The wildflowers at a national park have been decreasing in numbers. There were 300 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year. Create the sigma notation showing the infinite growth of the wildflowers and find the sum, if possible.

Year

New flowers

1

1200

2

300

3

75

Answers

Answer 1
Although the number of new wildflowers is decreasing, the total number of flowers is increasing every year (assuming flowers aren't dying or otherwise being removed). Every year, 25% of the number of new flowers from the previous year are added.
The sigma notation would be:
∑ (from n=1 to ∞) 4800 * (1/4)ⁿ , where n is the year. 
Remember that this notation should give us the sum of all new flowers from year 1 to infinite, and the values of new flowers for each year should match those given in the table for years 1, 2, and 3
This means the total number of flowers equals:
Year 1: 4800 * 1/4 = 1200 ]
+
Year 2: 4800 * (1/4)² = 300

Year 3: 4800 * (1/4)³ = 75
+  
Year 4: 4800 * (1/4)⁴ = 18.75 = ~19 (we can't have a part of a flower)
+
Year 5: 4800 * (1/4)⁵ = 4.68 = ~ 5

Year 6: 4800 * (1/4)⁶ = 1.17 = ~1
And so on. As you can see, it in the years that follow the number of flowers added approaches zero. Thus, we can approximate the infinite sum of new flowers using just Years 1-6:
1200 + 300 + 75 + 19 + 5 + 1 = 1,600


Related Questions

what is 86 divided by 9

Answers

Hello There!

86/9 = 9.5555555556

Hope This Helps You!
Good Luck :) 

- Hannah ❤
9.5 repeated is you answer

Roman has 2 red pencils in his backpack if this is 25% of the total number of pencils how many pencils are in his backpack. you dont have to but if you can explain

Answers

8 because 25% is 1/4 of how much he has so just multiply 2 by 4

The equation d=rt is used to calculate distance, rate, or time, where dd is the distance (in meters), r is the rate (in meters per minute), and tt is the time (in minutes). Consider the statements below that describe the walking rates for three people. Graph the equation that represents the rate of the fastest person. Tomas walks 1200 meters in 8 minutes. Becky walks for 10 minutes and goes 1400 meters. Derrick walks at a rate of 145 meters per minute.

Answers

We know derrick walks 145 m/min to get the other we simply divide how far they went in how much time
Tomas: 1200/8= 150 m/min
Becky: 1400/10= 140m/min
therefore Tomas is the fastest walker so we will write the equation based on his speed
y = 150x
you should start at the origin (0,0) and got up 150 meters for and over 1 for every minute they run!

Tomas is the fastest walker so we will write the equation based on his speed.

What is speed?

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that the equation d=rt is used to calculate distance, rate, or time, where dd is the distance (in meters), r is the rate (in meters per minute), and t is the time (in minutes).

Tomas: 1200/8= 150 m/min

Becky: 1400/10= 140m/min

Tomas is the fastest walker so we will write the equation based on his speed

y = 150x

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7 berries are 5 less than twice the number of berries Mickey had for lunch.

Answers

Final answer:

The subject of this question is Mathematics.

Explanation:

To define the subject of the question, we can see that it involves a mathematical problem. The question asks about the relationship between the number of berries a student has and the number of berries Mickey had for lunch. Therefore, the subject of this question is Mathematics.

7 berries are 5 less than twice the number of berries Mickey had for lunch can be represented as 7 = 2m - 5. Therefore, the correct option is c.

The problem states: "7 berries are 5 less than twice the number of berries Mickey had for lunch."

Let's represent the number of berries Mickey had for lunch as 'm'.

Now, translate the problem into an equation based on the information given:

"7 berries are 5 less than twice the number of berries Mickey had for lunch."

Twice the number of berries Mickey had for lunch is 2 times 'm', which is 2m.

"5 less than twice the number of berries Mickey had for lunch" means subtracting 5 from twice the number, so it's 2m - 5.

And finally, the equation becomes:

7 = 2m - 5

So, the correct representation of the situation in an equation is option C: [tex]$7 = 2m - 5$[/tex].

The complete question is given below:
7 berries are 5 less than twice the number of berries Mickey had for lunch. Choose the correct linear equation.

A. [tex]$7=5-2 m$[/tex]

C. [tex]$7=2 m-5$[/tex]

B. [tex]$5=2 m-7$[/tex]

D. [tex]$12=\frac{m}{2}$[/tex]

How do I add unlike denominators?

Answers

find the LCD ( Less Common Multipale)
multiply one or both of them until their denominator is the same. in this case, times 2/3 by 2 and 1/2 by 3. then add them
(please mark brainiest)

A family of four want to go to Cat Island.But their boat only can fit two individuals if they are BOTH children. How do all four people get to the island in the smallest amount of trips?

Answers

im not sure but maybe 1 adult and one child but im not sure if this is a trick question

The boat can fit two children at one time but not two  adults. Then we have the issue of it not specifying if they are all adults or two adults and two children or 1 adult with three children.  so solution have a child and adult go together. with a child in the adults lap. while it is not safe it is possible (warning this is a answer that could irritate any teacher with sense) or presuming this is a family of two adults ad two children, send the two children first together then send the adults separate 3 trips in total 

Give an example of a problem that could be solved using the 9.5x(8+12.5)

Answers


ALI-A needs to make 8 videos on COD WW2 for YouTube. IMMARKSMAN needs to make 12.5 videos on COD WW2 for YouTube. They need to do this every day for 9.5 days. How many shirts in total (ALI-A and IMMARKSMAN combined) do they make by the end of the 9.5 days

Check them out

At midnight, the temperature was 31.2°F. In the morning, the temperature was −6.7°F. Which statement describes the temperatures?
A. At midnight, the temperature was 31.2 degrees above 0, and in the morning, it was 6.7 degrees lower.
B.At midnight, the temperature was 31.2 degrees below 0, and in the morning, it was 6.7 degrees higher.
C. At midnight, the temperature was 31.2 degrees above 0, and in the morning, it was 6.7 degrees below 0.
D At midnight, the temperature was 31.2 degrees below 0, and in the morning, it was 6.7 degrees above 0.

Answers

C. At midnight, the temperature was 31.2 degrees above 0, and in the morning, it was 6.7 degrees below 0.

Which influence on food involves the availability of certain types of food in your local area?



A.


personal taste


B.


geography


C.


advertising


D.


None of these answers are correct.

Answers

B. geography if you are talking local foods

Seven ounces of liver contains 42grams of protein. How many ounces a liver will provide 90gm of protein

Answers

Hello!

You must convert 90 grams to ounces.

90 gm = 3.175 ounces.

So, it will provide 3.175 oz of protein.

I really hope you found this helpful! :)

On a circle graph, a section with an angle measuring 180 represents A:18%, B:50%, C:90% of the whole.

Answers

B; 50% because the whole circle measures 360, and 180 is half of 360 (180+180 =360)

Consider the two functions which statement is true

Answers

The answer would be the last one because function one has a slope of 1/2 (use rise/run) and function 2 has a slope of 2 (subtract the 2nd y value by the one above it)

The slope of the line in the graph is 1/2, and for the table the slope is 2.

Which is true about the two functions?

We can se two linear functions, remember that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of the line is given by the formula:

a = (y₂ - y₁)/(x₂ - x₁)

For the first line we can see it passes through (-4, 0) and (0, 2), then the slope is.

a = (2 - 0)/(0 + 4) = 1/2

For line b we can use the first two pairs in the table (2, 3) and (3, 5)

So the slope is:

a = (5 - 3)/(3 - 2) = 2

These are the slopes of the lines.

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Which set of ordered pairs represents a function? Question 1 options: {(0, 0), (2, 3), (1, -4), (2, -2)} {(5, 6), (2, 6), (-3, 4), (-1, 4)} {(-5, 1), (-4, 2), (-5, 3), (-4, 4)} {(3, -2), (-4, -1), (0, 3), (0, 5)}

Answers

The second option because there isn't the same domain in every other one there is 2 of the same first numbers in the pairs

Solve for v . 3 /9= v/ 12

Answers

Cross multiply. So
12x3=9x
36=9x
x=4
(If you want to check, both fractions simplify to 1/3)

0.06 is 10 times as much as

Answers

0.060 is the answer if you're wondering

a piece of yellow yarn was 230 inches long. After 90 inches had een cut from it,,, the piece of yellow yarn was twice as longas a piece of blue yarn. How much longer than the blue yarn was the yellow yarn at first?  

Answers

Okay. So 90 yds was cut from the 230 yd yarn. 230 - 90 = 140. 1/2 of 140 is 70. 230 - 70 = 160. The yellow yarn was 160 yds longer than the blue yarn at first.

Answer:

160 inches longer.

Step-by-step explanation:

Let x represent the length of the blue yarn.

We have been given that a piece of yellow yarn was 230 inches long. After 90 inches had been cut from it, the piece of yellow yarn was twice as long as a piece of blue yarn.

Twice the length of blue yarn would be [tex]2x[/tex].

We can represent this information in an equation as:  

[tex]2x+90=230[/tex]  

[tex]2x+90-90=230-90[/tex]

[tex]2x=140[/tex]

[tex]\frac{2x}{2}=\frac{140}{2}[/tex]

[tex]x=70[/tex]

Therefore, the length of blue yarn is 70 inches long.

Now, we will subtract 70 from 230 as:

[tex]230-70=160[/tex]

Therefore, the yellow yarn was 160 inches longer than the blue yarn.

Bethany is baking cookies for her school's bake sale. She plans to bake more than 185 cookies, in batches of 12 cookies. So far, Bethany has baked a total of 48 cookies. What inequality describes this situation, if b represents the number of batches of cookies Bethany has left to bake?

Answers

The inequality that describes this situation is "b > 12", where b represents the number of batches of cookies Bethany has left to bake.

What is inequality?

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

As per the question, we can start by subtracting the number of cookies that Bethany has already baked (48) from the total number of cookies she plans to bake (185).

This gives us a difference of 185 - 48 = 137 cookies.

Dividing this number by the number of cookies per batch, we get 137 / 12 = 11.41.

Since Bethany is baking whole batches of cookies, the number of batches she has left to bake must be at least 12.

This means b > 12

Therefore, the inequality "b > 12" accurately describes the situation, where b is the number of batches Bethany has left to bake.

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The ratio of pens to pencils in Mrs. Bosworth's desk is 4:1. What does this mean?

Answers

pens : pencils = 4 : 1

This means that for every 4 pens there is 1 pencil.  Another way to say that is that there are 4 times as many pens as pencils.

What would be farthest right on a the number Line??
-3.25 or -1.75
-9.7 or -9
4/5 or 0
-70 or -70 4/5
-15 or -5
1/2 or -2
-99, -100 or -99.3
0.05 or 0.5
0, -3/4 or -1/4
-0.02 -0.04

Each pair or the ones with three numbers in them are a separate group...please try to answer correctly

Answers

-1.75 is farthest to right, -9 is farthest to the right, 0 is farthest to the right, -70 is farthest to the right, -5 is farthest to the right, 1/2 is farthest to the right, -99 is farthest to the right, 0.5 is farthest to the right, 0 is farthest to the right, -0.02 is farthest to the right. ;) let me know if this helped and if you want an explanation

Is 4 to 7 the same as 7 to 4 when explaining ratios. And why or not.

Answers

Ratio shows the quantity of the relative 2 or more values. No, it would not be the same. The following example will answer your doubt:

There are 500 students in a class. 400 of them are girls, and 100 of them are boys. What is the ratio of girls to boys?

The are asking the quantity of GIRLS to BOYS, means that you will be writing the ratio of girls, and then the boys. If you write the other way around, it would be incorrect because you are not writing the answer as the question says. The ratio of girls to boys is [tex]400:500[/tex] after simplified it is [tex] \frac{4}{5} [/tex]

Hope this helps you!

Have a great day!

determine the percent of the change in the cost of gasoline from 1970 to 2010 round to the nearest whole percent if necessary

Answers

Since the 2010 price is greater ($2.95) than the 1970 price ($1.30) this is a percent of increased. 
Step 1: Find the amount of increased.
Step 2: Find the percent of increased.

The cost of gasoline increased by about 127% from 1970 to 2010.

weight varies directly with gravity a Mars Lander Wade 767 pounds on Earth but only 291 lb on Mars the accompanying Mars Rover weigh 155 lb on Mars how how much did it weigh on Earth round your answer to the nearest pound

Answers

You need to be more specific.

Pls help hurry *Math* will give crown to best answer pls explain!

Answers

Its going to be B, a+14
Collect like terms
13a^2-12a^2-a^2-17a+12a+6a+14
Solve
a^2 is cancelled out (13-12-1=0)
12a+6a=18a-17a=1a
Bring the 14
The answer is a+14
j agree with the answer above

answer a b and c math question

Answers

If the cut off fractions are 1 1/2, 3/4, 1/3 then these answers should be right.

(A) so if there is 1 1/2 cups of flour for 6 servings then you need to divide 1 1/2 by 6 to get 1/4 of a cup

(B) there are 1 1/12 cups of sugar (white & brown) then divide 1 1/12 by 6 to get 13/72 cups 

(C) To make the recipe serve 9 people you could divide all the fractions by six to see how much would make one serving then multiply by 9. 
the new fractions for 1 serving are 1/4, 1/8, and 1/18 
when multiplied by 9 the fractions become   2 1/4 1 1/18 1/2 

Hope i could help

here are 8 hamsters at Crazy Pete's Pet Shop that are completely brown. The rest of the hamsters at the shop are mixed colors. The 8 brown hamsters represent 25 2/5 of the total number of hamsters at the pet shop. Write and solve an equation, using the variable h, to find the total number of hamsters at the pet shop.

Answers

If the total number of hamsters is h, then h * 2/5 = 8. This means that h= 8 * 5/2 = 20 hamsters in total.


Write the difference 57 – (–38) as a sum. Then simplify.

Answers

the answer is 95 because when you have two negative you add
When you have a negative minus a positive you add
57-(-38)=
57+38=
=95

Hope this helps

help me solve this equation! and please tell me how you did it step by step, please!!!

-3(2u+5)+3.5u=-1u

a.u=10
b.u=-10
c.u=4
d.u=-4


Please don't plug in the numbers! I'm really confused and I need help on how I could solve this step by step.

Answers

I got you!
First distribute.
-6u-15+3.5u=-1u
Add like terms
-2.5u-15=-1u
Get the u’s on one side and the regular number on the other
-1.5u=15
Divide
U=-10

a school bought 831 boxes of computer paper for the computer lab. Each box has 59 sheets of paper inside it. how many sheets of paper were bought in total?

Answers

 831 *59=49,029

hope this helps!
Hey there!

All you have to do is simply multiply!

831*59= 49,029

49,029 total sheets of paper were bought

Lainey wrote the prime factorization of 60 as 2 x 5 x 6. Is she correct? If not, what is the prime factorization of 60? explain

Answers

She is wrong because "6" is not prime. it is composite. The answer for the prime factorization of 60 is 2^2 × 3 × 5. or 2, 3 and 5
she is not correct because 6 is not prime, correct is 2*2*5*3

1. 4^2+25
2.55−4⋅5+12

Answers

For the first one here is my work:

16 + 25
41


For the second one here is my work

62.5 

(The bold numbers are the answers)
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