The population of a type of local dragonfly can be found using an infinite geometric series where a1 = 65 and the common ratio is 1/6. Find the sum of this infinite series that will be the upper limit of this population.

Answers

Answer 1

In mathematics, number sequencing of the same pattern are called progression. There are three types of progression: arithmetic, harmonic and geometric. The pattern in arithmetic is called common difference, while the pattern in geometric is called common ratio. Harmonic progression is just the reciprocal of the arithmetic sequence.

The common ratio is denoted as r. For values of r<1, the sum of the infinite series is equal to

S∞ = A₁/(1-r), where A1 is the first term of the sequence. Substituting A₁=65 and r=1/6:

S∞ = A₁/(1-r) = 65/(1-1/6)
S∞ = 78

Related Questions

Subtract.

14x-(6+7x)

(Simplify answer)

Answers

14x-(6+7x)
=14x-6-7x
=14x-7x-6
=(14x-7x)-6
=7x-6x

We can simplify an expression by distributing if needed and combing terms if needed.

In the expression 14x - 6 + 7x the terms 14x and 7x are like terms. Because they both have the same variable and are to the same power.

14x - 6 + 7x
21x - 6

So, 21x - 6 is the answer.

Sydney applied the steps below to find the product of (3.1)(–1.6).

Step 1: (3.1)(–1.6) = (–1.6)(3.1)
Step 2: = _______________
Step 3: = (–4.8) + (–0.16)
Step 4: = –4.96

Which expression correctly fills in the blank in Step 2?
(1.6)(3) – (1.6)(0.1)
(–1)(3) + (–0.6)(0.1)
(1)(3) – (0.6)(0.1)
(–1.6)(3) + (–1.6)(0.1

Answers

(-1.6)(3)+(-1.6)(0.1)

Answer with explanation:

We have to find the product of

⇒(3.1)× (-1.6)

Step 1:→ (3.1)(–1.6) = (–1.6)(3.1)

Step 2: = -1.6×(3 + 0.1)=(-1.6) ×3 + (-1.6)×(0.1)→→We have used Distributive property of addition with respect to Multiplication, which is , a × (b + c)=a×b + a × c

Step 3: = (–4.8) + (–0.16)

Step 4: = –4.96

The expression which correctly fills the blank is:

Option D: →→ (–1.6)(3) + (–1.6)(0.1)

6x34 in distributrive property

Answers

6*34=204! Multiply 6 times 10 which is 60 then 60*3 which is 180 of 6* 4 which is 24! 180+24=204

6x34 in distributive property? I gotcha...
It's 204!
Why?

Well just Multiply 6 times 10 which is 60

Then 60*3 which is 180 of 6* 4 which is 24!

180+24=204!

And there is your answer!

-Hope It Helps! :3

C+1/c-2 = 4/7 please show how you got the answer which is 5

Answers

Assuming the equation is (c+1)/(c-2) = 4/7, the answer is actually c = -5

(c+1)/(c-2) = 4/7
7*(c+1) = 4*(c-2) ... cross multiply
7c+7 = 4c-8
7c+7-7 = 4c-8-7 ... subtract 7 from both sides
7c = 4c-15
7c-4c = 4c-15-4c ... subtract 4c from both sides
3c = -15
3c/3 = -15/3 ... divide both sides by 3
c = -5

----------------------------

Check:

(c+1)/(c-2) = 4/7
(-5+1)/(-5-2) = 4/7 ... replace every copy of 'c' with '-5'
(-4)/(-7) = 4/7
4/7 = 4/7 .. true equation; answer checks out

So the answer of c = -5 has been confirmed.

how many 1/4 pound patties can be made from 5 pounds of chicken?

i will give brainliest to 1 out of how ever many answer!

Answers

20patties(^o^)lellelelel

What is the point-slope form of a line with slope -3 that contains the point (10,-1)?

Answers

The point slope form is y+1=-3(x-10).

-3x-y+29=0 The point (10,-0) is (h,k) to set up the problem it will be y-h=m(x-k)
while m is the slope and then you just simplify.

Sue and Kim earn $52 per week for delivering magazines. Sue worked for x weeks and earned an additional total bonus of $12. Kim worked for y weeks. Which expression shows the total money, in dollars, that Sue and Kim earned for delivering magazines? 64x + 52y 52x − 12 + 52y 52x + 64y 52x + 12 + 52y

Answers

52x+12+52y or the last option, is the correct answer

What is the answer to 6,007,200 in exspanded form

Answers

6,000,000 + 7,000+ 200 is your expanded form

hope this helps

The number 6,007,200 in expanded form is written as 6,000,000 + 7,000 + 200, breaking down the number by each digit's place value.

To write the number 6,007,200 in expanded form, we break it down based on the place value of each digit. Here is how you would write it:

Identify the value of each digit in the number.

Starting from the left, write each digit multiplied by its place value.

Add each of these values together.

Applying this to the number 6,007,200, we get:

6,000,000 (6 millions) + 7,000 (7 thousands) + 200 (2 hundreds)

Therefore, the expanded form of 6,007,200 is:

6,000,000 + 7,000 + 200

Answer this for 10 points

Answers

answer: Bottom right is not true (last one)

rate = 26/6.5 = 4
4 in per minute (b) -
so it's constant rate (a)
15 x 4 = 60 (60 inch. in 15 minutes) (c)

The set of ordered pairs described in the table below can be described as which of the following?
x y
1 5
2 2
3 5

a relation only

a function only

both a relation and a function

neither a relation nor a function

Answers

The set of ordered pairs are both relation and function

It is a function because, for every value of x, there is one unique value of y

It is a 'relation' because there is a relation between two sets of values; set of x-values and set of y-values

A function is one example of a 'relation'.

Pre-image point N(6, -3) was dilated to point N'(2, -1). What was the scale factor used?

1/2
1/3
3
2

Answers

1/3 because:

(1/3)(6, -3)=(2, -1)

The answer to this question is 1/3

An equilateral triangle has a perimeter of 15x3 + 33x5 feet. What is the length of each side? x3 feet

Answers

In any case, divide by three: equilateral=same sides, triangle=3 sides

Let x represent one side of equilateral triangle.
Next, we know that the perimeter of the equilateral triangle= side+side+side,so
P=x+x+x with the P=15x^3+33x^5 feet
15x^3+33x^5=3x
Divided both side by 3
(15x^3+33x^5)/3=3x/3
x=5x^3+11x^5
x=x³(5+11x²) feet. As a result, the length of each side is x³(5+11x²) feet. Hope it help!

A man owned 5/8 of an interest in a house. He sold 1/5 of his interest, at a cost for $1000. What is the total value of the house? Explain how u solved it.

Answers

First you would have to find a common denominator with 1/5 and 5/8, which would be 40. So, they would now be 8/40 and 25/40. If 8/40 is $1,000, then you need to figure out how many 8/40 you need to get 40/40. You need 5 8/40, so you multiply $1,000 by 5 to get $5,000, which is the answer.

2/7 times 2/6 = what

Answers

4/7 or 0.571429 :) :)

2/7 x 2/6 = 4/42

simplified = 2/21

hope this helps

an airplane flies 105 miles in 1/2 hour . how far can it fly in1 1/4 hours at the same rate of speed.

Answers

262.5 miles in 1 [tex] \frac{1}{4} [/tex] hour because the airplane can fly 210 mph, and to find the rate it flies in 1[tex] \frac{1}{4} [/tex] hours, all you have to do is to multiply the unit rate by 1.25

The answer is 262.50 miles

The airplane flies 210 in one hour
1/4 of 210 is 52.5
52.5 x 5 = 262.5

Fraction 14 divided into 18

Answers

Since we need to find how many times 18 goes into 212, we do 212/18=11 and some more

Round 992,449 to the nearest hundred thousand

Answers

Hey! Hope that this helps.

992,449 rounded nearest to 100,000 is 1000,000.

After 9, we have another 9 which is greater than 5, so we must add 1 to the 9. The rounded value must have 5 zeros. On adding 1, the value becomes ten hundred thousand.

Hope it helped!

Mary has twice as many pencils as she has pens. Tom borrows a pen. Now, Mary has ten less pens than pencils. How many pencils does Mary does?

Answers

Mary has 18 pencils. 18/2 = 9. 9 - 1 = 8. 18 - 10 = 8.

Roman mixes 12 liters of 8% acid solution with a 20% acid solution, which results in a 16% acid solution. Find the number of liters of 20% acid solution in the new mixture. Construct a table to organize the information, and show all of your work to solve the problem

Answers

(12(0.08)+x(0.2))/(12+x)=0.16 perform indicated multiplication on left side

(0.96+0.2x)/(12+x)=0.16 multiply both sides by (12+x)

0.96+0.2x=1.92+0.16x subtract 0.16x from both sides

0.96+0.04x=1.92 subtract 0.96 from both sides

0.04x=0.96 divide both sides by 0.04

x=24

So 24 liters of 20% acid solution is in the new mixture.

Find the area of the figure shown. Use 3.14 to approximate pi

Answers

alrighty

we gots 1/4 circle and paralellogram

area circle=pi times radius^2
area paralelogram=base times height

1/4 circle is
radius is 10 so
area part circle is 1/4 times pi times 10^2=100/4pi=25pi=78.5 m²

area paralllogram is
10 times 3 because 3 is height and 10 is base length or 30

30+78.5=108.5 m² is the area

A carton has a length of fraction 2 1/6 feet, width of fraction 1 and 1/5 and height of fraction 2 and 1/2 feet. What is the volume of the carton

Answers

he volume of the carton = length * width * height
= 2 1/6 * 1 1/5 * 2 1/5 = 13/2 = 6 1/2 = 6.5 cubic feet

hope that helps

The weight of 10 identical samples of a substance is 0.01 pound what is the weight of 10,000 samples

Answers

We use ratios here.

For every 10 samples, the total weight is 0.01 lb.

We write
10 / 0.01.

We want to find the weight of 10,000 samples.

We write
10,000/?

These two ratios must equal each other.

(10 / 0.01) = (10,000 / ?)

If you know how to cross-multiply, then we can do that here.
0.01 * 10000 = 10 * ?
100 = 10 * ?

The unknown value is 10, which is your answer.

Answer:

The weight of 10,000 samples is:

10 pounds.

Step-by-step explanation:

It is given that:

The weight of 10 identical samples of a substance is 0.01 pound.

i.e. 10 samples= 0.01 pound.

Now we are asked to find the weight of 10,000 samples.

Since,

10 samples= 0.01 pound.

1000×10 samples= 1000×0.01 pounds

i.e.

10000 samples= 10 pounds.

Hence, the answer is: 10 pounds.

−5=−8−x What is x? Solve for x

Answers

Hello there!

-5 = -8 -x
First, we need to get x isolated (put on one side of the equation by itself), and then divide by -1 to get rid of the negative sign.
Add 8 to both sides.
-5 + 8 = 3
-8 + 8 = 0
You are left with:
-x = 3
Now, we must divide both sides by -1 to solve for x.
-x / -1 = x
3 / -1 = -3
You are now left with the following solution:
x = -3

I hope this helps!

What are the x-intercepts of the graph of the function f(x) = x2 + 4x – 12?

(–6, 0), (2,0)
(–2, –16), (0, –12)
(–6, 0), (–2, –16), (2, 0)
(0, –12), (–6, 0), (2, 0)

Answers

Answer:

x-intercepts are (-6,0 and (2,0)

First option is correct.

Step-by-step explanation:

The given equation is [tex]y=x^2+4x-12[/tex]

For x-intercept, y=f(x)=0. Thus, we have

[tex]0=x^2+4x-12[/tex]

We can split the middle term as 4x = 6x-2x

Thus, the equation becomes

[tex]x^2+6x-2x-12=0[/tex]

Now, we make group

[tex](x^2+6x)+(-2x-12)=0[/tex]

Take GCF from each of the group

[tex]x(x+6)-2(x+6)=0[/tex]

Factored out the common term

[tex](x+6)(x-2)=0[/tex]

Apply the zero product property,

[tex]x+6=0,x-2=0[/tex]

Solve for x

[tex]x-6,x=2[/tex]

Thus, x-intercepts are (-6,0 and (2,0)

First option is correct.

Answer:

Step-by-step explanation:

What are the factors of 4x2 + 23x − 6? (4x − 6)(x + 1) (4x − 1)(x + 6) (4x − 2)(x + 3) (4x − 3)(x + 2)

Answers

[tex]4x^2 + 23x- 6 = \\ 4x^2 +24x - x-6=\\4x(x+6)-(x+6)=\\(x+6)(4x-1)[/tex]

The factors of 4x^2 + 23x − 6 are (4x-1)and (x+6).

We have given that,

[tex]4x^2 + 23x - 6[/tex]

We have to determine the factors of given expression

What is the quadratic formula?

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4\cdot \:a\left(c\right)}}{2\cdot \:a}[/tex]

[tex]x_{1,\:2}=\frac{-23\pm \sqrt{23^2-4\cdot \:4\left(-6\right)}}{2\cdot \:4}[/tex]

[tex]x_{1,\:2}=\frac{-23\pm \:25}{2\cdot \:4}[/tex]

[tex]x_1=\frac{-23+25}{2\cdot \:4},\:x_2=\frac{-23-25}{2\cdot \:4}[/tex]

[tex]=\frac{-23+25}{2\cdot \:4}[/tex]

[tex]=\frac{2}{2\cdot \:4}[/tex]

[tex]=\frac{1}{4}[/tex]

[tex]x=\frac{1}{4},\:x=-6[/tex]

Therefore the factors are(4x-1)and (x+6)

To learn more about the expression visit:

https://brainly.com/question/723406

#SPJ2

Kevin had six nickels and 4 dimes in his pocket. If he took out one coin and then a second coin without replacing the first coin-- a) what is the probability that both coins were nickels. b) what is the probability that both coins were dimes. c) what is the probability that the first coin was a nickel and the second a dime

Answers

Alright so A is 6/10 * 5/9 = 1/3
B is 4/10 * 7/9 = 2/15
C is 6/10 * 4/9 = 4/15

I hope this helps

an airplane is flying from montreal to vancouver. the wind is blowing from the west at 60km/h. the airplane flies at an airspeed of 750km/h and must stay on a heading of 65 degrees west of north. what heading should the pilot take to compensate for the wind? what is the speed of the airplane relative to the ground?

Answers

Refer to the diagram shown below.

In order for the airplane to maintain a heading of 65° west of north, it actually heads at (65° +x) west of north at a speed of 750 km/h, to compensate for the wind blowing from west t east at 60 km/h.

The actual speed of the airplane relative to the ground is V km/h.

From geometry, obtain the triangle shown.
The speed of 750 km/h is opposite an angle of 155°, and the unknown angle x is opposite the wind speed of 60 km/h.

From the Law of Sines, obtain
[tex] \frac{sin(x)}{60}= \frac{sin(155^{o}}{750} \\ sin(x)= (\frac{60}{750})sin(155^{o})=0.0338[/tex]
[tex]x=sin^{-1}0.0338=1.937^{o}[/tex]

The heading that the pilot should take is 65 + 1.937 = 66.94° west of north.

The third angle of the triangle is 180 - (155 + 1.937) = 23.063°.
Use the Law of Sines to calculate V.
[tex] \frac{V}{sin(23.063^{o})}= \frac{750}{sin(155^{o})} [/tex]
[tex]V=( \frac{sin(23.063)}{sin(155)} )750=695.21\,km/h[/tex]

Answer:
The pilot heads approximately 67° (nearest integer) west of north.
The speed of the airplane relative to ground is 695.2 km/h (nearest tenth)

Find the perimeter of the following shape, rounded to the nearest tenth: Shape ABCD is shown. Point A is at -3,5. Point B is at 2,6. Point C is at 0, 2. Point D is at -5, 1.

Answers

By turning the points into triangles and using Pythagorean theorem you can solve for the lonest side(of the triangle) which is Equal to that side.
AB [(3-2)^2]+[(6-1)^2]=square root of (1+25)=Square root of 26= 5.099
If you do this for all 4 sides and add them up you get the answer:
P(perimeter)=19.1

Miguel typed 270 words in 6 minutes. His paper is 630 words. If he keeps typing at the same rate, in how many more minutes will Miguel finish typing his paper?

A. 8 minutes
B. 14 minutes
C. 16 minutes
D. 22 minutes

Answers

630-270 = 360 words remaining

Rate = 270words/6min=45wpm

Time left = 360words/45wpm = 8mins.

270/6, 630/x
you just cross multiply
270x=6*630
x=6*630/270
x=14

If the width of a rectangle is x + 2 and the length is twice as long, what is the area?

Answers

[tex]A=(x+2)(2(x+2)=(x+2)(2x+4)=2x^2+4x+4x+8=\\ =x^2+8x+8[/tex]

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