one half of the water is poured out of a full container. then one third of the remainder us poured out Continue the process: one fourth of the remainder for the third pouring, one fifth of the remainder for the fourth pouring, etc. After how many pourings does exactly one ninth of the origiNl water remain?

Therefore the common difference in this AP series is 4 and the next 3 terms are  1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.

Rows with a defined pattern, in which the difference between two consecutive terms is equal and fixed, are referred to as arithmetic sequences and series, also known as rows and counting series. In other words, by adding a fixed integer to the previous term, each term in the arithmetic arrangement is obtained from the previous term. To put it another way, every term in the arithmetic series (except from the first term) is obtained by adding a specific integer to the term that comes before it.

Here,

This mathematical sequence can be written as follows:

A, A+D, A+2D, A+3D, A+4D, etc. , a+(n-1)d or

where:

First term: a

d stands for common variation.

It is stated that the arithmetic sequence formula is

a = a + (n-1)d

where

First term: a

n = the number of terms

d stands for common variation.

Common Difference

In mathematical terminology, the common difference is the difference between two words.

2, 5, 8, 11, and more problems

Answer: To determine if a row is an arithmetic sequence or not, first identify the similarities between the rows.

d = 5 - 2 d = 8 - 5 d = 11-8

d = 3.

Each of them differs by 3 points.

The following three words are then 2, 5, 8, 11, 11+3, 11+6, 11+9 or 2, 5, 8, 11, 14, 17, and 20.

Issues 2, 4, 6, 8, and 10 exist.

Answer:

d = -4 - 2 = -6

d = 6 - (-4) = 10

It does not contain arithmetic sequences because there is no common difference.

Challenge: -6, -10, -14, -18,...

Answer:

d = -10 - (-6) = -4

d= -14 - (-10) = -4

d= -18 - (-14) = -4

There is a -4 difference between them all.

The following three terms are then 6, 10, 14, 18, -18, -18 + (-4), -18 + (-8), -18 + (-12), or 6, 10, 14, 18, -18, -22, -26, -30.

Issues 40, 42, 44, 46,...

Answer:

d = 42 - 40 = 2

d = 44 - 42 = 2

d = 46 - 44 = 2

All of them differ by 2 points.

The subsequent three words are either 40, 42, 44, 46, 48, 50, 52 or 40, 42, 44, 46, 46 + 2, 46 + 4, 46 + 6.

Issues: 1.2, 1.8, 2.4,...

Answer:

d = 1.8 - 1.2 = 0.6

d = 2.4 - 1.8 = 0.6

They are all separated by 0.6.

1.2, 1.8, 2.4, 2.4 + 0.6, 2.4 + 1.2, 2.4 + 1.8 or 1.2, 1.8, 2.4, 3.0, 3.6, 4.2 are the following three words.

Issues 1, 5, and 9,13

Answer:

d = 5 - 1 = 4

d = 9 - 5 = 4

d = 13 - 9 = 4

They are all divided by 4 in common.

The subsequent three terms are either 1, 5, 9, 13, 17, 21, or 25. These are 1, 5, 9, 13, 13 + 4, 13, 8, 13, and 12.

Therefore the common difference in this AP series is 4 and the next 3 terms are  1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.

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Answer:

[tex]\frac{-8}{9}[/tex]

Step-by-step explanation:

Substitute in 7 for x

[tex]\frac{7^{2}-5(7) -6 }{7^{2}-6(7) - 16 }[/tex]

[tex]\frac{49-35-6}{49-42-16}[/tex]

[tex]\frac{-8}{9}[/tex]

Container B needs to be filled faster in order for both containers to gain the same amount of water per minute , and by 1/6 water per minute .

Since water enters container A at a rate of 2/3 cup per 1/2 minute, then we can say that;

Rate of Filling container A = (2/3)/(1/2) = 4/3 cups per minute

We are also told that in container A, water leaks out at a rate of 1/4 cup per 3/4 minute. Thus;

Rate of leaking container A = (1/4)/(3/4) = 1/3 cups per minute

Amount of water in Container A in one minute = (4/3) - (1/3)

= 1

Similarly;

Since water enters container B at a rate of 3/4 cup per 1/2 minute, then we can say that;

Rate of Filling container B = (3/4)/(1/2) = 3/2 cups per minute

We are also told that in container B, water leaks out at a rate of 1/2 cup per 3/4 minute. Thus;

Rate of leaking container B = (1/2)/(3/4) = 2/3 cups per minute

Amount of water in Container B in one minute = (3/2) - (2/3) = 5/6

Since amount of water per minute in container A is 1 and the amount of water per minute in container B is 5/6 , then it means that container A fills faster by container B by; 1 - 5/6 = 1/6

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Complete question is;

two leaky containers are filling with water. water enters container a at a rate of 2/3 cup per 1/2 minute and leaks out at a rate of 1/4 cup per 3/4 minute. water enters container b at a rate of 3/4 cup per 1/2 minute and leaks out at a rate of 1/2 cup per 3/4 minute. which container needs to be filled faster in order for both containers to gain the same amount of water per minute? by how much more water per minute? explain

The sampling method is independent as the rain samples were taken from two different locations. As the sample sizes are small, they can be approximately considered normal distributions and t-test can be used to check the hypothesis.

Used in inferential statistics, t test can be used when we need to compare two different sets value to check if their is a significant difference between them.

T tests can be paired and dependent, like measuring the weight of a same patient before and after a diet or they can be unpaired an independent. Unpaired datasets might sometime have the same variance or unequal variance. Different formular are used to calculate the t-tests involving different datasets. To prove a null or alternate hypothesis, the t values must be checked with t- test table.

As the following datasets measuring rain pH at different cities are indepent and have unequal variances, the following formula should be used for calculating the t-score and the degree of freedom:

T-value= [tex]\frac{Mean1-Mean2}{\sqrt(\frac{var1}{n1})+(\frac{var2}{n2})}[/tex]

Substituing the values of Mean1=4.77; Mean2=4.50, Var1=0.1366, Var2= 0.0242, n1= 12, n2= 14, we get the t value as 2.27

Now calculating degree of freedom, which comes around

Δ=14

At x=0.05, from the table, t value=2.145

Hence as the calculated t vale is more than critical t value, null hypothesis can be rejected and alternate hypothesis can be accepeted proving that their is a significant visible difference in pH in the rain of Chicago and Huston.

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The given expression 9x(46+70)5 - 32(40-219) is equal to = 10948.

What is mathematical expression?

A mathematical sentence that contains at least one operation, numbers, and/or variables without the equal sign is known as a mathematical expression.

Expressions does not have equal sign as the equations have.

Considering the given question as:

9x(46+70)5 - 32(40-219) = ?

At first we will solve the expressions inside of the brackets:

= 9x(116)5 - 32(-179)

Now, ,we will solve the rest of the expressions

= 9x580 + 5728

= 5220 + 5728

= 10948

Therefore, the answer of the given question is 10948

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The result of the following summation is 114.

We are given the following summation, i = 1 to 6 ∑(4i + 5)

To determine the sum by adding the values, we will substitute the values of i, starting from i = 1 to i = 6, in the expression.

= 4(1) + 5 + 4(2) + 5 + 4(3) + 5 + 4(4) + 5 + 4(5) + 5 + 4(6) + 5

= 4(1) + 4(2) +  4(3) + 4(4) + 4(5) + 4(6) + 30

= 4 + 8 + 12 + 16 + 20 + 24 + 30

= 114

Thus, the result of the sum is 114.

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The given statement is FALSE.

Given info,

In addition to the strength and direction of an association between two numerical variables, correlation analyses allow us to predict one variable's value based on the other variable.

⇒ The statement is FALSE.

Finding the degree and direction of the link between two numerical variables is made easier with the use of correlation analysis.

The value of one variable can be predicted based on the value of another using regression analysis.

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We can take Samanta's equation and rewrite it in such a way that we get Phil's equation, then the equations are equivalent.

Two equations are equivalent if we can rewrite one of them and get the other one.

We know that the equations are:

Samantha's equation: f(x)=(x+12)^2−16

Phil's equation: f(x)=(x+16)(x+8)

We can find the zeros of Samantha's equation by solving the quadratic equation:

(x+12)^2−16 = 0

(x + 12)^2 = 16

(x + 12) = ±√16

x + 12 = ± 4

x = ±4 - 12

Then the two zeros are:

x = (+4 - 12) = -8

x = (-4 - 12) = -16

Then we can factorize the quadratic function of Samantha as:

y = (x - (-8))*(x - (-16))

x = (x + 8)*(x + 16)

That is Phil's equation, then the equations are equivalent.

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If the triangle ABC is an equilateral triangle having the length as (4x - 3) , and perimeter as 63 in , then the value of x is 6 .

The triangle having all the sides of equal measure is termed as Equilateral triangle.

The triangle ABC is equilateral triangle,

The measure of length of side of triangle ABC is = 4x - 3 ;

The perimeter of the triangle is = 63

So, According to the question,

(4x - 3) + (4x - 3) + (4x - 3) = 63

12x - 9 = 63

12x = 63 + 9

12x = 72

x = 72/12

x = 6

Therefore, the value of x in the given triangle  is 6.

-- The given question is incomplete, the complete question is

"Find the value of x, if the triangle ABC is an equilateral triangle with length of each side as (4x - 3), and the perimeter of the equilateral triangle ABC is 63 inches." --

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Answer: Attached to the post.

Step-by-step explanation:

First, label points A and B--given as (3, -3) and (3, 1) respectively. Now connect the points to form line segment AB.

We need to reflect this line segment over the line y = x. To visualize this easier, let's draw line y = x. Two coordinates on this line is (1, 1) and (0, 0). Plot these points and connect them to form line y = x.

Finally, we need to reflect line segment AB over y = x. Imagine the line y = x is a mirror and reflect the line segment AB over it. In my diagram, line segment A'B' is the answer.

So one angle is of measurement 130 degree and the other angle is of measurement 50 degree.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "pening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question-

One angle's measurement is 15 less than its supplement's measurement.

Let's say that the supplement angle is measured in degrees.

So the measurement of the other angle is

And the sum of the measurement of supplementary angles is 180.

Multiplying both sides by 2

Therefore, one angle is 130 degrees in length and the other is 50 degrees.

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Answer:

i don't know?please tell me in breif i didn't understand?

Graph of ​y+6=45(x+3)​ using the point and slope is given.

The slope of a line in mathematics, usually referred to as its gradient, is a numerical representation of the steepness and direction of the line.

Standard form of the slope-intercept form;

y = mx + b,

where m is the slope and b is the y-intercept.

We have the equation,

​y+6=45(x+3)​

Simplifying,

y = 45x + 135 - 6

y = 45x + 129.

Now, comparing the equation to the slop-intercept form;

we get,

m = 45,

and b = 129

And point slope form is the slope-intercept form.

And the graph is given in the image.

Therefore, y = 45x + 129 is the required equation.

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The given confidence interval is correct and it is between 22% to 38%.

The formula for calculating the confidence interval of population proportion is

[tex]C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }[/tex]

Here the sample proportion is represented by [tex]\bar{p}[/tex].

It is given that,

The 95% confidence interval has a sample size of n = 120 and the number of successes = 36.

So, the sample proportion [tex]\bar{p}[/tex] = 36/120 = 0.3

For the 95% confidence interval, α = 1 - 0.95 = 0.05

And α/2 = 0.05/2 = 0.025

Then, the z-score for α/2 = 0.025 is [tex]z{\alpha/2|=1.96[/tex].

And the standard deviation, [tex]\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }=\sqrt{\frac{0.3(1-0.3)}{120} }[/tex] = 0.0418

So, the interval is in between

C.I = 0.3 ± 1.96 × 0.0418

Upper limit = 0.3 + 1.96 × 0.0418 = 0.38 = 38%

Lower limit = 0.3 - 1.96 × 0.0418 = 0.218 = 0.22 = 22%

Therefore, the given confidence interval is correct.

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To beat the school long jump record, John must jump an additional 5 1/4 inches

From the given question, we are to determine how farther John must jump in order to break the record

From the given information,

"A high school track team's long jump record is 23 ft 1 3/4 in"

and

"John's best long jump is 22 ft 8 1/2 in"

First, we will convert the distances to inches

NOTE: 1 ft = 12 inches

23 ft 1 3/4 in = 276 + 1 3/4 in = 277 3/4 in

22 ft 8 1/2 in = 264 + 8 1/2 in = 272 1/2 in

Now, to determine how farther John must jump, we will subtract the distances

277 3/4 in - 272 1/2 in = 5 1/4 in

Hence, he must jump 5 1/4 in farther

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Hence, the amount of dividends in arrears that is still owed to preferred stockholders is $ [tex]50000[/tex].

What are the dividends?

The dividend is the value that is divided by another value to get the result. The dividend is the base of any division method.

The dividend is one of the four important parts of the division process. It is the whole which is to be divided into different equal parts.

Here given that,

Cumulative preferred stockholders of Rale Company receive $ [tex]80[/tex]per share. The company has [tex]70,000[/tex] shares outstanding. For the last [tex]9[/tex] years, Rale paid no dividends. This year, Rale paid $[tex]400,000[/tex] in dividends.

They are receiving $ [tex]80[/tex]per share and total amount they are receiving $ [tex]875[/tex].

So, when the Rale paid  $[tex]400,000[/tex] in dividends then the amount they are receiving is

[tex]\frac{400000}{80}=50000[/tex]

Hence, the amount of dividends in arrears that is still owed to preferred stockholders is $ [tex]50000[/tex].

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Answer: -4, -4

Step-by-step explanation:

-4 x -4 = 16

-4 + -4 = -8

Solving a system of equations we will see that Edmund will plant 4 yellow tulips and 8 white lilies.

Let's define our variables as:

We know that for each yellow tulip he will plant two white lilies, then:

y  = 2x

And we also know that he wants to plant 12 flowers, so:

x + y = 12

Then we have a system of equations:

x + y = 12

y  = 2x

Substituting the second equation into the first one, we will get:

x + 2x = 12

3x = 12

x = 12/3

x = 4

Then the value of y is:

y = 2x

y = 2*4 = 8

Then he will plant 4 yellow tulips and 8 white lilies.

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To begin, let's find how much the book is including tax and the student discount.  Once we find this, we can see if Lara or Alex is correct and if they can afford it.

First, we want to compute the student discount. The student discount is 35%. Thus, we can do 0.65 x 28.50 = 18.525. With 10% tax, we have 18.525 x 1.1 = 20.3775. Which will round up to $20.38.

Now, lets see what Alex did and if he got the same answer. First he takes 35% of $28.50 and subtracts it from the normal price.

.35 x 28.50 = 9.975

28.50 - 9.975 = 18.525

Then he takes 10% of this number and adds it back.

.10 x 18.525 = 1.8525

18.525 + 1.8525 = 20.3775

Alex has the correct answer.

Next, we will see if Lara computed it correctly.

First she takes 65% of the normal price.

0.65 x 28.50 = 18.525

Then she computes 110% of the reduced price.

18.525 x 1.10 = 20.3775

Lara also gets the correct answer.

So, do they have enough money to purchase the book?

YES:

$20.38 < $21

Is Alex correct?

YES

Is Lara correct?

YES

Although they used different methods to get the answer, they both got the right one!

As per the concept of vector, the while loop for integers is written below.

The term vector refers  a quantity or phenomenon that has two independent properties: magnitude and direction.

Here we need to write the  a quantity or phenomenon that has two independent properties: magnitude and direction.

While we looking into the given question, we have know that,

Here the input is 1 6 5 3 -1, then

the output is: 1 6 5 3

Then the function for the given statement is written as,

while ((char1 = getchar()) != '-1')  

    {  

        if (char1 == ' ')  

            sp_ct1++;  

        else if (char1 == '\n')  

            nl_ct1++;  

        else  

            other1++;  

    }  

Therefore, the above function is used to  read integers from input until -1 is read.

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The system of equations that describes Tammy and Luke's outcomes is written below

It can be deduced form the question that

x represents the number of points for a catch

y to represent the number of points for a miss

Tammy makes 5 catches and misses 1, ending the game with 23 points

5x - y = 23

Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points

8x - 5y = 30

The system of equations required are

5x - y = 23

8x - 5y = 30

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Answer:

[tex]1 - x = 16 - 4 \\ 1 - x = 12 \\ - x = 1 - 12 \\ - x = - 11 \\ x = 11[/tex]

it's that answer

The value of that guarantees the equation has exactly one real root is Zero

A quadratic equation has exactly one real number solution, then the value of its discriminant is always zero.

Quadratic

The word Quadratic is derived from the word Quad which means square. In other words, a quadratic polynomial is a polynomial function of degree 2.There are many scenarios where quadratic polynomials are used. When a rocket is launched, its path is described by the zero of a quadratic polynomial.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

A quadratic equation in variable x is of the form ax2 + bx + c = 0, where a ≠ 0.

In the case of one real solution, the value of discriminant b2 - 4ac is zero.

For example, x2 + 2x + 1 = 0 has only one solution x = -1.

Discriminant = b2 - 4ac = 22 - 4 (1) (1) = 0

Thus,  a quadratic equation has exactly one real number solution, then the value of the discriminant is always zero.

The value of that guarantees the equation has exactly one real root is Zero.

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Answer:

d = h(cot1 - cot2)

d = 100(cot30 - cot45))

d = 100* (1.732 - 1)

d = 100*0.732

d = 73.2 m

The probability that the buyer waits more than 10 minutes is 0.0271

From the question, we have the following parameters that can be used in our computation:

Probability function:

fy(y)=0.2e^(-0.2y), y ≥ 0

The inequality expression y ≥ 0 means that

The value of y is atleast 0

The probability that the buyer waits more than 10 minutes means that

y = 10

So, we have the following representation

y = 10 in fy(y)=0.2e^(-0.2y)

Substitute the known values in the above equation, so, we have the following representation

fy(10)=0.2e^(-0.2 * 10)

Evaluate the exponents

fy(10)=0.2 * 0.13533528323

Evaluate the products

fy(10) = 0.0271

Hence, the probability is 0.0271

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the trigonometric function of all the given question is obtained.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

Given: Cos θ = (3/5), Find: Csc θ = 5/4

Given: Sin θ = (5/6), Find: Cot θ = 11/5

Given: tan θ = (3/4), Find: Cot θ= 4/3

Given: Sec θ = (7/2), Find: Cos θ= 2/7

Given: Sin θ = (2/3), Find: Cosec θ=3/2

Given: Sin θ = (2/3), Find: Cos θ=5/3

Given: Tan θ = (6/4), Find: Sin θ=6/7.21

Given: Tan θ = (7/5), Find: Cos θ=5/8.6

Given: Tan θ = (7/5), Find: Sec θ= 8.6/5

Hence the above trigonometric function of all the given question is obtained.

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Calculating interest on the principal borrowed as well as any prior interest. $6,000 for six years at a daily compounded rate is None of these. No option is correct. The amount is $991.15.

Annual interest compounding adjective finance. If you borrow $100,000 at 5% interest compounded annually, you would owe $5,250 after the first year on a principal of $105,000. This method involves calculating and adding interest to an investment or loan once a year rather than for a longer period.

The formula to determine how much an investment will grow to overtime when it is placed in an account for years during which it generates dollar-compound interest is:

A = P(1 +r/m) m t

The values for each of these variables are provided as follows, presuming that a year has 365 days: m =365 t=6r  8.5% = 0.085The investment's worth is then computed after six years, as illustrated below.

A =991.15

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The measures of the angles formed by the parallel lines and their common transversal are;

Part A; B. c is equal to b

Part B; c = 60°

Second part; Angle P is 80°

Third part; The missing reason in step 3 is the option D.

Fourth part; Angle B is 72°

Parallel lines are lines in the same plane that have the same slope. The perpendicular distance between parallel is constant, such that they do not meet.

D. Vertical angles are congruent

Fourth part; Angle B is

Part A; JK is parallel to LM

Angle ∠c and angle ∠b are corresponding angles, therefore;

∠c and ∠b are congruent

∠c = ∠b

Therefore;

B. c is equal to b

Part B

Angle ∠b and 2·∠b are linear pair angles

Linear pair angles are supplementary, therefore

∠b + 2·∠b = 180°

3·∠b = 180°

∠b = 180°/3 = 60°

∠b = 60°

∠c = ∠b = 60°

B. c = 60°

Second part;

Angle P and the vertical angle to  the 100° angle are same side interior angles.

Vertical angles are congruent, therefore;

Angle P and 100° are same side interior angles

Same side interior angles are supplementary, therefore;

m∠P + 100° = 180°

m∠P = 180° - 100° = 80°

Third part;

Angle ∠2 and angle ∠3 are formed by the transversal t and w, therefore, they are vertical angles

Vertical angles theorem states that two sets of linear pair angles, that have congruent angles are formed from the intersection of two lines.

Therefore:

∠2 ≅ ∠3, reason: D. Vertical angles are congruent

Fourth part;

Line A is parallel to line B

The angles, 4·m -24, and 3·m are corresponding angles

Corresponding lines formed by the transversal and two parallel lines are congruent, therefore;

4·m - 24 = 3·m

4·m - 3·m = 24

m = 24 degrees

Taking angle ∠B as the angle formed at the intersection of line B and the transversal, 4·m - 24 we get;

∠B = 4·m - 24

∠B = 4 × 24 = 72°

Angle ∠B = 72°

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The community will contain 15,000 people with the gene that causes a triangle on their forehead after 20 days.

The rate of change of n (t) with respect to time is 500 people per day. This means that the equation for n (t) is given by:

n (t) = 5,000 + 500t

where t is the number of days since time t. At time t, n (t) = 5,000, and as time passes, the number of people with the gene that causes a triangle on their forehead increases. After 20 days, n (t) = 5,000 +500*20 = 15,000, meaning that after 20 days, the community will contain 15,000 people with the gene that causes a triangle on their forehead.

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