Evaluate:
20
Σ 4(8/9)^n-1 = [?]
1
Round to the nearest hundredth.

Answers

Answer 1

Answer:

32.59 (nearest hundredth)

Step-by-step explanation:

Geometric sequence

General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]

(where a is the first term and r is the common ratio)

Given:

[tex]\displaystyle \sum^{20}_{n=1} 4 \left(\dfrac{8}{9}\right)^{n-1}[/tex]

Therefore:

a = 4r = 8/9

Sum of the first n terms of a geometric series:

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

To find the sum of the first 20 terms, substitute the found values of a and r, together with n = 20, into the formula:

[tex]\implies S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}[/tex]

[tex]\implies S_{20}=32.58609013...[/tex]

[tex]\implies S_{20}=32.59\:\: \sf (nearest\:hundredth)[/tex]                    

Answer 2

General form of geometric progression

ar^n-1

On comparing to the summation

a=4r=8/9

Apply Sum formula

[tex]\boxed{\sf S_n=\dfrac{a(1-r^n)}{1-r}}[/tex]

[tex]\\ \implies \sf S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}[/tex]

[tex]\\ \implies\sf S_{20}=32.586[/tex]

[tex]\\ \sf\mplies S_{20}=32.59[/tex]


Related Questions

neeeed helppp asapp

Answers

Answer:

y=3x-1

Step-by-step explanation:

the answer is: y = 3x-1

you use the equation y=mx + b. b is your y intercept. in this question, -1 is your y intercept, because the graph passes the y axis at the point (0, -1).

m is also the slope, which is rise over run. so you go up 3 units and 1 unit to the right, which is 3/1 as your m .

overall, your equation of the line is:
y = 3x - 1

You are going on vacation with your family to the beach. You already spent $160 on
groceries for the week, and you know that each time you eat out you will spend another
$40. Does The relationship between the number of the Times eating out in the total budget represent a linear function?

Answers

Answer:$440, 9

Step-by-step explanation:

The relationship between the number of the times eating out in the total budget represent a linear function.

What is a linear function?

"A linear functions are those whose graph is a straight line."

Given, I already spent $160 on groceries for the week.

Each time I eat out you will spend another $40.

Let, I eat 'x' times during vacation.

Therefore, the required function will be:

f(x) = 160 + 40x

Hence, the function is a linear function.

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Which graph is an example of a function whose parent function is y = StartRoot x EndRoot?
On a coordinate plane, a curve starts at (negative 1, negative 1) and then curves up and to the right into quadrant 1.
On a coordinate plane, a parabola has a vertex at (0, 1).
On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = negative 1. One curved decreases from quadrant 2 into quadrant 1 and approaches y = 1. It crosses the y-axis at (0, 2). The other curve approaches y = 1 in quadrant 1 and then curves down and approaches y = negative 1 in quadrant 3. It crosses the x-axis at (negative 2, 0).
On a coordinate plane, a curve starts in quadrant 3 and then increases into quadrant 1. It crosses the y-axis at (0, negative 2) and crosses the x-axis at (1.5, 0).

Answers

Using translation concepts, the graph of a translated function of [tex]y = \sqrt{x}[/tex] is given by:

On a coordinate plane, a curve starts in quadrant 3 and then increases into quadrant 1. It crosses the y-axis at (0, negative 2) and crosses the x-axis at (1.5, 0).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

[tex]y = \sqrt{x}[/tex] starts at (0,0) and in it's entirety, is in quadrant 1. When it is shifted down and left, it will start on quadrant 3 and increase into quadrant 1, hence the correct option is given by:

On a coordinate plane, a curve starts in quadrant 3 and then increases into quadrant 1. It crosses the y-axis at (0, negative 2) and crosses the x-axis at (1.5, 0).

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Answer:

A

Step-by-step explanation:

I took it

On a number line, 1.43 would be located ______. Choose all answers that make a true statement.


1.43
《--|----|----|----|----|----|----|----|----|----|--》

A. to the left of 1.41
B. between 1 and 2
C. between 1.42 and 1.44
D. to the right of 1.45 ​

Answers

Answer:

B and C

Step-by-step explanation:

C because it tells you the true statement

There are 135 people in a sport centre.
73 people use the gym.
59 people use the swimming pool.
31 people use the track.
19 people use the gym and the pool.
9 people use the pool and the track.
16 people use the gym and the track.
4 people use all three facilities.
How many people didn't use any facilities?

Answers

Answer:

200wuwusjjdhsuauuaiajjduwiqisidiwiwia

Answer:

n(U) = n(G)+n(S)+n(T)-n(GnS)-n(GnT)-n(TnS)+n(GnTnS) + n(GnTnS)^c

135= 73+59+31-19-9-16+4+ n(GnTnS)^c

no. of people not using any facility =12

The diagram shows a swimming course set out on a lake. Angle BCA = 90°. B 80m 145m C A Not to scale C is due north of A. Calculate the bearing of B from A.

Answers

the pronunciation of this question is wrong make it right first then I will answer

Step-by-step explanation:

please send this question again because I I think you want to write it fast and by mistake you are wright wrong

please help me with this. put the shapes in their correct place on the Venn diagram. Screen shot and edit if you have to.

Answers

View the answer in the Venn Diagram below.

A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a quadrilateral ABCD are A, B, C, and D. A quadrilateral has the following sides: AB, BC, CD, and DA.

A simple (non-self-intersecting) quadrilateral with two sets of parallel sides is known as a parallelogram in Euclidean geometry.

A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and breadth of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

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Which inequality describes the acceptable weights for the suitcase?
x≤ 32.5 or x ≤ 47.5
32.52x2 47.5
x≤ 32.5 or x ≥ 47.5
32.5 ≤ x ≤ 47.5

Answers

Based on the given options, the inequality for the acceptable weights of the suitcase is 32.5 ≤ x ≤ 47.5.

What is the acceptable weight for the suitcase?

You didn't include the full question but this question can be answered based on the given options.

When inequalities are written, there is no inclusion of "or" which eliminates options A and C.

It is illogical to have an inequality as 32.5 ≥ x ≥ 47.5. This is because if 32.5 is larger or equal to x, then x cannot be larger than 47.5. This is mathematically impossible.

This leaves the likely answer as 32.5 ≤ x ≤ 47.5 which means that the weight of the suitcase has to be larger than or equal to 32.5 but less than or equal to 47.5.

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Answer:

32.5 ≤ x ≤ 47.5

Step-by-step explanation:

Xander needs to collect at least 120 cans for a food drive to earn community service credit. He has already collected 64 items.

Part A
Choose the inequality and solution to represent the number of cans, c, that Xander must still collect.

Answers

Answer:

Inequality: 64+C[tex]\geq 120\\\\[/tex]

               - 64.       -64

We subtract to isolate variable

Solution: [tex]C\geq 56[/tex]

if x + 3y = 25 write y in terms of x and also find the two solutions of this equation

Answers

Answer:

y= 25/3 - x/3

Step-by-step explanation:

y= 25/3 - x/3

If you draw all hearts from a deck of 52 cards,
what is the ratio of the remaining cards to the
whole deck?

Answers

Answer:

39

Step-by-step explanation:

Okay so there are 52 cards in a deck and there are 4 of each card. 4 kings 4 Queens 4 Jacks 4 Ace 4 Twos 4 Threes 4 fours 4 fives 4 sixes 4 sevens 4 eights 4 nines 4 tens. One from each group is a heart there are 13 groups so therefore subtract 13 from 52.

A cylindrical barrel of water has a base radius of 30 cm and is 110 cm high.
a) Find it’s volume in cm³.
b) Find it’s capacity in litres
( Hint is 1 cm³= 1 ml )
c) Find the number of bottles of water that can be filled from the barrel if each bottle holds 0.73 litres.

Answers

The volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.

What is a cylinder?

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

We have:

The radius of the cylindrical barrel r = 30 cm

Height of the cylindrical barrel h = 110 cm

Volume:

[tex]\rm V = \pi (30)^2 (110)[/tex]

V = 311017.67 cubic cm

The volume of litres:

V = 311.017 cubic ml  (1 liter = 1000 cubic cm)

Number of bottles = 311.017 /0.73= 426 bottles

Thus, the volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.

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Add.
(−2+6x^3−3x^2)+(4x^3−5+x^2)

Answers

Answer:

10x^3 - 2x^2 -7

Step-by-step explanation:

To subtract polynomials, you want to subtract the biggest exponent from the first polynomial to the second

so 6x^3 + 4x^3 and that would be 10x^3

then -3x^2 + x^2 and the negative is larger so it would be -2x^2

and finally -2 + -5 and that is -7

hope this helps! :)

Ten years ago Victors age WAs half of the age he will be in 10 years how old is he now?

Answers

By solving a linear equation, we will see that Victor is 30 years old.

How old is Victor now?

Let's say that Victor is x years old.

We know that 10 years ago, (x - 10), his age was half of what it will be in 10 years (x + 10).

Then we can write the linear equation:

(x - 10) = (x + 10)/2

Now we can solve that equation for x:

2*(x - 10) = x + 10

2x - 20 = x + 10

2x - x = 10 + 20

x = 30

So we conclude that Victor is 30 years old.

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Which table can be created using the equation below?
-2 + 4x = y
X
y
-5-22
0
3
X
y
-22 -5
-2 0
10
3
X
-5
0
-2
10
03
y
-18
-2
10

Answers

Answer:

h

Step-by-step explanation:

h

Josh and Bella picked apples from a tree. Josh had 3 less than 2/3 of Bellas apples. If Josh had 7 apples, how many apples did Bella have?

Answers

Answer:

Bella had 15 apples

Step-by-step explanation:

First, you see that Josh has 3 less than 2/3 of Bellas apples. If Josh has 7 apples you would add 3 to 7 which = 10. Assuming that 10 = 2/3 of Bellas apples, then you would subtract half of 10 and get 5. 1/3 = 5 apples. Lastly, you should do 5 * 3 which = 15. Bella had 15 apples.

Work out the equation of line B. Give your answer in the form y = mx + c, where m and care integers or fractions in their simplest forms. Work out the equation of line B. Give your answer in the form y = mx + c , where m and care integers or fractions in their simplest forms .​

Answers

Answer:

y = -3x + 1

Step-by-step explanation:

the line crosses the y-axis at (0,1) then c = 1

The points (0,1) and (1,-2) lie on the line then

m = slope = [(-2)-1]÷(1-0) = [-3]÷(1) = -3÷1 = -3

Therefore,

The equation of the line is : y = -3x + 1

What is the intersection of line CA a and line XA?

Answers

Answer:

point A is the intersection point between XA and AC

2x+y=8
y+3z=5
z+2w=1
5w+3x=9

what is x,y,z,w

Answers

Answer:

Systems of equations:

x=3

y=2

z=1

w=0

Probability and Two-Way Tables

Answers

Answer:

the answer are A and Y , B and X.

 A and X are two independent events  , Option A is the correct answer.

When is Probability ?

Probability is the likelihood of an event to happen

A two way table is given

The two events will be independent when

If A is the first event and B is the second event , then

P(A) = P(A|B)

Here the P(A) = 30/100 = 0.3

P(B) = 20/100 = 0.2

P(A|X) = 15/50 = 0.3

P(A) = P(A|X)

Therefore A and X are two independent events , Option A is the correct answer.

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Solve for x.



Enter your answer in the box.

x = ...°

(Please refer to attached image.)

Answers

Answer:

132

Step-by-step explanation:

6 angles plug in for n

(n-2)*180

4*180

720 degrees in all

subtract all other angles

What is the sum of 4 + (-6)?

Answers

Answer:

-2

Step-by-step explanation:

4 + (-6) = -2

Answer = -2

Explanation: since your starting with a positive and adding a negative number you just subtract it.

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answers

The correct representations are - 6x + 15 < 10 - 5x  , An open circle is at 5 and a bold line starts at 5 and is pointing to the right , Option C and E are the right answers.

What is Inequality ?

Inequality are the mathematical statements where algebraic expressions are equated by another algebraic expression or a constant using an Inequality Operator.

The given statement is

–3(2x – 5) < 5(2 – x)

On simplifying can be written as

- 6x + 15 < 10 - 5x

- 6x + 15 < 10 - 5x

- 6x < -5 - 5x

- x < - 5

 x > 5

An open circle is at 5 and a bold line starts at 5 and is pointing to the right .

Therefore Option C and E are the right answers.

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What is the solution of the inequality sh
below?
9+b≤2

Answers

Answer:

b≤-7

Step-by-step explanation:

b+9≤2

Subtract 9 from both sides:

b+9-9≤2-9b≤-7

9+b≤2

subtract 9 on each side which will be -7

the answer will be b≤-7

You’re planning to place an order from an online boutique. Leggings are $12 each and shipping is a flat rate of $5. Write an expression that represents the total cost of your order (not including tax) based on the number of leggings (l) you buy.

Answers

Answer:

For the cost of each legging to be $12, and the shipping of $5, the expression is a straight line C = 12x + 5 where x is the number of leggings.

Step-by-step explanation:

It is given that each legging costs $12. This means that for x number of leggings, the cost will be $12x. Now there is an additional cost of shipping that is $5. So, total cost will be a linear equation and can be written as

C = 12x + 5

This equation represents a straight line like y = mx + c. Here y = C, m = 12 and c = 5.

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help please i dont know this

Answers

Answer:

150 yd

Step-by-step explanation:

the angle bisector divides the opposite sides into segments that are proportional to the other 2 sides .

let x be the distance from the oak tree to the hole, then

[tex]\frac{225}{x}[/tex] = [tex]\frac{375}{250}[/tex] ( cross- multiply )

375x = 56250 ( divide both sides by 375 )

x = 150 yd

If triangle DAB = Triangle CBA

Angle D = 132 degrees and Angle C = x + 18

x = ?

please help

Answers

Answer:

x = 114

Step-by-step explanation:

since the triangles are congruent, then corresponding angles are congruent, that is

∠ C = ∠ D

x + 18 = 132 ( subtract 18 from both sides )

x = 114

Mai bought a wedge with a central angle of 45 degrees and radius 10 centimeters. what is the area of the top surface of this wedge? , 1 of 2. select choice square centimeters

Answers

Using the area of a sector formula, we get the area to be:

[tex]\pi (10)^{2} \left(\frac{45}{360} \right)=\boxed{12.5\pi \text{ cm}^{2}}[/tex]

On. map with a scale of 1:75 000 the distance between a hotel and the airport is 3 cm

What is the actual distance I'm km?

a. 2.25

b. 2.5

c. 22.5

d. 25 km

please help​

Answers

Answer:

a. 2.25 km

Step-by-step explanation:

the scale on a map means how many units in the mapp corresponds to how many units in reality.

in this case

1 cm on the map = 75000 cm in reality =

= 75000/100 m = 750 m =

= 750/1000 km = 0.75 km

3 cm = 3×1 cm = 3 × 0.75 km = 2.25 km

Which of the following parent functions has a domain and range of all real
numbers, excluding the origin?

Answers

Sorry, I think my answer to your question is wrong.

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