By the year 2025, the town of Ellison is frustrated and wants to get

rid of their cats, so they send them over to Clarkville. The Clarkville

residents love cats and can use the cats to catch all the mice. The

mouse-catch-rate for each cat is 72%


The function f(x) = 5719(0. 28)^x represents this change in the cat

population.

a) Explain what the 0. 28 means in this problem, based on the

information is given.

(hint: think about if this function is increasing or decreasing)

Answer:

see below

Step-by-step explanation:

year 1

7000*(1+13%) = 7910

year 2

7910*(1+13%) =8940

Answer:

10 years

Step-by-step explanation:

principal = 6000

int = 7.5% annual compounding CONTINUOUSLY = everyday

so every day of the year he gets 7.5% / 365

so annual effective rate =7.7876%

so to get to 12500 it'll take t years

12500 = 6000* (1+ 7.7876% )^t

2.0833=1.077876^t

solve for t

approximately 10 years

First-principle differentiation of sec x results in ten times sec x.

Regarding the variable x, y = f(x). Wherever the limit occurs is defined to be the derivative of f at x if this limit exists and is finite. The first principle of derivative is another name for this definition.

Sec x tan x is, as far as we are aware, the derivative of sec x. Determining that sec x equals the integral of sec x tan x. Specifically, sec x tan x dx = sec x + C

On a graph, the first derivative shows the slope of the function at a particular position, while the second derivative shows how the slope changes as the independent variable is changed. The second derivative accounts for the curve in the above graph for a function with a variable slope.

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If  you know the volume of the solid and the length of two of the three sides, b and c the length of the remaining side, a can be calculated by putting this values in the formula of volume(height*breadth*length).

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these shapes.

Volume = a× b× c

a = V / b×c

Cubic units are used to quantify a solid's volume. For instance, the volume will be given in cubic metres if the dimensions are given in metres. The International System of Units uses this as the reference unit for volume (SI). Cubic metres, cubic feet, cubic inches, etc. are additional volume units.

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Unfortunately, without more context about the origin of the value 0.0004, it is not possible to provide a detailed explanation of how it was obtained. The method for obtaining this value will depend on the context in which it is used.

For example, if 0.0004 is a decimal fraction, it may have been obtained by dividing a small number by a larger number. If it is a monetary amount, it may have been the result of a calculation involving currencies, exchange rates, or taxes. If it is a measurement of physical quantity, it may have been obtained using a scale, ruler, or other measuring device.

The value 0.0004 can have different meanings depending on the context in which it is used. For example, it could represent a decimal fraction, a monetary amount, or a measurement of physical quantity.

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Answer:

Step-by-step explanation:

Slowest growing plant is plant A.

The Slope (also called Gradient) of a line shows how steep it is.

To calculate the Slope:

Divide the change in vertical distance by the change in horizontal distance

Given,

Amir grows three plants,

Graph of plant A is given with straight line,

Height is denoted on x axis,

Time is denoted on y axis

Slope of the line will represent growth rate.

Line passes through (1,2) and (2,4)

slope of the line

= y-y'/x-x'

= 2 - 4/1 - 2

= - 2 / - 1

= 2

Growth rate = 2 inches per month

For plant 2

by the table,

Height  is 15 inches in 6 months.

Growth rate = 15/6 = 2.5 inches per month

Equation for plant 3

h = 3.5t

Slope of the equation = 3.5

Growth rate = 3.5 inches per month

By the above calculation,

Growth rate of plant A is least.

Hence, Plant A is growing slowest.

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Answer: 900 peaches

Step-by-step explanation:

cuz please thank

I redrawn the line in the picture. Hopefully this helps you

Percentage of sandwiches out of all lunch orders = 61%

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Order of sandwich = 61%

Total lunch order = 100%

Percentage of sandwiches = 61%

Hence, There are 61% of sandwiches out of all lunch orders.

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Equation of the sphere with center (-5, -3, 0) and radius 1 is (x + 5)² + (y + 3)² + z² = 1.

All points on a sphere are at a set distance from the centre, making it a three-dimensional geometric object. It is thought to be one of the most basic three-dimensional shapes and is a perfect circle.

Both a circle and a sphere are round, if you compare them. The fact that we can measure the volume and area of a sphere is due to the fact that a sphere is three-dimensional as opposed to a circle, which is a two-dimensional shape.

It is possible to formulate the equation for a sphere with centre (h, k, l) and radius r as follows:

(x - h)² + (y - k)² + (z - l)² = r²

Using the given center (-5, -3, 0) and radius 1, we can write the equation of the sphere as:

(x + 5)² + (y + 3)² + (z)² = 1²

which simplifies to:

(x + 5)² + (y + 3)² + z² = 1.

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The value of b is 4.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

We can make the ordered pairs (x, y).

Where x is the number of quarters and y is the number of playable characters.

Now,

A video game was released with 4 playable characters.

This means,

(0, 4)

Now,

The video game company has a plan to add 6 new characters every quarter (every 3 months).

This means,

(1, 10)

(2, 16)

(3, 22)

Now,

y = mx + b

Now,

Take any two ordered pairs:

(1, 10)

(2, 16)

m = (16 - 10) / (2 - 1)

m = 6

Now,

(0, 4) = (x, y)

4 = 6 x 0 + b

b = 4

Thus,

4 is the value of b.

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Based on the information provided, the two whose is 101 are 1010 and 1313.

?

The is the highest common factor or in other words, the highest by which two numbers can be divided. Let's start by listing the four digits that can be the related to 101.

101 x 10 = 1010

101 x 11 = 1111

101 x 12 = 1212

101 x 13 = 1313

Now, from these numbers, there are two numbers whose difference is

1313 - 1010 = 303

Based on this, the two numbers are and

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Find two numbers whose difference is 303, hcf is 101 and are 4 digits long.

Start by writing down two 4-digit numbers that have a difference of 303. The two numbers should be close together, but not the same number. For example, you could choose 9801 and 9498.

Next, find the factors of each number. For 9801, the factors are 3 x 3 x 11 x 101 and for 9498 the factors are 2 x 7 x 13 x 101.

Now, find the Highest Common Factor (HCF) of the two numbers. To do this, you can look at the factors of both numbers and find which ones are the same. In this case, the HCF is 101.

Finally, check if the difference between the two numbers is still 303. As 9801-9498 = 303, this is correct. Therefore, 9801 and 9498 are the smallest pair of 4-digit numbers with a difference of 303 and an HCF of 101.

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The APR, given the finance charge, the amount borrowed, and the number of months, is b. 16. 19 %

You can find the APR by using the RATE function on Spreadsheet.

The number of periods = 40 months

The Payment per month was:

= ( Loan amount + Finance charge )

= ( 22, 500 + 6, 743 .25 ) / 40 months

= $ 731.08125

The present value is the loan amount of $ 22, 500

The monthly rate is 1. 13456 %

The APR is:

= 1. 3456 x 12 %

= 16. 19 %

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The length of line segment Dc is equal to 35 units.

In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.

Since side length DE is parallel to AB and side DE is 5 less than side length DC, we have the following:

DE = DC - 5

In Geometry, the corresponding side lengths of two similar geometric figures are proportionate and as such, we have the following:

DC/AC = DE/AB

DC/56 = DC - 5/48

48DC = 56(DC - 5)

48DC = 56DC - 280

56DC - 48DC = 280

8DC = 280

DC = 280/8

DC = 35 units.

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According to the Function, p(-2) = -29 and p(3) = 73 are the values that we have.

The vertical line test has been used to determine if a graph accurately depicts a function. If a trendline created across the chart is moved and only ever hits it once, the chart is functional. If the line graph crosses the chart at least once, it is not a function.

The core concept of mathematics' calculus is functions. The functions are special types of relations. A function is a rule that generates a unique outcome for each input x in mathematics. A mapping or transformation in mathematics represents a function. Usually, letters like f, g, and h are used to designate these functions. The domain is the set of all possible values that can be passed into a function while it is specified. The term "range" refers to the whole set of values that the function's output is capable of producing. The co-domain is the set of possible values for a function's outputs.

put the value of x = -2 and x = 3 into the polynomials .

[tex]p(-2) = -7(-2)^{2} + 5(-2) + 9 = -7 \times 4 + (-10) + 9 = -28 + (-10) + 9 = -29\\p(3) = 3(3)^{3} - (3)^{2} + 2(3) - 5 = 3 \times 27 - 9 + 6 - 5 = 81 - 9 + 6 - 5 = 73\\So, for p(x) = -7x^{2} + 5x + 9, p(-2) = -29 $and$ p(3) = 73.\\For p(x) = 3x^3 - x^{2} + 2x - 5, p(-2) = -29 $and$ p(3) = 73.\\For p(x) = 3x^{3} - x^{2} + 2x - 5, p(-2) = -29 $and$ p(3) = 73.\\[/tex]

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Answer:

B = 10/19 it's a fraction btw

[tex](\stackrel{x}{1}~~,~~\stackrel{y}{4})\hspace{5em}y=4x \\\\[-0.35em] ~\dotfill\\\\ \underset{y}{4}~~ = ~~4(\underset{x}{1})\implies 4~~ = ~~4\textit{\LARGE \checkmark}[/tex]

Answer:

y = 4x; (1, 4) = TRUE

Step-by-step explanation:

(1, 4) basically means:

x = 1

y = 4

So we put these values into our equation:

4 = 4 x 1

4 = 4

The length of the large base of the trapezoid is 18cm.

An isosceles trapezoid is simply a convex quadrilateral having a line of symmetry equally dividing one pair of opposite sides.

Given the data in the question

Let the large base be represented by 'x'

The perimeter of the trapezoid is the sum of all the sides of all its sides.

Perimeter = side a + side b + side c + side d

Hence;

43 = x + ( x - 11 ) + 9 + 9

Solve for x

43 + x + x - 11 + 18

43 = 2x + 7

43 - 7 = 2x

36 = 2x

2x = 36

x = 36/2

x = 18

Hence;

Large base = x = 18cm.

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The probability that exactly 10 of the 20 women have dark eyes is 0.2051.

The theory used in this question is the binomial probability formula, which is used to calculate the probability of a certain number of successes in a given number of trials.

The steps for this process are as follows

Step 1: Calculate the binomial formula: (n!)/(x!(n-x)!) * p^x * (1-p)^(n-x),

where n is the number of trials (in this case, 20), x is the number of successes (10), p is the probability of a success (0.40 in this case), and n-x is the number of failures (10).

Step 2: Plug the values into the formula: (20!)/(10!(20-10)!) * 0.40^10 * (1-0.40)^(20-10)

Step 3: Simplify the formula: (20*19*18*17*16*15*14*13*12*11) / (10*9*8*7*6*5*4*3*2*1) * 0.40^10 * 0.60^10

Step 4: Calculate the result: 0.2051

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The zeros of a function can be obtained by factor method, by solving equation or on a graph.

What are zeros of a function?

The values of x for which a function f(x) becomes zero, or f(x)=0, are known as the zeros of the function.

There are 3 different ways by which we can find zeros of a function.

The 3 ways are:

1. By factor method

In order to use this strategy, we must first identify a function's factors. The roots of a function are then obtained by equating the factors with zero.

2. By solving an equation

In some functions, it can be challenging to identify the factors directly. In these situations, we first create an equation by equating the polynomial function with zero. The equation is then resolved. A function's roots are the roots of an equation.

3. On a graph

This is the simplest method for locating a function's zeros. With this approach, we must identify the point at which a function's graph touches or cuts the x-axis (i.e., the x-intercept). The zeros of a function are the locations where the graph cuts or touches the x-axis.

Hence, by these ways we can find the zeros of a function.

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you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

What is meant by arithmetic ?

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Answer:

A' (-2, -1.5)

B' (-2, 1.5)

C' (1, 1.5)

D' (1, -1.5)

Step-by-step explanation:

If you start at (0,0) and go to Point A, you go 4 to the left and down 2.  Half of that is left 3 and down 1.5.  That is where A' will go.  Do the same thing to the other 3 points.

Answer:If Rafael has saved $16, which is one-fourth of the total cost of the game, then the total cost of the game is 4 times the amount he has saved. So, the game costs:

$16 * 4 = $64

Therefore, the game costs $64.

Step-by-step explanation:

If Rafael has saved $16, which is one-fourth of the total cost of the game, then the total cost of the game is 4 times the amount he has saved. So, the game costs:

$16 * 4 = $64

Therefore, the game costs $64.

The sixth number in the data is 24.

Mean is an arithmetic average of the data set, and it can be calculated by dividing a sum of all the data points with the number of data points in the data.

Given that, the mean of 6 numbers is 36, we need to find the 6th number if 5 of the numbers are 27, 42, 43, 45, and 35

We know that,

Mean = (sum of observations) ÷ (total number of observations)

Let the sixth number be x,

Therefore,

36 = (27 + 42 + 43 + 45 + 35 + x) / 6

216 = 192 + x

x = 24

Hence, the sixth number in the data is 24.

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Answer:

see below

Step-by-step explanation:

Opposite sides are congruent (AB = DC).

Opposite angels are congruent (D = B).

Consecutive angles are supplementary (A + D = 180°).

If one angle is right, then all angles are right.

The four properties of parallelogram are:

i) Opposite sides are parallel & equal.

ii) Sum of adjacent interior angles is 180°

iii) Opposite angles are equal.

iv) Diagonals bisect each other.

The quadrilateral with two pairs of parallel sides is known as a parallelogram. Equal in length and width on both sides is required. Four vertices make up a parallelogram, which also has four edges.

A parallelogram is a two-dimensional (2D) shape that has two matching pairs of opposite sides that are parallel and equal in length. The angles inside the two sides of the shape must add up to 180 degrees, which means that all of the angles must add up to 360 degrees.

A rectangle that has been pushed over slightly is all that a parallelogram really is. Because of this, finding the area of a parallelogram can be done using the same formula as finding the area of a rectangle.

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The point-slope formula can be used to get the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30).

To get the slope at the position (1, -30), first take the derivative of the function:

f'(x) = (x2 - 9) (x2 - 9)

(x - 4)' = 2x - 9/x - 4

Check the derivative at x = 1 now:

f'(1) = 2(1) - 9/(1) - 4 = -93

The line has a -93 slope.

Now, enter the point-slope formula the point (1, -30) and the slope (-93):

y - (-30) = -93(x - 1) (x - 1)

If we simplify, we get:

y = -93x + 22

As a result, y = -93x + 22 is the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30).

The point-slope formula can be used to get the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30). According to the point-slope formula, the equation of the line is y - y1 = m for a given point (x1, y1) and slope (m) (x - x1). The specified point in this instance is (1, -30), and the slope of the line may be calculated by calculating the function's derivative and evaluating it at x = 1. The derivative of the function f(x) is 2x - 9/x - 4, which for x = 1 translates to -93. When the point and slope are entered into the point-slope equation, we obtain the result y - (-30) = -93(x - 1), which is abbreviated to y = -93x + 22. As a result, y = -93x + 22 is the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30).

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Using the concept of ratio in the similar triangles, the length scale factor is 1:25

Similar triangles are triangles that have the same shape but may be scaled differently. Two triangles are considered similar if and only if their corresponding angles are congruent (equal in measure) and the ratio of their corresponding sides is the same. This property is known as the "AA Similarity Postulate" or "Angle-Angle Similarity".

In other words, similar triangles have the same shape and proportional sides. This means that if two triangles are similar, corresponding sides are in proportion and corresponding angles are equal in measure.

In the given figures, the two triangles have areas of 3m² and 75m²

The formula of area of a triangle is given as ;

A = 1/2 (b * h)

Assuming the side lengths are equal, we can apply heron's formula which is given as;

S = [a + b + c / 2]

A = √s(s - a)(s - b)(s - c)

But a = b = c

Using the two triangles to find the ratio between the ratios;

Q : R = 3 : 75 = 1 : 25

The length will be given as;

Area = 1/2 b * h

b = h

75 = 1/2 * a * a

a² = 75 * 2

a² = 150

a = √150

In the second triangle;

3 = 1/2(b²)

6 = b²

b = √6

The ratio between Q to R = √6 : √150 = 1 : 25

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The initial valuation of each asset Samtech acquired in transactions:

Value capitalized  = $4,000,000 + $16,000 + $5,000 + $4,000

Value capitalized   = $4,025,000

Assets              Fair value       Total percentage      Proportional value

1.Land           $3,300,000             75%                        $2,475,000

2.Building       $1,100,000             25%                        $275,000

Total              $4,400,000           100 %                      $2,750,000

Working Notes :

Land =($3,300,000 ÷ $4,400,000) =75%

Building =($1,100,000 ÷ $4,400,000) = 25%

Land Improvement =$82,000 + $40,000 =$122,000

2) The initial valuation of each asset assumes that immediately after acquisition that Samtech demolished the building:

  Entries                                                               Amounts

1. Purchase cost                                                  $4,000,000

2. Add: Title insurance of                                     $16,000

3. Add: Legal fees for drawing the contract         $5,000

4. Add: State transfer fee of                                  $4,000

5. Add: Demolition cost                                        $250,000

6. Add: Cleaning and grading cost                     $86,000

7. Less: Salvage material                                     $6,000

    Total Cost of land                                          $4,355,000

Land Improvement = $82,000 + $40,000 = $122,000

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The complete question is:

Samtech Manufacturing purchased land and building for $4 million. In addition to the purchase price, Samtech made the following expenditures in connection with the purchase of the land and building: Title insurance $ 16,000 Legal fees for drawing the contract 5,000 Pro-rated property taxes for the period after acquisition 36,000 State transfer fees 4,000 An independent appraisal estimated the fair values of the land and building if purchased separately, at $3.3 and $1.1 million, respectively. Shortly after the acquisition, Samtech spent $82,000 to construct a parking lot and $40,000 for landscaping. Required: 1. Determine the initial valuation of each asset Samtech acquired in these transactions. 2. Determine the initial valuation of each asset, assuming that immediately after acquisition, Samtech demolished the building. Demolition costs were $250,000 and the salvaged materials were sold for $6,000. In addition, Samtech spent $86,000 clearing and grading the land in preparation for the construction of a new building.