Use a double-angle identity to find the exact value of each expression.

cos 120°

Answer:

A≈1633.63

Step-by-step explanation:

d Diameter 26

h heigth 7

A=2πd

2h+2π(d

2)2=2·π·26

2·7+2·π·(26

2)2≈1633.62818

a. To show that f(n) is O(n^5), we need to find positive constants c and no such that |f(n)| ≤ c * n^5 for all n > no.

b. To show that f(n) is O(n^3), we need to find positive constants c and no such that f(n) ≤ c * n^3 for all n > no.

a. To find c and no to show f(n) is O(n^5), we can start by simplifying the expression for f(n):

f(n) = (1/2)n - 100n^3 + 3n

We can see that the dominant term in this polynomial is -100n^3, which means that as n gets very large, this term will dominate the behavior of the function.

To show that f(n) is O(n^5), we need to find constants c and no such that |f(n)| ≤ c * n^5 for all n > no.

Let's choose c = 101/2 and no = 1. Then, for all n > no:

|f(n)| = |(1/2)n - 100n^3 + 3n| ≤ 101/2 * n^3.5

Since n^3.5 < n^5 for all n > 1, this means that f(n) is O(n^5).

b. To find c and no to show that f(n) is O(n^3), we can start by simplifying the expression for f(n):

f(n) = n^3 + 3n^2 + 4

We can see that all terms in this polynomial are positive, which means that the dominant term is simply n^3.

To show that f(n) is O(n^3), we need to find constants c and no such that f(n) ≤ c * n^3 for all n > no.

Let's choose c = 8 and no = 1. Then, for all n > no:

f(n) = n^3 + 3n^2 + 4 ≤ 8n^3

This means that f(n) is O(n^3).

In conclusion, we found constants c and no to show that f(n) is O(n^5) and O(n^3) for parts a and b, respectively.

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Answer:

it can travel 352 feet in 8 seconds

Step-by-step explanation:

what you have to do is divide 220 by 5 and get 44 then you multiply 44 by 8 and get 352

Please mark me as brainliest

Answer:

352ft

Step-by-step explanation:

220ft for 5 seconds which means it travels 220/5 ft in one second which is 44 ft/s

in eight seconds its gonna travel 44×8=352 ft

The seller purchased the product at a cost of 7500 and sold it for 7950, which resulted in a gain of 6%. So, the cost price is 7500.

In business, it is essential to keep track of cost prices and profit margins to ensure profitability. If the selling price is 7950 and the gain is 6%, we can use the following formula to calculate the cost price:

Cost price = Selling price / (1 + Gain%)

Substituting the given values, we get:

Cost price = 7950 / (1 + 0.06)

Cost price = 7500

Therefore, the cost price of the product is 7500, the gain percentage is calculated based on the cost price and not the selling price.

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In linear equation, The solution to this system is (80, 120)

What is a linear equation example?

The following system of equations represents the given situation

x + y = 200

x = y - 40; substituting x from this equation to the first:

y - 40 + y = 200

2y = 240

y = 120

Corresponding value of x:

x = 120 - 40

x = 80

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You are 18 years old this year.

Let's call your age this year "x". Next year, your age will be "x + 1".

We know that the sum of the digits of "x" is three times bigger than the sum of the digits of "x + 1". Let's call the sum of the digits of "x" "s1", and the sum of the digits of "x + 1" "s2".

So we have the equation:

s1 = 3 * s2

If we add the digits of "x + 1", we get "s2 = a + b", where "a" and "b" are the digits of "x + 1".

Expanding the equation and substituting "s2":

s1 = 3 * (a + b)

Expanding the left side of the equation:

s1 = 3a + 3b

So the sum of the digits of "x" is three times the sum of the digits of "x + 1".

Now we need to find the values of "x" for which "s1" is three times bigger than "s2".

One possible solution is "x = 18", because:

So the answer is that you are 18 years old this year.

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You are 18 years old this year.

Let's call your age this year "x". Next year, your age will be "x + 1".

We know that the sum of the digits of "x" is three times bigger than the sum of the digits of "x + 1". Let's call the sum of the digits of "x" "s1", and the sum of the digits of "x + 1" "s2".

So we have the equation:

s1 = 3 * s2

If we add the digits of "x + 1", we get "s2 = a + b", where "a" and "b" are the digits of "x + 1".

Expanding the equation and substituting "s2":

s1 = 3 * (a + b)

Expanding the left side of the equation:

s1 = 3a + 3b

So the sum of the digits of "x" is three times the sum of the digits of "x + 1".

Now we need to find the values of "x" for which "s1" is three times bigger than "s2".

One possible solution is "x = 18", because:

"s1" = 1 + 8 = 9

"s2" = 1 + 9 = 10

9 = 3 * 10

So the answer is that you are 18 years old this year.

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Answer:

1. h = V/lb

2. y = (m - 7x)/3

3. m = P/gh

Answer:

1 real solution.

Step-by-step explanation:

The solution is the point where the 2 graphs intersect  (close to the point

(4, 3).

The equation have one real solution.

the correct option is (B)

Two or more lines which share exactly one common point are called intersecting lines.

Given:

y = 2x - 5 and y = √{3x - 1}

As seen from the graph the lines of both given equation is intersecting line.

So, the type of lines are intersecting lines.

and, intersecting lines give one real solution where the lines intersect.

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Wilson's Theorem states that if p is a prime number, then (p-1)! ≡ -1 (mod p). Using this theorem, we can find the least nonnegative residue modulo m for the given cases.

For a) with 36! and m = 37, the least nonnegative residue is 36.

For b) with 64! and m = 67, use Wilson's Theorem to construct a congruence and solve for the least nonnegative residue, which is 66.

a) To find the least nonnegative residue of 36! modulo 37, we apply Wilson's Theorem, which states that (37-1)! ≡ -1 (mod 37). Since 37 is a prime number:

36! ≡ -1 (mod 37)

By subtracting multiples of 37 from -1, we find that 36! ≡ 36 (mod 37). Therefore, the least nonnegative residue of 36! modulo 37 is 36.

b) To find the least nonnegative residue of 64! modulo 67, use Wilson's Theorem indirectly. Since 67 is a prime number,

(67-1)! ≡ -1 (mod 67). We can rewrite 64! as a product of integers modulo 67:

64! ≡ (64)(63)(62)(61)...(2)(1) (mod 67)

By evaluating the expression modulo 67, we find that 64! ≡ 66 (mod 67). Hence, the least nonnegative residue of 64! modulo 67 is 66.

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For a prime p ≡ 1 (mod 4), the quadratic residue of -1 in the finite field \($\mathbb{F}_p$\) exists, i.e., -1 is a square in\($\mathbb{F}_p$\).

Let p be a prime such that p ≡ 1 (mod 4). We need to prove that -1 is a quadratic residue modulo p, i.e., there exists an integer a such that \($a^2 \equiv -1 \pmod p$.\)

We know that the Legendre symbol $\left(\frac{-1}{p}\right)$ is equal to 1 if p ≡ 1 (mod 4), and -1 if p ≡ 3 (mod 4). Since p ≡ 1 (mod 4), we have \($\left(\frac{-1}{p}\right) = 1$.\)

By Euler's criterion, we have

\($\left(\frac{-1}{p}\right) \equiv (-1)^{\frac{p-1}{2}} \pmod p$.\)

Since \($\left(\frac{-1}{p}\right) = 1$\),

we have \($(-1)^{\frac{p-1}{2}} \equiv 1 \pmod p$.\)

This implies that  \($\frac{p-1}{2}$ is even, i.e., $p \equiv 1 \pmod 8$.\)

Now, let's consider the field \($\mathbb{F}_p$,\)

which is a finite field of order p. Since p ≡ 1 (mod 4), we have\($p = 4k+1$\) for some integer k. Let's define a subgroup of order 4 in \($\mathbb{F}_p^{\times}$ as $H = {1,-1,i,-i}$, where $i^2 \equiv -1 \pmod p$.\)

Since H is a subgroup of \($\mathbb{F}_p^{\times}$\)  of order 4, any element of \($\mathbb{F}_p^{\times}$\) can be written as a power of i multiplied by a power of -1. That is, for any\($x \in \mathbb{F}_p^{\times}$\), there exist integers m and n such that \($x = i^m(-1)^n$.\)

Since $p \equiv 1 \pmod 8$, we have \($2^{(p-1)/2} \equiv 1 \pmod p$\)  by Euler's criterion. This implies that \($i^{p-1} = (i^2)^{(p-1)/2} \equiv 1 \pmod p$\). Thus, \($i^p \equiv i \pmod p$.\)

Now, consider the element \($(-i)^2 = i^2(-1)^2 = -1$\). This shows that -1 is a quadratic residue modulo p, i.e., there exists an integer a such that \($a^2 \equiv -1 \pmod p$\). Therefore, we have proved that −1 is a square in \($\mathbb{F}_p$.\)

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Percentage Change = (ΔV/IV₁I) × 100

Constant rate of Change = (y₂ - y₁)/ (x₂ - x₁)

Constant Percentage Change:

This means that after t period the something has grown to \(g^{t} = 1.10^{t}\) it original value .

percentage change formula equals the change in value divided by the absolute value of the original value multiplied by 100.

Constant rate of Change:

In which the rate does not change between different points in the function. in short, constant rate of change refers to the comparison of the way two quantities changes. in equation, the constant rate of change can be seen as a slope.

An exponential function is a function that changes at a constant percentage rate.

An exponential function y of t is characterized by the following property:

when t increases by 1 to find the new value of y the current value by the base.

                 y- value for t +1 = Base of y - value for t

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Answer:

x=21

Step-by-step explanation:

Answer: B

Step-by-step explanation: Adjacency Matrix is a square matrix representing a simple graph with 0 or 1 according to the condition given.

In this diagram, 0 corresponds to no connection between airports and 1 corresponds to connections between airports.

In other words, analysing the image, we see that:

1) Albany just have connection with Atlanta, so in the position of line Albany with column At, it must be a 1. The other columns, there are 0.

The Line for Albany in the matrix will be: [0 1 0 0 0 0]

2) Atlanta has connections with Albany, Dalton, Macon and Augusta. So corresponding position (line and column) must be 1. The only two airports Atlanta doesn't have connection with its own and Waycross, so at the corresponding column and line, it is written 0.

The line for Atlanta in the matrix is [1 0 1 1 1 0]

3) Augusta: connections with Atlanta, Macon, Waycross. At those positions, it will be written 1. At positions related to itself, Albany and Dalton is 0.

The line in the matrix will be [0 1 0 0 1 1]

4) Dalton: connection with Atlanta only. That position will be 1 while the others will be 0.

The line is [0 1 0 0 0 0]

5) Macon: connections with Atlanta, Augusta and Waycon: those positions will have 1 and the other 0.

The line is [0 1 1 0 0 1]

6) Waycross: connections with Macon and Augusta. Those positions will be 1 and the others 0.

The line is [0 0 1 0 1 0]

In conclusion, the adjacency matrix matching the scenario is

\(A=\left[\begin{array}{cccccc}0&1&0&0&0&0\\1&0&1&1&1&0\\0&1&0&0&1&1\\0&1&0&0&0&0\\0&1&1&0&0&1\\0&0&1&0&1&0\end{array}\right]\)

The distance from Observer B to the sailboat is approximately 0.485 miles.

We have,

We know that the distance from observer A to sailboat C is 0.47 miles, and the observers are 1/2 mile apart.

Let's call the distance from observer B to sailboat C "x".

From observer A's perspective, the sailboat is at an angle of 63 degrees. We can use the tangent function to find the distance from observer A to sailboat C:

tan(63) = opposite / adjacent

tan(63) = 0.47 / adjacent

adjacent = 0.47 / tan(63)

adjacent ≈ 0.261 miles

Now we can use the Pythagorean theorem to find the distance from observer B to sailboat C:

x^2 + (1/2 - adjacent)^2 = (1/2)^2

x^2 + (1/2 - 0.261)^2 = 1/4

x^2 + 0.014721 = 0.25

x^2 = 0.235279

x ≈ 0.485 miles

Therefore,

The distance from Observer B to the sailboat is approximately 0.485 miles.

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Answer:

.2 Cm

Step-by-step explanation:

The quadrilateral is a parallelogram so it is Yes.

If a quadrilateral has a pair of parallel opposite sides, it’s a special polygon called parallelogram .The properties of a parallelogram are as follows:

The opposite sides are parallel and equal

The opposite angles are equal

The consecutive or adjacent angles are supplementary

If any one of the angles is a right angle, then all the other angles will be at right angle.

The quadrilateral is a parallelogram since the adjacent interior angles 75° and 105° are supplementary meaning they sum up to 180°

In conclusion, yes, the figure is a parallelogram.

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If the length of rectangular school hall is 4 times the width and the perimeter be 55m, then the length is 22m and the width of the school hall be 5.5m.

Given that the length of  rectangular school hall is 4 times the width.

We are required to find the length and breadth of the rectangle which has the length be 4 times the width.

Perimeter of rectangle is the sum of all the length and breadth of that rectangles.

Perimeter of rectangle is given as 55m

Perimeter=2(L+B)

let the width of rectangle be x.

Length of that rectangle be 4x.

According to question,

2(x+4x)=55

2*5x=55

10x=55

x=55/10

x=5.5 m

Width be 5.5 m.

Length of rectangle be 4*5.5=22m.

Hence if the length of rectangular school hall is 4 times the width then the length is 22m and the width of the school hall be 5.5m.

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Answer:

The question is very not detailed but I assume that because the path will finish does not mean that the whole thing/project will finish.

Step-by-step explanation:

The "d" format specifier is used to denote a signed decimal integer in various programming languages and formatting systems.

When used in format strings or printf-style functions, the "d" specifier indicates that the corresponding argument should be formatted as a signed decimal integer. It allows for the representation of both positive and negative whole numbers, including zero.

For example, in C programming, the printf function can be used with the "%d" format specifier to display a signed decimal integer value. Similarly, in other languages such as Python, the "{:d}" format specifier can be used with the format() function or string interpolation to represent a signed decimal integer.

Using the "d" specifier ensures that the output is formatted as a base-10 representation of a signed integer, taking into account the sign of the number.

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The area of the surface obtained by rotating the curve x = 20 cos(3θ), y = 20 sin(3θ), where 0 ≤ θ ≤ π/2, about the x-axis is calculated using the formulA for surface area of revolution

To find the area of the surface, we can use the formula for the surface area of revolution. Given a curve defined parametrically by x = f(θ) and y = g(θ), where α ≤ θ ≤ β, the surface area obtained by rotating the curve about the x-axis is given by:

A = ∫[α,β] 2πy √(1 + (f'(θ))²) dθ

In this case, we have x = 20 cos(3θ) and y = 20 sin(3θ), with 0 ≤ θ ≤ π/2. Taking the derivatives, we find f'(θ) = -60 sin(3θ) and g'(θ) = 60 cos(3θ).

Plugging these values into the surface area formula and simplifying, we get:

A = ∫[0,π/2] 2π(20 sin(3θ))(√(1 + (-60 sin(3θ))²)) dθ

Evaluating this integral will give us the exact value of the surface area of the rotated curve about the x-axis within the given range of θ.

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A. Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

B. The recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

(a) If Manager B always truthfully reports the state of the economy (s = 0.7), Manager A would send a recommendation that minimizes their disutility Ua. In this case, Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

(b) In a Nash equilibrium, both managers strategically make their recommendations based on their own utility. Manager A wants to minimize their disutility Ua, which increases as the decision deviates from 0.4. Manager B wants to minimize their disutility UB, which increases as the decision deviates from 0.7.

To find the Nash equilibrium, we need to consider the recommendations made by both managers simultaneously. Let's denote the recommendations as rA (from Manager A) and rB (from Manager B). The principal's decision, d, would be the average of the recommendations, so d = (rA + rB) / 2.

Given that both managers strategically choose their recommendations, they will aim to minimize their disutility. In this case, Manager A would recommend a decision of 0.4 (as it minimizes Ua), and Manager B would recommend a decision of 0.7 (as it minimizes UB). Therefore, the recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

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Answer:

x=20-y

y=20-x

Step-by-step explanation:

divide by 2 on both sides: x+y=20

to find x, subtract y:

x=20-y

to find y, subtract x:

y=20-x

nothing else can be done unless you know either y or x.

The possible lengths( in whole elevation) for the third side is

9 elevation< x< 45 elevation, i.e in between 9 and 45 elevation.

 For the below question, we've a rule from the properties of triangle, the sum of the length of any two  sides of the triangle must be lesser than the length of the third side.

Hence

She has two sides of length 18 elevation and 27 elevation

Let the third side = x

Hence

a) 18 27> x

45> x

b) 18 x> 27

x> 27- 18

x> 9

thus, the possible lengths( in whole elevation) for the third side is

elevation< x< 45 elevation

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The function that generates the table of values shown below is (8/3)ˣ. The values in the table are obtained by raising (8/3) to the power of x.

To determine which function generates the given table of values, we can examine the pattern and compare it to the given options.

The values in the table are increasing exponentially. By observing the relationship between the input (x) and output (y) values, we can see that each output is obtained by raising (8/3) to the power of the corresponding input value.

Option h, (8/3)ˣ, matches this pattern and generates the values in the table. When we substitute each x value into the function, we obtain the corresponding y values.

Therefore, the function (8/3)ˣ generates the table of values shown.

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The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.

Answer:

B

Step-by-step explanation:

The probability that all three balls drawn from the bag are red is 6/273.

Prοbability is a measure οf the likelihοοd οr chance that a particular event will οccur. It quantifies the uncertainty assοciated with an οutcοme in a given situatiοn οr experiment.

Given:

- Total number of balls in the bag: 4 white + 5 red + 6 blue = 15 balls

- Number of red balls: 5

For the first draw, the probability of selecting a red ball is 5 red / 15 total balls = 1/3.

After the first red ball is drawn, there are 4 red balls left and 14 total balls remaining in the bag. Therefore, for the second draw, the probability of selecting another red ball is 4 red / 14 total balls = 2/7.

After the second red ball is drawn, there are 3 red balls left and 13 total balls remaining in the bag. Therefore, for the third draw, the probability of selecting the final red ball is 3 red / 13 total balls.

To find the probability of all three balls being red, we multiply the individual probabilities together:

P(all red) = (1/3) * (2/7) * (3/13)

Simplifying the expression, we get:

P(all red) = 6/273

Therefore, the probability that all three balls drawn from the bag are red is 6/273.

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Answer:

A (4x-12)

Step-by-step explanation:

Still think of PEMDAS: 8-4(-x=5)

a) Multiply -4(-x + 5)

* -4(-x) = 4x (remember a neg x neg = pos)

* -4(5) = - 20

b) Now it reads = 8 +4x - 20

c) put all like terms together

* 8 - 20 = -12