Devise a recursive algorithm to find a2n, where a is a real number and n is a positive integer (hint: use the equality a2n+1 = (a2n)2

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

They buy at wholesale and sell at an 80% markup. The retail prices are;

0 - 20 pairs.

= 25 * 1.80

= $45.00

21 - 40 pairs

= 23 * 1.80

= $41.40

41 - 60 pairs

= 21 * 1.80

= $37.80

61 - 80 pairs

= 19 * 1.80

= $34.20

81 or more pairs

= 17 * 1.80

= $30.60

Answer:

x² + \(\frac{1}{x^2}\) = 5

Step-by-step explanation:

using the identity

(a - b)² = a² + b² - 2ab , then given

(x - \(\frac{1}{x}\) ) = \(\sqrt{3}\) ( square both sides )

(x - \(\frac{1}{x}\) )² = (\(\sqrt{3}\) )² , that is using the above identity

x² + \(\frac{1}{x^2}\) - 2(x × \(\frac{1}{x}\) ) = 3

x² + \(\frac{1}{x^2}\) - 2(1) = 3

x² + \(\frac{1}{x^2}\) - 2 = 3 ( add 2 to both sides )

x² + \(\frac{1}{x^2}\) = 5

\(\displaystyle\\Answer:\ x^2+\frac{1}{x^2}=5\)

Step-by-step explanation:

\(\displaystyle\\(x-\frac{1}{x} )=\sqrt{3} \\\)

Let's square both parts of the equation:

\(\displaystyle\\(x-\frac{1}{x} )^2=(\sqrt{3})^2 \\(x)^2-2*x*\frac{1}{x} +(\frac{1}{x})^2 =3\\x^2-2*1+\frac{1}{x^2}=3\\ x^2-2+\frac{1}{x^2}+2 =3+2\\x^2+\frac{1}{x^2}=5\)

Since c is a scalar, 2c is also a scalar. Therefore, the sum of u and v is in W if and only if 80 + 2c = 40, which is not true for all values of c. Therefore, W does not satisfy condition (i) and is not a subspace of R2.

To determine if W is a subspace of R2, we need to check if it satisfies the two conditions for a subspace:

(i) If u and v are vectors in W, then u + v is also in W.

Let u = (a1, a2) and v = (b1, b2) be vectors in W. Then we have:

(a1)^2 + (a2)^2 = 40 and (b1)^2 + (b2)^2 = 40

We need to show that u + v is also in W.

The sum of u and v is:

u + v = (a1 + b1, a2 + b2)

The magnitude of u + v is:

|(u + v)|^2 = (a1 + b1)^2 + (a2 + b2)^2

Expanding the squares, we get:

|(u + v)|^2 = (a1)^2 + 2a1b1 + (b1)^2 + (a2)^2 + 2a2b2 + (b2)^2

Since (a1)^2 + (a2)^2 = 40 and (b1)^2 + (b2)^2 = 40, we can substitute these values to get:

|(u + v)|^2 = 40 + 2a1b1 + 2a2b2 + 40

Simplifying, we get:

|(u + v)|^2 = 80 + 2(a1b1 + a2b2)

Since (a1b1 + a2b2) is a scalar, we can write it as c. Therefore:

|(u + v)|^2 = 80 + 2c

Since c is a scalar, 2c is also a scalar. Therefore, the sum of u and v is in W if and only if 80 + 2c = 40, which is not true for all values of c. Therefore, W does not satisfy condition (i) and is not a subspace of R2.

(ii) If u is in W and c is a scalar, then the vector cu is also in W.

We do not need to check this condition since W does not satisfy condition (i) and is therefore not a subspace of R2.

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Using statistical concepts, it is found that:

From their concepts above, we have that the mean and the range are influenced by outliers.

In this problem, the outlier is at the low end, of 15, hence:

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Terms are 4b, 7b, 5 coefficient are 4 , 7 and constant = 4, 7 , 5

What are the parts in expression?

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

Given expression:

4b+7b+5

As. term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Terms are 4b, 7b, 5

Now, coefficient is a number that is multiplied by a variable in an expression.

coefficient are 4 , 7

As a constant is a fixed numerical value,

So, constant = 4, 7 , 5

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The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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Answer:

3 r 44

51+51=102

102+51=153

197-153=44

44 does not go into 51 as a whole number, leaving it as a remainder.

Answer:

3 r 8

Step-by-step explanation:

When you divide 197 by 51 you get 3 r 8. Hope it helped!! :]

Answer:

10 x 6,000 is 60,000. now divide it by ten. its 6,000 because its 1/10 of it so yes, 6,000

The concept that a message gives different meanings to different objects is called option (b) polymorphism.

Polymorphism is a fundamental concept in object-oriented programming (OOP) that allows different objects to respond to the same message or method invocation in different ways. In other words, it allows objects of different classes to be treated as if they were of the same class, as long as they implement the same method or message.

This can make code more flexible, reusable, and easier to maintain. Polymorphism is achieved through inheritance, interfaces, or overloading methods. For example, a "draw" method could be implemented differently for different shapes, such as circles, rectangles, or triangles.

Therefore, the correct option is (b) polymorphism

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\(3 \sqrt{3} \)

please mark me as brainlist

Answer:

I think the answer is B because I've come across these kind of question and they add up to 180.

Rectangle ABCD is a square.

Relation between rectangle and square?

Squares and rectangles each have four straight sides. However, a square's and a rectangle's mathematical characteristics are very dissimilar. For instance, a common distinction is that squares have equal sides on each side, whereas only the opposite sides of a rectangle are equal.

Radius of circle R = 4cm

let sides of rectangle is a,b

let rectangle be ABCD in which AB =CD= a , AC=BD=b

ACD is right angled triangle on C.

Then,

\(AD^{2} =AC^{2} +CD^{2} \\\\8^{2} =b^{2} +a^{2} \\\\64=b^{2} +a^{2} \\\\b^{2} =\sqrt{64-a^{2} }\)------(1)

Area of rectangle = Area of ΔACD + ΔABD

                             = \(\frac{1}{2} \times a\times b + \frac{1}{2} \times a\times b\)

Area of rectangle = a×b

by eqn (1)

             Area = \(a\times (\sqrt{64-a^{2} } )\)

For maximum area

\(\frac{dA}{da} =0\\\\a \times \frac{1}{\sqrt{64-a^{2} } } (-a)+(\sqrt{64-a^{2} } )\times(1)=0\)

\(\sqrt{64-a^2} -\frac{a^2}{\sqrt{64-a^2} } =0\\\\\frac{64-a^2-a^2}{\sqrt{64-a^2} } =0\\\\64-2a^2=0\\\\a^2=32\\\\a=\sqrt{32} \\\\In (1) eqn\\b=\sqrt{64-a^2} \\\\b=\sqrt{64-32} \\\\b=32\)

So, a=b

Means Rectangle ABCD is a square.

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Answer:

180, i already commented it but like i even looked it up a straight line is 180

Step-by-step explanation:

The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

Given,The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam.

For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section.

The strength of an oak beam is 69, when the beam is 7 inches wide and 3 inches deep.Thus, we can conclude that k, a constant of proportionality exists, such that: S=k(W x D²), where W is the width, D is the depth of the rectangular cross-section and S is the strength of the beam.

Let's use this to calculate k: When the beam is 7 inches wide and 3 inches deep, S=69. Thus, we get:k = S/W x D²=69/(7 x 3²)=1.

Thus, the equation for S becomes:S = W x D²The radius of the oak tree is 28/2 = 14 inches and the beam must be 14 inches wide.

This implies that the rectangular cross-section of the beam must be square (or the largest rectangular cross-section is a square). Let the side of the square cross-section be x.

Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inchesWe need to determine the depth of the beam. The depth of the beam is half the height of the cylindrical log from which the beam is cut. The cylindrical log has a diameter of 28 inches. The beam has a width of 14 inches.

The largest rectangular cross-section is a square with sides of length x. This cross-section can be obtained by cutting the log at a height of x/2 from its center.Since the diameter is 28 inches, the radius is 14 inches. The height at which the beam is cut is h = 14 - x/2.

Thus, the depth of the rectangular beam cut from the cylindrical log is given by: D = 2(h) = 2(14 - x/2) = 28 - x.Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69Simplifying the above equation,x⁴ - 56x³ + 784x² - 69 = 0.

Using polynomial long division, we get:(x² + 16x - 69)(x² - 40x + 1) = 0The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.Therefore, the  answer is (b) S = 2231.

The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. Let the side of the square cross-section be x. Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inches. Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69.The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

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The equation of the function is represented by the graph is f(x)=2^x−3.

From the picture, we can see when x = 0, y = -2

First we take function is,

A.  f(x)=2^x−2

We can write,

f(x) = \(2^{x} -2\)

When x = 0,

y = \(2^{0}\) - 2

\(2^{0}\) = 1

y = 1-2 = -1x

B.  f(x)=−2^x−3

We can write,

f(x) = \(-2^{x} -3\)

When x = 0,

y = \(2^{0}\) - 3

\(2^{0}\) = 1

When x = 0,

y = -1-3 = -4x

C.  f(x)=2^x−3

We can write,

f(x) = \(2^{x} -3\)

When x = 0,

y = \(2^{0}\) - 3

\(2^{0}\) = 1

When x = 0,

y = 1-3 = -2x

D.  f(x)=−2^x−2

We can write,

f(x) = \(-2^{x} -2\)

When x = 0,

y = \(2^{0}\) - 2

\(2^{0}\) = 1

When x = 0,

y = -1 - 2 = -3x

You can immediately cross out options A and B because it cannot be negative. If it was negative, the graph would be going the opposite direction, it would curve closer to the negative numbers that the positive. We can cross out C because if it was -2, then it would cross the y-axis at -1 rather than -2.

Therefore,

The function equation is represented by the graph is f(x)=2^x−3.

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The interesting or surprising thing we can learn about converting between improper fractions and mixed numbers is that to know how large or small a fraction formed from mixed number.

A mixed number, or fraction is a number having two parts one is integer (whole number) and other is a proper fraction (having numerator is less than its denominator). An example of a mixed number is \(2\frac{1}{\\ 2} \\ \). An improper fraction is defined when the top number (numerator) is larger than the bottom number (denominator). For example, \( \frac{8}{5} \).

To change an improper fraction to a mixed number follow these steps.

The conversion between improper fractions and mixed numbers or mixed to improper is a best way to be able to understand fractions and recognize how large or small a fraction is.

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Okay, let's break this down step-by-step:

* The object has a mass of 2000 G

* Its acceleration is 11.5 m/s2

* To find the force acting on the object, we use Newton's 2nd law:

Force = Mass x Acceleration

So in this case:

F = 2000 G x 11.5 m/s2

= 23,000 N

Therefore, the unknown force acting on the 2000 G mass to produce an acceleration of 11.5 m/s2 is 23,000 N.

Let me know if you have any other questions!

Pythagorean theorem tells us how the side lengths of right triangles are related.

The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.

This relationship can be written as the equation:

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

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As per the given question, it is stated that the length of a rectangle is 5 m less than twice the breadth.

Assumption : Let us assume the length as "l" and width as "b". So,

\( \twoheadrightarrow \quad\sf{ Length =2(Width)-5} \)

\( \twoheadrightarrow \quad\sf{ \ell=(2b-5) \; m} \)

Also, we are given that the perimeter of the rectangle is 50 m. Basically, we need to apply here the formula of perimeter of rectangle which will act as a linear equation here.

\(\\ \twoheadrightarrow \quad\sf{ Perimeter_{(Rectangle)} = 2(\ell +b) } \\\)

\(\\ \twoheadrightarrow \quad\sf{50= 2(2b-5+b)} \\\)

\(\\ \twoheadrightarrow \quad\sf{50= 2(3b-5)} \\\)

\(\\ \twoheadrightarrow \quad\sf{50= 6b - 10} \\\)

\(\\ \twoheadrightarrow \quad\sf{50+10= 6b} \\\)

\(\\ \twoheadrightarrow \quad\sf{60= 6b} \\\)

\(\\ \twoheadrightarrow \quad\sf{\cancel{\dfrac{60}{6}}=b} \\\)

\(\\ \twoheadrightarrow \quad\underline{\bf{10\; m = Width }} \\\)

Now, finding the length. According to the question,

\( \twoheadrightarrow \quad\sf{ \ell=(2b-5) \; m} \)

\( \twoheadrightarrow \quad\sf{ \ell=2(10)-5\; m} \)

\( \twoheadrightarrow \quad\sf{ \ell=20-5\; m} \)

\(\\ \twoheadrightarrow \quad\underline{\bf{15\; m = Length }} \\\)

Therefore, length and breadth of the rectangle is 15 m and 10 m.

All equations of a line that is perpendicular to AB and passes through the points A or B are:

A. y = -2x + 13

D. y = -2x + 3

In Mathematics and Geometry, perpendicular lines are two (2) lines that intersect or meet each other at an angle of 90° (right angles).

From the information provided above, the slope for the equation of line m is given  by:

y = 1/2(x) - 2

slope (m) of line m = 1/2

In Mathematics and Geometry, a condition that must be true for two lines to be perpendicular include the following:

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

Slope, m₂ of perpendicular line = -2

Therefore, the required equations are;

y = -2x + 13

y = -2x + 3

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Answer:

390.66 meters

Step-by-step explanation:

perimeter = 2(87) + 3.14(69)

= 174 + 216.66

= 390.66

Answer:

The Coombs test checks your blood for antibodies that attack red blood cells. It can help prevent and diagnose problems.

ummmm

also what cu.ms out of a co.ck

lm.ao

Answer:

5

Step-by-step explanation:

125 breaks down into 5×5×5, which proves that it's 5.

Answer:

5 is the right answer

Step-by-step explanation:

Answer:

7% my answer i think if im mistake please dont report me

Based on the information provided, Railway Cabooses paid an annual dividend of $2.50 per share. However, the company has been reducing its dividends by 11.7 percent each year.

To calculate the current annual dividend, we can use the formula: current dividend = previous dividend * (1 - dividend reduction rate).
So, the current annual dividend would be $2.50 * (1 - 0.117) = $2.21 per share. To determine how much you should pay to purchase stock in this company, we need to use the dividend discount model.
The formula for this model is stock price = annual dividend / (required rate of return - dividend growth rate).
Plugging in the values from the problem, we get:
Stock price = $2.21 / (0.13 - 0.117) = $34.15 per share.
Therefore, if your required rate of return is 13 percent, you should be willing to pay $34.15 per share to purchase stock in Railway Cabooses.

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Answer:

The answer is 9 (B)

Step-by-step explanation:

I got 9 because you have to plug in answer (7, 9, 11, 8) in each equation than add them both together. I first plugged in 7 for x in the equation 9x-5. I got 58. I plugged in 7 for x in the equation 5x+12 and got 47. When I added both the answers together I got 105. The answer was to low because SU has to be 133. I plugged in 9 for x in both equations then added them both and got 133 for SU. I hope this helps.

Answer:

B

Step-by-step explanation: