The polynomial equation with the given zeros is something like:
p(x) = a*(x - 1)²*(x + 2)²*(x - 5)²
How to find the function that can represent the situation?Remember that for a polynomial of degree a with the zeros {x₁, x₂, ...} the polynomial can be written as:
p(x) = a*(x - x₁)*(x - x₂)*...
Here we don't know the leading coefficient, and we know that the zeros are:
{1, 1, -2, -2, 5, 5}
These appear twice because all have a multiplicity of 2.
Then the equation is:
p(x) = a*(x - 1)*(x - 1)*(x + 2)*(x + 2)*(x - 5)*(x - 5)
p(x) = a*(x - 1)²*(x + 2)²*(x - 5)²
Where a can be any real number different than zero.
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Kiran surveyed a random sample of students in her school district, and she found these statistics:
P{rides bike to school})=0.14
P{has crossing guard})=0.48
P{rides bike and crossing guard})=0.12
Find the probability that a student rides a bike to school, given that the student's school has a crossing guard.
The probability that a student rides a bike to school, given that the student's school has a crossing guard is given by 0.25.
What is the addition rule of probability for two events?For two events A and B, we have:
Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.
We know that;
For two events A and B:
The chain rule states that the probability that A and B both occur is given by:
⇒ P (A∩B) = P (A) P (B|A) = P (B) P (A|B)
You can remember this fact by using a trick that when A is on left, it is behind B in next term P(A) P(B|A)
And when B is on left, then it is behind A in next term P(B)P(A|B)
P(A|B) = Probability that A will happen given B has already happened.
P(B|A) = Probability that B will happen given A has already happened.
Using those above stated rules, we have
Let the event A be that a student rides bike to school.
Let the event B be that the student's school has a crossing guard
Then we are given that:
P(A) = P{rides bike to school}) = 0.14
P(B) = P{has crossing guard}) = 0.48
P{rides bike and crossing guard}) = 0.12
We have to find P(a student rides a bike to school, given that the student's school has a crossing guard) = P(A | B)
From the chain rule of probability, we have;
⇒ P (A ∩ B) = P (B) P (A |B)
⇒ 0.12 = 0.48 × P (A|B)
⇒ P (A|B) = 0.12 / 0.48
⇒ P (A|B) = 0.25
Thus, The probability that a student rides a bike to school, given that the student's school has a crossing guard is given by 0.25.
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$7,300 is invested in an account earning 6.6% interest (APR), compounded
monthly. Write a function showing the value of the account after t years, where the
annual growth rate can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the percentage of
growth per year (APY), to the nearest hundredth of a percent.
Answer:
see below
Step-by-step explanation:
7300 investment
annual rate 6.6% compounded monthly = 6.6/12 months = 0.55% per month
t years = t*12 months
so function is = 7300 * (1+6.6%/12)^12t
APY = (1+0.55%)^12 - 1 = 1.068-1 = 0.068 = 6.8%
Construct segment so that it is perpendicular to segment and segment so that it is perpendicular to segment .
Complete the proof.
The completed proof for the two triangles is as follows -
ST bisects ∠UTV - Given
∠UTS ≅ ∠VTS - Angle Bisection Theorem
∠TUS and ∠TVS are right angles - Given
∠TUS ≅ ∠TVS - All right angles are congruent
ST ≅ ST - Reflexive property of congruence
ΔUTS ≅ ΔVTS - Angle Angle Side (AAS) Theorem
SU ≅ SV - CPCTC Rule
SU = SV - Congruence Theorem
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
Two right angle triangles ΔSUT and ΔSVT are given with line segment ST being the common.
It is given that line segment ST bisects ∠UTV as ST is the common line between the two triangles.
∠UTS ≅ ∠VTS as it is bisected by the line segment ST and it follows the rule of angle bisection theorem.
∠TUS and ∠TVS similar as they both are right-angles which is denoted by the small square symbol in the diagram.
∠TUS ≅ ∠TVS as they both are right-angles and all the right angles are equal and congruent having a measure of 90°.
ST ≅ ST since it is mid line segment of both the triangles and it follows the rule of reflexive property of congruency.
ΔUTS ≅ ΔVTS as they satisfy the AAS theorem, where two angles of a triangle and side between them are equal. Here, ∠UTS ≅ ∠VTS, ∠UTS ≅ ∠VTS and ST ≅ ST.
SU ≅ SV as corresponding parts of the congruent triangles are congruent. So, the CPCTC rule is applied.
SU = SV as they are part of the congruent triangles, so the line segments must be equal.
Therefore, ΔUTS is equal and congruent to ΔVTS.
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Answer: Hope this helps sorry for answering late ^ ^
Step-by-step explanation: i got it right
F = {equilateral triangles} and G = {isosceles triangles}.
What is F ∩ G? Can you simplify F ∩ G in any way?
∩= intersection
The set of items that are part of both sets F and G is indicated by the symbol F G. It is the group of equilateral triangles that are also isosceles triangles, to put it another way.
How are these sets determined?Due to its three congruent sides, every equilateral triangle is an isosceles triangle. F G = F hence equals "equilateral triangles." By eliminating the unnecessary component, we can make F G simpler.
Consequently, F G = "equilateral triangles"
How is a set defined?When seen collectively, a set is a group of items. The elements or members of the set are the things that make it up. Any mathematical object, such as integers, functions, or other sets, may be one of the elements of a set.
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=. A boy walked 7km on a bearing of 060°. Represent this information on a diagram.
A boy walked 7km on a bearing of 60°. Represented this information on a diagram given below.
What are bearing rules in maths?A bearing in mathematics is the angle, measured in degrees and anticlockwise from north. Typically, bearings are given as a three-figure bearing. For instance, 30° clockwise from north is typically expressed as 0°.
"Pieces that aid objects' rotation" are bearings. They support the rotating shaft that moves the machinery. Cars, planes, power generators, and other devices all use bearings.
To lessen friction between two spinning or sliding surfaces, a bearing is a mechanical component.
There are many different types of bearings, including ball and roller bearings, linear bearings, and mounted versions that may use either, and they are used for rotating or linear shaft applications. Bearings are mechanical assemblies that include rolling elements and typically inner and outer races.
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Derek tried to solve an equation step by step. 8d=72 8d/8 = 72/8 d=8 Find Derek's mistake
The mistake Derek did was d = 8.
The correct step is d = 9.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 55 is an equation.
We have,
8d = 72
Step 1:
Divide both sides with 8.
8d/8 = 72/8
[ 8 x 9 = 72 ]
So,
d = (8 x 9)/ 8
d = 9
Thus,
Derek's mistake is d = 8.
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enter the recursive rule for the geometric sequence 2, -6, 18, -54 a1=; an=
The value for a1 in geometric series 2, -6, 18, -54, ..... is a1 = 2, and the recursive formula is a(n) =a^(n-1)·(-3) for n≥2.
What is geometric series?
A geometric series is a collection of terms in mathematics that have an unlimited number and a fixed ratio between each term. A geometric series is typically expressed as a + ar + ar² + ar³ + ..., where r is the common ratio between neighbouring terms and a is the coefficient of each term.
The given geometric series is -
2, -6, 18, -54, ..... (1)
Let A(n) be the geometric series defined in (1).
Then the first term A(1) = 2
The second term A(2) = -6
We need to find the common ratio from one term to the next.
r = common ratio
The formula for r is -
r = subsequent term / previous term = -6/2 = -3
The third term A(3) = 18
The r value for A(3) is -
r = subsequent term / previous term = 18/-6 = -3
The fourth term A(4) = -54
The r value for A(4) is -
r = subsequent term / previous term = -54/18 = -3
The formula for a(n) terms will be -
a(n) =a^(n-1)·(-3)
Therefore, the recursive formula is a(n) =a^(n-1)·(-3).
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You wish to test the claim that μ>20 at a level of significance of
α=0.05 and are given sample statistics n=50 and x=20.3.
Assume the population standard deviation is 1.2. Compute the value of the standardized test statistic. Round your answer to two decimal places.
A. 2.31
B. 3.11
C. 0.98
D. 1.77
The value of the standardized test statistic is D. 1.77.
A standardized test statistic is a measure of the difference between a sample statistic and the population parameter it estimates, expressed in units of the standard deviation.
The value of the standardized test statistic can be calculated using the formula:
(x - μ) / (s / √n)
where x is the sample mean, μ is the population mean, s is the population standard deviation, and n is the sample size.
Given the information provided in the question, the standardized test statistic is:
(20.3 - 20) / (1.2 / √50) = 1.7678
Rounding to two decimal places, the answer is D. 1.77.
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Find three consecutive odd
three times the
integers such that the sum of one times the first,
two times the second, and
third is 334. List the numbers in order from smallest to in largest.
The numbers in order from smallest to in largest are 65.6, 66.6. and 67.6 respectively
What are algebraic expression?Algebraic expression are expressions comprising of terms, variables, coefficients, constants and factors.
These algebraic expressions are also composed of arithmetic operation, such as;
DivisionSubtractionAdditionMultiplicationFloor divisionBracketParenthesesFrom the information given as;
x+1 + 2x + 4 + 2x + 6 = 334
collect like terms
x + 2x + 2x = 334 - 11
add or subtract like terms
5x = 323
Make 'x' the subject of formula
x = 64. 6
The numbers are;
x + 1 = 65.6
x+ 2 = 66. 6
x + 3 = 67. 6
Hence, the numbers are 65.6, 66.6. and 67.6
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simplify 4 x 5p
plssssssss
dont need step by step
Answer:
4 × 5p = 20p
(Multiply the terms; don't have to be like terms)
Reason:
I'm assuming the x refers to multiplication. If so, then 4 x 5 = 4 times 5 = 20. The p doesn't change.
A real world example would be that 5p represents a box with 5 pens inside it. Then imagine 4 such boxes to get 4 x 5 = 20 pens total.
i need an answer fast and correct and ill mark for brainiest
The correct orientation and location of triangle DEF is option B (as shown in the attachment to this answer).
Rotation of an object.Rotation is one of the types of solid transformation which involves turning a given object about a reference point or line at a certain required measure of angle. Other types of transformation are: dilation, translation and reflection.
Dilation: This is a process in which the dimensions of an object is either increased or decreased to produce its image.
Translation: This is a procedure that requires moving a given object a number of units in a specified direction.
Reflection: This requires flipping an object over a line to produce an image.
In the question, after rotating triangle ABC 90^o clockwise; the correct orientation and location of triangle DEF is option B.
A sketch of this is attached to this answer for clarity.
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which of the following are correct ways ofg determining of two compound propositions p and q are equailivanet
Two compound propositions p and q are logically equivalent if p↔q is a tautology. Alternatively, p and q are equivalent if and only if the columns in a truth table giving their truth values agree.
Two compound propositions p and q are logically equivalent if and only if p logically implies q and q logically implies p. In other words: two compound propositions are logically equivalent if and only if they have the same truth table.
let us consider,
T be the truth and F be the false of a problem statement.
Then the compound propositions p and q are logically equivalent if :
P q P→q
T T T
F F T
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The complete question is :
What is the correct way of determining of two compound propositions p and q are equivalent.
construct a truth table for p→q if the proposition is tautology.
Please see attached math problem.
a) The table is given below..
b) x + y = 45
c) 5.20x + 9y = 291
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
Cost of small box x = $5.20
Cost of large box y = $9
Now,
Number of boxes sold in one hour = 45
Total amount earned = $291
We can make two equations.
x + y = 45
x = 45 - y
Substituting
5.20x + 9y = 291
5.20 (45 - y) + 9y = 291
234 - 5.20y + 9y = 291
234 + 3.8y = 291
3.8y = 291 - 234
3.8y = 57
y = 15
Now,
x = 45 - y
x = 45 - 15
x = 30
Table:
Categories Value Number Amount
Small box 5.20 30 30 x 5.20 = 156
Large box 9 15 15 x 9 = 135
Thus,
The table is given above.
The equation is x + y = 45
The equation is 5.20x + 9y = 291
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A fifth degree polynomial with a root of multiplicity 3 at x = 2, and a root of multiplicity to at x = -3, can be written as the function y=(x - 2) ^a (x - b)^c where:
A=
B=
C=
the y-intercept of this polynomial is (0, )
Note: your answer should be integers.
When a fifth degree polynomial with a root of multiplicity 3 at x = 2, and a root of multiplicity to at x = -3. The polynomial can be written in the form
a = 3, b = -3c = 2How to write the polynomialEach zero's multiplicity is the quantity that indicates how frequently its corresponding factor appears. In other words, the powers are the multiplicities.
The polynomial is expressed as y = (x - 2) ^a (x - b)^c
for x = 2, x - 2, and the multiplicity is 3 hence
(x - 2)³
for x = -3, x + 3 and the multiplicity is will be 2 hence
(x + 3)²
Because of this we can say that
a = 3, b = -3 and c = 2
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sauv drove 296 miles in 8 hours.If he continued at the same rate,how far would he travel in 10 hours.
If he continued at the same rate, he would travel 370 miles in 10 hours.
What is proportion?A proportion is described as an equation having two ratios that are set equal to each other.
It is the mathematical comparison of numbers or variables.
In mathematics, the different types of fractions are;
Direct ProportionInverse ProportionCompound ProportionContinued ProportionFrom the information given, we have that;
sauv drove 296 miles in 8 hours
Then,
If 296 miles = 8 hours
x miles = 10 hours
cross multiply
8x = 2960
Make 'x' the subject of formula
x = 370 miles
Hence, the value is 370 miles
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What is 1+1 This question has to be the hardest question I ever done in Math. Please help me.
Answer:
2
Step-by-step explanation:
due to power failure, components of two states became mixed, given a boc containing both the components and two deectors can tou disginuish the two components
Yes, you can distinguish the two components if you have two detectors. The detectors can measure different properties of the components, such as:
SizeDensityElectrical chargeEven chemical compositionBy using the two detectors and measuring different properties of the components, you can identify which components belong to which state. For example, a detector can measure the size of the components, and another detector can measure the density of the components. If the components from one state have a larger size or a higher density than the components from another state, then the detectors can distinguish between the two components.
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Charmaine wants to rent a boat and spend at most $56. The boat costs $6 per hour, and Charmaine has a discount coupon for $4 off. What are the possible numbers of hours Charmaine could rent the boat.
Use t for the number of hours.
Write your answer as an equality solved for t.
Which of the following are like terms?
The like terms are listed as follows:
-y, 7y and y/2.
What are like terms?Like terms are terms that share these two features:
Same letters. (algebraic variables).Same exponents.If two terms are like terms, then they can be either added or subtracted.
Hence the first option is the only option in which all the three terms are like terms, as:
The letter of each expression is of y.The exponent of each term with the letter y is of 1.The remaining options have terms with different letters(second and third), or different exponents (fourth), hence they are not like terms.
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(50 POINTS AND BRAINLYEST)
Recall that the side length of the square was 14 units long. What is the base area of the prism?
Answer:
196 unit squareStep-by-step Explaination:
Area of base section of prism = area of square
Area of square = a²
side = 14 unit
=> (14)²
=> 196 unit square
hope it helps<3Sidney made b braided bracelets. she split them evenly among 4 gift boxes. Write an expression that shows how many bracelets were in each box answerlets.
Answer: We can use the distributive property to write an expression that shows how many bracelets were in each box.
Let b be the total number of bracelets that Sidney made.
The number of bracelets in each box can be represented as:
b/4
This expression means that Sidney divided the total number of bracelets she made, represented by b, by 4, the number of gift boxes.
So, the total number of bracelets in each box is b/4 bracelets.
Step-by-step explanation:
Josh invested in shares of four different companies at the beginning of the year. At the end of the year the share values had increased or decreased as follows:
SunBlush Technologies Stiller Co. PhotoFinish Co. Cola Company
7.62%
-4.17%
-0.83%
3.70%
For full marks your answers should be given as percents accurate to at least two decimal places.
a) What is the total rate of return if Josh invests the same amount in each company?
Return = 0.00 %
b) What is the total rate of return if Josh invests three times as much in Stiller Co. as in the other companies?
Return 0.00 %
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Answer: a) To calculate the total rate of return if Josh invests the same amount in each company, we need to add up the individual rates of return from each company and divide by the number of companies.
The total rate of return for the four companies is: (7.62% + -4.17% + -0.83% + 3.70%) / 4 = 2.52%
So the total rate of return if Josh invests the same amount in each company is 2.52%.
b) To calculate the total rate of return if Josh invests three times as much in Stiller Co. as in the other companies, we need to multiply the rate of return for Stiller Co. by 3 and add it to the rates of return for the other companies.
The total rate of return for the four companies is: (-4.17% x 3) + 7.62% + -0.83% + 3.70% = -7.32%
So the total rate of return if Josh invests three times as much in Stiller Co. as in the other companies is -7.32%.
It's important to note that the answer may change if the investment amount on each company is different.
Step-by-step explanation:
If RS = x + 5, ST = 14x − 15, and RT = 20, what is RS?
please help as fast as you can.
The Length of RS = 7 units.
Collinear points:The set of points that lie on a straight line is known as Collinear points. In other words, two or more points that lie on the same straight line are said to be Collinear points.
Here we have
RS = x + 5, ST = 14x − 15, and RT = 20
When R, S, and T are considered as 3 collinear points
=> RT = RS + ST
From the given data,
=> 20 = x + 5 + 14x − 15
=> 15x − 10 = 20
=> 15x = 30
=> x = 2
Length of RS = x + 5 = 2 + 5 = 7
Therefore,
The Length of RS = 7 units
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based on the results of the mouse coloration case study, suggest another hypothesis researchers might use to study the role of predators in natural selection.
Researchers might study the role of predators in natural selection by testing the hypothesis that animals with camouflage colorings have a greater chance of survival when they are exposed to predators.
They can do this by setting up an experiment in which they expose animals with different colorings, including camouflage, to predators and then measure the survival rate of the different colorings. This would test if animals with camouflage colorings have a higher chance of survival when they are exposed to predators.
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1. Henry and his sister Miranda are walking in the Jimmy Fund Walk-a-Thon to
money for cancer research. They are each collecting sponsors, who
pledge to donate a certain amount of money per mile they walk. Henry
has collected enough sponsors so that he'll earn $5.50 per mile for her
walks. If they both plan to walk all 20 miles of the Walk-A-Thon, and they
hope to raise a total $200, what does Miranda's per-mile sponsorship rate
need to be?
be Maps Desmos) Graphing
Analyzing Intersections of Lines and Planes
y
Z
x
B
Schoology
O
w
A
E
Use the given diagram to answer the question.
Which line is the intersection of two of the planes
shown?
Which line intersects one of the planes shown?
VZv
Which line has points on three of the planes shown?
Note that:
There are three separate planes and three different lines in the diagram. Line X crosses two of the planes, whereas Line Z intersects just one of the planes, and Line Y has points on all three planes.
Line y has points A and B in each of the three planes.
A plane is a flat surface that can be sliced across by a straight line connecting any two locations on the plane.
As a result of the diagram, we may deduce that
Line X is the line that connects two planes.Line Z is the line that intersects one of the planes.Line Y is the line with points on three of the planes displayed.Learn more about Planes:
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a software engineer owns 3 pair of pants, 4 shirts, and 3 pair of shoes. How many days can the software engineer go without wearing the same combination of three items?
The number of days a software engineer can go without wearing the same combination of three items will be 36.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
A software engineer owns 3 pairs of pants, 4 shirts, and 3 pairs of shoes. Then the number of different ways is given as,
⇒ ³C₁ × ⁴C₁ × ³C₁
⇒ 3 x 4 x 3
⇒ 36
The number of days a software engineer can go without wearing the same combination of three items will be 36.
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Find the scale factor of W X YI 2 QRST, if both quadrilaterals are similar.
We come to the conclusion that if the scale factor from S to M is 3/2, the scale factor from M to S must be 2/4.
What is the scale factor going from M to S?Assume we have a figure S. If we apply a stretch of scale factor K to our figure S, we may say that all of figure S's dimensions have been multiplied by K.
Following the stretch, we will have a bar of length M, such that:
M = S*K
If the scale factor is 3/2, the following scenario arises:
M = (3/2)*S
In the relationship mentioned above, S can be separated out as follows:
(2/3)*M = S
We now have an equation (similar to the first one).
As of right now, the scaling factor from M to S is 2/3, according to an equation (like the first one).
After that, we draw the conclusion that if the scale factor from S to M is 3/2, the scale factor from M to S must be 2/4.
The complete question is,
Scale factor is 3/2 for the range of S to M. How many are there in the scale from M to S?
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help please im really confused
Check the picture below.
so following the inscribed quadrilateral conjecture, let's get those equations that add up to 180°.
[tex](2y+74)+(7x+1)=180\implies 2y+7x+75=180\implies \underline{2y+7x=105} \\\\[-0.35em] ~\dotfill\\\\ (2y+100)+(6x-10)=180\implies 2y+6x+90=180\implies \underline{2y+6x=90} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{2y+7x=105}\implies 2y=105-7x \\\\\\ \stackrel{\textit{using the 2nd equation}}{2y+6x=90}\implies 2y=90-6x\implies \stackrel{\textit{substituting from above}}{105-7x=90-6x} \\\\\\ 105=90+x\implies \boxed{15=x}[/tex]
[tex]\stackrel{\textit{since we know that}}{2y+7x=105}\implies 2y+7(15)=105\implies 2y+105=105 \\\\\\ 2y=0\implies y=\cfrac{0}{2}\implies \boxed{y=0}[/tex]
The current population of a small town is
4709
people. It is believed that town's population is tripling every
9
years. Approximate the population of the town
4
years from now.
The number of people in the town in the next four years is 7610.
What is the population growth rate?We know that the population growth rate can be obtained when we apply the exponential growth formula. In this case we would have;
P= Poe^rt
P = Population at time t
Po = Initial population
r = Population growth rate
t = time taken
3(4709) =4709e^9r
3 = e^9r
ln3 = 9r
r = ln3/9
r = 0.12 or 12%
In the next four years;
P =4709e^4 * 0.12
P = 7610
The population can be obtained as 7610.
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