what is the sum of the geometric series?

a. 21/2
b. 21/8
c. 21
d. 10

Answer:

255

Step-by-step explanation:

EXPLANATION We are looking for the number of adult tickets sold. number of adult tickets sold =x We are given that there were 61 more student tickets sold than adult tickets. number of student tickets sold =+x61 The total number of tickets sold was 511.

Answer:

they are equivalent

Step-by-step explanation:

8/6

Divide the top and bottom by 2

4/3

16/12

Divide the top and bottom by 4

4/3

They are  the same so they are equivalent

Answer:

5/4

Step-by-step explanation:

Slope is y1-y2/x1-x2 so if you plug in the coordinates you get 4-(-1)/4-0 which you would get 5/4

Answer:

225/4 sqrt(3) in ^3

Step-by-step explanation:

The volume is found by

V = Bh

The B is the triangle

B = s^2 sqrt(3)/4

  = 5^2 sqrt(3)/4

  25/4  sqrt(3)

We know the height is 9

V =  25/4  sqrt(3) *9

V = 225/4 sqrt(3)

this is approximately 97.42785793 in^3

Answer:

because

most people like green apples

Answer:

18 x 15 x 3 is 810. The volume is 810.

Step-by-step explanation:

Volume of cuboid= Length*Width*Breadth

Volume of container= 18 cm X 15 cm X 3cm

Volume of container=810

Hope i helped

Answer:

[tex]810[/tex] centimeters cubed.

Step-by-step explanation:

The formula: [tex]Length * width * height[/tex]

[tex]18 *15*3 =810[/tex] centimeters cubed

Answer: f(2) = g(-2)

Step-by-step explanation: f(x) line if u go to the x axis you see that it’s 2 the x intercept.....

The g(x) line you go to the x axis and see it is -2, that is the x intercept

Answer:

Step-by-step explanation:

4x and 5x are supplementary, so they add up to 180.

4x + 5x = 180 and

9x = 180 so

x = 20.

Because DE and BA are parallel, then 2y and 70 degrees are alternate interior and are equal to one another.

2y = 70 so

y = 35

Answer:

C many solutions

Answer:

3/2

Step-by-step explanation:

Since the lines goes through the point (0,0)

We have a point (2,3)

The slope is y/x = 3/2

Answer:

In total there are 30 cups and there are 2 left over

Step-by-step explanation:

The first thing is to clarify the equivalences, we have to:

1 gallon = 4 quarts

1 quart = 2 pints

1 pint = 2 cups

We will pass everything to cups,

1 gallon of orange juice = 16 cups

3 pints of pineapple juice = 6 cups

2 quarts of lemon ‐ lime soda = 8 cups

So in total they would be 16 + 6 + 8 = 30 cups

How to get 2 cups for 14 guests in total would be 28 cups, which means that if 2 cups are left and left over.

Answer:

The answer is D.

Step-by-step explanation:

By the time 4 seconds has passed, the line is at the bottom of the graph, which represents the time the ball has landed. I hope this helps.

Answer:

In most cases u are either given the value of "t" or the question would be written this way: y=sin20t where as, when comparing we would get the exact value of T(period) at the end

Answer:

Possible

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

thank u god!

Answer:

5+3 = 8!!!! :D

Step-by-step explanation:

Five plus three, is going to equal to eight total.

Answer:

a. 6.48 miles   b. 9.54 miles

Step-by-step explanation:

a. 7/x=x/6

x^2=42

x=6.48

b. 13/x=x/7

x^2=91

x=9.54

Answer:

A. 6.48 miles  

B. 9.54 miles

Step-by-step explanation:

hope this helps :-)

Answer:

B. to show the general tendency of the points in a scatterplot

Step-by-step explanation:

Answer:

C. A condition in which a quantity increases at a rate that is

proportional to the current value of the quantity

Step-by-step explanation:

Exponential growth is increasing, but not at a steady rate. On a graph, it has a curve instead of being a straight line.

Answer:

y = 400 (amt invested at 4%)

x = 500 (amt invested at 7%)

Step-by-step explanation:

Kindly check attached picture for detailed explanation

Answer:

the answer is attached to the picture

The volume of a sphere with a radius of 9.9 ft is 4062.3 cubic foot.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of the sphere is 4/3πr³

Radius is 9.9 ft.

Volume =4/3×3.14×(9.9)³

=4/3×3.14×970.3

=12187/3

=4062.3

Hence, the volume of a sphere with a radius of 9.9 ft is 4062.3 cubic foot.

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Answer:

d. 40

Step-by-step explanation:

2x + x +( x + 20) have to all equal 180 degrees in a triangle.

2x + x + x + 20 = 180

2x + 2x + 20 = 180

4x + 20 = 180

4x = 180 - 20

x = (180-20) / 4

x = 160 / 4

x = 40

Answer:

Step-by-step explanation:

This is the answer that was right for me, I just did this question :) Hope this helps! :D

Answer:

a) Total distance travelled to the nearest foot = 105ft

b) First 5 terms = 12, 9, 6.75, 5.0625, 3.796875

Step-by-step explanation:

From the question above, we can see that this is a geometric series or progression

Formula for geometric progression:

Tn = arⁿ-¹

Where

a = first term

r = common ration

n = number of terms

From the question, we are told that the ball dropped from 16 feet

Hence First term(a) = 16

We are told that the ball rebounds to 3/4 of it's previous height anytime it hits the surface.

Hence, common ratio(r) = 3/4

a) We are told to find total distance to the nearest foot that the ball travelled when it strikes the ground for the 10th time

This means we are to find the sum of the first 10 terms.

Because the ball rises and falls, we would use the rises form

Where the first term = 12 and the number of times is 9 because it rises 9 times

The formula we would use to find this sum is based on if the common ratio is less than or greater than 1

Our common ratio = 3/4, hence it is less than 1.

When r< 1, sum of n terms =

Sn = a(1 - rⁿ)/ 1 - r

It is important to

Where a = 12

r = 3/4

n = 9

Sn = 12( 1 - (3/4)^9) / 1- 3/4

Sn = 104.79ft

Approximately = 105ft

b) First five terms

Using the formula

Tn = arⁿ-¹

Where

a = first term = 12

r = common ration

n = number of terms

First term, n = 1 = 12 × 3/4^(1-1)

= 12 × 3/4 ^(0)

= 12× 1

= 12

Second term, n = 2 = 12 × 3/4^(2-1)

= 12 × 3/4 ^(1)

= 36/4

= 9

Third term, n = 3 = 12 × 3/4^(3-1)

= 12 × (3/4)²

= 6.75

Fourth term, n = 4= 12 × 3/4^(4-1)

= 12 × (3/4)³

= 5.0625

Fifth term, n = 5 = 12 × 3/4^(5-1)

= 12 × (3/4)⁴

= 3.796875

Therefore, the first 5 terms = 12, 9, 6.75, 5.0625, 3.796875

The rebound of the ball from the height is an illustration of a geometric series

(a) The total vertical distance

The given parameters are:

[tex]\mathbf{a = 16}[/tex] -- the first term

[tex]\mathbf{r = \frac 34}[/tex] -- the common ratio

[tex]\mathbf{n = 10}[/tex] -- number of terms

The total vertical distance when it strikes for the 10th time is the sum of nth terms of the geometric series.

So, we have:

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

Substitute values for (a), (r) and n

[tex]\mathbf{S_{10} = \frac{16(1 - 3/4^{10)}}{1- 3/4}}[/tex]

Simplify

[tex]\mathbf{S_{10} = \frac{16(0.943)}{0.25}}[/tex]

[tex]\mathbf{S_{10} = 60.352}[/tex]

Hence, the total vertical distance at the 10th rebound is 60.352 feet

(b) The first five terms of this sum

The nth term of a geometric series is:

[tex]\mathbf{T_n = ar^{n-1}}[/tex]

So, we have:

[tex]\mathbf{T_1 = 16}[/tex]

[tex]\mathbf{T_2 = 16 * 3/4 = 12}[/tex]

[tex]\mathbf{T_3 = 12 * 3/4 = 9}[/tex]

[tex]\mathbf{T_4 = 9 * 3/4 = 6.75}[/tex]

[tex]\mathbf{T_5 = 6.75 * 3/4 = 5.0625}[/tex]

Hence, the first five terms of the sum are 16, 12, 9, 6.75 and 5.0625

Read more about geometric series at:

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Answer:

Number of nickels: 2,

Number of dimes: 6

Step-by-step explanation:

Say d ⇒ number of dimes, n ⇒ number of nickels; from this we can formulate two equation knowing the cost per dime ⇒ $ 0.1, and the cost per nickel ⇒ $0.05

d + n = 8,

0.1 * d + 0.05 * n = 0.7 ⇒ Let us solve through substitution

d = 8 - n into 0.1 * d + 0.05 * n = 0.7,

0.1 * ( 8 - n ) + 0.05 * n = 0.7,

0.8 - 0.1 * n + 0.05 * n = 0.7,

0.8 - 0.1n + 0.05n = 0.7,

- 0.05n = - 0.1,

Number of nickels: 2 ⇒ Now let us substitute this value into the first equation as to solve for d, dimes

d = 8 - 2,

Number of dimes: 6

Answer:

1/ 6

Step-by-step explanation:

Therefore, the required probability is 1/6.

Answer:

1/6

Step-by-step explanation:

Think of drawing 1 student at a time without replacement.

First drawing:

p(boy) = 6/10

Second drawing:

p(boy) = 5/9

Third drawing:

p(boy) = 4/8

p(3 boys) = 6/10 * 5/9 * 4/8 = 3/5 * 5/9 * 1/2 = 3/18 = 1/6

Answer: 1/6

Answer:

The complete table is shown below.

Step-by-step explanation:

The data provided is:

Number Rolled       Observed Frequency       Relative frequency

          1                                     10                                [tex]\frac{10}{60}=\frac{1}{6}[/tex]

         2                                     12                                [tex]\frac{12}{60}=\frac{1}{5}[/tex]

         3                                     10                                [tex]\frac{10}{60}=\frac{1}{6}[/tex]

         4                                     10                                [tex]\frac{10}{60}=\frac{1}{6}[/tex]

         5                                      8                                [tex]\frac{8}{60}=\frac{2}{15}[/tex]

         6                                     10                                [tex]\frac{10}{60}=\frac{1}{6}[/tex]

    TOTAL                                60                                     1

The complete table is shown above.

Answer:

A= 1/5

B.2/15

Step-by-step explanation:

trust me i got it right on edg

Answer:

18-6×10=-42

Step-by-step explanation:

all i did was put it in my calculator

Answer:

13.015625

Step-by-step explanation:

Answer:

13 remainder 1.

I have attached the work to your question.

Please see the attachment below.

I hope this helps!

Answer:

Slope (m) =0

Slope (m) =  

ΔY

ΔX

= 0

θ =  

arctan( ΔY )

ΔX

= 0°

ΔX = 3 – 13 = -10

ΔY = -2 – -2 = 0

Distance (d) = √ΔX2 + ΔY2 = √100 = 10

Answer:

1. 1/2 * 5 * 5

2. 4

3. 7

4. 79

Step-by-step explanation:

IReady test

The volume of the paperweight will be 79.17 cubic inch

A solid geometric figure whose two end faces are similar, equal, and parallel rectilinear figures, and whose sides are parallelograms is known as prism

The steps are as follow:

∴ Area of floor = Area of triangle = ah/2

Where a=5 and h=5 from figure given

∴ Area of floor = (5*5)/2 = 12.5 sq.inch

[tex]V_{1} = \frac{1}{3}sh \\V_{1} = \frac{1}{3}*7*\frac{1}{2}*5*5\\V_{1} = 29.17[/tex]

[tex]V_{2} = sh\\V_{2} = 4*\frac{1}{2}*5*5 \\V_{2} = 50[/tex]

∴ Total volume

[tex]=50+29.17\\=79.17[/tex]

Therefore the total volume of paperweight will be 79.17 cubic inch

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Answer:

10

Step-by-step explanation:

assuming those are meant to be absolute value brackets you have -5 x 2 which is -10 but because it is in the absolute value lines all answers become positive =10