer:

5v is an equivalent expression for 6v + -1 ?

Answer:

5v is equivalent expression for 6v + -1

The area of a rectangular parking lot is 3960 m²
If the length of the parking lot is 72 m, what is its width?

Answers

Answer:

3816m

Step-by-step explanation:

72 + 72= 144

8960 - 144= 3816

what is the value of x?​

Answers

Answer:

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180 degrees

so

70 + 35 + x = 180 add like terms

105 + x = 180 subtract 105 from both sides

x = 75

Answer:

75  degrees

Step-by-step explanation

triangles add up to 180 degrees so, 70+35= 105 degrees, 180-105= 75 degrees

Whats the y-intercept of -2x - y=3

Answers

Let’s first write this in the slope form: y=mx+b.
m is the slope and b is the y intercept.
-2x-y=3
y=-2x-3
So the b, or the y intercept is -3

Which of the following is RS? pls answer asap thank you

Answers

Answer:

not sure

Step-by-step explanation:

but I think it's c tell me if I'm correct please but I'm not sure if u have no time just click C)

Answer:

c

Step-by-step explanation:

What is the product?

Answers

Answer:

[tex]21x^{7}y^{11}[/tex]

Step-by-step explanation:

Remove the parentheses and take out the constansts.

[tex](7 x 3) x^{2} x^{5} y^{3} y^{8}[/tex]

Simplify 7 x 3 to 21.

[tex]21x^{2} x^{5} y^{3} y^{8}[/tex]

Use the product rule: [tex]x^{a} x^{b} = x^{a + b}[/tex]

[tex]21x^{2 + 5}y^{3+8}[/tex]

Simplify 2+5 to 7.

[tex]21x^{7}y^{3+8}[/tex]

Simplfiy 3 + 8 to 11.

[tex]21x^{7}y^{11}[/tex]

PLEASE HELP!! The green line below *blank*. Check all that apply.

A. is parallel to the x-axis

B. crosses the origin

C. is in the xy-plane

D. crosses the y-axis

Answers

Answer:

D. crosses the y-axis

[tex]{ \tt{crosses \: y - axis \: at \: y = 5}}[/tex]

Hi can someone please help me with these questions.

Answers

Answer:x=3, x=18, x=29, x=30, x=27

Step-by-step explanation: for problems like the first one, the angles add up to 180 since it’s just a straight line.

The second problem is a right angle so 90°. It gives you 2x and 3x. Part + part =whole so you have 5x=90 then just solve.

Angles across from each other are the same so just 145=5x then solve.

HELP ASAP PLEASE!!!!!

Answers

I think the answer is (6,-4)
i think it will be (4,-4)

x = 4 and y = 2, what is the value of x^2 + y^3 ?

Answers

Answer:

14

Step-by-step explanation:

x * 2 = 8

y * 3 = 6

6 + 8 = 14

Lines J and k intersect at point Q and h is a straight line. What is the value of X ?

Answers

Answer:

Step-by-step explanation:

Angles on a straight line add up to 180 so 180-135 equals 45. Vertically opposite angles are equal so the second angle inside the triangle equals 100. Henceforth, we can solve this equation:

x +45+100 = 180 (angles in triangle add up to 180)

x+145=180

x=35

Vertically opposite angles are equal so x will become 35.

Hope this helps!

for freshman year Nick had 3.5 for a gpa. what gpa does Nick needs for sophomore, junior, senior year to get the average of at least 4.0?

Answers

Answer:4.0

Step-by-step explanation:

Math help please urgent

Answers

Answer:

THREE AND SIX OR FOUR AND FIVE

Step-by-step explanation:

They're just opposite ends !

Step-by-step explanation:

Alternate Interior Angles: 3 and 6

Alternate Exterior Angles: 2 and 7

¿¡ Cuanto es "(8 x 7 + 5 x (-8)) : (-4)" ??

Answers

Answer:

-4

Step-by-step explanation:

So like ur last problem do it in order left to right.

[8x7]+5x(-8)/(-4)

56+[5x(-8)/-4

56+(-40)/-4

16/-4=(-4)

Sorry if i did in wrong order.

Answer: 4(14x-11) hop that can help you

A person runs 1/4 mile in 1/28 hour. What is the persons speed

Answers

Answer:

7

Step-by-step explanation:

speed x time = distance

? x time = distance

1/28x = 1/4

1/28x          1/4

_____ =  _____

1/28          1/28

1/4 ÷ 1/28

(reciprocal method) 28/1

1/4 × 28/1 (change the equation into multiplication)

1/4 × 28/1 = 28/4 (multiply)

(Simplify) 28/4 ---> 7/1 or 7

final answer:

The persons speed would be 7.

En un sistema masa resorte (masa atada a un muelle) ¿en qué punto la masa alcanza su máxima velocidad?

Answers

Answer:

yo just search up Spanish translator

A cylinder-shaped drainage pipe 66 in. long measures 25.12 in. around.


What is the volume of the drainage pipe?

Answers

Answer:

Step-by-step explanation:

25.12 inches around means diameter. So radius = 12.56 inches

   volume  [tex]= \pi r^2 \times h =\pi \times 12.56^2 \times 66 = 32709.44 \ in^3[/tex]

Answer:

The volume of the drained pipe is 32692.11 in ³.

Step-by-step explanation:

Given :-

Diameter of drainage pipe = 25.12 in

So, radius , r = 25.12 in = 12.56 in

Height of drainage pipe, h = 66 in.

To Find :-

Volume of the drainage pipe

Solution :-

We know that,

Volume of cylinder = π × r ² × h

substitute the values

Volume of pipe = 3.14 × (12.56 in)² × 66 in

simplify

Volume of pipe =3.14 ×157.7536 in² × 66in

multiplying ✖ the values

Volume of the pipe = 32,692.11 in ³

Therefore, the volume of the drained pipe is 32692.11 in ³.

Anyone know how to do this

Answers

Answer:

77

Step-by-step explanation:

3+2*49-24

3+98-24

101-24

77

Good luck

Answer:

77

Step-by-step explanation

3+2X7^2-4X6

First complete the exponent

3+2X49-4X6

Then multiply

3+2X49-24

Multiply

3+98-24

Calculate the rest of the equation

101-24=77

Therefore the answer is 77.

Please don't be mad if this is incorrect

Also the x's are multiplication symbols and NOT variables

I’m struggling in finding the nearest cent, May you please help me

Answers

Answer:

$88.48

Step-by-step explanation:

First, we can check the formula for compound interest, which is

[tex]A = P (1 + r)^{n}[/tex] , with A representing the end amount, r representing the interest rate, and n representing the amount of times compounded. We know that the interest rate is 9% (to convert this to a decimal, we can divide it by 100, resulting in 0.09), the end amount is 700, and the amount of times compounded is however many months are in 2 years (there are 12 months per year, and 12 *2 = 24, so 24 times).

Thus, our equation is

[tex]700 = P (1 + 0.09)^{24}\\700 = P (7.911083)\\[/tex]

Divide both sides by 7.911083 to isolate P, and we get

P = 88.48 (rounded to the nearest cent)

A track coach records the number of miles that he ran per day over the month. The stem-and-leaf plot below summarizes this data.

Answers

Answer:

[tex]Mean = 6.70[/tex]

Step-by-step explanation:

Given

See attachment for plot

Required

The mean of the plot

Mean is calculated as:

[tex]Mean = \frac{\sum x}{n}[/tex]

Where

[tex]n = 20[/tex]

Using the given key to read, the plot;

We have:

[tex]Mean = \frac{3.00+3.25+4.25+5.00+..........+8.75+9.50}{20}[/tex]

[tex]Mean = \frac{134.00}{20}[/tex]

[tex]Mean = 6.70[/tex]

The diagram shows the locations of Cody and Reese after running
different directions from a tree. How far did Cody run?

Answers

Answer: 80yd

Step-by-step explanation:

Coach Peters has 12 gallons of water to fill buckets for field day. If
each bucket needs of a gallon to fill, how many buckets can he fill?

Answers

Answer:

Step-by-step explanation:

D.36

because 12 divided by 1/3 is 36

Dois triângulos semelhantes possuem razão entre suas áreas igual a 9. Se o perímetro de um deles é 10, o perímetro do outro deve ser:

Answers

Answer:

O perímetro do outro triângulo deve ser ou de 30 unidades de comprimento, ou de 3.33 unidades de comprimento.

Step-by-step explanation:

Dois triângulos semelhantes possuem razão entre suas áreas igual a 9.

O perímetro tem grau um, enquanto a área tem grau 2. Isto implica que a razão entre os perímetros é a raiz quadrada da razão entre as áreas, então a razão entre os perímetros é de 3.

Se o perímetro de um deles é 10, o perímetro do outro deve ser:

Ou 10*3 = 30, ou [tex]\frac{10}{3} = 3.33[/tex]

O perímetro do outro triângulo deve ser ou de 30 unidades de comprimento, ou de 3.33 unidades de comprimento.

The solution is {-8, 3} but I’m not sure how to graph it on a line, is it A B C or D?

Answers

Answer:

-8 < x< 3

Step-by-step explanation:

|2x+5| <11

there are two solutions, one positive and one negative ( remember to flip the inequality for the negative)

2x+5 <11  and   2x+5 > -11

Subtract 5 from each side

2x+5-5 < 11-5 and    2x+5-5 > -11-5

2x< 6           and           2x>-16

Divide by 2

2x/2 <6/2        and       2x/2 >-16/2

x <3                  and             x>-8

-8 < x< 3

x is less than 3 and x is greater than -8

open circles and -8 and 3 and a line between

pls help me pls and thank u

Answers

94 step by step below

What is the median for this set of data?
28, 32, 15, 19, 24, 26, 22, 32, 30

Answers

Step-by-step explanation:

according order 15 , 19,22, 24,26,28,30,32,32. answer is 26

Answer:

Hello There!!

Step-by-step explanation:

26 is the median as you order the numbers smallest to largest.Therefore,it is 15,19,22, 24, 26,28,30,32,32 and the amount of numbers are odd so the median is the middle number.If it was even the two middle numbers would be added together and then divided by 2.

hope this helps,have a great day!!

~Pinky~

Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for
recycling. Abha collected 178 more cans than Shane did.
Write an inequality to determine the number of cans, S, that Shane could have collected.
What is the solution set of the inequality?

Answers

Answer:

s + 178 = Abha's Can's

Step-by-step explanation:

Well since Abha collected 178 more cans than Shane, it would be Shane's amount of cans they collected AND 178 cans on top of that.

(i didnt know if you wanted the solution of s or just the equation on how to find s)

Please help with these problems

Answers

Answer:

thank you for thissssssss

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