Find s10 for a geometric series with first term 10 and a common ratio 4

Answers

Answer 1
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ n=10\\ r=4\\ a_1=10 \end{cases} \\\\\\ S_{10}=10\left( \cfrac{1-4^{10}}{1-4} \right)[/tex]
Answer 2
the sum of a geometric sequence where the first term is a1 and the common ratio is r and n is which term is
[tex]S_{n}=\frac{a_1(1-r^n)}{1-r}[/tex]

so
given first term of 10 and common ratio 4 and n=10

[tex]S_{10}=\frac{10(1-4^{10})}{1-4}[/tex]
[tex]S_{10}=\frac{10(1-1048576)}{-3}[/tex]
[tex]S_{10}=\frac{10(-1048575)}{-3}[/tex]
[tex]S_{10}=\frac{-10485750}{-3}[/tex]
[tex]S_{10}=3495250[/tex]

Related Questions

Does anyone know the answer to this question?

Answers

f(x) = x-3

g(x) = 2f(x)

g(2)  = 2(2-3) = 2 * -1 = -2

The table below represents a linear function f(x) and the equation represents a function g(x):

x f(x)
−1 −3
0 0
1 3


g(x)

g(x) = 7x + 2

Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

Answers

A. The slope of g(x) is greater. Because g(x) is written in slope intercept form (mx+b), we know that the slope is simply the m value, which, in this case, is 7. For f(x) we know that the slope is 3 because for each increment of x, y increases by 3. 7>3
B. g(x) has a greater y intercept. Because g(x) is written in slope intercept form, we know that the intercept is simply the b value, which is 2 in this case. For f(x), we know that slope interceot is the value of y when x=0. When x=0 in this case, y=0. 2>0

A man paid $71.40 for a radio. The radio was marked 15% off the original selling price. What was the original selling price?

Answers

the original price is $84

If conner spent $36 to buy a new collar for each of his dogs.if each collar cost $6,how many dogs dose conner have?

Answers

6*6=36 you simply just divide the 36 by 6 and you get 6 as your answer

what is this answer

Answers

50=16t^2

Divide both sides by 16
3.125=t^2

Find the square root of both sides (approximated)
1.77= t

Final answer: F

Can square root of 32 be simplified

Answers

Well let's check

√32 = √8*4 = 4√2

Yes it can
Hey!

First, we have to break 32 into its primes.
[tex]32=2^5[/tex]
[tex]=\sqrt{2^5}[/tex]
Since we don't want an odd number, we can split it into two.
[tex]=\sqrt{2^4\cdot \:2}[/tex]
[tex]=\sqrt{2}\sqrt{2^4}[/tex]
Since we want to remove one of the square roots, we have to do something like this: [tex]\sqrt{2^4}=2^{\frac{4}{2}}=2^2[/tex]
We would be left with,
[tex]=2^2\sqrt{2}[/tex]
Simplify the exponent.
[tex]=4\sqrt{2}[/tex]
This tells us that the square root of 32 can be simplified.

Thanks!
-TetraFish

True or false the difference of two numbers is less than either of those two numbers

Answers

The difference of two numbers is not always less at either of the two numbers. (especially for negative numbers)

Take fo example, 40 - 30 = 10.
Here the difference is less than both two numbers.

But in 40 - 15 = 25
Here the difference is less than one of the numbers but greater than the other number.

Now consider, -3 and -5, their difference is given by (-3) - (-5) = -3 + 5 = 2.
Here, 2 is greater than both -3 and -5.

Therefore, The difference of two numbers is not always less than either of those two numbers.

Your answer is False.

How would I solve this?

Answers

2*(3(5+2)-1)
2*(3(7)-1)
2*(21-1)
2*20
40

Final answer: 40

Remember the order of operations. Parentheses, then multiplication and division, followed by addition and subtraction.

A triangle has side lengths of 20 cm, 99 cm, and 108 cm. Classify it as acute, obtuse, or right.

A. acute
B. obtuse
C. right

Answers

B. Obtuse

If draw it out in your head, it's obviously obtuse.
Let "a", "b" and "с"  be sides of the triangle ("с" is the longest side).
The triangle will be:
right if       a² + b² = c²
аcute if     a² + b² > c²    
obtuse if   a² + b² < c²    

We have a=20, b=99 and c=108
20² + 99² = 400 + 9801 = 10201
and
108² = 11664

10201 < 11664   ⇒  obtuse triangle.

Convert: 52 cups = ________ qt.

Answers

1 cup = 0.25 quarts

52 *0.25 = 13 quarts


13 is the answer HOPE THAT HELPS


The field hockey coach is purchasing new uniforms for the team. Company A charges a one-time printing fee of $100 and $12 per uniform. Company B charges a one-time fee of $61 and $15 per uniform. How many uniforms must the coach buy to get a better deal from Company A?

Answers

You can make this into an inequality, using x as the number of uniforms.
100 + 12x < 61 + 15x
39 < 3x
13 < x, so they must buy more than 13 to get a better deal.

which best describes the diameter of a circle?

A. The distance from the center to any point of the circle
B. The length of a chord that contains the center of the circle
C. The distance around the circle
D. The length of a chord that does not contain the center of the circle

Answers

Which best describes the diameter of a circle?

Statements

A. The distance from the center to any point of the circle

This statement describes the radius of the circle

B. The length of a chord that contains the center of the circle

This statement describes the diameter of the circle

C. The distance around the circle

This statement describes the circumference of the circle

D. The length of a chord that does not contain the center of the circle

This statement describes a line segment linking any two points on a circle that does not contain the center of the circle

therefore

the answer is the option

B. The length of a chord that contains the center of the circle


The correct answer is:

B) The length of a chord that contains the center of the circle

Explanation:

A chord is a segment that goes across a circle, with both endpoints on the circle.

A diameter goes through the center of a circle and has both endpoints on the circle; this makes it a chord that goes through the center.

Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 17 ft by 17 ft by 2 in. for a patio if the concrete costs $40.00 per cubic yard? (1 cubic yard = 27 cubic feet)

Answers

Answer:

It will cost approximately $71.360.

Step-by-step explanation:

Given,

The dimension of the concrete is 17 ft by 17 ft by 2 in.

1 ft = 12 inches ⇒ 2 inches = 1/12 × 2 = 1/6 ft.

Thus, the dimension of the concrete is 17 ft by 17 ft by 1/6 ft.

Now, the volume of the concrete = 17 × 17 × 1/6

[tex]=\frac{289}{6}\text{ cubic ft}[/tex]

We know that,

1 cubic yard = 27 cubic feet

[tex]\implies 1 \text{ cubic feet}=\frac{1}{27}\text{ cubic yards}[/tex]

[tex]\implies \frac{289}{6}\text{ cubic ft}=\frac{289}{6}\times \frac{1}{27} = \frac{289}{162}\text{ cubic yards}[/tex]

Since,  the concrete costs $40.00 per cubic yard.

Hence, the total cost of concrete = [tex]\frac{289}{162}\times 40=\frac{11560}{162}=\$71.3580247\approx \$71.360[/tex]

The total cost of concrete is,

C = $71.4

We have to give that,

Dimensions of the concrete are,

17 ft by 17 ft by 2 in.

And, the concrete costs $40.00 per cubic yard.

Since we know that,

1 feet = 12 inches

Hence,

2 inches = 2/12 = 1/6 feet

Thus, the dimension of the concrete is 17 ft by 17 ft by 1/6 ft.

So, the Volume of the concrete,

V = 17 x 17 x 1/6

V = 48.2 cubic feet

Here, 1 cubic yard = 27 cubic feet

And, the concrete costs $40.00 per cubic yard.

Hence, the total cost of concrete is,

C = 48.2 × 40 / 27

C = $71.4

To learn more about the volume visit:

brainly.com/question/24372707

#SPJ6

A square garden plot has an area of 75 ft2. a. Find the length of each side in simplest radical form. b. Calculate the length of each side to the nearest tenth of a foot.

Answers

A square garden plot has an area of 75 ft2.
a. Find the length of each side in simplest radical form.
First, a square area (A) = length (l)^2
A(ft2) = l^2 --> so l(ft) = square root (sr) of A
l = srA = sr75
Next, factor out 75 into number with even roots: 25•3 = 75
So l = sr25•sr3 --> l = 5•sr3 ft
5•sr3 is in the simplest radical form

b. Calculate the length of each side to the nearest tenth of a foot.
l = sr3 = 1.732 --> so 5•1.732 = 8.66ft
Tenth is one place to the right of the decimal, so l = 8.7 ft

Answer:

a)the length of each side is [tex]5\sqrt3[/tex] feet

b)In the nearest tenth the length of the side is 8.7 feet.

Step-by-step explanation:

The area of the square garden is 75 square feet.

a) Let x  be the length of each side.

We know that,

[tex]\text{Area of square}=\text{(Side)}^2[/tex]

Hence, we have

[tex]75=x^2\\\\x=\sqrt{75}\\\\x=5\sqrt{3}[/tex]

Thus, the length of each side is [tex]5\sqrt3[/tex] feet

b)

In the nearest tenth the length of the side is 8.7 feet.

Two sandboxes with the same area are shown. The equation w(3w+1)=5^2 represents the area of Sandbox 2 in terms of its width. Which is the approximate length of the longest side of Sandbox 2? Round the answer to the nearest hundredth of a meter.

A.) 2.72 meters

B.) 3.06 meters

C.) 9.16 meters

D.) 10.18 meters

Answers

sandbox 1 area = 5*5 = 25 square m

sandbox 2

25=w*(3w+1)=

3w^2+w-25=0

w=2.7248 (round to 2.72 m)

2.72*3=8.16+1 = 9.16

Longest side = 9.16 meters

Answer:

C.) 9.16 meters

Step-by-step explanation:

We are given that the two sandboxes have same area and the equation is given by 25 = w*(3w+1).

Now, we simplify this equation in order to find the value of unknown variable 'w'.

i.e. 25 = 3[tex]w^{2}[/tex]+w

i.e. 3[tex]w^{2}[/tex]+w-25=0

The two factors of this quadratic equation are w=2.72 and w= -3.05.

But, as 'w' represents the length of the box, so it cannot be negative.

Therefore, w = 2.72

So, the longest side of the box is (3w+1) = 3*2.72+1 = 9.16 meter

Hence, the length of longest side to the nearest hundredth is 9.16 meter.


HELP Please THANKS:((((

Answers

answer is C.

w + c <= 27

hope it helps
More than 5 acres will be planted with wheat, so
w>5.

Up to 27 acres will be filled with wheat and corn, so
w+c<=27

Final answer: A C

Not sure ^^^^^^^^^^^

Answers

To factor the trinomial, use slip and slide.
y^2-7y-30
(y-10)(y+3)
(y-5)(2y+3)
If you divide out y-5, you are left with 2y+3
B

- ( 1 + 7x ) - 6 ( -7 - x ) = 36

Please solve and show work

Answers

 -(1 + 7x) - 6(-7 - x) = 36
 -1(1+7x) - 6(-7 - x) = 36
    -1 - 7x + 42 + 6x = 36
                     41 - x = 36
                          41 = 36 + x
                            5 = x
-(1 + 7x) - 6(-7 - x) = 36

Simplify.

-1 - 7x + 42 + 6x = 36

Add 1 to both sides.

-7x + 42 + 6x = 36 + 1

Simplify.

-x + 42= 37

Subtract 42 from both sides.

-x = 37 - 42

Simplify.

-x = -5

Divide both sides by -1.

x = 5

~Hope I helped!~

How many different pizzas can be ordered if the restaurant offers 15 different toppings and there is no limit to
the number of toppings on the pizza?

Answers

Final answer:

Using the formula for combinations with repetition, with 15 different toppings and no limit on the number of toppings per pizza, we find that there can be 32,768 different possible pizzas.

Explanation:

The question you're asking relates to combinations with repetition, a topic in combinatorics, a branch of mathematics. Given 15 different pizza toppings and the possibility of choosing any number of these toppings for a single pizza (including the possibility of a pizza with no toppings at all), we're essentially looking at how many different pizzas can be created.

To calculate the total number of different pizzas that can be ordered, we use the formula for combinations with repetition, which is (n+r-1)C(r), where 'n' is the number of toppings to choose from (15 in this case), 'r' is the number of toppings chosen, and 'C' represents the combination function. Since there's no limit to the number of toppings, 'r' can vary from 0 (a pizza with no toppings) to 15 (a pizza with all the toppings). However, because the question allows any number of toppings and we consider repetitions, the calculation simplifies to 2ⁿ, where n is the number of toppings.

Therefore, calculating this gives us 2¹⁵, which equals 32,768 different possible pizzas. This includes every combination from no toppings at all to a pizza with all 15 toppings.

An angle measures 7pi/9 radians. What is the degree measure of the angle?

Answers

To convert into degrees:

1. You should know the percentage of the angle with respect to 2pi:

(7pi/9) / (2pi) = 7/18

2. Then, multiply the ratio to the 2pi angle in degrees, which is 360

360 * (7/18) = 140
(7pi/9)(180/pi)
140°

multiplying by 180/pi give you a degree measure

Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain.


n | an
1 | 9
2 | 3
3 | −3

Answers

an = 1 + -6(n - 1) Restrictions to the domain are integers greater than or equal to 1

Choose the missing exponent to create a polynomial: 3x^4+4x^2-9x^-?+2
A)2
B)3
C)-9
D)7
E)4

Answers

any given polynomial must have all positive exponents over the placeholder
we see we are given 9x^-?
so (-) times what=positive?
the answer is negative
so we must pick a negative exponent

so the answer is C -9

For a Polynominal 3x^4+4x^2-9x^-?+2 the missing part is mathematically given as

3x^4+4x^2-9x^-(-9)+2

-9, Option C is correct

What is a Polynomial?

Polynomials are summations of elements of the format of kxn, having k as any digit and n is +ve integer

Generally, the expression for the Polynominal  is mathematically given as

3x^4+4x^2-9x^-?+2

In conclusion, the Polynominal must have all positive exponents, hence the value must be negative to give a positive exponent

Hence, -9 is correct

Read more about Polynomial

https://brainly.com/question/17822016

Colby took out a sinlge payment loan for $550 that charged a $60 fee. How much does he have to pay by the time the loan reaches maturity?

Answers

He has to pay by the time the loan reaches maturity
550+60=610

Answer:

Step-by-step explanation610:

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.

A(n) = 12 + (n – 1)(3)


A.12, 21, 39

B. 0, 9, 27

C. 12, 24, 42

D. 3, 24, 27

Answers

[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ 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} \end{cases}\\\\ -------------------------------\\\\[/tex]

[tex]\bf A(n)=12+(n-1)(3)\qquad \begin{cases} n=n^{th}\ term\\ 12=\textit{first term's value}\\ 3=\textit{common difference} \end{cases} \\\\\\ n=1,4\ and\ 10\implies \begin{cases} A(\underline{1})=12+(\underline{1}-1)(3)\\ A(\underline{4})=12+(\underline{4}-1)(3)\\ A(\underline{10})=12+(\underline{10}-1)(3) \end{cases}[/tex]

For the graphed function f(x) = (2)x + 2 + 1, calculate the average rate of change from x = −1 to x = 0. graph of f of x equals 2 to the x plus 2 power, plus 1. (6 points) −2 2 3 −3

Answers

Next time you should write the correct form of equation because it affects greatly the answer. I believe the correct form would be:

f (x) = 2 * x^2 + 1

where the second 2 is a power of x

The average rate of change is also defined as the slope of the equation. Therefore:

average rate of change = slope

Where slope is:

m = (y2 – y1) / (x2 – x1) = [f (0) – f (-1)] / (x2 – x1)

 

Calculating for f (0): x2 = 0

f (0) = 2 * 0^2 + 1 = 1

Calculating for f (-1): x1 = -1

f (-1) = 2 * (-1)^2 + 1 = 3

 

Substituting the known values to the slope equation:

average rate of change = (1 – 3) / (0 – 1)

average rate of change = -2 / -1

average rate of change = 2

 

Answer: 2

Answer:

I believe the proper form of this question is actually... as I have also come across this question.

"For the graphed function f(x) = (2)^(x + 2) + 1, calculate the average rate of change from x = −1 to x = 0."

Step-by-step explanation:

the y2 - y1/ x2 - x1, will actually be (-1,3) and (0,5).

This means you will get a 5 + 1 (because subtracting a -1 is the same as adding 1) over 0 - 3.

Next you have 6/-3 which will give you a answer of -2

Now I do believe the proper answer is actually 2 because the graph shows a chart that is growth, not decay, but the math gives a -2 which is confusing.

Find a and b so that the polynomial, p(x)=x^2+ax-b passes through the points (6,-9) and (1, 16)

Answers

The given equation is:

p(x) = x^2 + ax - b

We write this in terms of y:

y = x^2 + ax – b

To solve for the values of the constants a and b, we are given the following conditions:

When x = 6, y = -9

When x = 1, y = 16

From these conditions, we can formulate two equation by substituting the values of y:

-9 = 6^2 + a(6) – b

6a = b – 45                           ---> 1

 

16 = 1^2 + a(1) – b

a = b + 15                             ---> 2

 

Combining equations 1 and 2:

6 (b + 15) = b – 45

6b + 90 = b – 45

5b = -135

b = -27

 

calculating for a using equation 1:

a = b + 15

a = -27 + 15

a = -12

 

Answers:

a = -12

b = -27

WILL GIVE A BRAINLIEST!!

Find the range of the parent function below.

y=1/x

A.
all real numbers
B.
all real numbers except 0
C.
all positive numbers
D.
all negative numbers

Answers

(the Domain of the function is clearly all Real numbers - {0})

The Range is the set of all values that the function can take.

let c be any value in the range. So c=1/x for some x in the domain, 

and so x=1/c.

For example, is c=10 in the range of the function?
yes, for x=1/10, f(1/10)=1/(1/10)=10.

Consider again x=1/c, the only value of c that cannot be in the Range is c=0, because to produce 0 in the range, x would need to be 1/0, which is undefined.


Answer: 

B.
all real numbers except 0

(-3,1) perpendicular to y=2/5x-4

Answers

(-3, 1)             y = 2/5x - 4 
 x₁  y₁              slope (m) = 2/5x

Since the equation we are looking for is perpendicular to y = 2/5x - 4, we need to find the opposite reciprocal slope. We have to flip the slope upside down and turn it negative.

2/5 ⇒ 5/2 ⇒ -5/2

So far, we have the equation y = -5/2.

Now, we need to find the y intercept by plugging in the given point into point slope form, which is...

y - y₁ = m(x - x₁) 

The subscripts in the y and x are just the x and y in (-3,1). They are just placeholders, not exponents.

y - 1 = -5/2(x + 3)
 y - 1 = -5/2x - 15/2
   + 1               +     1
------------------------------
 y = -5/2x - 13/2 ⇒ final equation


If the discriminant of an equation is negative, which of the following is true of the equation

A it has two complex solutions
B it has one real solution
C it had two real solutions

Answers

The answer is A. it has two complex solutions

Answer:

A. It has two complex roots.

Step-by-step explanation:

We are given that

Discriminant of an equation =negative

We have to find which is  true about the equation .

Let quadratic equation

[tex]ax^2+bx+c=0[/tex]

Discriminant=[tex]D=b^2-4ac[/tex]

If D < 0 , then the equation has complex roots.

Therefore, if the discriminant of an equation is negative then the equation has two complex roots.

Answer:A. It has two complex roots.

If (44)x = 432, what is the value of x?

4
7
8
28

Answers

44 x 4 = 176

44 x 7 =308

44 x 8 = 352

44 x 28 =1232


 none of those will =432

 are you sure you have the right numbers?


(44)x=432

x=432/44 = 9.8181


28 would be your vaule for x
Other Questions
What was the role of viceroys in early Spanish coloniesA. superviseB. cookC. hunt NEED HELP PLEASE In Ellen's math class, there are 2 boys for every 3 girls . What is the the following ratio of boys to girls in the class ?A . 17/21B . 14/21C . 7/14D. 11/17 Which event provided an opportunity for L'Ouverture to establish power and rid Haiti of both British and Spanish influence? A.) Great Britain's takeover of the Spanish colony of Santa Domingo in Haiti B.) Laws passed by the French National Convention to abolish slavery in Haiti C.) Napoleon Bonaparte's recapture of Haiti and his reinstitution of slavery D.) The Haitians' reoccupation of the Dominican Republic establishing independence Sal bought three CDs for 1598 each a computer cable for 3995 and a case for his MP3 player for 2499 sales tax is 7% to the nearest cent what is the total cost of his purchasesPleaseee helppppppp The number of particles in 1 mole of hydrogen gas is ________. Suppose you are walking home from the skating ring , you have to walk 6 miles east and 9 miles north , use the Pythagorean theorem how far is the skating ring from where u are.plzzzzz!!!!!help (15+23)+7=15+(___+7) Why does Truman feel the act is radical and not moderate, as some in Congress claim? In the early years of the industrial revolution factory owners paid women ___ higher wages the same wages as men lower wages then men in material goods and food stuffs Museoa.marta va al ________ para escuchar la orquesta. teatrob.el pintor es un _________. cinec.ella es una cantante en ___________. instrumentosd.pedro va al ________ para ver obras de arte. murale.paco va al _______ para ver una pelcula nueva. artista f) la orquesta hace un _________ bellsimo. actor g) los msicos tocan muchos ________. el coro h) la persona que ensaya es un _________. sonido i) me gusta visitar las ________ de arte. galeras j) una pintura muy grande en la pared es un _________. what country gained independence from Portugal True or False: The future tense is formed the same way in all 4 conjugations. In the short story "Son," author John UpdikeA.purposely confuses the reader by going back and forth in time.B.makes a deliberate choice to manipulate the story structure in order to support his themes.C.develops characters that span generations in order to add depth to the story.D.combines setting, characterization, and plot to create a suspenseful mood. Consider the words typically associated with geometry. Are there any words that would be hard to precisely define? What words can you think of? 1.Determine the value of n from: nP3 = 5 (4P2)2.Consider the experiment of throwing of two coins, a) establish the probability distribution b) determine the expected value c) determine the standard deviation Two saturated aqueous solutions are prepared at 25 C.One is made by dissolving lithium carbonate (Ksp = 8.15 x 10) in 100.0 mL of water until excess solid is present, while the other is prepared by dissolving lithium phosphate (Ksp = 2.37 x 10) in 200.0 mL of water until excess solid is present.1) What is the molar concentration of Li in the lithium carbonate solution?2) What is the molar concentration of Li in the lithium phosphate solution?Please, show all calculation with comments. Thanks! Australias arid and semiarid climate regions can receive less than 5 inches of rain a year.True or False Cultural diffusion is the process by which a cultural custom, item, or concept is modified or hybridized to fit the cultural context of a society that borrows it. Solve for v 14v-8v=24 What is the ratio of 2.5 million to 1.5 million Steam Workshop Downloader