Find the sum of the geometric series 100+20+…+0.16

Find The Sum Of The Geometric Series 100+20++0.16

Answers

Answer 1

Answer:

c)  124.96

Step-by-step explanation:

Geometric series:  100 + 20 + ... + 0.16

First we need to find which term 0.16 is.

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)

To find the common ratio r, divide one term by the previous term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{20}{100}=0.2[/tex]

Therefore, [tex]a_n=100(0.2)^{n-1}[/tex]

Substitute [tex]a_n=0.16[/tex] into the equation and solve for n:

[tex]\implies 100(0.2)^{n-1}=0.16[/tex]

[tex]\implies (0.2)^{n-1}=0.0016[/tex]

[tex]\implies \ln(0.2)^{n-1}=\ln0.0016[/tex]

[tex]\implies (n-1)\ln(0.2)=\ln0.0016[/tex]

[tex]\implies n-1=\dfrac{\ln0.0016}{\ln(0.2)}[/tex]

[tex]\implies n=\dfrac{\ln0.0016}{\ln(0.2)}+1[/tex]

[tex]\implies n=5[/tex]

Therefore, we need to find the sum of the first 5 terms.

Sum of the first n terms of a geometric series:

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

Therefore, sum of the first 5 terms:

[tex]\implies S_5=\dfrac{100(1-0.2^5)}{1-0.2}[/tex]

[tex]\implies S_5=124.96[/tex]


Related Questions

A spinner is divided into 4 equal sectors that are colored green, red, yellow, and blue. The number of times the spinner lands on each color is listed below. image Which statement best explains whether the results listed in the table should cause the probability model for the given situation to be questioned?

Answers

The probability of landing on the 4 spinners divided into four equal parts will be P=25%

What is probability?

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Here the spinner is divided into four parts of the colours green, red, yellow, and blue.So the number of the sample variable are:-

P(S)=[red,green,yellow,blue]=[4]

The favourable outcome is given as:-

F[s]=[1]

So the probability will be given by:-

P={1}÷{4}=0.25=0.25x 100=25\%

Hence the probability of landing on the 4 spinners divided into four equal parts will be P=25%

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One angle of a right triangle measures 24°. What is the measure of the other acute angle?

Answers

Answer:

66 °

Step-by-step explanation:

Given:

One angle of a right triangle measures 24°.

To Find:

What is the measure of the other acute angle?

Solve:

Note:

Total angles in a triangle 180 degree

Right Triangle ⇒ 90 degree

Let "x" be the measure of the other acute angle

90° + 24° + x = 360°

114° + x = 180°

x = 66°

Kavinsky~

A square based pyramid has a surface area of 111.6 in2. The sides of the base
of the pyramid measure 4 inches. What is the slant height of the figure?

Answers

Answer:

  11.95 in

Step-by-step explanation:

We can find the slant height of a square-based pyramid by solving the area formula for the unknown value.

__

The formula for the area of a square-based pyramid can be written ...

  A = s(s +2h)

where s is the side of the square base, and h is the slant height.

Filling in the given values, we can solve for h:

  111.6 = 4(4 +2h)

  27.9 = 4 +2h . . . . . divide by 4

  13.95 = 2 +h . . . . . divide by 2

  11.95 = h . . . . . . . . subtract 2

The slant height of the figure is 11.95 inches.

b) 7 of these cuboids of side 3 cm are put together to make this shape. Find the surface area of this shape. (3) Total marks: 5

Answers

Answer:  504 cm^2

The surface area of the shape is:

3 3 * 3=9

9 * 7=63

63+9=72 * 7

=504cm^2

Solve for v in terms of w, x, y, and z.
ZW = -yxv
V=

Answers

Answer:

V= -WZ/xy

Step-by-step explanation:

-yxV=ZW

V=-ZW/yx

V=-ZW/yx

V=-WZ/xy

Select all the rational numbers

Answers

Answer:

B. 3.14

C. .33

E. 3.46

remember rational number are can be measured from decimals and even fractions.

find the values of x and y. then find the measures of the interior angles of the polygon​

Answers

The value of x and y are 9 and 6. Then the measure of the angles ∠A, ∠B, ∠C, and ∠D will be 54°, 36°, 126°, and 144°.

What is a cyclic quadrilateral?

If the quadrilateral is inscribed in a circle then the quadrilateral is known as a cyclic quadrilateral.

We know the sum of the opposite angle of the cyclic quadrilateral is 180°.

Then we have

14x + 9y = 180 ...1

4x + 24y = 180 ...2

By solving the equations 1 and 2, we have

x = 9 and y = 6

Then the measure of the angle will be

∠A = 9y = 9 × 6 = 54°

∠B = 4x = 4 × 9 = 36°

∠C = 14x = 14 × 9 = 126°

∠D = 24y = 24 × 6 = 144°

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What percent is equivalent to the fraction 7/10

Enter your answer in the box.

Answers

Answer:

70%

Step-by-step explanation:

Two Steps to Convert a Fraction to a Percent

Use division to convert the fraction to a decimal:

7/10 = 7 ÷ 10 = 0.7

Multiply by 100 to get the percent value:

0.7 × 100 = 70%

Therefore the answer is 70%.

10) A rhombus has a
diagonal 8.6 mm long
and an area of 81.7 mm. what is the
perimeter?


Answers

Answer:

P=41.72

Step-by-step explanation:

S=ACxDB/2

81.7=8.6xDB/2

81.7=4.3xDB|:4.3

19(mm)=DB

DO=19/2=9.5

OC=8.6/2=4.3

(O is the center of the rhombus, where two diagonals meet)

a²+b²=c² (DO²+OC²=DC²)

9.5²+4.3²=c²

90.25+18,49=c²

√108,74=√c²

c≈10.43

P=4c

P=4x10.43

P=41.72

Hope it helps:)

help ya girl out real quick!! 50 points for rewardd!

Answers

Answer:

Slope is 1

Step-by-step explanation:

Slope=RISE/RUN

You can see the slope is constant. To clarify we can do an example.

So rise can be 2

And run is also 2

Change in y is equal to change in x

so 2/2=1

Hope it helps

(4,0)(6,2)

Slope

m=y2-y1/x2-x1m=2-0/6-4m=2/2m=1

Can some one please help me ?

Answers

Answer:

B. 13.5 in ^2

Just use the formula : 1/2 h ( a + b )

If in the case you need any other help , let me know. [ You need to pay me] :) Thanks!

If Madison had 10 apple and gave 3 away to Zack how many apples does she have

Answers

Answer:

7 i think because 10-3 =7

also 3+7 =10

Step-by-step explanation:

Answer:

Its 7 because it you do 10-3 it would equal up to 7

Step-by-step explanation:

a photograph measuring 8 cm by 10cm costs 440 naira. what will be the cost of an enlargement measuring 20cm by 25cm

Answers

Answer:

2750

Step-by-step explanation:

Remark

You have to assume that this can be solved by using a proportion. A proportion is 2 equal ratios. Three parts of the 2 ratios must be known and your job is to find the 4th one.

Equation

w*L/C1 = w1*L1 / x

Solution

w = 8

L = 10

w1 = 20

L1  = 25

C1 = 449

C2= x

Solution

8*10/440 = 20*25/x          Combine

80/440 = 500 / x               Cross Multiply

80x = 440*500                  Combine

80x = 220000                  Divide by 80

x = 220000/80

Answer

x = 2750

A delivery truck drove 40 miles per hour. It took 2 hours to travel between two towns. What is the distance between the two​ towns

Answers

Answer:

80 miles

Step-by-step explanation:

40 miles per hour means you move 40 miles in one hour.

If it took 2 hours to travel between the two towns at 40 mph, multiply 40 by 2 and you get 80.

Hope this helps!

Answer:

your answer would be 80 miles

What number comes
next in the pattern? The rule is "Multiply
the position number by itself." Describe a
feature of the pattern.
1,4,9,16,

Answers

Answer:

25 comes next

Step-by-step explanation:

okay so when it says "position" it means the numbers place in the order, for example "4" in this case would be the in the second position and "16" in the fourth position.

to get 1 you do: 1*1 because 1 is the first number and it is in the first (1) position.

To get the second number (4) you do: 2*2 because two is the second number (it comes after 1) and it is in the second position.

For 9, you do 3*3; the pattern here is squares, 1^2=1 2^2=4, 3^2=9, 4^2=16.

If we follow that pattern we will get 5^2=25

Please answer these questions for me

Answers

Answer:

Do reciprocal of that and diameter formula and when your answer will come me just do square multiple of that

What is the solution to the equation?
5 = 2/5 a

O 2

O 4 3/5

O 12 1/2

O 25

Answers

Answer:

Option C, [tex]12\frac{1}{2}[/tex]

Step-by-step explanation:

Step 1:  Multiply both sides by 5/2

[tex]5 = \frac{2}{5}a[/tex]

[tex]5 * \frac{5}{2} = \frac{2}{5}a * \frac{5}{2}[/tex]

[tex]\frac{25}{2}=a[/tex]

[tex]12\frac{1}{2}=a[/tex]

Answer: Option C, [tex]12\frac{1}{2}[/tex]

Hope this helps!  Let me know if you have any questions

Which figure has two bases and one lateral face that is rectangular?

Answers

a prism

Step-by-step explanation:

it has two parallel, congruent bases that are connected by a lateral face

What is the value of x in the triangle?
2xº
25°
25°

Answers

Answer:

130 degrees

Step-by-step explanation:

2x+25+25=180

2x=130

Answer:

65°

Step-by-step explanation:

25+25+2x= 180(sum of all the angles of a triangle)

2x= 180-50

x=130/2= 65

What are all the rational roots of the polynomial f(x) = 20x4 x3 8x2 x – 12? negative four-fifths and three-fourths negative four-fifths and negative three-fourths –1, negative four-fifths, three-fourths, and 1 –1, negative four-fifths, negative three-fourths, and 1

Answers

The root of the polynomial f(x) = 20x⁴ + x³ + 8x² + x - 12 is at the point -4/5 and 3/4

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the polynomial:

f(x) = 20x⁴ + x³ + 8x² + x - 12

The root of the polynomials is at the point the graph of f(x) intersects with the x axis. This is at -4/5 and 3/4

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Answer:

A

Step-by-step explanation:

Did it on edge :)))

A hat contains four slips of paper. The slips of paper are numbered 3, 3, 6, and 8. One slip of paper is randomly selected and not replaced, and then a second slip of paper is selected. the numbers on the two slips of paper are added together.

A fair decision is to be made about which one of three sizes of coffee will be ordered, using the sum of the numbers on the slips of paper.

The coffee size options are small, medium, and large.

Which description accurately explains how a fair decision can be made in this situation?

A.) If the sum of the slips of paper is 9, a small coffee will be ordered. if the sum of the slips of paper is 11, a medium coffee will be ordered. If the sum of the slips of paper is 6 or 14, a large coffee will be ordered.

B.) If the sum of the slips of paper is 9, a small coffee will be ordered. if the sum of the slips of paper is 6, a medium coffee will be ordered. If the sum of the slips of paper is 11 or 14, a large coffee will be ordered.

C.) If the sum of the slips of paper is 9, a small coffee will be ordered. if the sum of the slips of paper is 14, a medium coffee will be ordered. If the sum of the slips of paper is 6 or 11, a large coffee will be ordered.

D.) If the sum of the slips of paper is 14, a small coffee will be ordered. if the sum of the slips of paper is 9, a medium coffee will be ordered. If the sum of the slips of paper is 6 or 11, a large coffee will be ordered.

Answers

The option that  accurately  fit the description that  explains how a fair decision can be made in this situation is option A - the sum of the slips of paper is 9.

What is Random selection?

This is known to be  scientific method used when each unit in a population is known or said to have an equal chance of been selection for  any inclusion into a sample.

The option that  accurately  fit the description that  explains how a fair decision can be made in this situation is option A - the sum of the slips of paper is 9, a small coffee will be ordered. if the sum of the slips of paper is 11, a medium coffee will be ordered. If the sum of the slips of paper is 6 or 14, a large coffee will be ordered.

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Multiplying by which number is equivalent to finding 80%?

Answers

Answer:

80% is equivalent to 80/100 which is the same as 0.8 and we can just take a number, for example 10, and we can multiply it by 0.8 and we would get 8 which is 80% of the original value.

draw the line 3y-4x=12 for values of x from -3 to 3

Answers

Answer:

Step-by-step explanation:

Explanation:

Notice that the terms are linear or constant, so this equation represents a straight line.

We can find the intersections with the

x

and

y

axes by setting

y

or

x

equal to zero, or equivalently covering up the corresponding term and solving the resultant equation.

So putting

x

=

0

we get:

3

y

=

12

Dividing both sides by

3

, we find:

y

=

4

So the line intercepts the

y

axis (which has equation

x

=

0

) at the point

(

0

,

4

)

If we instead put

y

=

0

then we get:

4

x

=

12

The functions f(x) and g(x) are described using the following equation and table:

f(x) = −3(1.02)x

x g(x)
−1 −5
0 −3
1 −1
2 1
Which statement best compares the y-intercepts of f(x) and g(x)? (5 points)

Group of answer choices

The y-intercept of f(x) is equal to the y-intercept of g(x).

The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).

The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).

The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).

Answers

Answer:

A) The y-intercept of f(x) is equal to the y-intercept of g(x).

Step-by-step explanation:

Given functions f(x) and g(x).

What is the y-intercept?

The y-intercept is the output of the function with the input of zero.

In other words the y -intercept is:

f(0) for f(x) and g(0) for g(x)

Let's determine the y-intercept of the given functions:

f(0) = - 3(1.02)⁰ = - 3(1) = - 3

g(0) = - 3 according to table

We see both functions have same y-intercept with the value of -3.

The matching answer choice is A.

Stacy recorded the number of minutes she used her
smartphone each day for one week before using an
app that awards points for decreased phone usage,
and for one week after using the app. Stacy's
alternative hypothesis is Ha:X< 114.6.
Before 103 127 87 12495 136 130
After 83 94 1201057598 96
Stacy used a simulation to randomize her data 200
times. She found that the difference between sample
means over 200 trials is approximately normally-
distributed, with a mean of -0.2 and a standard
deviation of 9.1. Which of the following conclusions
is most appropriate?
Phone use did not change.
Phone use increased and then decreased.
Phone use increased.
Phone use decreased.

Answers

Using the t-distribution, it is found that the most appropriate conclusion for the hypotesis test is given by:

Phone use did not change.

What are the hypothesis tested?

At the null hypothesis, we test if the mean has not changed, that is:

[tex]H_0: \mu = 0[/tex]

At the alternative hypothesis, we test if it has changed, that is:

[tex]H_1: \mu \neq 0[/tex].

What is the test statistic?

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.

In this problem, the values of those parameters are as follows:

[tex]\overline{x} = -0.2, \mu = 0, s = 9.1, s = 200[/tex]

Hence, the test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{-0.2 - 0}{\frac{9.1}{\sqrt{200}}}[/tex]

t = 0.31.

What is the conclusion?

Considering a two-tailed test, as we are testing if the mean is different of a value, with a standard significance level of 0.05 and 200 - 1 = 199 df, the critical value is of [tex]|t^{\ast}| = 1.972[/tex].

Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis and the conclusion is:

Phone use did not change.

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What is the trigonometric ratio for sin Z?
Enter your answer, as a simplified fraction, in the boxes.

Answers

Answer:

[tex] \large { \purple{ \sf {The \: value \: of \: sin \: Z \: is} \sf \frac{3}{5} }}[/tex]

Step-by-step explanation:

[tex] \large{\underline{\underline{\pink{\sf{To \: \: find :-}}}}}[/tex]

[tex] \textsf{The value of Sin Z}[/tex]

[tex]\large{\red{\underline{\textsf{Given :-}}}}[/tex]

YZ (B) = 32 (which the base of the triangle)

XZ (H) = 40 (which is the hypotenuse of the triangle)

[tex] \textsf{ \huge { \underline{ \orange{Solution :-}}}}[/tex]

[tex] \sf{The \: formula \: to \: find} \sin Z = \frac{P}{H} \\ \textsf{which \: means} \\ \sf \rightarrow \frac{perpendicular}{hypotenuse} [/tex]

But here we don't have perpendicular so we use Pythagoras theorem to find perpendicular

[tex]{ \sf {(perpendicular)}^{2} + \sf{(base)}^{2} = \sf {(hypotenuse)}^{2} } \\ \sf {(P)}^{2} + \sf {(B)}^{2} = \sf {(H)}^{2} [/tex]

let here P = P

[tex] \sf {(P)}^{2} + {(32)}^{2} = {(40)}^{2} \\ \sf {P}^{2} + 1024 = 1600 \\ \sf {P}^{2} = 1600 - 1024 \\ \sf {P}^{2} = 576 \\ \sf P = \sqrt{576} \\ \sf P = 24[/tex]

Now we to find Sin ZPH

[tex] \sf \ \sin Z = \frac{P}{H} \\ \implies \frac{24}{40} \\ \implies \frac{6}{10} \\ \implies \frac{3}{5} [/tex]

PLEASE ANSWER AS SOON AS U Can

Answers

Answer:  3082.2

Step-by-step explanation:

Answer: 3,082.2 ft

Step-by-step explanation:

You must apply the formula for calculate the perimeter of a circle, which is:

P=πd where,

P is the perimeter of the circle. (P=9,687 ft)

d is the diameter of the circle.

When you solve for d, you get:

d = P/π

d = (9,687 ft)/(22/7)

d = 3,082.2 ft

Therefore, the answer is: 3,082.2 ft

Mr. conner is placing stone tiles to make a patio. each tile is 1 square foot. the drawing shows the dimensions of his patio. a quadrilateral is broken into a triangle and rectangle. the triangle has a base of 20 feet and a height of 6 feet. the rectangle has a base of 20 feet and a height of 12 feet. how many total stone tiles will mr. connor need for the patio? 240 stone tiles 300 stone tiles 360 stone tiles 480 stone tiles

Answers

300 stone tiles would be needed to make a patio that has a total area of 300 ft²

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Area of triangle = (1/2) * base * height = 0.5 * 20 ft * 6 ft = 60 ft²

Area of rectangle = base * height = 20 ft * 12 ft = 240 ft²

Total area of patio = 60 ft² + 240 ft² = 300 ft²

Number of stone tiles needed = 300 ft² / 1 ft² = 300

300 stone tiles would be needed to make a patio that has a total area of 300 ft²

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Answer:

300

Step-by-step explanation:

B

Apply green’s theorem to evaluate the integral 3ydx 2xdy

Answers

The value of the integral 3ydx+2xdy using Green's theorem be - xy

The value of    [tex]\int\limits_c 3ydx+2xdy[/tex]  be -xy

What is Green's theorem?

Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C.

If M and N are functions of (x, y) defined on an open region containing D and having continuous partial derivatives there, then

[tex]\int\limits_c Mdx+Ndy[/tex] = [tex]\int\int\〖(N_{x}-M_{y}) \;dxdy[/tex]

Using green's theorem, we have

[tex]\int\limits_c Mdx+Ndy[/tex] = [tex]\int\int\〖(N_{x}-M_{y}) \;dxdy[/tex] ............................... (1)

Here [tex]N_{x}[/tex] = differentiation of function N w.r.t. x

          [tex]M_{y}[/tex]= differentiation of function M w.r.t. y

Given function is: 3ydx + 2xdy

On comparing with equation (1), we get

M = 3y, N = 2x

Now, [tex]N_{x}[/tex] = [tex]\Luge\frac{dN}{dx}[/tex]

               = [tex]\frac{d}{dx} (2x)[/tex]

              = 2

and, [tex]M_{y}[/tex] = [tex]\Huge\frac{dM}{dy}[/tex]

             = [tex]\frac{d}{dy} (3y)[/tex]

             = 3

Now using Green's theorem

= [tex]\int\int\〖(2 -3) dx dy[/tex]

= [tex]\int\int\ -dxdy[/tex]

= [tex]-\int\ x dy[/tex]

=[tex]-xy[/tex]

The value of  [tex]\int\limits_c 3ydx+2xdy[/tex]  be -xy.

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Which choice is equal to 66
6
6
+ 66
6
6
+ 66
6
6
+ 36
3
6
+ 26
2
6
?

Answers

There are 11 1/8 picec that equals 1 3/8

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