why does area and perimeter change in different ways

Answer:

For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.

Step by Step:

Keep this in mind >>

Consider the unit circle > The sine and cosine ratios are the only ratios that have 1 (the radius or hypotenuse) as the denominator. The numerators (sides) vary between 0 and 1, thus determining that the sine and cosine do the same.

All of the other ratios (tangent, cotangent, secant, cosecant) have a side as the denominator, varying between 0 and 1. As any denominator approaches 0, the value of the ratio approaches infinity.

From the given information, the probability that either event will occur is 0.7.

From the given Venn diagram,

Number of A = 4

Number of B = 24

Number of others  = 12

Total number = A + B + others = 4 + 24 + 12 = 40

Probability of event A occurring = number of A / Total number = 4/40 = 1/10 = 0.1

Probability of event B occuring = number of B / Total number = 24/40 = 3/5 = 0.6

Now, the probability of either event will occur = P(A or B) = P(A) + P(B)

P(A or B)  = 0.1 +0.6 = 0.7

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Answer:

The best choice is:

Circular-flow model

The circular-flow model demonstrates how consumer demand and production supply influence each other in a market economy. Some key points:

• Consumers demand goods and services by spending money (aggregate demand). This drives production.

• Producers supply goods and services to meet demand (aggregate supply). But supply depends on and influences demand.

• There is a continuous flow and feedback loop between consumers, producers, and the money/resources flowing between them.

The circular-flow model highlights this interconnectedness and interdependence. It shows how consumer spending drives production, which in turn enables more consumer spending, and so on. Changes in demand, supply, spending or consumption ripple through the economy.

The other choices do not accurately represent this relationship:

• Assembly line - Focuses on supply-side production process, not the demand-supply feedback loop.

• Downward spiral - Implies a negative, self-defeating cycle rather than the mutually supporting feedback in the circular-flow model.

• Flow chart - Too generic. A flow chart could represent any process, not specifically the demand-supply relationship.

So in summary, the circular-flow model is the best choice as it demonstrates the way consumer demand and producer supply interact with and influence each other in a free market system. The circular flow of money, resources, supply and demand relies on this interconnection.

Does this help explain the circular-flow model and why it is the best choice? Let me know if you have any other questions!

Step-by-step explanation:

The estimated number of the 160 ducks that have blue marks would be 5 ducks.

Assuming none of the 50 people have received a considerable reward, it is probable that winning a small prize bears higher odds than claiming a more substantial one. Estimating, the probability of achieving a large prize may be considered half as likely to succeed as obtaining a smaller sum:

P ( large prize ) :

= 0.5 x P(small prize)

= 0.5 x 0.06 = 0.03

Number of ducks with blue marks (large prize):

= ( total number of ducks ) x P( large prize )

= 160 x 0.03

= 4.8

= 5 ducks

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Answer:46

Step-by-step explanation:

traingle ABD = 53 + 24 + 47 + x = 180

134+x=180

x=180-134

x=46

The 95% confidence interval is (22.8876, 49.1124)..

To find the 95% confidence interval for the difference in means between two populations, we can use the formula:

CI = (x1 - x2) ± z*(SE)

where x1 and x2 are the sample means of the two populations, SE is the standard error, z is the critical value from the standard normal distribution corresponding to the level of confidence.

Substituting the given values into the formula, we have:

CI = (264 - 228) ± 1.96*(6.69)

Simplifying this expression, we have:

CI = 36 ± 13.1124

Therefore, the 95% confidence interval for the difference in means between the two populations is (22.8876, 49.1124).

This means that we are 95% confident that the true population difference in means falls between 22.8876 and 49.1124. We can interpret this interval as a range of plausible values for the population difference in means, based on the sample data.

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Answer:

To find a splitting field for f, we first factor f completely over Q:

f = (2x^2 − 4x + 1)(x^4 + 1) = 2(x - 1/2)^2(x^4 + 1)

The roots of the quadratic factor are x = 1/2 ± 1/2√2, which are real, and the roots of the quartic factor are x = ±i. Therefore, a splitting field for f is Q(i, √2).

(a) Q(√2): The roots of the quadratic factor are real, so they are already in Q(√2). The roots of the quartic factor are ±i, which are not in Q(√2). Therefore, the Galois group of f over Q(√2) is isomorphic to Z/2Z.

(b) Q(2): The roots of the quadratic factor are not in Q(2). However, both i and √2 are in Q(2), so Q(2) contains a splitting field for f. Therefore, the Galois group of f over Q(2) is trivial, since there is only one automorphism of Q(2) that fixes Q.

(c) Q(i): The roots of the quadratic factor are not in Q(i). However, √2 is in Q(i), so Q(i) contains a splitting field for f. The Galois group of f over Q(i) is isomorphic to Z/2Z × Z/2Z, since there are two complex roots and two real roots, and the complex roots are conjugates of each other.

(d) Q(ζ): The roots of the quadratic factor are not in Q(ζ). However, both i and √2 are in Q(ζ), since ζ^4 = i and ζ^8 = √2. Therefore, Q(ζ) contains a splitting field for f. The Galois group of f over Q(ζ) is isomorphic to Z/2Z × Z/2Z, since there are two complex roots and two real roots, and the complex roots are conjugates of each other.

(e) R: The roots of the quadratic factor are real, so they are already in R. The roots of the quartic factor are ±i, which are not in R. Therefore, the Galois group of f over R is isomorphic to Z/2Z.

The proportional relationship used to find B, the area of the base with a volume of V, is given as follows:

B = V/6.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the table given in the image at the end of the answer, we have that the base area is a sixth of the volume, hence the equation is:

B = V/6.

The table is given by the image presented at the end of the answer.

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From the graph, Jerimiah walks along 44 city blocks.

Hence the correct option is (D).

It is given that each unit on the grid represents 1 city block.

From the given graph we can see that

Number of city block between Restaurant and Museum = 7

Number of city blocks between Museum and Hotel = 4

Number of city blocks between Hotel and Arena = 7

Number of city blocks between Arena and Restaurant = 4

Total number of city blocks along the rectangular path = (7 + 4 + 7 + 4) = 22 city blocks.

Jerimiah walks twice around the rectangular path.

So Jerimiah walks through = 2*22 = 44 city blocks.

Hence the correct option will be (D).

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The question is incomplete. The complete question will be -

Answer:

23

Step-by-step explanation:

Assume the digits are

1, 4 or 2,3

The number can be 14, 41, 23, 32

Test each one:

14 + 9 = 23 does not work

41 + 9 = 50 does not work

23 + 9 = 32 works

32 + 9 = 41 does not work

Answer:

78.947%

Step-by-step explanation:

It says A OR B, so:

5/19 + 6/19 + 4/19

11/19 + 4/19

15/19 = approx. 0.78947 = 78.947%

The perimeter of rectangle W'X'Y'Z is 16 units

he rectangle has four sides. There are two lengths and two widths in a rectangle. Therefore, the perimeter of the rectangle is twice the sum of two adjacent sides that are length and width. The formula is given by:

Perimeter of rectangle = 2(l + b)

We have :

Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'

So, By the image:

The analysis will be the:

Rectangle of WXYZ = 2 × 4

and, The rectangle of W'X'Y'Z' = 2 × WXYZ

                                                   = 16

W'X' = 4

W'Z' = 4

Hence, The perimeter of rectangle is = 4 + 4 + 4 + 4 = 16

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The given question is incomplete, So i take the similar question :

Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'. What is the perimeter of rectangle W'X'Y'Z?

And also to see the attachment.

Answer:

Step-by-step explanation:

To find an equivalent ratio with smaller numbers, we can divide both 25 and 2 by their greatest common factor, which is 1:25 ÷ 1 = 25

2 ÷ 1 = 2Therefore, the ratio can be written as:25 : 2To write this ratio as a rational number, we can divide 25 by 2:25 ÷ 2 = 12.5So an equivalent representation of the ratio 25 : 2 is the rational number 12.5.

The value of distance between two points on graph is,

⇒ d = √32 units

We have to given that;

The coordinates of two points are,

⇒ (9, - 4) and (5, -8)

We know that;

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, The value of distance between two points on graph is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (5 - 9)² + (- 8 - (-4))²

⇒ d = √ 16 + 16

⇒ d = √32

Thus, The value of distance between two points on graph is,

⇒ d = √32 units

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The maximum value of the data = 64

We know that in the box and whisker plot with the left end of the whisker represents the minimum value of the data and the right end of the whisker represents the maximum value.

From the attached box and whisker plot, we can observe that between two numbers on the number line there are 5 equal units.

So, the value of each unit length = 4 unit

Here, the left end of the whisker has value 8 and the right end of the whisker has value 64

This means that the meaximum value = 64

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The angles of rotation for a regular pentagon are:

A Regular Pentagon has five equal sides and five equal angles.

Since the sum of the interior angles of a polygon with n sides is given as:

(n-2) x 180°, then we have:

(5-2) x 180 = 540°.

Note that n = sides of pentagon which is 5

Since all angles in a regular pentagon are equal, each angle measures (540/5) = 108°.

The angles of rotation for a regular polygon are given by the formula 360/n, where n is the number of sides.

Therefore, the angles of rotation for a regular pentagon is:

360/5 = 72°,

Any other angles will be in the multiple of 72. Therefore we have:

Note that a full rotation is 360°.

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Answer: 2, 2, 135, 9, 5, 35, 15, 10, 15, 15

Step-by-step explanation:

Answer:

Step-by-step explanation:

tan theta=5/6

theta=tan-1(5/6)

        =39.8º

i Got u Bro! Answer:X=8x/15+77/15

:D

I Got u Bro Answer: x2-7x+14=0

Answer:

Step-by-step explanation:

X^2-7x+14=0

The radius of curvature of the curve [tex]a^{2y[/tex]=x³-a³ at the point where the curve intersects the x-axis is 27[tex]a^{\frac{3}{2}[/tex].

To find the radius of curvature of the curve [tex]a^{2y[/tex]=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.

When the curve intersects the x-axis, y=0. Therefore, we have:

a⁰ = x³ - a³

x³ = a³

x = a

Next, we need to find the derivative of y with respect to x:

dy/dx = -2x/(3a²√(x³-a³))

At the point where x=a and y=0, we have:

dy/dx = -2a/(3a²√(a³-a³)) = 0

Therefore, the radius of curvature is given by:

R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)

To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:

d/dx(dy/dx) = -2/(3a²(x³-a³[tex])^{\frac{3}{2}[/tex]) + 4x²/(9a⁴(x³-a³[tex])^{\frac{1}{2}[/tex])

At x=a, we have:

d/dx(dy/dx) = -2/(3a²(a³-a³[tex])^{\frac{3}{2}[/tex]) + 4a²/(9a⁴(a³-a³[tex])^{\frac{1}{2}[/tex]) = -2/27a³

Therefore, the radius of curvature is:

R = (1/|-2/27a³|) = 27[tex]a^{\frac{3}{2}[/tex]

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The 12th term of the geometric sequence is -1,240,029

The general formula for the nth therm is:

A(n) = A(1)*(r)^(n - 1)

Where A(1) is the first term, in this case 7.

r is the common ratio, to get it, take the quotient between two consecutive terms:

-21/7 = -3

Then the formula is:

A(n) = 7*(-3)^(n - 1)

The 12th term will be:

A(12) = 7*(-3)^(12 - 1) = -1,240,029

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Answer:

To find A + B, we need to add the corresponding entries of A and B. That is,

A + B = [a_ij + b_ij],

where a_ij and b_ij are the entries of A and B, respectively, in the ith row and jth column.

Using this formula, we get:

A + B = 7 + (-8) -6 + (-7) 2 + 5

6 + (-1) 6 + (-9) -5 + 4

-5 + 9 -7 + 5 8 + (-4)

= -1 -7 7

5 1

4

Therefore, A + B is the matrix:

-1 -7 7

5 1

4

The height of the pyramid is 30.14 in

We have,

Using the Pythagorean theorem,

Hypotenuse = 32.6 in

Base = 24.8/2 = 12.4 in

Height = x

Now,

32.6² = 12.4² + x²

x² = 1062.76 - 153.76

x² = 909

x = 30.15

Thus,'

The height of the pyramid is 30.14 in

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Answer:

Step-by-step explanation:

the median would be 9.