a circular treehouse has a floor that is 490.625ft.to add a thin strip of waterproofing around the floor how many feet are needed

The value of k given sequence is =300 and the value of the term Sk=4875,

In mathematics, we may come across different types of numbers, and patterns. One of the number patterns includes sequences. The sequence is a specified collection of objects in which repetitions are allowed and order matters. Formally, a sequence is a function from natural numbers to the elements at each position. Similar to a set, it contains members, and they are called elements or terms. The number of elements is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and the order does matter.

value of k

U1 =1.3

U2= 1.4

Uk = 31.2

a = 1.3

d = 1.4 - 1.3 = 0.1

Uk = 1.3 + (k - 1)(0.1)

=> 1.3 + (k - 1)(0.1) = 31.2

=>  (k - 1)(0.1) = 29.9

=> k - 1 = 299

=> k = 300

Sk  = (300/2)(1.3 + 31.2)

= 150 * (32.5)

= 4875

F is the sum of the terms for which the term is not a multiple of 3

3rd term = 1.5

6th term = 1.8

300th term = 31.2

Total terms = 100

Sum = (100/2)(1.5 + 31.2)  =  1635

F = 4875 - 1635   = 3240

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The sound and unsound deductive reasoning is differentiated below.

Deductive reasoning is a logical approach where you go from general ideas to specific conclusions.

Given is the difference between sound and unsound deductive reasoning.

Sound deductive reasoning -

If an argument is both valid and has all true premises, we will say that the argument is sound.

Unsound deductive reasoning -

An argument is unsound if it either has a false premise, or is invalid.

Therefore, the sound and unsound deductive reasoning is differentiated above.

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The ratio of their volumes is 3: 1

If two solids are identical, their volume ratio is equal to the cube of their corresponding side ratio. (It should be noted that volume is a 3-D measurement, not a “length” measurement. When the base and height of a pyramid and a prism are the same, their volumes are always in the ratio of 1:3Volume of prism.

A triangular prism and a triangular pyramid with identical bases and heights with the volume of the prism being three times that of the pyramid. Students should use manipulatives such as water, rice, or beans to physically represent this connection.

The volume of a prism =Base Area× Height and Volume of Pyramid = 1/3 × base area × Height

Given:

Height of both pyramid and a prism is 8.2 cm.

Area of base is 22.3 cm cube.

Volume of Prism = 22.3 × 8.2

Volume of Pyramid = 1/3 × 22.3 × 8.2

Ratio of volume of prism and volume of pyramid = (22.3 × 8.2) : 1/3 × (22.3 × 8.2)

Ratio of volume of prism and volume of pyramid = 1: 1/3

Ratio of volume of prism and volume of pyramid = 3: 1

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The vector C is 1.00 x + 3.00 y

Therefore, the correct answer is C) 1.00 x + 3.00 y.

In mathematics and computer science, a vector is an ordered list of numbers that can be used to represent things like position, direction, and magnitude. Vectors can be added and subtracted, and they can be multiplied by scalars (numbers).

To subtract two vectors, we need to subtract the corresponding components. So, the x-component of vector C is

(-3.00 x) - (-2.00 x) = -3.00 + 2.00

= 1.00

and the y-component of vector C is

(4.00 y) - (1.00 y) = 4.00 - 1.00

= 3.00.

Therefore, vector C = 1.00 x + 3.00 y.

--The question is incomplete, answering to the question below--

"Vector A = -2.00x + 1.00y and vector B = -3.00x + 4.00y .What is vector C =  B - A?

A) 1.00x+5.00y

B) -100x+-3.00y

C) 1.00x+3.00y

D) -100x+3.00y

E) -100x+-5.00y"

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16 is the number which shows a proportional relationship between x and y.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

the ratio of x:y = 0.8 : 4

let, the number for y be a

so that, x: y is  proportional .

i.e. 3.2 : a = 0.8 : 4

or, a = 16

Hence, 16 is the solution.

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The surface area of square pyramid is 207.04 square inches.

Surface area is the area of all outer facing surfaces on an object. The total surface area is calculated by adding all the areas on the surface: the areas of the base, top, and lateral surfaces (sides) of the object.

The formula to find the surface area of square pyramid is A=a²+2a√(a²/4+h²)

Here, a=8 inches and h=8 inches

Now, A= a²+2a√(a²/4+h²)

A= a²+2a√(a²/4+h²)

A= 8²+2×8√(8²/4+8²)

A= 64+16√(16+64)

A= 64+16√80

A= 64+16×8.94

A= 207.04 square inches

Therefore, the surface area of square pyramid is 207.04 square inches.

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The value of c for the given function at x = 0 to be continuous is c = 8/15.

The following three requirements must all be met for a function to be regarded as continuous at a point:

In other words, a function is continuous at a place if you can draw it without moving your hand and the function's graph doesn't have any gaps or leaps at that location. Calculus' central idea of continuity is crucial for defining derivatives and integrals.

According to the question

Given function =  f(x)= 12x−4sin(3x)/5x3

We require f(0) = c, where c is the value given to the function at x = 0, in order to make the function continuous at that point. We may assess the limit of f(x) as x gets closer to zero to determine c.

The limit of f(x) as x approaches 0 may be determined using L'Hopital's rule as follows:

lim x→0 f(x) = lim x→0 (12x - 4 * sin(3x)) / (5x^3)

= lim x→0 (12 - 4 * 3 * cos(3x)) / (15x^2)

= 8 / 15.

So, c = 8 / 15. Therefore, the function f(x) = (12x - 4 * sin(3x)) / (5x^3), x ≠ 0 and c, x = 0 is continuous at x = 0 with c = 8 / 15.

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The measure of angle D is ∠D = 65°.

Two triangles are said to be similar if there corresponding sides are proportional and their corresponding angles are equal.

Given is that triangle ΔABC is similar to triangle ΔDEF.

We can write -

∠D + x + 90° = 180°

∠D = 90° - x

Since both the triangles are similar, we can write -

∠D = ∠A

{90° - x} = {2x + 15}°

3x = 75°

x = 25°

∠D = 90 - x = 65°

∠D = 65°

Therefore, the measure of angle D is ∠D = 65°.

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S = {(t, 1, 1), (1, 0, 1), (1, 1, 3t)} is linearly independent of t.

Therefore the answer is b) S = {(t, 1, 1), (1, 0, 1), (1, 1, 3t)}.

(a) S is linearly independent for all values of t if the following equation has a non-trivial solution:

a(t, 1, 1) + b(1, t, 1) + c(1, 1, t) = (0, 0, 0).

Expanding this equation, we get:

at + b + c = 0

a + bt + c = 0

a + b + ct = 0.

Solving this system of linear equations, we find that a = b = c = 0. This implies that any linear combination of the vectors in S results in the zero vector, so S is linearly dependent for all values of t.

(b) S is linearly independent if the following equation has a non-trivial solution:

a(t, 1, 1) + b(1, 0, 1) + c(1, 1, 3t) = (0, 0, 0).

Expanding this equation, we get:

at + b + 3ct = 0

b = 0

a + c = 0.

Since a and c cannot both be zero, this system has no trivial solution, which means that S is linearly independent for all values of t.

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The elevation represents a distance from the sea level greater than 5 feet, because the original description specifies a distance greater than 5 feet below sea level.

Physical quantities like mass and electric charge are examples of scalar quantities because they only have magnitudes. In contrast, a vector quantity is a physical quantity like force or weight that has both magnitudes and directions.

The elevation is the height or distance above sea level and is expressed as a distance.

Given that it contains both magnitude (distance) and direction, elevation in the previous description is a vector (above sea level).

Distance is a scalar quantity with only one magnitude that describes the area travelled by a moving object.

A height of less than 5 feet denotes a location that is less than 5 feet above sea level, which is equivalent to a location that is more than 5 feet below sea level.

Greater than 5 feet below sea level = less than -5 feet above sea level, therefore;

A distance from (below) sea level of more than 5 feet is represented by an elevation of less than -5 feet.

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The value of h for which b in the plane spanned by a1 and a2 is 11.

A vector b is in the plane spanned by two vectors a1 and a2 if it can be written as a linear combination of a1 and a2. This means that there exist scalars x and y such that:

b = xa1 + ya2

[5, 4, h] = x[1, 4, -1] + y[-6, -20, 2]

Solving for x and y, we have:

5 = x - 6y

4 = 4x - 20y

h = -x + 2y

Using the first two equations, we can solve for x and y:

x = 5 + 6y

20y + 4 = 4x = 4(5 + 6y)

20y + 4 = 20 + 24y

4y = -16

y = -16/4 = -4

Substituting this value of y back into the first equation:

x = 5 + 6y

= 5 + 6 * -4

= 5 - 24

= -19

Finally, substituting x and y into the third equation:

h = -x + 2y

= -(-19) + 2 * (-4)

= 19 - 8

= 11

So for h = 11, the vector b is in the plane spanned by a1 and a2.

--The question is incomplete, answering to the question below--

"Let a1 = [1 4 -1], a2 = [-6 -20 2], and b = [5 4 h]. For what value(s) of h is b in the plane spanned by a1 and a2?"

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The area bounded by the given curve is =4.44.

There are several ways to calculate the area under the curve, but the antiderivative approach is the most widely used. Knowing the curve's equation, its bounds, and its enclosing axis will allow you to determine the area under the curve. In general, there are formulas for calculating the areas of standard shapes like squares, rectangles, quadrilaterals, polygons, and circles, but there isn't one specifically designated for calculating the area beneath curves. The integration method aids in equation solution and area determination.

The antiderivative methods are highly useful for locating the regions of irregular plane surfaces. In this lesson, we'll learn how to calculate the curve's area under the axis.

the area of the region that is bounded above by the curve f(x)=(x- 9)2 and the line g(x)=x−7.

The area enclosed by the curves is-

[tex]A=\int_a^b[{f(x)-g(x)]dx[/tex]

[tex](x-9)^2=x-7\\\\x^2-19x+88=0\\(x-8)(x-11)=0\\x=8 , x=11\\\\\int_8^{11}[(x-9)^2-(x-7)]dx\\\\=\int_8^{11}[x^2-19x+88]dx\\\\\\=[x^3/3-19x^2/2+88x]_8^{11}\\\\=4.44[/tex]

The area bounded by the given curve is =4.44.

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The pair of variables with an inverse relationship is y = 1/x. This relationship can be seen by graphing the two variables on a coordinate plane and observing the shape of the graph.

As x increases, y decreases and as x decreases, y increases. This is because the equation y = 1/x can be written as y = c/x, where c is a constant. Since c is a constant, as the value of x increases, the value of y decreases, and vice versa.

For example, if x = 4, then y = 1/4, or 0.25. If x increases to 8, then y decreases to 1/8, or 0.125. On the other hand, if x decreases to 2, then y increases to 1/2, or 0.5. As can be seen, as x increases, y decreases, and as x decreases, y increases, which shows the inverse relationship between the two variables.

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The value of x in the given equation, 3/5x - 1/3x = 42, is x = 157.5

From the question, we are to determine the value of x in the given equation.

The given equation is

3/5x - 1/3x = 42

To determine the value of x,

First, we will eliminate the denominators.

Multiply through by 15

15 × 3/5x - 15 × 1/3x = 15 × 42

3 × 3x - 5 × x = 630

9x - 5x = 630

4x = 630

Divide both sides by 4

4x/4 = 630/4

x = 157.5

Hence, the value of x is 157.5

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Probability determines the likelihood of an event occurring: P(A) = f / N

P(A) = f / N indicates the likelihood of an event occuring. Odds and probability are connected, but odds are affected by probability. Before calculating the chances of an event occurring, you must first calculate probability.

Finding the chance of a simple event occurring is simple: add the probabilities together. For instance, if you have a 10% chance of winning $10 and a 25% chance of winning $20, your total chances of winning are 10% + 25% = 35%. According to probability, heads have a 12 chance, thus we may expect 50 heads. But when we attempt it, we could get 48 heads, or 55 heads, or anything else, but in most circumstances, we’ll get something close to 50.

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The required equation is C = 8 + 0.25m, where m represents the number of mats used per month and C represents the total cost in dollars.

Let's use "m" to represent the number of center floor mats used per month, and "C" to represent the total cost in dollars. The total cost can be expressed as the sum of a fixed monthly fee of $8 and an additional fee of $0.25 per center floor mat used:

C = 8 + 0.25m

This equation expresses the relationship between the number of center floor mats used (m) and the total cost (C) in dollars.

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Step-by-step explanation:

3/4*7.5

5.625

7.5-5.625

1.875

of blue pints

The measure of angle B is m∠B = 71°

If ABCD is a kite, then ∠A and ∠C must be equal to each other.

∠A = ∠C, so ∠C = 87°.

ABCD is a quadrilateral, so all of its interior angles must add up to 360°. We know 3 of the 4 angles, so we'll add them up and subtract the answer from 360.

∠A + ∠C + ∠D ⇒ 87 + 87 + 115 = 289

360 - 289 = 71

m∠B = 71°

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Therefore , the solution of the given problem of ratio comes out to be

x has length of 5.2 .

The simple formula "a / b" can be used to create a pair of similar variables "a" and "b," where "b" may also be greater than zero. One ratio is created by combining two ratios. If there were only one man and three women, the ratio would be 1:1. There are 1/4 boys and 3/4 girls in the group. A separation between a or more objects, a numeral, or a piece of a component's volume are all examples of parts.

Here,

Given :

A figure of star shape

having diameter of 3.6 and length x

and other star having same shape but

having diameter 5.76 and length 8.32

Since , both the figures are same ,

Thus , there length ratio will also be same.

=> 8.32/5.76 =  x / 3.6

=> 832/576 =  10x/36

=>  832/576 * 36 /10 = x

=> x = 1.44 * 3.6 =5.2

Therefore , the solution of the given problem of ratio  comes out to be

x has length of 5.2 .

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// Returns an array C[1..n] of the number of coins of each value, where

// the sum from 1 to n of C[i]*A[i] will equal t.

Greedy-Coins( t, A )

Define array C as an array of length n with all values zero for i = 1 to n

C[i] = t / A[i] // Note use INTEGER arithmetic here

t = C[i] mod A[i] // Note using integer modulo here to get the remainder

end fo ... ro

return C

An easy counterexample would be to use V = ( 5, 3, 1 ), and t= 9. The greedy algorithm will return values ( 1, 0, 4), but a little intuition shows that the array ( 0, 3, 0 ) will use fewer coins.

c) If we consider the array A = ( kn-1, kn-2, ..., k0), and k >0, then we can see that for any k < (n-1), there will be at most (k-1) coins of that value; if there had been sufficient \"value\" remaining to select k coins o that value, the greedy algorithm would have selected one more coin of the next coin up. Another way to look at this is that for any selection by the greedy algorithm from ki ... k0, the value MUST be less than ki+1, since ki+1 is by definition a multiple of k.

Complete question:

Let An = { a1, a2, ..., an } be a finite set of distinct cointypes (e.g., a1= 50 cents, a2= 25 cents, a3= 10 cents etc.). We assume each ai is an integer and that a1 > a2 > ... > an. Each type is available in unlimited quantity. The coin-changing problem is to make up an exact amount C using a minimum total number of coins. C is an integer > 0.

(a) Explain that if an != 1 then there exists a finite set of coin types and a C for which there is no solution to the coin-changing problem.

(b) When an = 1 a greedy solution to the problem will make a change by using the coin types in the order a1, a2, ..., an. When coin type ai is being considered, as many coins of this type as possible will be given. Write an algorithm based on this strategy.

(c) Give a counterexample to show that the algorithm in (b)doesn\'t necessarily generate solutions that use the minimum total number of coins

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We can prove this using the product rule. Let y(x) = y1(x) y2(x). Then:

y'(x) = y1'(x) y2(x) + y1(x) y2'(x)

y''(x) = y1''(x) y2(x) + 2y1'(x) y2'(x) + y1(x) y2''(x)

Substituting into the equation yields:

y'' p(x)y' q(x)y = [y1''(x) y2(x) + 2y1'(x) y2'(x) + y1(x) y2''(x)] p(x) [y1'(x) y2(x) + y1(x) y2'(x)] q(x) [y1(x) y2(x)]

= [y1''(x) p(x)y1'(x) + 2y1'(x) p(x)y2'(x) + y1(x) y2''(x) p(x)] q(x) [y1(x) y2(x)]

= [r1(x) + r2(x)] q(x) [y1(x) y2(x)]

= r1(x)r2(x) q(x) [y1(x) y2(x)]

Since this is equal to y″ p(x)y′ q(x)y, it follows that y(x) = y1(x) y2(x) is a solution of y″ p(x)y′ q(x)y = r1(x) r2(x). We can prove this using the product rule. Let y(x) = y1(x) y2(x). Then:

y'(x) = y1'(x) y2(x) + y1(x) y2'(x)

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To find the width of Wyoming, we need to find the area of the state and divide by the width.

Area = population density x total population

Area = 2.16 x 564,000 people

Area = 1,222,624 square kilometers

Width = Area / Length

We don't have the length, so we'll have to rearrange the formula to solve for it:

Width = Area / Length

Length = Area / Width

Length = 1,222,624 square kilometers / Width

We'll solve for width:

Width = 1,222,624 square kilometers / Length

Since we don't know the length, we cannot solve for width.

One square mile contains 640 acres. 640 acres in a square mile.

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The value of the variable x for the function f(x) = x² + 4x for which

f(f(x) ) = f(x) is equal to x = -1 or x = -3.

The function f(x) = x² + 4x

Substitute the value in the required function we get,

Right hand side

= f ( f(x))

= f ( x² + 4x )

= ( x² + 4x )² + 4 ( x² + 4x )

= x⁴ + 8x³ + 16x² + 4x² + 16x

= x⁴ + 8x³ + 20x² + 16x

Left hand side

f(x)

= x² + 4x

Equate left hand side is equal to right hand side we get,

x⁴ + 8x³ + 20x² + 16x = x² + 4x

⇒x⁴ + 4x³ + 4x³ + 16x² + 4x² + 16x =  x² + 4x

⇒x² ( x² +4x ) + 4x ( x² + 4x )+ 4 ( x² + 4x ) = x² + 4x

⇒( x² + 4x ) ( x² + 4x + 4 ) = x² + 4x

⇒ x² + 4x + 4 = 1

⇒ ( x + 2 )²  - 1² =0

⇒ ( x + 2 -1 ) ( x+ 2 + 1) = 0

⇒ ( x+ 1 ) ( x+ 3 ) = 0

⇒ x = -1  or x = -3

Therefore, the value of x = -1 or x = -3 for the condition f(f(x)) = f(x).

The above question is incomplete , the complete question is:

Let function f(x) = x² + 4x for what value of x is f(f(x)) = f(x).

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The Volume of Each Shape is Shown below.

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m³, cm³, in³ etc.

Given:

1. r = 6 inch, height = 6 inch

So, Volume of Cone = 1/3 πr²h

                                  = 1/3 x 3.14 x 6 x 6 x 6

                                   = 226.08 inch³

2. diameter = 6cm

r = 3 cm,

so, volume of each piece

= 4/3 πr³

= 4/3 x 3.14 x 3 x 3 x 3

= 113 cm³

now, volume of 20 candies

= 20 x 113

=  2260 cm³ of chocolate.

3. The height of the cone shape, h = 84 inches

radius = 8 inches

The cost per cubic inch is $2.25.

The cost of nickel for the sculpture is given by

= 2.25 x 1/3πr²h

= 2.25 x 1/3 x 3.14 x 8 x 8 x 84

= $12660.48.

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The limit as h→0 of f(x+h) − f(x) / h is 0. the denominator of the fraction is 0, the limit is undefined.

To evaluate this limit, we need to plug in the given value for x and the function f(x). We are given that f(x) = x2 and x = 3.

Therefore, we have:

limh→0 f(3+h)−f(3) h

Since f(3) = 3^2 = 9, we can rewrite the limit as:

limh→0 f(3+h)−9

We can now plug in the value of h=0 to get the value of the limit:

limh→0 f(3+0)−9 0

Since the denominator of the fraction is 0, the limit is undefined.

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92% is the percent of decrease.

A relation is a function if it has only One y-value for each x-value.

The function [tex]M(t)=975.(0.92)^{t}[/tex]

Function represents the number of milligrams of a medication in a patients body as a function of time.

t represents the time.

0.92×100=92%

975 is the initial value and 0.92 is the percent of decrease.

Hence, 92% is the percent of decrease.

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