How do I do this problem with the summary table​

The estimated fox population in the year 2008 is 19498.

A function is a mathematical concept that describes the relationship between two sets of variables, where each input value (independent variable) corresponds to a unique output value (dependent variable).

(a) The continuous growth rate of 5% per year means that the fox population is increasing at a rate proportional to its current size. Let P(t) be the fox population t years after 2000. Then, we can model the population using the differential equation:

dP/dt = kP

where k is the constant of proportionality. To solve this differential equation, we can separate the variables and integrate:

dP/P = k dt

ln|P| = kt + C

where C is the constant of integration. To find the value of C, we use the initial condition that the population in the year 2000 (t=0) was 12500:

ln|12500| = 0 + C

C = ln|12500|

Therefore, the solution to the differential equation is:

ln|P| = kt + ln|12500|

Simplifying, we get:

P(t) = [tex]e^(kt + ln|12500|)[/tex]

P(t) = 12500 [tex]e^(kt)[/tex]

where P(t) is the fox population t years after 2000.

We know that the population grows at a continuous rate of 5% per year, so we can use this information to find the value of k. Since the continuous growth rate is given by r = 0.05, we have:

k = ln(1 + r) = ln(1.05)

As a result, the following function represents the fox population t years after 2000:

p(t) = 12500 [tex]e^(0.05t)[/tex]

(b) Since t is the number of years after 2000, we must determine the value of p(8) in order to calculate the fox population in 2008. We have the following using the function from section (a):

p(8)  = 12500 [tex]e^(0.05(8))[/tex]

       = 19498

Therefore, the estimated fox population in the year 2008 is 19498.

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Answer:

0.625

Step-by-step explanation:

you divide 5 by 8

The amount of butter that Simon has left is given as follows:

0.75 cups.

The amount of butter that Simon has left is obtained applying the proportions in the context of the problem.

The pack has 8 sticks of butter that are each 1/2 of a cup, hence the number of cups purchased is given as follows:

8 x 1/2 = 4 cups.

Simon used 1 1/4 of butter to make brownies , 3/4 cup of butter to make a cake , and 1 1/4 cup of butter to make cookies, hence the number of cups used is given as follows:

1.25 + 0.75 + 1.25 = 3.25.

Hence the amount of butter that Simon has left is given as follows:

4 - 3.25 = 0.75 cups.

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Mnemonic expressions can be useful for remembering mathematical concepts, formulas, and equations.

PEMDAS: This acronym stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It is used to remember the order of operations in mathematical calculations.

SOH-CAH-TOA: This acronym is used to remember the trigonometric ratios for sine, cosine, and tangent. SOH stands for Sine = Opposite/Hypotenuse, CAH stands for Cosine = Adjacent/Hypotenuse, and TOA stands for Tangent = Opposite/Adjacent.

FOIL: This acronym is used to remember the process of multiplying two binomials. It stands for First, Outer, Inner, Last, and represents the order in which you multiply the terms of the two binomials.

Please Excuse My Dear Aunt Sally: This sentence is used to remember the order of operations in mathematical calculations. It stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

My Dear Aunt Sally Loves Ice Cream: This sentence is used to remember the signs of trigonometric functions in each quadrant of the unit circle. It stands for positive for cosine and ice cream, negative for sine and loves, and alternating for tangent.

These are just a few examples of mnemonic expressions in mathematics, and there are many more that can be used to help remember mathematical concepts and formulas.

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οther valid transfοrmatiοn sequences cοuld Sequences achieve the same result, and the specific sequence used wοuld depend οn the specific shapes and οrientatiοns οf figures M and N.

A sequence is an οrdered list οf elements in mathematics. Numbers, functiοns, and οther mathematical οbjects can be used as elements. A series is frequently denοted by stating its terms in parenthesis, separated by cοmmas. The series οf natural numbers, fοr example, can be denοted as: (1, 2, 3, 4, 5, ...) Similarly, the series οf even numbers is denοted as fοllοws: (2, 4, 6, 8, 10, ...) Depending οn whether it has a finite οr infinite number οf terms, a sequence might be finite οr infinite.

Here's an example transfοrmatiοn sequence that cοuld pοtentially cοnvert figure M intο its cοngruent image figure N:

Figure M shοuld be mοved tο a new lοcatiοn in space sο that it aligns with the cοrrespοnding pοrtiοn οf figure N.

Figure M shοuld be rοtated abοut a pοint until it aligns with the οrientatiοn οf figure N.

Figure M shοuld be mirrοred acrοss a line οf symmetry tο match the mirrοr image οf figure N.

Figure M shοuld be translated tο its final lοcatiοn sο that it exactly cοincides with figure N.

It shοuld be nοted that many οther valid transfοrmatiοn sequences cοuld achieve the same result, and the specific sequence used wοuld depend οn the specific shapes and οrientatiοns οf figures M and N.

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Answer: [1]   G,D,L,K    [2] HF and AB    [3] X-Y Plane  [4] CE and LA

[5] A,L,B

Step-by-step explanation:

16.8 gallons

2.85 dollars/gallons

[tex]16.8 \times \frac{2.85 \: dollars}{gallons} = 47.88 \\ [/tex]

Alyssa paid a total of $47.88 for 16.8 gallons of gas when each gallon costs $2.85

The subject of this question is mathematics. Let's start by identifying what we know. We know that Alyssa filled her tank with 16.8 gallons of gas and that the cost of gas is $2.85 per gallon.

To find out how much Alyssa paid in total, we need to multiply the number of gallons by the cost per gallon:

Now, we are asked to round to the nearest cent. Rounding $47.88 doesn't change anything because the digits following the decimal point are 88, which is less than 100. So, the total amount Alyssa paid is $47.88.

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The angle subtended by each of the 8 equal parts at the center of the circle is 45 degrees.

What is circle and how to find its angle?

A circle is a two-dimensional shape that consists of all points in a plane that are equidistant from a given point called the center. A circle is defined by its radius (the distance from the center to any point on the circle) or its diameter (the distance across the circle passing through the center).

The angles in a circle can be measured in degrees or radians. There are several types of angles that are important in circles:

Central angle: A central angle is an angle whose vertex is at the center of the circle. The measure of a central angle is equal to the measure of the arc it subtends.

Inscribed angle: An inscribed angle is an angle whose vertex is on the circle and whose sides are chords of the circle. The measure of an inscribed angle is half the measure of the arc it subtends.

Arc: An arc is a portion of the circumference of a circle. The measure of an arc is equal to the measure of the central angle that subtends it.

To find the measure of an angle in a circle, you need to know the type of angle and the information given about the circle. The formulas and methods used to find the measure of an angle in a circle depend on the type of angle and the given information.

For example, to find the measure of a central angle, you can use the formula:

measure of central angle = (arc length / radius) * 180 / pi

To find the measure of an inscribed angle, you can use the formula:

measure of inscribed angle = 1/2 * measure of arc it subtends

In general, to find the measure of an angle in a circle, you need to use the information given about the circle and apply the appropriate formula or method based on the type of angle.

If a circle is divided into 8 equal parts, this means that the circle is divided into 8 congruent sectors. Since the sum of all angles at the center of a circle is 360 degrees, we can find the measure of the angle subtended by each sector at the center by dividing 360 degrees by the number of sectors:

angle subtended by each sector at the center = 360 degrees / 8 = 45 degrees

Therefore, the angle subtended by each of the 8 equal parts at the center of the circle is 45 degrees

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Your complete question is :-a circle is divided into 8 equal parts, what is the angle subtended by each at the center?

Answer:

Step-by-step explanation:

From the property of logarithm the input cannot be negative.

Therefore Z should be negative

As from the given question both sides have the (ln)
operator thus we can remove it.

-5Z=z^2-7Z

2Z=Z^2

Z^2=2Z

Z=2

Answer:

$12

Step-by-step explanation:

Parents=x Children=Y 2(4)y+2y=120 10y=120 y=12

Answer:

y =  [tex]\frac{1}{16}[/tex] ( x + 5 )² - 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k , (h, k) are coordinates of the vertex.

If a parabola passes through the point A ( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) , then

[tex]y_{1}[/tex] = a( [tex]x_{1}[/tex] - h )² + k

a = [tex]\frac{y_{1} -k }{ (x_{1} -h)^2}[/tex]

~~~~~~~~~~~~~~~~~~

Vertex at ( - 5, - 5 )

A( - 19, [tex]\frac{29}{4}[/tex] )

a = [ [tex]\frac{29}{4}[/tex] - ( - 5)] ÷ [ - 19 - ( - 5)]² = ( [tex]\frac{29}{4}[/tex] + 5 ) ÷ ( - 14 )² = 0.0625 = [tex]\frac{1}{16}[/tex]

y = [tex]\frac{1}{16}[/tex] ( x + 5 )² - 5

Glorious Gadgets should order a lot size of 1 to minimize their total inventory costs, and the minimum total inventory cost is $42,501.50.

In mathematics, rate is commonly used in the context of describing how one quantity changes with respect to another quantity over time. For example, the rate of change of an object's position over time is its velocity, which is expressed in units of distance per unit of time (such as meters per second). Similarly, the rate of growth or decline of a population over time is often expressed as a percentage, such as an annual growth rate of 2% or a population decline rate of 1.5% per year.

To find the lot size that minimizes the total inventory cost, we need to find the value of "x" that minimizes the function C(x) = 1.5x + 25500x¹ + 17000.

To do this, we can take the derivative of C(x) with respect to x, set it equal to zero, and solve for "x":

C'(x) = 1.5 + 25500 + 0 = 25501.5

25501.5 = 0

x = -25500/1.5 = -17000

Since a negative value of "x" doesn't make sense in the context of the problem, we can conclude that there is no minimum value for C(x). Instead, the function C(x) increases as "x" increases, so Glorious Gadgets should order as small a lot size as possible to minimize their inventory costs.

To find the minimum total inventory cost, we can evaluate the function C(x) at a small lot size, such as x = 1:

C(1) = 1.5(1) + 25500(1)¹ + 17000

C(1) = 1.5 + 25500 + 17000

C(1) = 42501.5

Therefore, Glorious Gadgets should order a lot size of 1 to minimize their total inventory costs, and the minimum total inventory cost is $42,501.50.

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Answer:

3.5

Step-by-step explanation:

Answer: 3.5

Step-by-step explanation: In this scenario, the vertex would be the peak of the baseball throw. We can find the x value of the vertex by using -b/2a. With your equation of 112x-16x^2 we need to change the x^2 value to the front to make it -16x^+112x so that it is in standard form. Now take your b value (112), make it negative (-112), and divide that by 2 times -16. to get 3.5.

I should also include that the x value of the vertex is equal to t which is seconds.

Solution for b: The events "all boys," "all girls," "2 boys and 1 girl," and "2 girls and 1 boy" are equally likely because each has probability 1/8. Solution for c: The events "0 tails," "1 tail," "2 tails," "3 tails," and "4 tails" are equally likely because each has probability 1/16. Solution for d: the events are not equally likely.

b) For a family having 3 children, the sample space is {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}, where B represents a boy and G represents a girl. Each outcome in the sample space has probability 1/8. The events "all boys," "all girls," "2 boys and 1 girl," and "2 girls and 1 boy" are equally likely because each has probability 1/8.

c) For tossing four coins, the sample space is {TTTT, TTTH, TTTT, TTHH, TTHH, THHH, THHT, THHH, HHHH, HHTH, HHTT, HHHT, HHTH, HTHH, HTTH, HTTT}, where T represents tails and H represents heads. Each outcome in the sample space has probability 1/16. The events "0 tails," "1 tail," "2 tails," "3 tails," and "4 tails" are equally likely because each has probability 1/16.

d) For tossing a coin 10 times, the sample space is all possible sequences of 10 H's and T's. There are 2^10 = 1024 outcomes in the sample space, each with probability 1/1024. The events "longest run of heads is 1," "longest run of heads is 2," "longest run of heads is 3," "longest run of heads is 4," "longest run of heads is 5," and "longest run of heads is 6 or more" are not equally likely, because the probability of getting a long run of heads is much lower than the probability of getting a short run of heads. For example, the probability of getting a run of 6 heads in a row is (1/2)^6 = 1/64, while the probability of getting a run of 1 head is 1/2. Therefore, the events are not equally likely.

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So the shaded region represents 30% of the whole. Each individual square on the grid must represent 1/100 of the whole.

A grid is a network of horizontal and vertical lines that intersect at regular intervals to form a pattern of squares, rectangles, or other shapes. It is commonly used as a tool for visualizing and organizing information, such as in maps, charts, graphs, and other types of diagrams. A grid can be simple or complex, depending on its purpose and the level of detail required. Simple grids may consist of only a few lines, while complex grids may have many lines and sub-divisions. In many cases, grids are labeled with coordinates or numbers to facilitate navigation or data analysis.

Here,

If the grid represents 1 in a grid of 100 squares, then each individual square on the grid must represent 1/100 of the whole.

The shaded region covers 30 squares out of the 100 squares in the grid. So the shaded region represents a fraction of the whole that can be calculated by dividing the number of shaded squares by the total number of squares:

30/100

This fraction can be simplified to:

3/10

Therefore, the shaded region represents three-tenths (3/10) of the whole. Alternatively, we can also express this as a percentage by multiplying the fraction by 100:

(3/10) x 100 = 30%

So the shaded region represents 30% of the whole.

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Answer:

56.7%

Step-by-step explanation:

Total number of students = 30

Number of boys in the class = 13

Number of girls in the class = 30 - 13 = 17

Now we have to find the percent of girls of the class

Therefore

[tex]\dfrac{\text{Number of girls}}{\text{Total students}} \times100[/tex]

[tex]=\dfrac{17}{30}\times100=56.67\%[/tex]

[tex]56.67\implies56.7\%[/tex]

Hence, girls are 56.7% of the class.

For the given equation, the values of X and Y are X=4 and Y=-2, respectively.

What is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two expressions separated by an equal sign (=).

To find the values of X and Y, we need to separate the real and imaginary parts of the complex number on the right-hand side of the equation.

We have:

X + Yi = 3Y - 2Xi + 4i

Separating the real and imaginary parts, we get:

X = -2Y + 0

Y = 3Y + 4

Simplifying the second equation, we have:

-2Y = 4

Dividing by -2, we get:

Y = -2

Substituting this value of Y into the first equation, we have:

X = -2(-2) = 4

Therefore, the values of X and Y are X=4 and Y=-2, respectively.

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Since there are 12 face cards (4 J, 4 Q, 4K) those represent 12/52.  The nonface cards excluding aces (4 twos through 4 tens) represent 36/52.

The expected value is then:

(12/52)($3)+(36/52)(-$2)= -$36/52 or -$0.69 but rounding to one decimal would be -$0.70

The resulting function is : y = (1/3)[tex]e^{(-2x) }[/tex] - 2 + 0.

What is the function?

A function is a rule that assigns each input value (usually represented by the variable x) to a unique output value (usually represented by the variable y). A function is typically written as an equation in terms of x and y, such as y = f(x), where f is the name of the function.

Starting with the function y = [tex]e^{(-2x) }[/tex], here are the steps to transform it:

1. Vertically compress by a factor of 3: Multiply y by 1/3

2. Reflect across the y-axis: Multiply x by -1

3. Shift down 2 units: Subtract 2 from y

So the transformed function is:

y = (1/3)[tex]e^{(-2x) }[/tex] - 2

Simplifying the exponent and the coefficient of e, we get:

y = (1/3)[tex]e^{(-2x)}[/tex] - 2

Writing in the desired form, we get:

y = (1/3)[tex]e^{(-2x)}[/tex]- 2 + 0

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The required volume of the given cuboid is (B) 3/2 inches³.

A cuboid is a solid shape or a three-dimensional shape in geometry.

A cuboid is a convex polyhedron that has six rectangular faces, eight vertices, and twelve edges.

Another name for a cuboid is a rectangular prism.

A cube is a cuboid with six square faces.

For instance, furniture, books, and televisions all have rectangular frames. It is a cuboid shape.

On the other hand, the 3D shape known as a cube is represented by items like ice, dice, and Rubik's cube. In actuality, a cube is a particular kind of cuboid with square, identical sides.

So, the volume of cuboid:
V= l*w*h

V = 1*1.5*1

V = 1.5

V = 1/5 = 3/2

Therefore, the required volume of the given cuboid is (B) 3/2 inches³.

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Therefore, the surface area of the rectangular prism is 280 square meters.

Area is a measure of the size of a two-dimensional region or surface, typically expressed in square units. It is the amount of space inside a closed shape or figure, and is calculated by multiplying the length and width of the shape or by using a formula specific to the shape. For example, the area of a rectangle can be found by multiplying its length and width, while the area of a circle can be found by multiplying pi (3.14) by the square of its radius. Area is commonly used in mathematics, science, engineering, and other fields to calculate quantities such as surface area, volume, and density.

Here,

The rectangular prism has 6 faces, and each face is a rectangle. To find the surface area, we need to find the area of each rectangle and add them up. The net shows that the dimensions of the prism are:

length = 10 m

width = 6 m

height = 5 m

The area of the top and bottom faces (which are congruent) is:

A = length × width

= 10 m × 6 m

= 60 m²

The area of the front and back faces (which are congruent) is:

A = length × height

= 10 m × 5 m

= 50 m²

The area of the two side faces (which are congruent) is:

A = width × height

= 6 m × 5 m

= 30 m²

To find the surface area, we add up the areas of all six faces:

Surface Area = 2 × (top and bottom faces) + 2 × (front and back faces) + 2 × (side faces)

Surface Area = 2(60 m²) + 2(50 m²) + 2(30 m²)

Surface Area = 120 m² + 100 m² + 60 m²

Surface Area = 280 m²

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the answer is 1 5/8 inches shorter. To find the difference between the initial length of the pencil and the final length after the project, we need to subtract the final length from the initial length.

Initial length of the pencil = 7 1/2 inches

Final length of the pencil = 5 7/8 inches

To subtract these two values, we need to convert the mixed numbers to improper fractions.

7 1/2 = 15/2

5 7/8 = 47/8

Now we can subtract:

15/2 - 47/8

To subtract these fractions, we need to find a common denominator. The least common multiple of 2 and 8 is 8, so we can convert both fractions to have a denominator of 8.

15/2 = 60/8

47/8 = 47/8

Now we can subtract:

60/8 - 47/8 = 13/8

So the pencil is 13/8 inches shorter after the project. To write this as a mixed number, we divide the numerator by the denominator:

13 ÷ 8 = 1 with a remainder of 5

So the answer is 1 5/8 inches shorter.

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It would cost $13.02 to buy a Rectangle type frame for the painting.

What exactly is a rectangle?

A rectangle is a two-dimensional geometric shape that is characterized by having four sides and four right angles. It is a type of quadrilateral.

The opposite sides of a rectangle are parallel and equal in length, and the adjacent sides are perpendicular to each other. This means that the opposite sides of a rectangle have the same distance apart throughout their entire length. The Perimeter is given by 2(L+B), where L and B are length and breadth respectively.

Now,

The painting measures 1 meter by 2 meters, so the perimeter of the painting (the total length of its sides) is:

P = 2 x (1 + 2) = 2 x 3 = 6 meters

To frame the painting, we need to buy a wooden frame with a perimeter of 6 meters. The frame shop charges $2.17 per meter for the wooden frame, so the cost of the frame would be:

Cost = 6 x $2.17 = $13.02

Therefore, it would cost $13.02 to buy a frame for the painting.

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The probability of drawing a queen or a heart from a standard 52-card deck is 0.308 or 30.8%.

What is Probability ?

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The event is "drawing a queen or a heart from a standard 52-card deck".

There are 4 queens in a standard 52-card deck, and there are 13 hearts (including the queen of hearts) in the same deck. However, we need to be careful not to count the queen of hearts twice, since it is both a queen and a heart.

So, the number of cards that satisfy the given event is 4 queens + 12 hearts (not including the queen of hearts) = 16 cards.

The total number of cards in a standard deck is 52.

Therefore, the probability of drawing a queen or a heart from a standard 52-card deck is:

P(queen or heart) = number of cards that satisfy the event : total number of cards

P(queen or heart) = 16 : 52

P(queen or heart) =  0.308

Therefore, the probability of drawing a queen or a heart from a standard 52-card deck is  approximately 0.308 or 30.8%.

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The outcome that is most likely to occur after rolling the cube 100 times is that an even number would be rolled around 50 times.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

A fair number cube labeled with the numbers 1 - 6 is equally likely to land on any of its faces when rolled.

Therefore, we can use probability to determine which outcome is most likely to occur after rolling the cube 100 times.

"The number 6 would never be rolled." This outcome is highly unlikely, but not impossible.
If the cube is fair, each number has an equal probability of being rolled, so the probability of rolling a 6 on any given roll is 1/6.

The probability of rolling a non-6 on any given roll is 5/6. The probability of not rolling a 6 in 100 rolls is (5/6)¹⁰⁰, which is approximately 0.0001. So, while it is very unlikely that the number 6 would never be rolled, it is not impossible.

"All the numbers rolled would be odd." This outcome is even less likely than the first one.

The odd numbers on the cube are 1, 3, and 5, each with a probability of 1/2.

The probability of rolling an odd number on any given roll is 1/2.

The probability of rolling an odd number on 100 rolls is (1/2)¹⁰⁰, which is an extremely small number, approaching zero.

"An even number would be rolled 50 times." This outcome is more likely than the first two.

The even numbers on the cube are 2, 4, and 6, each with a probability of 1/2.

The probability of rolling an even number on any given roll is 1/2.

If we assume that each roll is independent of the others, the probability of rolling an even number exactly 50 times in 100 rolls can be calculated using the binomial distribution and is approximately 0.0796.

This means that this outcome is not very likely, but still possible.

"The number 7 would be rolled at least once."

This outcome is impossible since the cube is only labeled with the numbers 1 through 6.

Therefore, the number 7 cannot be rolled.

Hence, Based on the above analysis, the outcome that is most likely to occur after rolling the cube 100 times is that an even number would be rolled around 50 times.

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There are 45 monkeys in the zoo.

A percentage is a way of expressing a fraction or a portion of a whole as a number out of 100. The word "percent" means "per hundred."

Let's suppose x is the total number of monkeys in the zoo.

We know that 25 ≤ x ≤ 49, and that 20% of the monkeys are Langur monkeys and 1/4 of them are Colobus monkeys. This means that the number of Langur monkeys is 0.2x and the number of Colobus monkeys is (1/4)x

The total number of monkeys can be expressed as;

x = 0.2x + (1/4)x + other monkeys

Simplifying this, (11/20)x = other monkeys

Since we know that the number of monkeys is between 25 and 49, we can substitute these values into the equation and solve for "x":

25 ≤ (11/20)x ≤ 49

45.4 ≤ x ≤ 89.1

Since x must be an integer, the only solution in this range So, x = 45

Therefore, there are 45 monkeys in the zoo.

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