Finite geometric series:

Hi, I want to ask a question, is about... for example, take the sequence 1,2,4,8,... Notice that each number is twice the value of the previous number. So, a number in the sequence can be represented by the function f(n) = 2^n-1. One way to write the sum of the sequence through the 5th number in the sequence is E^5 n-1^2n-1. This equation can also be written as S5 = 2^0 + 2^1+2^2+2^3+2^4. If we multiply this equation by 2, the equation becomes 2(S5) = 2^1+2^2+2^3+2^4+2^5.

What happens if I subtract the two equations and solve for S5? Can I use this information to come up with a way to find any geometric series Sn in the form E^a n-1^bn-1?

Answer:

Justified ✔

Below is the justification.

Step-by-step explanation:

39 + 6 = 45

=> 45 = 45 ✔

This work justifies that y does equal to 39.

Hoped this helped.

Answer:

Step-by-step explanation:

Answer:

6.7679

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Step-by-step explanation:

Cube root of 310 can be represented as 3√310. The value of cube root of one is 310.The nearest previous perfect cube is 216 and the nearest next perfect cube is 343 .

Answer:

the cube too of 310 is 7

Step-by-step explanation:

as cube root of 310 is 6.76

Answer: All four friends would have to share paying the tip and the total so all of them would pay 1/4 of the bill and 1/4 of the tip

Step-by-step explanation: divide the bill and tip between the 4 friends and you get 1/4 which is how much of the bill and tip that all you and the friends have to pay

Answer:

n > 8/3

Step-by-step explanation:

Divide both sides of the equation by 3 to make n the only variable left, n> 8/3

Answer:

1. Sleep well

2. Eat a proper meal to increase your energy

3. Do the ones you are good at first. Skip the harder questions

4. There are 2 parts. One is ELA while the other is math. Do the one that you are good at first so you wouldn't be annoyed.

5. When you are finished filling out the test slip double-check your work that way you could see which one you got wrong.

6. Have faith in yourself. :)

Step-by-step explanation:

Step-by-step explanation

Answer:

A. 1

B. -1

C. 5

Step-by-step explanation:

A. Using the Formula, we get u sub 2 = 9-9+1, which is just 1

B. Using the Formula, we get u sub 3 = 1-3+1, which is equal to -1

C. Using the Formula, we get u sub 4 = 1-(-3)+1, which is just 1+3+1 = 5

The total amount of money Christian spends to download x xongs is y = 15 + 0.99x.

Christian initially pays $15 to join the music service.

Also, he pays $0.99 for each song he downloads from the service.

If he downloads x songs, the amount extra he pays per song he downloads is price per song × number of songs = $0.99 × x = $0.99x.

This amount is added to the initial $15 he pays to join the service. So, the total amount of money he pays is y = initial amount + extra per song = $15 + $0.99x = $0.99x + $15

So, the total amount of money Christian spends to download x xongs is y = 15 + 0.99x.

Learn more about linear equations here:

https://brainly.com/question/11767839

Answer:

$12/$28

Step-by-step explanation:

Let x and y represent the two amounts of money adding up to $40.

Assume that x is the smaller amount.  Then:

 x        3

----- = -----    Remembering that x + y = $40, we get x = $40 - y

 y        7

amd sp we have

 $40 - y          3

-------------- = ------   which, after cross-multiplication, is $280 - $7y = 3y

       y             7

Simplifying this, we get $280 = 10 y, so that y must be $28.  If y = $28, x must be $40 - $28, or $12.

                                                                             $12

Then $40, split in the ratio 3/7, is the ratio ----------------

                                                                            $28

Check:  Note that $12 + $28 = $40, as required, and that $12/$28 = 3/7.

The height of the radio station antenna is approximately 116 feet to the nearest foot.

From the diagram in the attached image

[tex]h=\text{the height of the radio station antenna}\\x=\text{the distance from the foot of the radio station antenna to where the man stood at first}[/tex]

we now have the following relationships

[tex]tan64^\circ=\frac{h}{x}\\\\\implies x=\frac{h}{tan64^\circ}[/tex]

and

[tex]tan43^\circ=\frac{h}{68+x}\\\\\implies x=\frac{h}{tan43^\circ}-68[/tex]

we can equate the two relationships to eliminate [tex]x[/tex].

[tex]\frac{h}{tan64^\circ}=\frac{h}{tan43^\circ}-68[/tex]

solving for the height of the radio station antenna, [tex]h[/tex], we get

[tex]h=\frac{68\times tan43^\circ \times tan64^\circ}{tan64^\circ -tan43^\circ}\approx 116ft\text{ (to the nearest foot)}[/tex]

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Answer:

answer=11 cm.

Step-by-step explanation:

Step-by-step explanation:

V = Volume of cube

a = edge

Formula of volume of cube:

V = a³

[tex]1331 = {a}^{3} \\ \sqrt[3]{1331} = a \\ a = 11[/tex]

The length of each edge is 11 cm.

Answer:

Step-by-step explanation:

First we must know this,

The length of the third side of a triangle must be less than than the sum of the lengths of any two sides of a triangle.

So, Now let us check one by one :

Option 1 : 5m, 6m, 8m

So, 5m, 6m, 8m can form a triangle .

Option 2 : 10m, 10, 2m

So, 10m, 10m, 2m can form a triangle .

Option 3 : 19m, 34m, 15m

So, 19m, 34m, 15m cannot form a triangle .

Option 4 : 3m, 16m, 14m

So, 3m, 16m, 14m can form a triangle .

Answer:

Read image

Step-by-step explanation:

Desmos

Answer:

Option D: [tex]y= -\frac34x+14[/tex]

Step-by-step explanation:

In order for two lines to be perpendicular, the product of the slopes has to be [tex]-1[/tex]. That allows you to rule out A and C. Let's plug the coordinate of the point in B. If the equality holds, we found or line. Else, it's D.

[tex]11 =-\frac34(4) +8 \rightarrow 11 = -3+8 \rightarrow 11=5[/tex] Which is obviously impossible. Our line has to be D

Answer:

Step-by-step explanation:

If u got two negative number such as (-6)+(-7) your answer will be positive 13.

If u got one negative number and one positive number like (-10)-(5) the answer will be negative like -5

Answer:

-6/5

Step-by-step explanation:

The slope of perpendicular lines multiply to -1

5/6 * p = -1

Multiply each side by 6/5

6/5 * 5/6 * p = -1 * 6/5

p = -6/5

The slope of the perpendicular line is -6/5

Answer:

For example, a borrower takes a $100,000 loan with a 6% annual interest rate for three years.

Step-by-step explanation:

Have a GREAT DAY !

Answer:

B : y = 0.1x + 5

Step-by-step explanation:

using the y = mx + b equation

b is the intercept on the y axis ( x = 0)

m is the slope of the line.

From the graph we can see that the intercept is (0,5), therefore b = 5;

To calculate slope (m) pick two pints on the line e.g (100, 15) and (0, 5)

m = (y2 - y1)/(x2 -x1) = (15 - 5)/(100 - 0) = 10/100 = 0.1

m = 0.1

therefore in y = mx + b

y = 0.1x + 5

Answer:

3

Step-by-step explanation:

Answer:

Answer 2

Step-by-step explanation:

Answer:

the answer is A since it forms a pattern :>

Answer:c

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The number of comic books is an illustration of a linear function

She had 17 comic books already.

So, we have:

[tex]\mathbf{Base\ Amount = 17}[/tex]

Her order of 65 books contains 8 comic books per collection.

So, we have:

[tex]\mathbf{Rate = 8}[/tex]

[tex]\mathbf{Total = 65}[/tex]

This is represented as:

[tex]\mathbf{Rate \times b + Base\ Amount =Total}[/tex]

So, we have:

[tex]\mathbf{8\times b + 17 =65}[/tex]

Rewrite as:

[tex]\mathbf{8b + 17 =65}[/tex]

Subtract 17 from both sides

[tex]\mathbf{8b =48}[/tex]

Divide both sides by 8

[tex]\mathbf{b =6}[/tex]

Assume she has 97 books in her collection, then the equation would be represented as:

[tex]\mathbf{8b + 17 = 97}[/tex]

Subtract 17 from both sides

[tex]\mathbf{8b = 80}[/tex]

Divide both sides by 8

[tex]\mathbf{b = 10}[/tex]

The values of b are 6 and 10.

The difference between 6 and 10 is 4

Hence, the value of b has increased by 4

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Answer: x = 48 minutes

Step-by-step explanation:

15 miles/72 min = 0.208 miles/min

(0.208 miles/min)x = 10 miles

x = 48 minutes

Answer:

its the second option under the first one... which is more than likely C.

Step-by-step explanation:

The easiest way to convert a fraction to a decimal is to divide the numerator (the top of the fraction) by the denominator (the bottom of the fraction) by using a calculator. The resulting answer will be the value of the fraction expressed as a decimal number.

Answer:

7

Step-by-step explanation:

5/45 = 3/2x+13

Answer:

3.9375 gallons per day or 4 gallons if you want to round up