50 points pls answer if you do answer include how you got the answer <3333

True. Based on the given information, it is possible that both triangles are acute triangles in which two of their angles measure 40 degrees and 80 degrees and all of the corresponding sides are congruent.

Firstly, let's recall some basic facts about triangles and angles. An acute triangle is a triangle in which all three angles are acute angles, i.e., all three angles measure less than 90 degrees. An angle is a measure of the amount of turn between two straight lines that meet at a common point. The unit used to measure angles is called degrees.

Now, let's consider the given information. We are told that both triangles are acute triangles, which means that all three angles in each triangle are acute angles. We are also told that two of the angles in each triangle measure 40 degrees and 80 degrees. This means that the third angle in each triangle must measure 60 degrees (since the sum of angles in a triangle is always 180 degrees).

Furthermore, we are told that all of the corresponding sides in the two triangles are congruent. This means that the triangles are similar triangles (since corresponding angles in similar triangles are congruent, and corresponding sides are proportional).

So, based on the given information, it is possible that both triangles are acute triangles in which two of their angles measure 40 degrees and 80 degrees, and all of the corresponding sides are congruent. Therefore, the statement "true" would be the correct answer.

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boo... it's length and weighs.

"What is the length of a dinosaur foot if the dinosaur weighs 40 tons.

Answer:

Step-by-step explanation:

What is the length of a dinosaur foot if the dinosaur weighs 40 tons?

Answer:

--------------------------

Angles ∠4 and 87° are vertically opposite angles and therefore are congruent:

Angles ∠6 and 87° are same side interior angles and therefore they are supplementary:

The statement "correlation is measured on a scale from 0 to 1, where 0 indicates no linear relationship between two variables, and 1 indicates a perfect linear relationship" is true.

The correlation coefficient, typically denoted as r, is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 represents a perfect negative linear relationship, 1 represents a perfect positive linear relationship, and 0 indicates no linear relationship or correlation between the variables.

A correlation coefficient of 0 means that there is no linear association between the variables being analyzed. As the correlation coefficient moves closer to 1 or -1, it indicates a stronger linear relationship between the variables. Therefore, the scale from 0 to 1 is commonly used to represent the extent of correlation, where 0 signifies no linear relationship and 1 signifies a perfect linear relationship.

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After 6 hours, there are approximately 41.6mg of ibuprofen left in the person's system. To determine how much ibuprofen is left in the person's system after 6 hours, we will use the formula A=P (1+ r/n) ^nt,

where A is the final amount, P is the initial amount, r is the rate of decrease, n is the number of times the interest is compounded per period, t is the number of periods, and nt is the total number of times the interest is compounded.

In this case, P = 400mg (initial amount of ibuprofen), r = -0.29 (rate of decrease, negative because it decreases), n = 1 (compounded once per hour), and t = 6 (hours).

Now, we'll plug these values into the formula: A = 400(1 - 0.29) ^6.

Step 1: Calculate (1 - 0.29), which is 0.71.
Step 2: Raise 0.71 to the power of 6, which is approximately 0.104.
Step 3: Multiply 400 by 0.104, which is approximately 41.6.

After 6 hours, there are approximately 41.6mg of ibuprofen left in the person's system.

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Answer:

f ^ -1 (x) =  -5x + 10

Step-by-step explanation:

Let's call f(x) = y.

so, y = -(1/5) x + 2

multiply all by -5

-5y = x - 10

get x on its own by adding 10 to both sides

x = -5y + 10

then convert back to f ^-1 (x) for inverse function and call y, x. (that's because graph of inverse function is reflected in the line y=x. a reflection of the original function, f (x)).

f ^ -1 (x) = - 5x + 10

The answer is the system of equations is x = 0.290566 and

y = 40.603774.

To solve this system of equations using a matrix, we have to write it in the form AX = B, where A will be coefficient matrix, X will be variable matrix, and B, constant matrix.

The system of equations is:

                                     y = 650x + 175

                                     y = 25,080 - 120x

To write it in matrix form, arrange coefficients and constants as follows:

| 650 -1 | | x | | 175 |

| -120 1 | * | y | = | 25,080 |

So, coefficient matrix A is:  | 650 -1 |

                                                  | -120 1 |

Variable matrix X is: | x |

                                         | y |

And constant matrix B is: | 175 |

                                                | 25,080 |

The coefficients in the first column of the matrix are coefficient of x in each equation, and coefficients in the second one are the coefficients of y. The constants in the matrix are constants from each equation.

To solve for X, we use matrix algebra to isolate X. First, we have find the inverse of matrix A:

[tex]A^{-1 }[/tex] = (1 / det(A)) * adj(A)

where, det(A) is determinant of A, and adj(A) represents adjugated of A (the transpose of the co-factor matrix of A).

We can calculate these as follows:

det(A) = (650 * 1) - (-120 *(-1)) = 530

adj(A) = | 1 120 |

          = |-1 650 |

So [tex]A^{-1 }[/tex]  = (1 / 530) * | 1 120 |

            = | 0.001887 0.226415 |

   [tex]A^{-1 }[/tex]   = |-1 650 | |-0.001887 1.226415|

Now we can solve for X:

X = [tex]A^{-1 }[/tex]* B

X = | 0.001887 0.226415 | * | 175 |

  = | 0.290566 |

  = |-0.001887 1.226415 | | 25,080 | | 40.603774|

So, the system of equations is x = 0.290566 and y = 40.603774.

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Final answer:

The given matrix does not match either the first equation 'y = 650x + 175' nor the second equation 'y = 25,080 - 120x'. There's a discrepancy between the coefficients given in the matrix and those in the equations.

Explanation:

The first step is to express both equations in terms of y to match the matrix provided. However, the equations already match this format.

The first equation is y = 650x + 175, so if we place the terms in matrix form, we'll get: Column 1 as -650 (the coefficient of x) and Column 2 as 1 (the coefficient of y) and Column 3 as -175 (the constant).

For the second equation, which is y = 25,080 - 120x, again converting all terms as per the columns in matrix form, the coefficients will be Row 2 - Column 1 as 120 (the coefficient of x), Column 2 as 1 (the coefficient of y), and Column 3 as 25,080 (the constant).

Given that the matrix provided doesn't match either of these equations, there must be a mistake in the matrix or in these equations.

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Answer: Q1 = 12.

Q3 = 18.

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Hence Bus 14 is the more consistent bus, due to the lower IQR.

Step-by-step explanation:

Her pupils were 2 * mm after being dilated.

Step 1: Identify the original size of Tori's pupils, which is "mm".
Step 2: Since her pupils were dilated to twice their normal size, multiply the original size by 2.

Calculation: mm * 2

If Tori's pupils were originally x mm in size, and they were dilated to twice their normal size, we can set up the following equation:

2x = size after dilation

To find the size of her pupils after dilation, we need to solve for "size after dilation" in the equation above.

Dividing both sides of the equation by 2, we get:

x = (size after dilation) / 2

Therefore, the size of Tori's pupils after being dilated is x/2 mm.

So, the size of Tori's pupils after being dilated would be 2 * mm, or simply 2mm.

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The joint probability mass distribution of x and y as well as the marginal distributions is 19/81, 25/81 and 7/36

To calculate P(X = x), we need to consider the probability of drawing x red balls out of the 2 balls. Since we are drawing with replacement, the probability of drawing a red ball on any given draw is 3/12 = 1/4. Therefore, the probability of drawing x red balls out of 2 is given by the binomial distribution:

P(X = x) = (2 choose x) * (1/4)ˣ * (3/4)²⁻ˣ

where (2 choose x) is the binomial coefficient.

Similarly, to calculate P(Y = y|X = x), we need to consider the probability of drawing y white balls given that we have already drawn x red balls. Since we are drawing with replacement, the probability of drawing a white ball on any given draw is 4/12 = 1/3. Therefore, the probability of drawing y white balls out of the remaining (2-x) balls is also given by the binomial distribution:

P(Y = y|X = x) = ((2-x) choose y) * (1/3)^y * (2/3)²⁻ˣ

The marginal distribution of x represents the probability distribution of drawing x red balls, irrespective of the number of white balls drawn. We can obtain this by summing the joint probabilities over all possible values of y:

P(X = 0) = P(X = 0, Y = 0) + P(X = 0, Y = 1) + P(X = 0, Y = 2) = 1/9 + 4/27 + 4/81 = 19/81

P(X = 1) = P(X = 1, Y = 0) + P(X = 1, Y = 1) + P(X = 1, Y = 2) = 2/9 + 4/27 + 4/81 = 25/81

P(X = 2) = P(X = 2, Y = 0) + P(X = 2, Y = 1) + P(X = 2, Y = 2) = 1/16 + 1/12 + 1/36 = 7/36

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Answer:

Step-by-step explanation:

The box method to distribute and simplify (6x - 4) (5x - 5). (6x - 4)(5x - 5) simplifies to 30x² - 50x + 20.

To use the box method to distribute and simplify (6x - 4)(5x - 5), we first draw a box and divide it into four sections:

     | 6x  | -4 |

------------------

5x  |     |    |

------------------

-5   |     |    |

Next, we multiply the terms on the top row and write the result in the top left section:

    | 6x  | -4 |

------------------

5x  | 30x²| -30x|

------------------

-5   |     |    |

Then, we multiply the terms on the bottom row and write the result in the bottom right section:

     | 6x  | -4 |

------------------

5x  | 30x²| -30x|

------------------

-5   | -20x|  20 |

Finally, we add the terms in each of the four sections to get the simplified expression:

     | 6x  | -4 |

------------------

5x  | 30x²| -30x|

------------------

-5   | -20x|  20 |

------------------

     | 30x² - 50x + 20 |

Therefore, (6x - 4)(5x - 5) simplifies to 30x² - 50x + 20.

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To align the decimals of the given numbers at the 1.5 inch mark, we can use the Decimal Tab stop feature in a word processor. This will help to ensure that the decimals of the numbers appear organized and uniform.

To align the decimals of the numbers at the 1.5 inch mark using the Decimal Tab stop feature, we first need to set the tab stop at the desired location on the ruler. In this case, we need to set it at 1.5 inches.

To do this, we can click on the ruler at the 1.5 inch mark, and a small L-shaped symbol will appear to indicate the location of the tab stop.

Next, we need to place the tab stops for each of the numbers. We can do this by clicking at the point in each number where we want the tab stop to be and then pressing the Tab key.

This will move the cursor to the next tab stop, which in this case is the Decimal Tab stop at the 1.5 inch mark. We can repeat this process for each number, ensuring that the decimals align vertically at the 1.5 inch mark.

Once we have set the tab stops for all the numbers, the decimals will be aligned uniformly at the 1.5 inch mark.

This will make the numbers easy to read and compare, providing a neat and organized appearance to the document. Using the Decimal Tab stop feature is an effective way to align decimals in a column and can save time and effort in formatting documents.

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The creation story in Christianity exemplifies commitment creativity, obligation, generosity and service.

These values are demonstrated through God's actions and intentions in creating the world and his instructions to humanity to care for it.

Commitment, creativity, obligation, generosity and service are exercised in the creation story of Christianity:

Commitment:

In Christianity, the creation story in Genesis 1 shows God's commitment to creating the world in six days and resting on the seventh day.

This story shows that God was committed to his creation and intended it to be good.

Creativity:

The creation story in Genesis 1 also shows God's creativity in designing and bringing forth the world.

The story describes how God created the heavens and the earth, light, the seas and all living creatures, demonstrating his power and creativity.

Obligation:

In Christianity the creation story also demonstrates God's obligation to care for and provide for his creation.

In Genesis 1:29-30, God gives humans and animals all the plants and fruits on the earth for food showing his obligation to provide for them.

Generosity:

Similarly God's generosity is displayed in the creation story of Christianity.

God creates a world filled with beauty and abundance, with all the resources necessary for life to thrive.

He also gives humans and animals the ability to reproduce and multiply showing his generosity in sustaining life.

Service:

The creation story in Christianity also highlights the importance of service.

In Genesis 2:15 God places Adam in the Garden of Eden and instructs him to work and take care of it.

This shows the value of serving and caring for God's creation.

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The vertex is (5, -96), the axis of symmetry is x = 5, and the function has a maximum value of -96.

To identify the vertex, axis of symmetry, and min/max value of the function f(x) = -2x² - 20x - 46, use the formula:

Vertex: (-b/2a, f(-b/2a))

Axis of symmetry: x = -b/2a

Max or min value: f(-b/2a)

where a, b, and c = coefficients of the quadratic function.

Using the formula, find:

a = -2

b = -20

c = -46

Axis of symmetry:

x = -b/2a

x = -(-20)/(2*(-2))

x = 5

Vertex:

(-b/2a, f(-b/2a))

(-20/(2*(-2)), -2(5)^2 - 20(5) - 46)

(5, -96)

Max or min value:

f(-b/2a) = f(5) = -2(5)^2 - 20(5) - 46

= -96

Therefore, the vertex is (5, -96), the axis of symmetry is x = 5, and the function has a maximum value of -96.

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The elements in GF(2^3) are {0, 1, x, x + 1, x^2, x^2 + 1, x^2 + x, x^2 + x + 1}, and (x^2 + x) * (x^2 + x + 1) in GF(2^3) simplifies to x.

To construct the Galois field GF(2^3), we consider the polynomial x^3 + x + 1 as an irreducible polynomial in Z2[x].

(1) To list all elements in GF(2^3), we can represent them as polynomials of degree 2 or lower in Z2[x]/(x^3 + x + 1). The elements are:

{0, 1, x, x + 1, x^2, x^2 + 1, x^2 + x, x^2 + x + 1}

(2) To compute (x^2 + x) * (x^2 + x + 1) in GF(2^3), we need to perform the multiplication using polynomial multiplication rules and reduce the result modulo (x^3 + x + 1).

(x^2 + x) * (x^2 + x + 1) = x^4 + x^3 + x^3 + x^2 + x^3 + x^2 + x^2 + x

= x^4 + (1 + 1 + 1)x^3 + (1 + 1 + 1)x^2 + x

= x^4 + x + x^2 + x

= x^4 + x^2 + 2x (in GF(2), 2 is equivalent to 0)

Next, we need to reduce the result modulo (x^3 + x + 1):

(x^4 + x^2 + 2x) mod (x^3 + x + 1) = (x^4 + x^2 + 2x) mod (x^3 + x + 1)

= (x^4 + x^2 + 2x) - (x^3 + x + 1)(x)

= x^4 + x^2 + 2x - x^4 - x^2 - x

= x

Therefore, (x^2 + x) * (x^2 + x + 1) in GF(2^3) is equivalent to x.

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Answer: Sam had $170 at first

Step-by-step explanation:

Let's use algebra to solve the problem.

Let J be the amount of money James had at first, and let S be the amount of money Sam had at first. We know from the problem that:

J = S + 240 (James had $240 more than Sam at first)

After their mother gave James $30 and Sam $50, James had twice as much money as Sam:

J + 30 = 2(S + 50)

Now we can substitute the first equation into the second equation to solve for S:

(S + 240) + 30 = 2(S + 50)

S + 270 = 2S + 100

S = 170

Therefore, Sam had $170 at first.

Answer:

y = 7

Step-by-step explanation:

y-4 = 3

Add 4 to both sides of the equation so the y is 'isolated' (alone).

y - 4 + 4 = 3 + 4

Now simplify

y-0 = 7

y = 7

Answer: y = 7

Step-by-step explanation:

y - 4 = 3

add 4 to both sides.

this becomes y - 4 + 4 = 3 +4

                       y + 0 = 7

                       y = 7

Answer:

x = 7

Step-by-step explanation:

looking at the vertical sides, the ratio is 25 : 20 which can be simplified to  5 : 4.

25 = 20 X 1.25.

so the sides of the top shape are 5/4 = 1.25 times longer then the side on the bottom shape.

5x-5 = 1.25 X 24 = 30

we now have 5x - 5 = 30

add 5 to both sides of the equation

5x = 35

divide by 5

x = 7

Measure of angle WVX is  7/9 π

Given,

circle with center V

Radius of circle = 2

Arc length = 14/9 π

Now to measure the central angle of the arc,

Arc length = 2πr × α/360°

α = central angle of arc = ∠WVX

Now,

Substitute the values in the formula,

14/9 π = 2π × 2 ×α/360

α = 7/9 π

Hence the value of ∠WVX = 7/9 π .

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Answer:

Since each score appears only once, there is no score that appears more frequently than the others. There is no mode for this data set.

Step-by-step explanation:

The score that the greatest number of people received is the mode of the data set. In this case, the mode is the score that appears most frequently.

Looking at the data set, we see that the score of 5 appears once, the score of 6 appears once, the score of 7 appears once, the score of 8 appears once, the score of 9 appears once, and the score of 10 appears once.

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Answer:

9 ft

Step-by-step explanation:

The area formula for a rectangle is:

[tex]A=lw[/tex]

We know the area and the width, so let's substitute:

72=l(8)

divide both sides by 8

9=l

So, the length is 9 ft.

Hope this helps! :)

The statements regarding the exponent rules are given as follows:

For the first statement, we have that that a positive exponent can generate both positive and negative numbers, according to the examples presented as follows:

The same is true for negative exponents, as follows:

For an exponent of zero, we have that 0 to the zero can be any number, while any other number has a result of one.

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The Mean Absolute Deviation (MAD) of the given set of numbers is 1.

The mean of the given set of numbers:

Mean = (1+1+1+...1+2+2+..+3+3+...+4+4+4+5+5)/30

Mean = 2.2

The absolute deviation of each number is the absolute value of the difference between the number and the mean.

Absolute deviation of 1 = |1 - 2.2| = 1.2

Absolute deviation of 2 = |2 - 2.2| = 0.2

Absolute deviation of 3 = |3 - 2.2| = 0.8

Absolute deviation of 4 = |4 - 2.2| = 1.8

Absolute deviation of 5 = |5 - 2.2| = 2.8

Now, take the mean of these absolute deviations:

MAD = (11×1.2+9×0.2+5×0.8+3×1.8+2×2.8)/30

MAD = 30.7/30 ≈ 1

Therefore, the Mean Absolute Deviation (MAD) of the given set of numbers is 1.

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A. System of equations describes a set of two or further equations with multiple variables.

A system of equations is a grouping of one or more equations having several variables.

The variable mappings that fulfill all element equations — that is, the points at which all of these equations intersect — are the results of equation systems.

To break a system, you must find all of these common outcomes or sites of intersection. Direct equation systems are a common and valuable subset of equation systems.

These systems can be regarded as two-dimensional lines in the case of two variables. However, if all lines meet in the same spot, the system is deemed to be harmonious and to have a result at that point of junction.

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Answer: system of equations

Step-by-step explanation:

The division shows that the quotient is -3x² - 4x + 2 and the remainder is 147x² + 74x - 6.

           -3x² - 4x + 2

     ---------------------------

x³ + 6x² - 3x - 5 | -3 - 22x⁴ - 13x³ + 39x² + 14x - 6

          3x + 18x⁴ - 9x³ - 15x²

          -------------------------

                   -4x⁴ - 4x³ + 39x² + 14x

                   -4x⁴ - 24x³ + 12x² + 20x

                   -----------------------

                           20x³ + 27x² + 14x - 6

                           20x³ + 120x² - 60x - 100

                           -----------------------

                                     147x² + 74x - 6

Hence, the quotient is -3x² - 4x + 2 and the remainder is 147x² + 74x - 6.

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(a) function of t: [tex]$x(t) = 2 - 3\cos(t)$[/tex]

(b) the equation of the tangent line at the point where [tex]$t = t_0$[/tex]:  [tex]$y - (3 + 2\sin(t_0)) = \frac{2\cos(t_0)}{3\sin(t_0)}(x - (2 - 3\cos(t_0)))$[/tex]

(c) The approximate length of the curve between the two y-intercepts is (3π)/2.

What is curve?

In mathematics, a curve is a continuous and smooth mathematical object that represents a path or a line in space. It can be thought of as a set of points that follow a certain pattern or equation.

(a) To find [tex]$x$[/tex] as a function of [tex]$t$[/tex], we use the parametric equation [tex]$x = 2 - 3\cos(t)$[/tex]. Therefore, [tex]$x(t) = 2 - 3\cos(t)$[/tex].

(b) To find the equation of the tangent line at a specific point where [tex]$t = t_0$[/tex], we need to find the values of [tex]$x$[/tex] and [tex]$y$[/tex] at that point.

Given: [tex]x = 2 - 3\cos(t)$ and $y = 3 + 2\sin(t)$.[/tex]

Substituting [tex]$t = t_0$[/tex] into these equations, we get:

[tex]x(t_0) = 2 - 3\cos(t_0)$ \\\\$y(t_0) = 3 + 2\sin(t_0)$[/tex]

These values represent the coordinates of the point on the curve at [tex]t = t_0$.[/tex]

To find the slope of the tangent line at that point, we differentiate [tex]$x$[/tex] and [tex]$y$[/tex] with respect to [tex]$t$[/tex]:

[tex]\frac{dx}{dt} = 3\sin(t_0)$ \\\\$\frac{dy}{dt} = 2\cos(t_0)$[/tex]

The slope of the tangent line is given by [tex]$\frac{dy}{dx}$[/tex]. To find [tex]$\frac{dy}{dx}$[/tex], we divide [tex]\frac{dy}{dt}$ by $\frac{dx}{dt}$:[/tex]

[tex]$\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{2\cos(t_0)}{3\sin(t_0)}$[/tex]

Now we have the slope of the tangent line at the point [tex]$t = t_0$[/tex]. To find the equation of the tangent line, we use the point-slope form of a line:

[tex]$y - y(t_0) = m(x - x(t_0))$[/tex]

where [tex]$m$[/tex] represents the slope. Substituting the values, we get:

[tex]$y - (3 + 2\sin(t_0)) = \frac{2\cos(t_0)}{3\sin(t_0)}(x - (2 - 3\cos(t_0)))$[/tex]

Simplifying the equation will give you the equation of the tangent line at the point where [tex]$t = t_0$[/tex].

(c) To find the length of the curve between the two [tex]$y$[/tex]-intercepts, we need to find the values of [tex]$t$[/tex] where the curve intersects the [tex]$y$[/tex]-axis. This occurs when [tex]$x = 0$[/tex].

Substituting [tex]$x = 0$[/tex] into the parametric equation [tex]$x = 2 - 3\cos(t)$[/tex], we get:

[tex]$0 = 2 - 3\cos(t)$[/tex]

Solving this equation for [tex]$t$[/tex] will give you the values of [tex]$t$[/tex] where the curve intersects the [tex]$y$[/tex]-axis. Let's assume the solutions are [tex]$t_1$[/tex] and [tex]$t_2$[/tex], with [tex]$t_1 < t_2$[/tex].

To approximate the length of the curve between the two [tex]$y$[/tex]-intercepts, we use the arc length formula for parametric curves:

[tex]$L = \int_{t_1}^{t_2} \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} dt$[/tex]

In this case, [tex]$\frac{dx}{dt}$[/tex] and [tex]$\frac{dy}{dt}$[/tex] are given as:

[tex]\frac{dx}{dt} = 3\sin(t)$ \\\\$\frac{dy}{dt} = 2\cos(t)$[/tex]

Substitute these values into the arc length formula and integrate from [tex]$t_1$[/tex] to [tex]$t_2$[/tex]. Evaluating this integral will give you an approximation of the length of the curve between the two [tex]$y$[/tex]-intercepts.

Hence, the approximate length of the curve between the two y-intercepts is (3π)/2.

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To find out how much the stock must regain to equal the value of $2.50, we need to calculate the total change in the stock's value over the week.
On Monday and Tuesday, the stock rose a total of $0.27 + $0.27 = $0.54 per share. Then, over the next 3 days, the stock dropped a total of $0.38 * 3 = $1.14 per share. So the net change in the stock's value over the week is $0.54 - $1.14 = -$0.60 per share.

To get back to the original value of $2.50 per share, the stock must regain the $0.60 per share it lost, plus the $2.50 it started at, for a total value of $3.10 per share.  

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For a decorative object as circular mirror, the area of piece of decorative contact paper that Araceli cut for the back of the circular mirror is equals to 38.534 square inches.

Area of a circle geometry is defined as pi(π) times the square of radius of circle, A = πr², where r is radius of circle.

Araceli glued has a ribbon and decorative contact paper for decoration of a circular mirror.

Length of ribbon = 22 inch

It is around the circular mirror like circumference. So, circumference of circle = 22 inch

Let the radius and area of circular mirror be r and A. As we know circumference of circle, C = 2πr

where r --> radius of circle

π--> math constant and π = 3.14

=> 22 inch = 2×3.14 × r

=> [tex]r = \frac{22}{6.28}[/tex]

= 3.50318 ~ 3.5 inch

Now, she used decorative contact paper to cover the back of the mirror. Area of piece of decorative contact paper that she cut for the back of the circular mirror is equals to the area of circular mirror. So, using the formula of area of circle is

A = πr² = 3.14 ( 3.5)²

= 38.5340 inch²

Hence, required area value is 38.534 inch².

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The probability that a random bus has a working radio given that it is ready for service is 75.3%.

Given that,

Probability that a city bus is ready for service = 85% = 0.85

Probability that a city bus is ready for service and has a working radio = 64% = 0.64

If A represents the event of ready for service and B represents the event for working radio,

P(A) = 0.85

P(A ∩ B) = 0.64

We have to find P(B | A).

P(B | A) = P(A ∩ B) / P(A) = 0.64 / 0.85 = 0.7529 = 75.29% ≈ 75.3%.

Hence the correct option is D.

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