Sue makes bracelets. she uses 8 1/4 inches of chain to make one bracelet. how many bracelets can she make from a chain that is 49 1/2 inches long?

The value of x is 17

The congruent arcs are (b) PQ and SR

The radius is 12 units

The value of PQ is 4

The length YZ is 19 units

In this question, we make use of the property of congruent sides

So, we have

3x - 24 = x + 10

When evaluated, we have

2x = 34

Divide by 2

x = 17

By the definition of congruent arcs, congruent arcs are arcs that have equal measures

In this figure, the congruent arcs are PQ and SR i.e. (b) PQ and SR

The radius of the circle is calculated as

r² = (25 + r)² - 35²

When expanded, we have

r² = 625 + 50r + r² - 1225

So, we have

50r = 600

Divide both sides by 50

r = 12

In this question, we make use of the property of congruent sides

So, we have

PQ = SR

Where

SR = 4

When evaluated, we have

PQ = 4

The length of YZ in the circle is calculated as

YZ² = (9 + 8)² + 8²

So, we have

YZ² = 17² + 8²

When expanded, we have

YZ² = 289 + 64

So, we have

YZ² = 353

Take the square root of both sides

YZ = 19

Hence, the length YZ is 19 units

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Step-by-step explanation:

z² +x² - y= -2²+ -1² - 3

4+ 1 - 3= 2

x²y²z²= -1²× 3²× -2²

1× 9× 4= 36

Answer:

38.16

Step-by-step explanation:

cosine = adjacent leg / hypotenuse

34 / x = cos 27

x = 34 / cos 27 deg

x ≈ 38.16

Answer:

we have

cos 27°=base/hypotenuse

cos27°=34/x

x=34/cos27°= 38.16is your answer

(a) The integral ∫ sec(x) tan(x) √(1 + sec(x)) dx is equal to √(1 + sec(x)) + C, where C is the constant of integration.

To solve this integral, we can use the substitution method. Let's substitute u = sec(x) + 1, which implies du = sec(x) tan(x) dx. By rearranging the equation, we have dx = du / (sec(x) tan(x)).

Substituting the values, the integral becomes:

∫ sec(x) tan(x) √(1 + sec(x)) dx = ∫ √u du

Integrating with respect to u, we get:

∫ √u du = (2/3)u^(3/2) + C

Now, substituting back u = sec(x) + 1, we have:

(2/3)(sec(x) + 1)^(3/2) + C

Simplifying further:

√(1 + sec(x)) + C

Therefore, the solution to the integral is √(1 + sec(x)) + C, where C represents the constant of integration.

(b) The given definite integral a∫ √(a² - x²) dx, when evaluated, represents the area of a semicircle with radius 'a'.

To evaluate the integral, we use the substitution method. Let z = a sin(θ), which implies dz = a cos(θ) dθ. By rearranging the equation, we have dx = dz / (a cos(θ)).

Substituting the values, the integral becomes:

a∫ √(a² - x²) dx = a∫ √(a² - (a sin(θ))²) (dz / (a cos(θ)))

Simplifying the expression inside the square root:

√(a² - (a sin(θ))²) = √(a² - a²sin²(θ)) = √(a²(1 - sin²(θ))) = √(a²cos²(θ)) = a cos(θ)

Substituting dx and simplifying further, the integral becomes:

a∫ a cos(θ) (dz / (a cos(θ))) = ∫^π a dz

Since the integration is with respect to z and not θ, the limits of integration do not change. Hence, the integral evaluates to:

a∫ √(a² - x²) dx = a∫^π a dz = a² [θ]₀^π = a²(π - 0) = a²π

Therefore, the given definite integral represents the area of a semicircle with radius 'a'.

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Answer:

-1,024

Step-by-step explanation:

-4,-8,-16,-32,-1024<- thats the 8th one

Answer:

52=x-15(being vertically opposite angle)

52+15=x

x=67

Answer:

2

Step-by-step explanation:

you take 1 and add 1 to it... and bam... 2

Answer:

2

Step-by-step explanation:

1+1=2 because 2-1=1 :0

Answer: In mathematics, prime and composite numbers are distinguished by the number of factors they contain. A prime number is one that has only two factors and a composite number has more than two factors. Factors are values that divide a number or expression evenly.

Suppose that triangles ABC and DFE are similar. Therefore, the ratio between their corresponding sides is constant. Let x and y be

Then,

Triangle DFE is impossible, the lengths of its sides are impossible to construct in such a manner that the result is a right triangle whose hypotenuse is 3. DFE is an impossible triangle, the hypotenuse of a right triangle is always its largest side.

However, we can algebraically find x and y, although it would not make any sense geometrically speaking.

Solving for x,

Similarly, solving for y,

Answer:answer what

Step-by-step explanation:

After 1 year, you have invested $977.28. The Option B

To find the total amount, we have to determine monthly investment required.

Let's represent monthly investment as M.

After 12 months of compounding, the final amount will be $1000. We will use formula for compound interest \(A = P(1 + r/n)^{nt}\)

To solve for monthly investment (M), we rearrange the formula as follows: \(A = M * ((1 + r/n)^{nt} - 1) / (r/n)\)

\(1000 = M * ((1 + 0.05/12)^{12*1} - 1) / (0.05/12)\\M = $1000 * (0.05/12) / ((1 + 0.05/12)^{12*1} - 1)\\M = $81.4408151 \\M = $81.44\)

To get total amount invested after 1 year, we will multiply investment by 12 months:

= $81.44 * 12

= $977.28.

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The scale factor is 10:3

And the value of X=30

A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller). For example, we can increase a rectangle with sides of 2 cm and 4 cm by multiplying each side by an integer, say 2.

Scale factor = new form dimension The basic formula for calculating the scale factor is the dimension of the former shape. The formula for scaling up the original figure is Scale factor = Larger figure dimensions. Figure dimensions are reduced.

From the figure,

Scale factor of AB:AB'

=40:12

=10:3

Therefore, BB':X≅10:3

100/X=10/3

X=(3×100)/10

X=30

Therefore, the scale factor is 10:3

And the value of X=30

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The area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ) is 294π square units.

To find the area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ), we need to evaluate the integral for half of the area and then double the result.

The curve of the limacon has a loop when 0 ≤ θ ≤ π, so we integrate from 0 to π. The area can be calculated as follows:

A = 2 ∫₀^π 1/2 r² dθ

Using the equation for r given, we can substitute and simplify:

A = 2 ∫₀^π 1/2 (7 - 14sin(θ))² dθ

A = 2 ∫₀^π 1/2 (49 - 196sin(θ) + 196sin²(θ)) dθ

A = ∫₀^π (98 - 392sin(θ) + 392sin²(θ)) dθ

Using the trigonometric identity 1 - cos(2θ) = 2sin²(θ), we can simplify further:

A = ∫₀^π (98 - 392sin(θ) + 196 - 196cos(2θ)) dθ

A = ∫₀^π (294 - 392sin(θ) - 196cos(2θ)) dθ

Integrating with respect to θ:

A = [294θ + 392cos(θ)sin(θ) + 98sin(θ)]₀^π

Evaluating at the limits of integration, we get:

A = [294π + 0 + 0] - [0 + 392cos(0)sin(0) + 98sin(0)]

A = 294π - 0 - 0 = 294π

Therefore, the area inside the loop of the limacon r = 7 - 14sin(θ) is 294π square units.

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The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Answer:

36 and 48 and 96

Step-by-step explanation:

add 3+4+8=15

all of the angles in a triangle have to add up to 180

so 180÷15=12

now for this ratio, each part will equal 12

so we have to multiply each of the parts by 12

3×12=36

4×12=48

8×12=96

those are the measures of the angles

you can add them up again and see that they equal 180

you can try dividing and you will see that they also equal the ratio

The yield of stock at yesterday's closing price is 3.43%.

Annual dividend is the profit of the stock which is divided among the shareholders, both common and preferred shareholders annually.

Given,

Annual dividend = $1.20

Today's closing price = $34.50

Net change = -$0.50

Let x be yesterday's closing price.

Net change = Today's closing price - yesterday's closing price

⇒ -0.50 = 34.50 - x

⇒ x = 34.50 + 0.50

⇒ x = 35

Yield = \(\frac{Annual dividend}{Price}\) × 100

         = \(\frac{1.2}{35}\) × 100

         = 3.4286 % ≈ 3.43 %

Hence the stock's yield at yesterday's closing price of preferred stock is 3.43 %.

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Answer:

its 2 to the 9th power

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

i just took the test

For all real numbers x, there exists a real number y such that x is less than y.

The given statement, ∀x∃y(x < y), can be translated into English as "For all x, there exists a y such that x is less than y."

This means that for every value of x, there is a value of y that is greater than x. This is true for all real numbers, as there are an infinite number of real numbers and there will always be a number greater than any given number.

In summary, the statement ∀x∃y(x < y) where x and y are real numbers can be translated into English as "For all x, there exists a y such that x is less than y."

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Respuesta:

x = 5.656854249

Explicación paso a paso:

[NOTA: Solo quería disculparme de antemano por cualquier mala gramática, ya que estoy usando un traductor para esto.]

x/Sen30°= 8/Sen45° [Multiplica ambos lados por Sen30°]

x = (8/Sen45°) * Sen30° [Resuelve usando una calculadora]

x = 5.656854249

Answer:

-38

Step-by-step explanation:

4-(3^4-6^2)+2(3)÷2

=>     4 - (81-36) + 2(3) ÷ 2      

=>     4 -  45 + 2(3)÷2

=>     4 -  45 + 6÷2

=>     4 -   45 + 3

=>     -41 + 3

=>     - 38

hope this helps :)

Answer:

14 hours

Step-by-step explanation:

Finding the rate of travel

Time taken to cover 889 km

Step-by-step explanation:

1. 35.7/0.07=510

2. 486.12/0.6=810.2 approximately 810

3. 3.43/0.035=98

4. 5418.54/0.009=602,060

5. 812.5/1.25=650

6. 17.343/36.9=0.47 approximately 1

Answer:

800.53

Step-by-step explanation:

The car was driven 105 miles.

What is rent?

An agreement where a fee is paid for the temporary use of a good, service, or property owned by another is known as renting, sometimes known as hiring, or letting.

In the given example the cost function is, c = 15 + 2m

Where, c is the total cost and m is the number of miles car driven.

The total cost was $225.

So, plug c = $225 in the above equation.

225 = 15 + 2m

210 = 2m

   m = 105

Therefore, the car was driven 105 miles.

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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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The net area A of the parametric curve f(t) from 0 ≤ t ≤ 1 is (1/3)e.

To find the net area A of the parametric curve f(t), we can use the concept of definite integration. Since the curve is defined by the parametric equations x = t^(2/3) and y = t^2e^(t^(1/3)), we need to integrate the y-coordinate with respect to the x-coordinate within the given range of t.

First, we need to express t in terms of x to determine the limits of integration. From the equation x = t^(2/3), we can solve for t as t = x^(3/2). Therefore, the limits of integration become x = 0 and x = 1^(2/3) = 1.

Next, we integrate the y-coordinate with respect to x within the given limits. The integral becomes ∫(t^2e^(t^(1/3))) dx, where t is replaced by x^(3/2). Simplifying the expression, we have ∫(x^(3/2))^2 * e^(x^(3/2)^(1/3)) dx, which further simplifies to ∫x^3 * e^(x^(1/2)) dx.

Evaluating this integral from x = 0 to x = 1, we obtain the net area A = (1/3)e.

Therefore, the net area A of the parametric curve f(t) from 0 ≤ t ≤ 1 is (1/3)e.

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"Create a new matrix by copying elements greater than or equal to 25 from the original matrix."

To process a given n×m matrix with the provided rules, we need to create a new matrix that retains only the elements greater than or equal to 25 from the original matrix. We can start by initializing an empty new matrix of the same size as the original matrix. Then, we iterate through each element of the original matrix. For each element, we check if it is greater than or equal to 25. If it satisfies this condition, we copy that element to the corresponding position in the new matrix.

By applying this process for all elements in the original matrix, we generate a new matrix that contains only the elements greater than or equal to 25. The new matrix will have the same dimensions as the original matrix, and the elements in the new matrix will be placed in the same positions as their corresponding elements in the original matrix

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Subtracting the extremes of each axis, it is found that the measure of angle ABC is of 170º.

Considering the given figure, the measure of angle ABC can be found subtracting the extremes of the balance, that is, axis C by axis A.

Looking at the balance, we have that:

Hence:

170º - 0º = 170º.

Thus the measure of angle ABC is of 170º.

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