Find the equation of the line.
Use exact numbers.

The nth term of the given sequence is 1/n².

An arithmetic progression (AP) is a sequence of numbers in which each term, starting from the second term, is obtained by adding a fixed constant value to the previous term. This constant value is called the common difference, and it remains the same throughout the sequence.

A geometric progression (GP) is a sequence of numbers in which each term, starting from the second term, is obtained by multiplying the previous term by a fixed constant value. This constant value is called the common ratio, and it remains the same throughout the sequence.

In the given question,

The given sequence is of the form:

1, 1/2², 1/3², 1/4², ...

So, the nth term can be written as:

1/n²

Therefore, the nth term of the given sequence is 1/n².

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It will take around 3.72 months to pay off the credit card debt.

The formula for APR is:

A = P * [tex](1 + r/n)^{nt}[/tex]

In which,

A = amount after compounding.

P = balance amount

r = rate of interest.

n = number of time compounded.

Initial balance: $30,000.

Payments per month = $200.

Expenses = $100

Balance amount = 30,000 - 12 *(200 - 100)

Balance amount = $28800

So, time taken for paying off credit card debt.

30,000 = 28800  [tex](1 + 0.24/1)^{1*t}[/tex]

[tex](1.24)^{t}[/tex] = 30,000 / 28800

[tex](1.24)^{t}[/tex] = 1.04

Solve by using logarithmic function.

t = ln (1.04) / 1.24

t = 0.31  year

t = 3.72 months

Thus, it will take around 3.72 months to pay off the credit card debt.

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Answer:

You can use trigonometry to solve this problem. The distance from the base of the tree to where you are standing forms the adjacent side of a right triangle, with the height of the tree being the opposite side and the angle of elevation being 39°.

Using the tangent function: tan(θ) = opposite/adjacent

tan(39°) = 390 / adjacent

Adjacent = 390 / tan(39°)

Adjacent ≈ 496.4 feet

So you are approximately 496.4 feet away from the base of the tree.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.  sinL = 3/5

3.  cosL = 4/5

4.  sinN = 4/3

5.  cos32 = x/14

     x = 14(cos32) = 11.9

7.  tan75 = 17/x

    x = 17/tan75 = 4.56 ≈ 4.6

The simulation suggests that the chef's estimation of 30% broccoli soup orders is reasonable, but actual orders will vary from one set of customers to the next.

The chef's estimation of 30% broccoli soup orders seems reasonable based on the probabilities given, but the actual number of broccoli soup orders will likely vary from one set of 10 customers to the next. To estimate the accuracy of the chef's estimation, she conducts a simulation by shuffling cards representing the soup choices and randomly selecting one for each of the 10 customers. She repeats this process five times.

Based on the simulation results, we can see that the actual number of broccoli soup orders varies quite a bit from the expected value of 1.5. However, this is to be expected due to the random nature of the simulation.

To further estimate the accuracy of the chef's estimation, we could calculate the mean and standard deviation of the results to get a better sense of the distribution of possible outcomes.

Overall, the simulation suggests that the chef's estimation of 30% broccoli soup orders is a reasonable estimate, but the actual number of broccoli soup orders will likely vary from one set of 10 customers to the next.

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Answer:

We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can write:

m∠A + m∠B + m∠C = 180

Substitute the given values:

5x+6 + 7x-18 + m∠C = 180

Combine like terms:

12x-12 + m∠C = 180

Add 12 to both sides:

12x + m∠C = 192

Subtract 12x from both sides:

m∠C = 192 - 12x

Therefore, m∠C is equal to 192 minus 12 times x.

Answer:

848,775 pounds

Step-by-step explanation:

The volume of a hemisphere with radius 8 feet is:

V = (2/3)πr^3 = (2/3)π(8^3) = 268.08 cubic feet

The weight of the liquid is given by:

W = V * ρ * g

where ρ is the density of the liquid and g is the acceleration due to gravity. Plugging in the values, we get:

W = 268.08 * 98.9 * 32.2 = 848,774.7 pounds

Rounding to the nearest full pound, the total weight of the liquid in the tank is 848,775 pounds.

Kenny will spend $4,593.75 on fencing the dilated rectangle.

What is rectangle ?

A rectangle is a quadrilateral with four right angles (90-degree angles) and opposite sides of equal length. It is a type of parallelogram in which both pairs of opposite sides are parallel and congruent (of equal length). The opposite sides of a rectangle are also perpendicular (form a right angle) to each other. The area of a rectangle is equal to the product of its length and width, while its perimeter is equal to the sum of the lengths of all its sides. Rectangles are commonly used in geometry, architecture, engineering, and many other fields.

According to the question:
Since each unit on the graph represents 25 feet, the dimensions of the original rectangle ABCD are:

AB = 4 units, which represents 4 x 25 = 100 feet

BC = 3 units, which represents 3 x 25 = 75 feet

Therefore, the perimeter of ABCD is 2(AB + BC) = 2(100 + 75) = 350 feet.

When dilating by a scale factor of 2.5, each dimension of ABCD will be multiplied by 2.5. Therefore, the dimensions of the dilated rectangle A'B'C'D' are:

A'B' = AB x 2.5 = 100 x 2.5 = 250 feet

B'C' = BC x 2.5 = 75 x 2.5 = 187.5 feet

The perimeter of A'B'C'D' is 2(A'B' + B'C') = 2(250 + 187.5) = 875 feet.

Therefore, Kenny will need to fence a perimeter of 875 feet. At a cost of $5.25 per foot, the total cost of fencing will be:

875 feet x $5.25/foot = $4,593.75

Therefore, Kenny will spend $4,593.75 on fencing the dilated rectangle.

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The area should the base of the new container must have option D that is, A = 2m-10.

In mathematics, area is a measurement of the size of a two-dimensional surface or shape, usually measured in square units such as square meters, square centimeters, or square feet. It is the amount of space inside the boundary of a flat object or shape.

Here,

To calculate the area of the base of the new container, we need to find the radius of the container first. Since the diameter is given as 10 cm, the radius would be half of that, which is 5 cm. The formula for the area of a circle is A = πr², where A is the area and r is the radius. So, substituting the values, we get:

A = π(5 cm)²

A = π(25 cm²)

A = 25π cm²

However, the answer choices are not in this format. To simplify the answer, we can use the value of π as approximately 3.14 (rounded to two decimal places). So, the area of the base would be:

A = 25π cm²

A ≈ 25(3.14) cm²

A ≈ 78.5 cm²

Now, we need to choose the answer option that represents this area in terms of variables. The only option that matches is:

d. A = 2m-10

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Complete question:

Question 6. One of the bases of a container for storing gasoline has broken and it is necessary to buy a new one. The diameter of the container is 10 cm. What area should the base of the new container have?

a. A = -10²

b. A = 2m-5

c. A = -5²

d. A = 2m-10

Based on the information provided, the total length of the worms would be 6 1/2 inches.

The graph presented shows the length of the worms Abe measured, based on the graph we know that the shortest worm was 2.125 inches, while the longest worm was 2.875 inches. Using this information, let's now add the three shortest worms together:

2.125  inches + 2.125  inches + 2.25 inches = 6.5 inches in total, which can be expressed ad 6 1/2.

Based on this, the total length of the three shortest worms would be 6 1/2.

Note: This question is incomplete; here is the complete question:

Abe measured the lengths of several worms. He made this line plot to display his measurements. Abe laid the three shortest worms together end to end. What is the total length of these three worms?

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Step-by-step explanation:

the width is 23.5ft and the length is 47ft

Answer:

X=-1 or 9

Step-by-step explanation:

using the quadratic formula:

[tex]X=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]

X=-1

X=9

The graph of f(x) is a parabola that opens downward and has a vertex at (-3/2, 3/4), while the graph of g(x) is a parabola that opens upwards and has a vertex at (-1/2, 7/4). They both intersect at the point (-3/2, -5/4).

Vertex is a mathematical term used to describe the point where two lines or line segments meet. It is the point of intersection for two or more lines. In a two-dimensional plane, a vertex is the point that marks the beginning and end of a line segment. In a three-dimensional plane, a vertex is the point of intersection of three or more lines. A vertex can also refer to a corner, such as the vertex of a triangle or a cube. In graph theory, a vertex is a node, or point, in a graph. Vertex can also refer to the highest point of a graph, such as the vertex of a parabola.

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Answer:

Width = 12

Length = 19

Step-by-step explanation:

They multiply to 228 and 19in is 7in larger than 12in.

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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Answer:

The quotient of 13 and 0.4 can be found by dividing 13 by 0.4.

13 ÷ 0.4 = (13/1) ÷ (2/5) = (13/1) × (5/2) = 65/2 = 32.5

So the answer is D. 32.5.

Step-by-step explanation:

The quotient of 13 and 0.4 is 32.5. The method involves directly dividing 13 by 0.4, either manually or using a calculator.

The student is asking for the quotient of 13 and 0.4. Quotient means the result of a division operation. In this case, we divide 13 by 0.4. Here's how:

So, the quotient of 13 and 0.4 is 32.5. Therefore, the answer is (D) 32.5.

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True. The length of AB can be gotten by 3^2 + b^2 = 4^2.

True.  The perimeter of the trapezoid shown is not 22 units.

The length of AB can be gotten by 3^2 + b^2 = 4^2.

9 + b^2 = 16

b^2 = 16 + 9

b = 5

Then we have to count the boxes to get the length of the other sides

CD = 4

AD = 8

BC = 5

AB = 5

Then the perimeter would be be 5 + 5 + 8 + 4

= 22

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Answer:4? Think

Step-by-step explanation:

Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

Answer:

A. To find the acceleration, we need to take the derivative of the velocity function with respect to time:

a(t) = v'(t) = 2(pi) - cos(t(pi))

B. To find the minimum acceleration, we need to find the critical points of the acceleration function in the interval [0, 3].

a'(t) = sin(t(pi))

The critical points occur when sin(t(pi)) = 0, which means t = 0, 1, 2, 3. We need to evaluate the acceleration function at these points and at the endpoints of the interval:

a(0) = 2(pi) - cos(0) = 2(pi)

a(1) = 2(pi) - cos(pi) = pi + 2

a(2) = 2(pi) - cos(2pi) = 2(pi)

a(3) = 2(pi) - cos(3pi) = pi - 2

The minimum acceleration occurs at t = 3, with a minimum value of pi - 2.

C. To find the maximum velocity, we need to find the critical points of the velocity function in the interval [0, 2].

v'(t) = 2(pi) - cos(t(pi)) = 0

The critical points occur when cos(t(pi)) = 2(pi). We can solve for t as follows:

cos(t(pi)) = 2(pi)

t(pi) = arccos(2(pi))

t = arccos(2(pi))/pi ≈ 1.58

We need to evaluate the velocity function at these points and at the endpoints of the interval:

v(0) = -sin(0) = 0

v(1.58) ≈ 1.69

v(2) = (2(pi) - 5)(2) - sin(2(pi)) = 4(pi) - 10

The maximum velocity occurs at t = 1.58, with a maximum value of approximately 1.69.

Answer:

The midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2) is given by the coordinates:

[(x1 + x2) / 2, (y1 + y2) / 2]

In this case, A is located at (1, 4) and B is located at (3, -6). So the midpoint M of AB is:

[(1 + 3) / 2, (4 + (-6)) / 2]

= [2, -1]

Therefore, the midpoint of AB is at the point (2, -1).

The coordinates of the midpoint of the line AB is [2, -1]

Section formula is used to find the ratio in which a line segment is divided by a point internally or externally.

It is used to find out the centroid, incenter and excenters of a triangle. In physics, it is used to find the center of mass of systems, equilibrium points, etc.

Given that, we need to find the midpoint of AB if A located at (1, 4) and B is located at (3, -6).​

The midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2) is given by the coordinates:

[(x1 + x2) / 2, (y1 + y2) / 2]

In this case, A is located at (1, 4) and B is located at (3, -6).

So the midpoint M of AB is:

= [(1 + 3) / 2, (4 + (-6)) / 2]

= [2, -1]

Hence, the midpoint of AB is at the point (2, -1).

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As a ladybug on the outer surface of the Klein bottle, there is no direct path to the inside. However, you can travel along a specific type of curve called a "cross-cap curve" to reach the inside. and using topology.

To do this, start by moving along the outer surface of the Klein bottle until you reach the point directly opposite to your starting position. Then, imagine folding the surface of the bottle in half along a line that runs through this point.

This folding will create a new surface that intersects with the original surface of the bottle along a cross-cap curve. Follow this curve until you reach the inside of the Klein bottle, where the special gentleman bug is waiting for you.

It's important to note that the Klein bottle is a non-orientable surface, which means that there is no "inside" or "outside" in the traditional sense. However, the concept of inside and outside can still be useful for navigation purposes.

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The exponential function system that intersects as x = 1, is  [tex]y = 3(1)^x[/tex] and [tex]y = \frac{6}{8} \times (4)^x[/tex].

The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The d Here are two different exponential functions of the required form that intersect at x = 1 -

[tex]y = 3(1)^x[/tex]

[tex]y = \frac{6}{8} \times (4)^x[/tex]

In the first equation, a = 3, and b = 2.

Plugging in x = 1, we get -

[tex]y = 3(1)^1[/tex]

y = 3 × 1

y = 3

So the point of intersection of this equation with the x-axis is (1, 3).

In the second equation, a = 6/8 , and b = 4.

Plugging in x = 1, we get -

[tex]y = \frac{6}{8} \times (4)^1[/tex]

y = 3/4 × 4

y = 3

So the point of intersection of this equation with the x-axis is also (1, 3).

So, both of these equations intersect at x = 1 and are of the form [tex]y = a \times b^x[/tex].

Therefore, the equations are [tex]y = 3(1)^x[/tex] and [tex]y = \frac{6}{8} \times (4)^x[/tex].

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Complete reference question:

To subtract 6/7 from 2 1/4, we need to find a common denominator. The least common multiple of 7 and 4 is 28, so we can convert 2 1/4 to 9/4 and 6/7 to 24/28. Then we can subtract:

9/4 - 24/28

= 63/28 - 24/28

= 39/28

Therefore, 2 1/4 - 6/7 = 39/28.

To solve for the blank in 2 5/12 - blank = 2/3, we can start by converting 2 5/12 to an improper fraction:

2 5/12 = (2*12 + 5)/12 = 29/12

Then we can subtract 2/3 from both sides:

2 5/12 - 2/3 = blank

To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 12 is 12, so we can convert 2/3 to 8/12. Then we can subtract:

29/12 - 8/12

= 21/12

= 7/4

Therefore, the blank in 2 5/12 - blank = 2/3 is 7/4.

To subtract 5 3/8 from 7 1/12, we need to find a common denominator. The least common multiple of 8 and 12 is 24, so we can convert both mixed numbers to improper fractions:

7 1/12 = (712 + 1)/12 = 85/12

5 3/8 = (58 + 3)/8 = 43/8

Then we can subtract:

85/12 - 43/8

= 85/12 - (433)/(83)

= 85/12 - 129/24

= 5/24

Therefore, 7 1/12 - 5 3/8 = 5/24.

To solve for the blank in blank + 7/10 = 2 9/20, we can start by converting 2 9/20 to an improper fraction:

2 9/20 = (2*20 + 9)/20 = 49/20

Then we can subtract 7/10 from both sides:

blank + 7/10 - 7/10 = 49/20 - 7/10

Simplifying the right side:

49/20 - 7/10 = (492)/(202) - (74)/(104) = 98/40 - 28/40 = 70/40 = 7/4

Therefore, blank + 7/10 - 7/10 = 7/4, and solving for blank:

blank = 7/4

Therefore, the blank in blank + 7/10 = 2 9/20 is 7/4.

The calclulated value of c to make a perfect square trinomial from 6x^2 + 60x + c is 150

To make a quadratic trinomial a perfect square trinomial, we need to add a constant term that is equal to half of the coefficient of the x-term, squared.

In other words, we need to find a value of c such that:

6x^2 + 60x + c = Perfect square trinomial

Divide through by 6

So, we have

x^2 + 10x + c/6 = Perfect square trinomial

Take the coefficient of x

k = 10

Divide by 2

So, we have

k/2 = 5

Square both sides

(k/2)^2 = 25

This means that

c/6 = 25

So, we have

c = 150

Therefore, to make the trinomial 6x^2 + 60x + c a perfect square trinomial, we need to choose c = 150.

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The required  derivative of [tex]f(x) = \frac{2x^3 - 1}{x}$[/tex] is [tex]$f'(x) = 4x + \frac{1}{x^2}$[/tex].

A technique for determining a function's derivative is differentiation. Mathematicians use a method called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.

The function [tex]f(x) = \frac{2x^3 - 1}{x}$[/tex] can be written as [tex]f(x) = 2x^2 - \frac{1}{x}$[/tex].

The derivative of f(x) can be found using the power rule and the derivative of 1/x, which is[tex]-\frac{1}{x^2}$[/tex].

Therefore, we have:

[tex]$f'(x) = 4x + \frac{1}{x^2}$$[/tex]

So the derivative of [tex]f(x) = \frac{2x^3 - 1}{x}$[/tex] is [tex]$f'(x) = 4x + \frac{1}{x^2}$[/tex].

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Complete question:

Find the derivative of the following, using differentiation from first principles. f(x) = 2x²-1/x​.

Simultaneous equations are a set of equations that are solved together to determine the values of the variables that satisfy both equations.

1) 4x + 5y = 3 ---(1)

y - 3x = -7 ----(2)

Using the substitution method;

y = -7 + 3x ----(3)

Thus

4x + 5(-7 + 3x) = 3

4x -35 +15x = 3

19x - 35 = 3

19x = 3 + 35

x = 2

Then

4(2) + 5y = 3

8 + 5y = 5

y = 13/5

y = 2 3/5

2) 2x - 4y = 24 ----- x 3

  -3x + 2y = -48 ----- x 2

   6x - 12 y = 72 ---- (3)

  -6x + 4y = -96 ---- (4)

Add 3 and 4

         16y = -24

y = -24/16

Substitute y = -24/16 into (1)

2x - 4(-24/16) = 24

2x + 6 = 24

x = 15

3) -x + y = 13 --- 1

  3x - 4y = 46 ---- 2

y = 13 + x ---- 3

Substitute 3 into 2

3x - 4(13 + x) = 46

3x - 52 - 4x = 46

-x - 52 = 46

x = 98

Substitute x = 98 into (1)

-98 + y = 13

y = 13 + 98

y = 111

Let C be x and D be y

x + y = 180

x = 33 + 6y

x - 6y = 33

x = 180 - y

Substitute and obtain;

180 - y - 6y = 33

180 - 7y = 33

y = 33 - 180/-7

y = 21

Then

x + 21 = 180

x = 180 - 21

x = 159

Lastly

Let small = x , medium = y

x + y = 150

4x + 6y = 764

x = 150 - y

4(150 - y) + 6y = 764

600 - 4y + 6y = 764

600 + 2y = 764

2y = 764 - 600

y = 82

Then;

x + 82 = 150

x = 68

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The solutions to the simultaneous equations are:

1) x = 2 and y = -1

2) x = 18 and y = 3

3) y = -7 and x = 6

There are three main methods in solving simultaneous equations and they are:

1) Elimination Method

2) Substitution Method

3) Graphical Method

1) 4x + 5y = 3

y = 3x - 7

Substitute 3x - 7 for y in the first equation to get:

4x + 5(3x - 7) = 3

4x + 15x - 35 = 3

19x - 35 = 3

19x = 35 + 3

19x = 38

x = 38/19

x = 2

Thus:

y = 3(2) - 7

y = -1

2) 2x - 4y = 24

-3x + 2y = -48

Multiply eq 2 by 2 and eq 1 by 1 to get:

2x - 4y = 24    -----(3)

-6x + 4y = -96   -----(4)

Add eq 3 to eq 4 to get:

-4x = -72

x = 18

2(18) - 4y = 24

36 - 4y = 24

36 - 24 = 4y

4y = 12

y = 3

3) -x + y = -13

3x - 4y = 46

From eq 1, x = y + 13

Thus:

3(y + 13) - 4y = 46

3y + 39 - 4y = 46

39 - y = 46

y = 39 - 46

y = -7

x = -7 + 13

x = 6

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The total distance that the water tanker has covered in March of 2022 is given as follows:

1860 kilometers.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The parameters for this problem are given as follows:

Hence the total distance is then obtained as follows:

d = v x t

d = 60 x 31

d = 1860 kilometers.

The complete question is:

"Assuming that the water tanker travels an average of 60 kilometers a day, calculate the total distance that the water tanker has covered in March 2022​".

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