The recursive equation for f(n) will be f(n) = 4242.42(1.65)ⁿ - 1300n.
What is an exponent?Let Consider the function:
y = a (1 ± r) ˣ
Where x is the number of times this growth/decay occurs,
a = initial amount, and r = fraction which this growth/decay occurs.
Lionfish are considered an invasive species, with an annual growth rate of 65%.
Then the equation will be
f(n) = P(1.65)ⁿ
P = initial population
A scientist estimates there are 7,000 lionfish in a certain bay after the first year.
7000 = P(1.65)
P = 4242.42
Then the equation will be,
f(n) = 4242.42(1.65)ⁿ
If scientists remove 1,300 fish per year from the bay after the first year.
Then the recursive equation for f(n) will be,
f(n) = 4242.42(1.65)ⁿ - 1300n
Learn More about the exponent link is given below.
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write 2^ 100 as a power with the following base of 16 brianly.
Pls answer quickly
Answer:
16^25
Step-by-step explanation:
The applicable relation is ...
(a^b)^c = a^(bc)
2^100 = 16^x = (2^4)^x = 2^(4x)
Equating exponents, we have ...
100 = 4x
25 = x
Then 2^100 = 16^25.
A 11 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth.
Check the picture below.
no link no bot right please
9514 1404 393
Answer:
10.49
Step-by-step explanation:
Since we know 110 = 10² +10, we can make a first approximation to the root as ...
√10 ≈ 10 +10/21 . . . . . where 21 = 1 + 2×integer portion of root
This is a little outside the desired approximation accuracy, so we need to refine the estimate. There are a couple of simple ways to do this.
One of the best is to use the Babylonian method: average this value with the value obtained by dividing 110 by it.
((220/21) + (110/(220/21)))/2 = 110/21 +21/4 = 881/84 ≈ 10.49
An approximation of √110 accurate to hundredths is 10.49.
__
The other simple way to refine the root estimate is to carry the continued fraction approximation to one more level.
For n = s² +r, the first approximation is ...
√n = s +r/(2s+1)
An iterated approximation is ...
s + r/(s +(s +r/(2s+1)))
The adds 's' to the approximate root to make the new fraction denominator.
For this root, the refined approximation is ...
√110 ≈ 10 + 10/(10 +(10 +10/21)) = 10 +10/(430/21) = 10 +21/43 ≈ 10.49
_____
Additional comment
Any square root can be represented as a repeating continued fraction.
[tex]\displaystyle\sqrt{n}=\sqrt{s^2+r}\approx s+\cfrac{r}{2s+\cfrac{r}{2s+\dots}}[/tex]
If "f" represents the fractional part of the root, it can be refined by the iteration ...
[tex]f'=\dfrac{r}{2s+f}[/tex]
__
The above continued fraction iteration adds 1+ good decimal places to the root with each iteration. The Babylonian method described above doubles the number of good decimal places with each iteration. It very quickly converges to a root limited only by the precision available in your calculator.
Please look at picture for question.
Answer:
Amount spent on breakfest each day: 2B+J
Amount spent on granola bars each day: 2B
Amount spend on juice each day: J
Number of days buys breakfast: 7
help me due today it is math
Answer:
2
Step-by-step explanation:
sum of digits=1+2+5+8=16
smallest term to be added to make it divisible by 9 is 2
∵16+2=18÷9=2
Christina has these two tiles. Draw a new shape she can create with both tiles. Then name the shape and how many sides the new shape has.
Square and triangle
Answer:
quadangle
Step-by-step explanation:
a square made of triangles and If a triangle is called a triangle, why is a square not called a quadangle?
Squares and triangles can be combined to form a pentagon
The new shape is a pentagon.The shape has 5 sides.The two shapes are given as:
SquareTriangleWhere the base of the square equals the side length of the triangle
When these shapes are combined i.e. when the base of the triangle is merged with the side length of the square, then it forms a pentagon.
See attachment for the image of the new shape.
From the attached image, we can see that the shape has 5 sides
Read more about pentagons at:
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-2.875 greater than or less than -2 7/8
Answer:
They are both the same.
Step-by-step explanation:
-2.875
7/8 = 0.875 thus -2 7/8 is equal to -2.875
What is a common denominator for 1 3/4 and 1 4/5
Answer:
20
Step-by-step explanation:
A common denominator is a number that is a multiple of both denominators.
To find it just write the multiplication table of the numbers and find a number that appears in both of them.
In this case, we have 4 and 5:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40
5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Since it only asks for a common denominator, it can be 20, 40, 60, 80... Although it's usually smarter to pick the lower number.
[tex]1\dfrac 34 =1+ \dfrac 34 =\dfrac 74 = \dfrac{35}{20}\\\\\\1\dfrac 45 = 1+ \dfrac 45 = \dfrac 95 =\dfrac{36}{20}\\\\\text{The answer is 20}[/tex]
Strawberries cost $3.00 per pound. For each question
a.
How many pounds of strawberries can you buy for $1.00?
b.
How many pounds of strawberries can you buy for $11.0
Answer:
A. 1/3 pound
B. 11/3 or 3.666666667
Step-by-step explanation:
:)
write the value of the underlined digit in words 6,302,450? 3 being the underlined number.
Answer:
Three hundred thousand
Step-by-step explanation:
Hope this helps
A scale model of a bicycle has a scale of 1 : 25. The real bicycle has a length of 1.75 m. What is the length of the model in cm?
Answer:
It's 7 I just did this question today and got it right
A package contains 12 ounces of cereal .If you use 1 portion of this cereal which is 1 1/3 how much would be left in the cereal box?
To answer this question, you would need to divide the total amount of cereal in the box by the serving size.
This would be 12 2/3 divided by 1 1/3.
We can write each mixed number as an improper fraction first before we divide:12 2/3 = 38/3 and 1 1/3 = 4/3
Now divide 38/3 by 4/3. Recall that dividing by a fraction is accomplished by multiplying by the reciprocal of the divisor: 38/3 * 3/4 = 114/12 = 38/4 OR 19/2
Also, 19/2 is equivalent to 9 and 1/2. There would be 9 and 1/2 servings in the box of cereal.
Hope this helps
20 feel from the ground i need a ladder placed 15 feet from the house what is the length
Answer:
helooo
Step-by-p explanation:
Please help I do not understand thanks
Simplify.
510√
2√
2√2
10√2
5√
Answer:if you know how to do this your smart and in two years if someone can Answer ill give you a mil in cash swear
Step-by-step explanation:
Answer:
√10/2
Step-by-step explanation:
I took le test
Please helpppp I will mark you branliest pleaseee
Answer:
no
Step-by-step explanation:
the ratios shown in this table are not proportionate. You will also never get (0,0) in this table.
1. What is the ratio of 10 notebooks to 5 ballpens in simplest form?
Answer:
2:1 or 2
Step-by-step explanation:
*** (Ratios can be written as " a : b", or can be written as a fraction " a / b".
>> therefore 10/5 can be simplified to 2/1 )***
For every 10 notebooks, there are 5 ballpens.
Therefore, for every 2 notebooks there is 1 ballpen (The simplification).
EXTRA:
**Also remember that the ratio of notebooks to ballpens cannot be reversed into ballpen to notebook ratio, because this would change the meaning.
2/1 is not the same as 1/2 **
If an item that originally cost $20 is increased to $27, what is the percentage of increase in the item?
Problem example: For the given sequence: -2,2,6,10,14,18
Write a recursive formula to find the nth term: a = an-1+4
Write a explicit formula to find the nth term: a = -2 + 4(n-1)
What is the 64th term in the sequence?
Answer:
250
Step-by-step explanation:
You can take the explicit formula and simply substitute the n value with 64:
-2 + 4 * (64 - 1)
-2 + 4 * (63)
-2 + 252
250
what is the distance between the coordinates (9, -2) and (9, 8) show your work on a coordinate grid pleas help mee
Answer:
10
Formular for finding distance between two points; (x2-x1)² + (y2-y1)² (all square root)
X1=9
X2=9
Y1=-2
Y2=8
Distance= (9-9)²+(-2-8)² (all square root)
=(0)²+(-10)² (all square root)
=0 + 100 (square root)
=100 square root
=10
A secured loan would most likely be used to pay for
A. college
B. a car
C. groceries
D. a phone
A secured loan would most likely be used to pay for a car, the correct option is B.
We are given that;
The four options
Now,
A secured loan is a loan that is backed up by collateral pledged by the borrower, such as a car or property.
The lender can sell the collateral to cover repayment of the loan if the borrower defaults.
Car, since it is a common type of collateral for secured loans.
College, groceries and a phone are less likely to be used as collateral for secured loans, since they are either intangible, perishable or low-value assets.
Therefore, by loan the answer will be car.
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In circle O, what is mArc A E?
Answer:
Step-by-step explanation:
By using the theorem of secants intersecting externally, Measure of angle formed by two secants, from a point outside the circle is half the difference of the measures of the intercepted arcs. m∠C =. 36° =. 72° = °. …
By using the theorem of secants intersecting externally, Measure of angle formed by two secants, from a point outside the circle is half the difference of the measures of the intercepted arcs. m∠C =. 36° =. 72° = °. …
Find the product. Simplify your answer.
(m+2)(3m+2)
there you go the answer is in the picture
82.1 / 7.8= What is the answer yall
Answer:
10.5
Step-by-step explanation:
Hope I helped please mark brainliest if I did and thanks! <3
What is 3.59 rounded to the nearest whole number?
Answer:
its 4 ezy
Step-by-step explanation:
please mark as brainlists
if there was a group of ten people the probability of them being born on the same day of the same year is 1, true or false and why
Answer:
True
Step-by-step explanation:
For instance, twins are born on the same day but imagine ten people instead of two being born on the same day.
Does anyone know this?
Answer:
I think 7.6 i remember i had something like this
Step-by-step explanation:
From a group of 15 men and 12 women, how many ways can you select a group of 2?
Answer:
The total number of ways this can be done together is 105 × 66 = 6930
This is a combination question question it has to do with selection.
In order to group 2 men from 15 men, this can be expressed using the combination formula as shown;
15C2 = 15!/(15-2)!2!
15C2 = 15!/13!2!
15C2 = 15×14/2
15C2 = 105 ways
Similarly in order to group 2 women from 12 men, this can be expressed using the combination formula as shown;
12C2 = 12!/(12-2)!2!
12C2 = 12!/10!2!
12C2 = 12×11/2
12C2 = 66 ways
The total number of ways this can be done together is 105 × 66 = 6930
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solve the equation 5/x+3 + 4/x+2 = 2
Answer:
5 + 4 = 9
x × x = X2
3 + 2 = 5
9/x + 5 = 2
Answer:
5/x+3+4/x+2=2
=9/x+5=2
9/x=-3
Multiply both sides by x
9= -3x
Divide by -3
Answer x= -3
Hope this helps
-
Find the equation of the line that
is parallel to y = 2x – 7 and
contains the point (-3,6).
Step-by-step explanation:
The first step is to Know the condition for two lines be parallel is that have the same slope, and this form the slope given is 2, therefore the new function has its slope too
2) with the slope and the two points givens, you can find the equation
Y-Y1 = m( X-X1) , Y-6 = 2[(X-(-3)] ⇒Y-6 = 2X+6 ⇒Y = 2X+12, AND THIS IS THE EQUATION PARALLEL TO THE LINE Y = 2X-7
