2n × r × 2 × 1 × s
for n = 2, r = 2, and s = 1.

a) The estimate for the total number of deer in the park is given as follows: 630 deers.

b) The assumption that he made was that the proportion was followed.

The total number of deer in the park is estimated applying the proportions in the context of this problem.

The next week, the gamekeeper caught 70 deer. 10 of the deer had a tag around one of their hooves, hence the fraction of marked deers is given as follows:

10/70 = 1/7.

He had marked 90 deers, hence the estimate for the total number of deers, considering a constant proportion, is given as follows:

1/7 x n = 90

n = 90 x 7

n = 630 deers.

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The explicit formula for the given geometric series will be [tex]a_n = -4(3)^{n-1}[/tex].

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

Given that the geometric series is -4,-12,-36,-108. The formula for the nth term of the geometric progression will be written as:-

[tex]a_n = a_1(r)^{n-1}\\[/tex]

Here, r is the common ratio of the series. The value of the common ratio is r = -12 / -4 = 3.

The formula will be:-

[tex]a_n = a_1(r)^{n-1}\\[/tex]

[tex]a_n = -4(3)^{n-1}\\[/tex]

Therefore, the formula for the nth term will be [tex]a_n = -4(3)^{n-1}\\[/tex].

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i'm to lazy to bored trying to do my work and I'm also very dumm

[tex]y=2\frac{2}{3}+16[/tex] is the answer as it passes perpendicular and through point A

Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°

Explaining quadrilaterals?

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals' internal angles add up to a constant 360 degrees.

What is quadrilateral formula?

When the diagonal and the sum of the lengths of the perpendiculars drawn from the remaining two vertices are known, the area of the quadrilateral can be determined as follows Area of quadrilateral = (12) diagonal length sum of the lengths of the perpendiculars drawn from the remaining two vertices.

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The complete question is -

Explain in your own words why it takes more to prove quadrilaterals congruent. Include examples demonstrating how ""just angles"" or ""just sides"" is not enough.

The value of A + B + C is 1.21 for the distribution function.

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x in probability theory and statistics.

From the given data the values of A, B, and C are 1 / 8, 3 / 8, and 23 / 32.

The value of the sum of A, B, and C is calculated as:-

E = A + B + C

E = 1 / 8 + 3 / 8 + 23 / 32

E = ( 4 + 12+ 32 ) / 32

E = 39 / 32

E = 1.21

Therefore, the solution for the distribution function is E = 1.21.

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Answer:

0.072337963 or 125/1728

Step-by-step explanation:

simply put it into a calculator

Answer:

20

Step-by-step explanation:

lets say width is 2x and the length is x

2x+x+2x+x=120

6x=120

x=20

thus, your answer is 20

The measure of side MK is 103.3.

To find the length of side MK, we need to use the concept of similar triangles. Similar triangles have the same shape but may be different sizes. In this case, the ratio of corresponding sides is the same.

Now, we can use the fact that the ratio of corresponding sides is the same for both triangles:

JI/JH = ML/MK

16/29 = 57/x

cross-multiply the expression, we get

16x = 57 × 29

x = (57 × 29)/16

x = 103.3125

Therefore the measure of side MK is 103.3 to the nearest tenth place.

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Answer:

k = 12

Step-by-step explanation:

Finding the unknown value:

    To find the value of 'k', isolate k

             2k + 36 = 6k - 12

                     2k = 6k - 12 - 36

                    2k = 6k - 48

                2k - 6k = -48

                      - 4k = -48

                          k = -48 ÷ (-4)

                          k = 12

Answer:

x = 13

Step-by-step explanation:

I put it into my calculator, let me know if that helped :)

The predicted cost of postage for 2013 is 45 cents.

We need to use the exponential regression model to predict the cost of postage for the year 2013, given that it was 63 years since 1950.

Let's assume that the cost of postage can be modeled using the exponential function:

C(t) = a * e^(kt)

where:

We can use the two data points we have to solve for a and k:

Using the above data points, we can solve for k as follows:

0.03 = a * e^(0 * k)

0.46 = a * e^(63k)

Dividing the second equation by the first equation, we get:

15.333 = e^(63k)

Taking the natural logarithm of both sides, we get:

k = ln(15.333)/63

Evaluate

k = 0.043

Now that we have k, we can use it to predict the cost of postage in 2013:

C(63) = a * e^(63k)

C(63) = 0.03 * e^(63 * 0.043)

C(63) = 0.45

Hence, according to the exponential regression model, the cost is 45 cents.

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Complete question

The cost of first-class postage in 2013 was raised to 46 cents.

According to the exponential regression model, what was the predicted cost for 2013 if the cost of postage was 3 cents in 1950

Start by noting that 2013 is 63 years since 1950.

The solution of a system of equations can be determined by dividing the coefficients of variables.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Solution of system of equations :-

Let the two system of equations be

a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0

1) Unique solution or one solution :-

The solution of the system of equations will be unique when,

a₁ / a₂ ≠ b₁ / b₂

2) Infinite solutions :-

The solution of the system of equations will have infinitely many solutions when,

a₁ / a₂ = b₁ / b₂ = c₁ / c₂

3) No solution :-

The solution of the system of equations will have no solutions when,

a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂

Hence, the solution of a system of equations can be determined by dividing the coefficients of variables.

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Answer:

4.81 meters

Step-by-step explanation:

1 m = 100 cm

where m = meters

         cm = centimeters

481 centimeters need to be converted:

= 481 cm × [tex](\frac{1 m}{100 cm})[/tex]

The cm in the numerator and denominator will completely cancel each other out:

= [tex]\frac{481}{100}[/tex] m

= 4.81 meters

Answer: -1/12

Step-by-step explanation:

Answer:

-1/12

Step-by-step explanation:

9/4 - 7/3

To start, we need to make the denominators the same number.  In order to do that, we need to identify the factor they have in common.

4, 8, 12

3, 6, 9, 12

Twelve is the common factor, so we will use this.  Remember, whatever you do to the bottom, you must do to the top, and vice versa.

4 * 3 = 12

/12

3 * 9 (numerator) = 27

27/12

     Now, we must figure out 7/3.

3 * 4 = 12

4 * -7 = -28

-28/12

Now, take the new fractions and subtract them.

27/12 - 28/12

-1/12

The area of the surface to be covered by the label = 904.32 mm²

We know that the formula for the surface area of cylinder is:

A =  2πrh + 2πr²

where r is the radius of the cylinder and h is the height of the cylinder

Here, the dimensions of the cylindrical battery:

radius r = 4 millimeters

height h = 32 millimeters

Using the above formula of surface area of cylider, the area of the surface to be covered by the label would be,

A =  2πrh + 2πr²

A =  2πr(h + r)

A = 2π × 4 × (32 + 4)

A = 2 × 3.14 × 4 × 36

A = 904.32 mm²

Therefore, the required area is 904.32 mm²

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The expression - 7 meters represents the 7 meters in the west direction.

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

If 20km represents 20 km due east.

We know that the opposite of the east direction will be the west direction.

Then we can conclude that if the east direction represents the positive values, then the west direction represents the negative value.

Then the expression - 7 meters represents the 7 meters in the west direction.

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The values of the terms, a₁, a₂, and a₁₀ of the sequence are;

(a) a₁ = 1, a₂ = 1/2, a₁₀ = 1/10

(b)  [tex]\lim\limits_{n\to {\infty}}[/tex] aₙ = 0

A sequence is an ordered collection of objects such as numbers in which repetition of the object is possible, and the objects (or numbers) are referred to as the terms of the sequence.  

The sequence, [tex]\{a_n\}^\infty_{n = 1}[/tex] with values, aₙ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{n + 1}} }[/tex]

(a) a₁ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{1 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^2} } = -[\frac{1}{x} ]^{\infty}_1[/tex]

[tex]-[\frac{1}{x} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{1} ) = 0 + 1 = 1[/tex]

Therefore; a₁ = 1

a₂ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{2 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^3} } = -[\frac{1}{2\cdot x^2} ]^{\infty}_1[/tex]

[tex]-[\frac{1}{2\cdot x} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{2 \times 1} ) = 0 + \frac{1}{2} = \frac{1}{2}[/tex]

Therefore; a₂ = 1/2

a₁₀ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{10 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^{11}} } = [-\frac{1}{10\cdot x^{10}} ]^{\infty}_1[/tex]

[tex][-\frac{1}{10\cdot x^{10}} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{10\times 1} ) = 0 + \frac{1}{10} = \frac{1}{10}[/tex]

Therefore; a₁₀ = 1/10

b) The limit, [tex]\lim \limits_{n\to \infty} a_n[/tex] can be evaluated as follows;

aₙ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{n+1} } } \, dx[/tex]

[tex]\int\limits^{\infty}_1 {\frac{dx}{x^{n+1} } } \, dx = [-\frac{1}{n\cdot x^n} ]^{\infty}_1 = -\frac{1}{n\times \infty } - (-\frac{1}{n\times 1^n} )= \frac{1}{n}[/tex]

aₙ = 1/n

Therefore;

[tex]\lim \limits_{n\to \infty} a_n = \frac{1}{\infty}[/tex] = 0

[tex]\lim\limits_{n\to {\infty}} a_n[/tex] = 0

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Answer:

Step-by-step explanation:

The dot product of two vectors u and v is given by the formula:

u · v = u[0] * v[0] + u[1] * v[1] + u[2] * v[2]

where u[0], u[1], and u[2] are the components of vector u and v[0], v[1], and v[2] are the components of vector v.

Plugging in the values from the vectors u = [2, 3, 4] and v = [5, 6, 7], we get:

u · v = 2 * 5 + 3 * 6 + 4 * 7 = 10 + 18 + 28 = 56

Therefore, the dot product of the vectors u and v is 56.

To design the table, you could create a "Sports" table and a "Patient-Sport" table with the following fields:

Sports table:                                      Patient-Sport table:

SportID (primary key)                        PatientID (foreign key)

SportName                                        SportID (foreign key)

A database is a collection of organized data stored and retrieved electronically. It is designed to allow efficient storage, retrieval, manipulation, and management of large amounts of data. Databases can be used to store information such as text, numbers, images, and other media. The data in a database is typically organized into tables, which are made up of rows and columns. Each row represents a single record, and each column represents a field of information within that record. There are many different types of databases, including relational databases, NoSQL databases, and in-memory databases, and they are used in a wide range of applications, such as online retail, finance, healthcare, and more.

The Patient-Sport table is used to connect the patient to the sport they are playing. This allows for multiple sports to be assigned to a single patient. In this way, you can track the sports played by each patient, while still maintaining the relationships between the patient and their data in the other tables.

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Answer: 37.5

Step-by-step explanation:

62.5 * (3/5) = 37.5

Answer:

Step-by-step explanation:

If there is a hole in the graph at x = -6, that means that there was initially an expression in both the numerator and the denominator that was the same, which is the hole very loosely defined. If the hole is at x = -6, then the factor for that solution is (x + 6). One of those has to be in both the numerator and denominator in order for them to cancel out. This is called a removeable discontinuity. Because the x-intercept is at x = 3, the factor for that zero is (x -3). That has to go in the numerator also. Our equation then for the rational function graphed is

[tex]y=\frac{(x+6)(x-3)}{(x+6)}[/tex] which FOILs to

[tex]y=\frac{x^2+3x-18}{x+6}[/tex]

There are several ways to find the zeros of the function x^4–18x^2+12x+80. You can graph the equation and see where it crosses the x axis.The graph crosses at x=-4,-2. This means that -4, and -2 are roots, and (x+4) and (x+2) are factors. I like synthetic division the best when it comes to factoring. I teach synthetic division when we get to problems like this, so I will assume that you are familiar with it.First take the coefficients of the equation x^4–18x^2+12x+80 I have to usex^4 +0 x^3 –18x^2+12x+80 : 1 0 -18 12 80. I will use -4 first.If you are not supposed to graph it, then you can use synthetic division. It can take longer because you have to “guess “ at the factors using an educated guess from the factors of =/- p/q . Where p is the last coefficient and q is the first coefficient.In this case we need to find the factors of 80/1 . These are 1,2,4,5,8,10,16,20,40,80. So possible roots are +/- (1,2,4,5,8,10,16,20,40,80). Students usually start with the smaller numbers and work up, So I would try 1 first then 2 etc.Now another way to find the factors is to use 10 as x and to see what the answer is, then try to factor the results. f(x)=x^4–18x^2+12x+80 f(10)=10,000–1800+120+80=8400I can factor 8400 into 100 *6 *14, or (10+0) *(10+0)*(10–4)*(10+4). 0 is not a factor from above, but +/- 4 is. So I could try those two numbers. Looking at the possible roots using 10 as my x, I would need to look at 9,11, 8,12, 0,20 -4,26, etc

The mapping above represents a function, since each number in Set A is mapped to only one number in Set B.

A relation represents a function when each input value is mapped to a single output value.

For the relation in this problem, we have that:

As there are no repeated inputs, the relation represents a function.

The diagram is given by the image presented at the end of the answer.

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Answer:

3000

Step-by-step explanation:

8 x 375 = 3000

Jeremy should choose Model A.

From the question, we have the following parameters:

These mean that:

Model A = 2 * Backpack (x)

Model B = 15 + Backpack (x)

18 + Model A = 28 + Model B

As equations, we have

A = 2x

B = 15 + x

18 + A = 28 + B

So, we have

18 + 2x = 28 + 15 + x

Evaluate

x = 25

So, we have

A = 2 * 25 = 50

B = 15 + 25 = 40

Hence, he should choose model A

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The length of BC is 6 inches.

There is a theorem in mathematics that:

If there is a circle O with tangent line L intersecting the circle at point A, then the radius OA is perpendicular to the line L.

Given;

Part a;

The length of the secant CD, times its external segment, FC, equals the square of the tangent segment CB;

Mathematically, it can be written as;

RT*ST=TU^2

Part b;

RT*ST=TU^2

TU^2=9*4

TU=6

Therefore, the distance of TU in circle will be 6 inches.

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Answer:

1.71 pounds of sugar per dollar.

Step-by-step explanation:

To calculate how many pounds of sugar Keisha got per dollar, we divide the total amount of sugar by the total amount of money spent. In this case, she bought 12 pounds of sugar for $7, so we divide 12 by 7:

12 ÷ 7 = 1.71

So, Keisha got 1.71 pounds of sugar per dollar.