What are the domain and range of

We can use log with different base value,It is not necessary to use log base 10 always.  

Positional notation is used to express numbers that are base-10 or decimal numbers. Powers of ten are represented as digit values (column values) in decimal notation. Any one of the 10 digits (0, 1, 2,...,.,.,.,.,.,.,. ) may be present in any place, indicating how many of each digit value is.

Therefore, base ten log is meant when you see log by itself. Ln stands for a natural logarithm; a definition of natural logarithms is provided below. Only base ten and natural logarithms will be used in this course.

Thus, We can use log with different base value.

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Answer:

B

Step-by-step explanation:

The best answer would be 213.

Assuming that the sign denotes summation, we are adding from k=4 to k=9.

To get, we change k=4 to k=9.

We simplify obtaining,

To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Summarizing mainly entails entering the values k=4, 5, 6, 7, 8, and 9 into the formula section 5K+3 and adding them all together.

So, the result is:

(5(4)+3)+(5(5) + 3) + (5(6) + 3) + (5(7) +3) + (5(8) + 3) + (5(9) + 3) 23+28+33 +38+43 + 48

= 213

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The volume of the prism is 387.9inch^3

Suppose you've got a triangle. Now, strech it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism. Usually, when we talk about triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

The volume of an equilateral triangular prism can be easily found out by using the formula, Volume = (√3/4)a2 × h, where,'a' is side length and 'h' is the height of the equilateral triangular prism.

Given;

Height= 4.5inches

Length= 8inches

Height of prism= 7inches

Volume = (√3/4)a2 × h

= (√3/4)(8)^2x 7

=387.9inch^3

Therefore, the volume  of triangular prisms will be 387.9inch^3

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There are several methods for factoring expressions, including factoring out the greatest common factor (GCF), by grouping, using the difference of squares or sum/difference of cubes, using the FOIL method or the reverse FOIL method or using special cases such as perfect square trinomials or difference of squares.

Factoring out the GCF: This method involves finding the greatest common factor of all the terms in an expression and then dividing it out of each term. For example, if we have the expression 12x^2 + 8x^2, the GCF is 4x^2, so we can factor it out and write the expression as 4x^2(3 + 2).

Factoring by grouping: This method involves grouping the terms of an expression into pairs and factoring out a common factor. For example, if we have the expression x^2 + 3x + 2x + 6, we can group the first two terms and the last two terms and factor out a common factor of x from the first group and 2 from the second group. This gives us x(x + 3) + 2(x + 3)

Factoring quadratics: There are a few methods to factor quadratics, such as factoring a difference of squares, or factoring a sum or difference of cubes. For example, if we have the expression x^2 - y^2, we can factor it as (x-y)(x+y) using difference of squares.

Factoring trinomials: There are a few methods to factor trinomials, such as FOIL method or reverse FOIL method. The FOIL method is a mnemonic acronym for first, outer, inner, and last, which is used to multiply two binomials. Reverse FOIL is used to factor a trinomial that is the product of two binomials. For example, if we have the expression x^2 + 5x + 6, we can factor it as (x+2)(x+3) using reverse FOIL method.

Factoring special cases: There are some special cases of factoring that have specific methods. For example, factoring perfect square trinomials such as x^2 + 2x + 1 is factored as (x+1)^2 and factoring difference of squares such as x^2 - y^2 is factored as (x-y)(x+y)

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Step-by-step explanation:

We know that the product of slopes of two perpendicular lines is -1 . So the slope of the line perpendicular to the given line will be negative reciprocal of the slope of the given line. The given line is,

[tex]\implies \rm y = -4x -4 [/tex]

on comparing it to the slope intercept form of the line we have,

[tex]\implies \rm m =-4\ (slope)[/tex]

so the slope of the perpendicular line would be,

[tex]\implies \rm m_{\perp}=\dfrac{1}{4} [/tex]

Now we may use the point slope form of the line ro to find out the equation of the line that passes through the given point as ,

[tex]\implies \rm y - y_1 = m(x-x_1)\\[/tex]

[tex]\implies \rm y -8=\dfrac{1}{4}\{ x -(-1)\}\\[/tex]

[tex]\implies \rm 4y -32 = x +1\\ [/tex]

[tex]\implies \rm x-4y +33=0 [/tex]

and we are done!

-rishabh

The value of x in the equation 9x+7=15+6x is 2.66

When we have an equation, we can divide it into two parts, the left and right sides. In short, we call the equation LHS and RHS.

If we get both LHS and RHS as equal values, we can say that the equation is true; otherwise, the equation does not hold for at least some real-number values.

Given that,

9x+7=15+6x

Bring x terms to LHS and constants to RHS

9x-6x=15-7

we get,

3x= 8

taking 3 to RHS

in LHS we multiply with two so it becomes divided on RHS

so

x=8/3

x=2.66

Thus, the value of x in the equation 9x-6x=15-7 is 2.66

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A function f(x) = ax^2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.

A function is a parabola. A parabola with an upward or downward opening is represented by the graph of a quadratic function. If the graph has the formula y = ax^2 + bx + c, then it is a parabola (where a is not zero). A parabola, however, is not a one-to-one function.

Additionally, because it violates the vertical line test, a "sideways" parabola of the form x = ay2 + by + c is not a function.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The answer would be 1 cm

Check out the solution in attachment ~

The 5 properties of matters can include things like density, color, odor, hardness, and volume.

Any item with mass and volume is considered to be matter, which includes all atoms and subatomic particles as well as all chemical combinations, everyday things, etc. Any characteristics that can be measured, such as an object's density, color, mass, volume, length, malleability, melting point, hardness, odor, temperature, and others, are considered to be part of its properties. Some characteristics of matter, like the density of gold, are constant, but others rely on the quantity of matter present (like the mass of a golf ball in comparison to that of a bowling ball) or the characteristics of the mixture. All atoms of a given element will share characteristics with that element, however chemical reactions have the power to significantly alter an element's characteristics.

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Trigonometric ratios are an important part of problem solving in mathematics.

They help us find the lengths of sides and angles of triangles when certain information is provided. Here is a step-by-step guide to solving trigonometric ratios:

1. Identify the ratio you need to solve. Do you need to find the sine, cosine, or tangent of an angle? Knowing which ratio you need to solve is the first step.

2. Figure out which side of the triangle you are given. Do you know the length of the adjacent side, the opposite side, or the hypotenuse? Knowing this will help you determine which trigonometric ratio to use.

3. Substitute the given information into the trigonometric ratios. Once you have identified the ratio you need to use and the information you have, you can substitute these into the equation.

4. Solve the equation. This step involves using algebra to solve the equation.

5. Check your answer. Once you have solved the equation, make sure to check your answer by plugging it back into the equation to verify that it is correct.

These are the basic steps for solving trigonometric ratios. With practice and a good understanding of the basics of trigonometry, you can become an expert in solving trigonometric ratios.

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The approximate value of the maximized profit include the following: D. 1100.

In Economics, profit can be defined as a measure of the amount of money (revenue) that is generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

Mathematically, the profit function P(x) of a company simply refers to the revenue function R(x) minus the cost function C(x):

P(x) = R(x) - C(x)

Where:

Based on the graph of the company's weekly profit, (y), we can logically deduce that its maximized profit would occur at point (40, 1100) because this is the vertex of profit function P(x).

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The product of 20 is 2,000. This is true no matter how many times you multiply 20 by itself. As long as the numbers you are multiplying are the same, the product will remain the same.

Product is the result of multiplying two or more numbers together.

20 x 1 = 20

20 x 10 = 200

20 x 100 = 2,000

Product is the result of multiplying two or more numbers together. When it comes to the product of 20, it is the result of multiplying 20 by 1, 10, or 100. For example, 20 multiplied by 1 equals 20, 20 multiplied by 10 equals 200, and 20 multiplied by 100 equals 2,000. Therefore, the product of 20 is 2,000. This is true no matter how many times you multiply 20 by itself. As long as the numbers you are multiplying are the same, the product will remain the same.

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Answer:Solve for x 2x-4=10 2x − 4 = 10 2 x - 4 = 10 Move all terms not containing x x to the right side of the equation. Tap for more steps... 2x = 14 2 x = 14 Divide each term in

Step-by-step explanation:

The distance of Julie from the base of the tower is 72.2 feet.

From the top of a tower, John sees his friend Julie on the ground at an angle of depression of 49 degrees. The height of the tower is 83 feet.

Therefore, the distance of Julie from the base of the tower can be calculated as follows:

This situation forms a right angle triangle.

Hence, using trigonometric ratios,

tan 49° = opposite / adjacent

tan 49° = 83 / a

cross multiply

a tan 49° = 83

divide both sides by tan 49°

a = 83 / tan 49°

a = 83 / 1.15036840722

a = 72.1507996916

Therefore,

distance of Julie from the tower = 72.2 feet

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A system of equation with no solution or zero solution equation is not considered as a dependent because it is inconsistent.

When the same line is written in two different forms so that there might be an infinite number of solutions, this is an example of what is known as a dependent system of equations. If the equations have the same slope and y-intercepts, a system is considered dependent. For the equations to represent the same line, the lines must coincide. Every point on the line is a coordinate pair that works with the system.

To establish whether a linear system is inconsistent, the first step is to determine whether the lines are parallel. If this is the case, you need to find out if the lines share a y-intercept. Since two parallel lines with distinct y-intercepts would never collide, this finding indicates that the system is inconsistent.

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The inequality for Graph 1 is y > -1x - 8.

The inequality for Graph 2 is y > (1/3)x - 2.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

We will pick two coordinates from each graph.

Graph 1.

(0, -8) and (-8, 0)

The equation of the graph y = mx + c

m = (0 - (-8)/(-8 - 0) = 8/-8 = -1

(0, - 8) = (x, y)

-8 = -1 x 0 + c

c = -8

y = -1x - 8

The inequality is y > -1x - 8.

Graph 2.

(6, 0) and (0, -2)

The equation of the graph y = mx + c

m = (-2 - 0)/(0 - 6) = -2/-6 = 1/3

(6, 0) = (x, y)

0 = (1/3) x 6 + c

0 = 2 + c

c = -2

y = (1/3)x - 2

The inequality is y > (1/3)x - 2

Thus,

Graph 1 inequality is y > -1x - 8.

Graph 2 inequality is y > (1/3)x - 2.

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the standard deviation of the weights of the fish in the lakex will be equal to 0.115 right so that that is approximately 0.12

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graphical form, the normal distribution appears as a "bell curve".

Formula

f(x)= {frac{1}{sigma\sqrt{2\pi}}}e^{- {frac {1}{2}} (frac {x-mu}{sigma})^2}

f(x) = probability density function

sigma = standard deviation

mu = mean

the question is that organizers of a fishing totame believe that the lake whole sizable population of large mouths they assumed the wives of these fish have modeled that is q to the right, with a mean of 2.3 and standard deviation of 1.67. So here the question first part is that why does the skewed model make sense here right? So the for this? The answer will be because a skeeto, the right model makes sense, because it would be expected that there are many small fishes and few larger ones in the lake right. So here the correct option would be the option a right now. The next part of the question here it says that explain why you cannot use the normal model to determine the probability that a large mouth, but some randomly selected from the lake, weighs over 2 pounds. So here the correct option will be option b only. That is because the distribution is not normal and the exact distribution is not given. So it is not possible to determine the probability right so here and the third part of the question. It says here that each contestant catches 15 fish each day. So is it possible to determine the probability that some 1 catches average more than 2 pounds? Okay, so here the answer will be here: the probability cannot be determined, since the distribution is q to the right and the sample size of 15 is not large enough to use the central limit theorem. So the correct option is option b now. The third part for d option is the next part here says that the 14 contestants competing each cot, the limit of 15 fish. So what is the standard? Deviation of the mean weight of the 210 fishes caught right now here the size of the sample is 14 into 15 point. That is equal to 210 point right. So this is the standard. Deviation here. Sorry, okay, so the standard deviation here for the mean will be equal to the population. Standard deviation upon square root of sample size, so this is the population. Standard deviation is 1.67. This is square root of 210 point,

so this will be equal to 0.115 right so that that is approximately 0.12

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the standard deviation of the weights of the fish in the lake will be equal to 0.115 right so that is approximately 0.12

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

Formula:

[tex]P(x) = \frac{1}{{\sigma \sqrt {2\pi } }}e^{{{ - \left( {x - \mu } \right)^2 } \mathord{\left/ {\vphantom {{ - \left( {x - \mu } \right)^2 } {2\sigma ^2 }}} \right. \kern-\nulldelimiterspace} {2\sigma ^2 }}}[/tex]

[tex]P(x)[/tex] = probability density function

σ = standard deviation

μ = mean

The issue is that the organizers of a tame fishing tournament think that the lake has a substantial population of large mouth bass, therefore they assumed that the spouses of these fish have modeled that is q to the right, with a mean of 2.3 and a standard deviation of 1.67. The first half of the inquiry is, therefore, why does the skewed model make sense in this situation? then what for this? The correct model, a skeeto, will provide the answer since it is reasonable to assume that the lake has a large number of little fish and few larger ones.

The following portion of the question asks you to clarify why you can't use the normal model to calculate the likelihood that a large mouth, but some randomly selected from the lake, weighs more than 2 pounds. So, in this case, the distribution is not normal and the precise distribution is not provided. Because of this, it is impossible to answer the third half of the question and establish the probability at this time. Each participant in the competition is said to capture 15 fish every day. Can we therefore calculate the likelihood that some 1 catches average more than 2 pounds? Okay, so this is where the response will be: The probability cannot be calculated because of the distribution  is q to the right and the sample size of 15 is not large enough to use the central limit theorem.

The next section of this question states that each of the 14 contenders has a catch limit of 15 fish. What then is the norm? The sample size's 14 to 15 point deviation from the mean weight of the 210 fish currently captured here. That is equivalent to 210 correct points. And so, this is the norm. this is a departure. Sorry, yeah, so the population's standard deviation will be the same as the mean in this case. This is the population based on standard deviation of sample size squared. There is a 1.67 standard deviation. This is the square root of 210.

So, this will be equal to 0.115 right so that that is approximately 0.12

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If one of the zeros in the quadratic polynomial is 4, then the value of k is 3.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. A polynomial is a mathematical expression that only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates in mathematics.

Here,

4 is a root/zero of polynomial

P(x)  =   (k-2) x²  - 2 x  - (k+5)

P(4) = 0

(k - 2) 4²  - 2 * 4 - (k+5)  = 0

15 k - 45 = 0  

k = 3

The value of k if 4 is one of the zeros of the quadratic polynomial is 3.

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Complete question:

If one of the zeros of a quadratic polynomial(k-2)x^2-2x-(k+5) is 4 , find value of k.

The table B would not be an appropriate model for the function shown here.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

A function is shown here.

In the graph:

When x = 2, then f(x) = 2 ≠ 0.

From the given choices:

The table B gives contradiction.

Therefore, the table D is not an appropriate model.

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The given quadratic equation yields a price per unit at demand of $7.89 when 1000 units are given.

Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known numbers, and where a 0 is true is known as a quadratic equation. x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer might be simple or complicated.

Here,

D=2000+100P-6P²

D=1000

2000+100P-6P²=1000

1000+50P-3P²=500

3P²-50P=500

3P²-50P-500=0

x=(-b±√(b²-4ac))/2a

a=3

b=-50

c=-500

x=(50±√((-50)²-(4*3*-500)))/2*3

x=$7.89

The price per unit at demand given as 1000 units is $7.89 by the given quadratic equation.

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Answer: 320

Step-by-step explanation: 812 divided by 203 is 4

203 min = 40 bacteria.

203 + 203 = 406

406 min = 80 bacteria because 40 times 2 is 80.

406 + 203 = 609

609 min = 160 bacteria because 80 time 2 is 160.

609 + 203 = 812

812 min = 320 bacteria because 160 time 2 is 320.

Step-by-step explanation:

[tex]area \: ofa \: circle = \pi {r}^{2} [/tex]

[tex]\pi {r}^{2} = \frac{22}{7} \times {r}^{2} \\ 153.86 = \frac{22}{7 } \times {r}^{2} \: \: \: \: \: \: \\ {r}^{2} = \frac{153.86 \times 7}{22} \\ {r}^{2} = \frac{1,077.02}{22}\\ r = \sqrt{48.95} \\ = 6.99[/tex]

So let's take r as 7

[tex]circumference \: of \: a \: circle = 2\pi r[/tex]

[tex]2\pi r = 2 \times \frac{22}{7} [/tex]

= 2× 22/7 × 7

= 44

Answer:

No, because 1999 at any time is 1999. If the time didn't officially occur at the year 2000, then you were born on the year 1999, not 2000.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Yes, if someone is born on December 31st at 11:59 p.m., they are regarded to be born in the next calendar year.

This is due to the fact that we utilize the Gregorian calendar, which is a solar calendar with 365 days in a normal year and 366 days in a leap year. The calendar year runs from January 1st to December 31st.

When a person is born at 11:59 p.m. on December 31st, they are born after the end of December 31st but before the start of January 1st. As a result, they are deemed to have been born in the following calendar year. In this situation, the individual is regarded to have been born in the year 2000.

The coordinates of the triangle STU will be -

S(- x₁ + 5, y₁)

T(- x₂ + 5, y₂)

U(- x₃ + 5, y₃)

Given is that triangle PQR is reflected across the line y = 0. The image is then translated 5 units to the right, resulting in triangle STU.

Since the triangle is not given, let the coordinates of the triangle be -

P(x₁, y₁)

Q(x₂, y₂)

R(x₃, y₃)

The reflection of point (x, y) across the y-axis is (-x, y). So, the new coordinates will be -

P'(- x₁, y₁)

Q'(- x₂, y₂)

R'(- x₃, y₃)

After the coordinates of the triangle are translated to right by 5 units, the coordinates will become -

P"(- x₁ + 5, y₁)

Q"(- x₂ + 5, y₂)

R"(- x₃ + 5, y₃)

Therefore, the coordinates of the triangle STU will be -

S(- x₁ + 5, y₁)

T(- x₂ + 5, y₂)

U(- x₃ + 5, y₃)

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The area of triangle WIN is also 84 square cm.

The idea applied in this problem is the triangle's area formula, A = 1/2bh, where b is the base and h is the height.

These are the steps in this procedure:

The first step is defining a triangle as a three-sided form with three sides and three angles.

Step 2: The equation A = 1/2bh, where b is the base and h is the height, is used to calculate the area of a triangle.

3. Since the area of triangle YOU is specified as being 84 square cm, triangle WIN's area must also be 84 square cm.

Step 4: The triangular WIN's area is 84 square centimeters as a result.

The idea applied in this problem is the triangle's area formula, A = 1/2bh, where b is the base and h is the height.

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To plot x = -1 on a graph, draw a vertical line at x = -1 and extend it infinitely in both directions.

To plot x = -1, start by drawing a horizontal line on the x-axis. Then, use a ruler to draw a vertical line at x = -1. Make sure that this vertical line extends infinitely in both directions, above and below the x-axis.

This line will represent x = -1. Now, draw a point at the intersection of the vertical and horizontal lines. This point will be the point where x = -1. To double-check your work, label the point as (-1, 0).

This means that the x-value is -1, and the y-value is 0. If you wish, you can extend the vertical line in both directions to get a better sense of the line's position. Congratulations, you have now plotted x = -1 on your graph!

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a. The number of student that pack a lunch is 12.

b. The number of student that pack a lunch is 400.

c. Each of these numbers is how many students you can expect to pack a lunch in each group

About 40% of students pack their lunch for school.

Let's solve the following question using the percentage above:

In a classroom with 30 students, how many do you expect to pack a lunch?

number of student that pack a lunch = 40% of 30

number of student that pack a lunch = 40 / 100 × 30

number of student that pack a lunch = 1200 / 100

Therefore,

number of student that pack a lunch = 12

In a school with 1,000 students, how many do you expect to pack a lunch?

number of student that pack a lunch = 40% of 1000

number of student that pack a lunch = 40 / 100 × 1000

number of student that pack a lunch = 40000 / 100

number of student that pack a lunch = 400

The number of student that pack a lunch is just a prediction.

Each of these numbers is how many students you can expect to pack a lunch in each group.

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So the area of the pupil after entering the room is (π(r/2)^2) = (πr^2)/4 and the area of the pupil after entering the room is 4 times smaller than the area of the pupil before entering the room.

a. The area of a circle can be represented by the formula A = πr^2, where A is the area and r is the radius of the circle. The radius of the pupil can change depending on the amount of light entering the eye, so we can represent the radius as a variable, r. Therefore, the polynomial that represents the area of the pupil is A = πr^2.

b. The width of the iris, x, decreases from 4 millimeters to 2 millimeters when you enter a dark room. Since the iris controls the size of the pupil, we can assume that the radius of the pupil also decreases by half when the width of the iris decreases. Therefore, the area of the pupil after entering the room is (πr^2) / 4, where r is the radius of the pupil before entering the room.

So the area of the pupil after entering the room is (π(r/2)^2) = (πr^2)/4.

Therefore the area of the pupil after entering the room is 4 times smaller than the area of the pupil before entering the room.

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