from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. how many different committees are possible if ross, sheldon. first course in probability, a (p. 16). pearson education. kindle edition.

In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it. This statement is False.

Hypothesis testing is an inferential procedure that uses data from a sample to draw a general conclusion about a population. It is a formal approach and a statistical method that uses sample data to evaluate hypotheses about a population. When interpreting a research question and statistical results, a natural question arises as to whether the finding could have occurred by chance. Hypothesis testing is a statistical procedure for testing whether chance (random events) is a reasonable explanation of an experimental finding.

In hypothesis testing, we will always set up a particular hypothesis that we want to demonstrate to be true. We then use probability to determine the likelihood of our hypothesis is correct. If it appears our original hypothesis was wrong, we reject it and accept the alternative hypothesis. The alternative hypothesis is usually the opposite of our original hypothesis. In Fisher’s case, his original hypothesis was that the lady was guessing. His alternative hypothesis was the lady was not guessing.

Generally speaking, the hypotheses that business researchers want to prove are stated in the alternative hypothesis.

Thus, the statement 'In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it' is False.

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Length of missing side is 8/9x² - 5/9

The steps for this process are as follows

Step 1: Add the two equations together to form a new equation.

10z² + 42 - 3 + 82² + 6x - 7 = 8/9x² - 5/9

Step 2: Simplify the expression on the left side of the equation.

92² + 48x - 10 = 8/9x² - 5/9

Step 3: Subtract 8/9x² from both sides of the equation.

92² + 48x - 10 - 8/9x² = - 5/9

Step 4: Simplify the left side of the equation.

92² + 40x - 10 = -5/9

Step 5: Add 10 to both sides of the equation.

92² + 40x = 5/9

Step 6: Divide both sides of the equation by 40.

92²/40 + x = 5/9

Step 7: Simplify the left side of the equation.

x = 5/9 - 92²/40

Step 8: The length of the missing side is 8/9x² - 5/9 = 8/9 (5/9 - 92²/40) - 5/9.

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Using the given equation, Length of missing side is 8/9x² - 5/9

The steps for this process are as follows

Step 1: Add the two equations together to form a new equation.

10z² + 42 - 3 + 82² + 6x - 7 = 8/9x² - 5/9

Step 2: Simplify the expression on the left side of the equation.

92² + 48x - 10 = 8/9x² - 5/9

Step 3: Subtract 8/9x² from both sides of the equation.

92² + 48x - 10 - 8/9x² = - 5/9

Step 4: Simplify the left side of the equation.

92² + 40x - 10 = -5/9

Step 5: Add 10 to both sides of the equation.

92² + 40x = 5/9

Step 6: Divide both sides of the equation by 40.

92²/40 + x = 5/9

Step 7: Simplify the left side of the equation.

x = 5/9 - 92²/40

Step 8: The length of the missing side is 8/9x² - 5/9 = 8/9 (5/9 - 92²/40) - 5/9.

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The values of the six trignometric functions for the angle are

The above sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (0,-2) is on the terminal side of θ. We have to determine the value of six

triganomertric functions at angle θ. As we see at terminal side point (0,-2) the value of angle θ = 3π/2. The six trigonometric functions are sine, cosine , secant , cosecant , tangent , cotangent .

= Sin ( 180° + π/2) = - sin(π/2) ( since, 180° + θ represents 3rd quadrant where sinθ is negative)

=> Sinθ = - 1

= Cos( 180° + π/2) = - Cos(π/2) ( since, 180° + θ represents 3rd quadrant where cosθ is negative)

=> Cosθ = Cos(π/2) = 0

= tan( 180° + π/2) = - tan(π/2) ( since, 180° + θ represents 3rd quadrant where tanθ is positive)

=> tanθ = - sin(π/2)/cos(π/2) = 1/0

= undefined

= Csc( 180° + π/2) = - Csc(π/2) ( since, 180° + θ represents 3rd quadrant where cscθ is negative)

=> Cscθ = - Csc (π/2) = - 1/sin(π/2) = 1

= Sec( 180° + π/2) = - Sec(π/2) ( since, 180° + θ represents 3rd quadrant where secθ is negative)

=> Secθ = -Sec(π/2) = -1/cos(π/2) = - 1/0

= undefined

= Cot( 180° + π/2) = Cot(π/2) ( since, 180° + θ represents 3rd quadrant where cotθ is positive)

=> Cotθ = cot(π/2) = Cos(π/2)/sin(π/2) = 0

Hence, we determined all required triganomertric functions value for θ=3π/2.

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The six trignometric functions' values for the angle are

Tan = tan(3/2) = undefined, Sin = Sin(3/2) = -1, Cos = Cos(3/2) = 0, and vice versa.

Cot = Cot(3/2), Csc = Csc(3/2), and Sec = Sec(3/2), respectively.

The above drawing shows an angle in standard position with the point (0,-2) on the angle's terminal side and the smallest positive measure achievable. We must calculate the value of six.

Triganomertric operates at an angle. As can be seen, the angle's value is 3/2 at the terminal side point (0,-2). In trigonometry, there are six different functions: sine, cosine, secant, cosecant, tangent, and cotangent.

At this point, Sin = Sin(3/2) = Sin( + /2)

= Sin ( 180° + π/2) Since 180° + denotes the third quadrant, where sin is negative, the expression is equal to - sin(/2).

=> Sinθ = - 1

Cos is equal to Cos(3/2) = Cos(+/2)

because 180 degrees, = Cos(180° + /2) = - Cos(/2)

Since 180° + denotes the third quadrant, where cos is negative, the equation is Cos(180° + /2) = - Cos(/2).

Hence, Cos = Cos(/2) = 0.

Tan is equal to Tan (3/2) = Tan (+/2)

= tan( 180° + π/2) Since 180° + denotes the third quadrant, where tan is positive, the expression is = - tan(/2).

Consequently, tan = - sin(/2)/cos(/2) = 1/0

not defined

Csc is equal to Csc(3/2) = Csc(+/2)

Since 180° + represents the third quadrant, where csc is negative, Csc(180° + /2) = - Csc(/2)

=> 1/sin(/2) = 1 = Csc = - Csc (/2)

Se( + /2) = Se( = Sec(3/2)

Since 180° + represents the third quadrant, where sec is negative, sec(180° + /2) = - Sec(/2)

The formula is: Sec = -Sec(/2) = -1/cos(/2) = -1/0.

not defined

Cot = Cot(3/2), which equals Cot(+/2)

Since 180° + denotes the third quadrant, where cot is positive, the equation is Cot(180° + /2) = Cot(/2).

Consequently, Cot = Cot(2/2) = Cos(2/2)/sin(2/2) = 0

As a result, we calculated the values for all necessary triganomertric functions for 3/2.

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The items in A or the elements included in set A are A = 1, 2, 3, 4.

What is an element in a set?

In mathematics, any one of the unique things that make up a set is referred to as an element (or member). A distinct object belonging to a set is referred to as an element (or member) of a set.

The items in A and B, or the elements included in both sets, make up its constituent parts.

Example The elements of the set A B should be listed if A = 1, 2, 3, 4 and B = 2, 4, 6, 8.

A little letter, like x, y, or z, is typically used to represent a set element.

By listing all of a set's components inside braces, a set can be explained.

A = 2, 4, 6, 8 for instance, if Set A is composed of the integers 2, 4, 6, and 8.

Hence, The items in A, or the elements included in set A are A = 1, 2, 3, 4.

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Please see the image attached below to know a representation of linear function y = - (1 / 3) · x - 6 in Cartesian plane.

Linear functions are polynomials of the form:

y = m · x + b

Where:

Graphically speaking, linear functions represents lines and lines can be generated from two points on Cartesian plane. The procedure is described below.

First, obtain two points from linear function:

x = 0

y = - (1 / 3) · 0 - 6

y = - 6

x = 1

y = - (1 / 3) · 1 - 6

y = - 1 / 3

Second, add the points on Cartesian plane.

Third, construct a line that passes through the two points added. Please see the image attached below.

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By performing a change of units, we will see that the cost is 161.36 US dollars.

Here we know that the cost of the dinner was 119 british pounds, and we want to change the units to US dollars.

We know that the exchange rates are:

Currency          Dollar per foreign.    Foreign per dollar.

British pound          1.356                              0.7376

That means that each british pound is equal to 1.356 US dollars, then 119 british pounds is equivalent to:

119*(1.356 ) = 161.36 US dollars.

That is the cost in US dollars.

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Answer:

70.824

Step-by-step explanation:

to solve, multiply the amount of pounds by 0.454.

EX:

156 * 0.454 = 70.824

what it actually equals:

70.7604 (answ on web)

vs

70.824 (answ with formula)

not bad eh?

hope this helps :)

Answer:

[tex]9x^2+14x+1[/tex]

Step-by-step explanation:

Hey there!

In order to find the answer to this problem, we must first form an equation; then we can solve/simplify it further

Our Equation:

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

[tex](9x^2+5x+8)+(9x-7)[/tex]

1. Distribute the positive sign: positive and positive make positive, positive and negative make negative, negative and negative make positive

[tex]9x^2+5x+8+9x-7[/tex]

2. Combine like terms in each parenthesis: This means combining the x values and the constants.

[tex]9x^2+14x+1[/tex]

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

This means that when you add the two given values, the answer you get is: [tex]9x^2+14x+1[/tex]

The function f(x) can shift for log (w ± dx) in any of the four directions

From the question, we have the following parameters that can be used in our computation:

log(DWX)

Express properly

log(w ± dx)

Where w and d are constants and x is the variable

The above function is a logarithmic function, and the parent function is

log(x)

The direction the function shifts is dependent on the values of w and d i.e.

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So, the correct ordering from smallest to largest is 17/15, 7/6, 28/25.

When comparing fractions, one way to determine which fraction is larger or smaller is by finding a common denominator and then comparing the numerators. A common denominator is a multiple of both denominators. The least common denominator (LCD) is the smallest common denominator.

In this case, the least common denominator for the fractions 7/6, 17/15, 28/25 is 30.

This is because 30 is the smallest multiple of 6 and 15 that is also a multiple of 25

So, 7/6 = 35/30, 17/15 = 17/15 and 28/25 = 84/75

The numerators of the fractions are 35, 17, and 84 respectively. Since 17 is the smallest numerator and 84 is the largest numerator, we can conclude that 17/15 is the smallest fraction and 84/75 is the largest fraction.

Therefore, the correct ordering from smallest to largest is 17/15, 7/6, 28/25.

In summary, to compare fractions, we can find a common denominator, then compare the numerators. In this case, we used the least common denominator 30, and then compared the numerators 35, 17, 84, which allowed us to order the fractions in an increasing order.

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Answer:

Step-by-step explanation:

The value of x is 900 and value of y is 300.

Two or more expressions with an Equal sign is called as Equation.

From the given information we form a system of linear equations.

1.4x+1.6y=1740..(1)

x-3y=0..(2)

x=3y

Plug in x =3y in the equation 1.

1.4(3y)+1.6y=1740

4.2y+1.6y=1740

5.8y=1740

Divide both sides by 5.8

y=300

x=3(300)=900

Hence, the value of x is 900 and value of y is 300.

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Answer:

Step-by-step explanation:

wwI effected fiction writing in many ways such as _________________.

Answer:

The First World War evoked a surge in literary output, which included poems, novels and drama. Whilst the poetry of Siegfried Sassoon, Rupert Brooke and Wilfred Owen immediately springs to mind, works by by Ivor Gurney, Edward Thomas, Charles Sorley, David Jones and Isaac Rosenberg are also widely anthologised.

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The total probability of filling oil is 0.60

a. P(oil) = 1 - P(no oil) = 1 - 0.40 = 0.60

b.P(soil ∩ high quality oil) = (0.45)(0.15) = 0.067

P(soil ∩ medium quality oil) = (0.15)(0.15) = 0.022

P(soil ∩ no oil) = (0.40)(0.40) = 0.16

New probabilities,

P(high quality oil | soil) = 0.067 / (0.067+0.022+0.16) = 0.067/0.269 = 0.269

P(medium quality oil | soil) = 0.022 / (0.067+0.022+0.16)  = 0.022/0.269 = 0.088

P(no oil | soil) = 0.09 / (0.067+0.022+0.16) = 0.09/0.269 = 0.361

New probability of finding oil,

P(oil|soil)= 1 - P(no oil | soil) = 1 - 0.361 = 0.639

So the company has a lower chance of finding oil given that they find the particular soil.

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x⁶y¹⁴ is the expression equivalent to (x³y⁷)², 12 is the equivalent expression of  [tex](144^{3}) ^{\frac{1}{6} }[/tex] and 6t+8 is equivalent expression of  2(3t+4).

An expression is combination of variables, numbers and operators.

Equivalent expressions are expressions that work the same even though they look different.

The given expression is (x³y⁷)²

(x³)²(y⁷)²

x⁶y¹⁴

x⁶y¹⁴ is the expression equivalent to (x³y⁷)²

Expression is [tex](144^{3}) ^{\frac{1}{6} }[/tex]

[tex]144^{\frac{3}{6} }[/tex]

[tex]144^{\frac{1}{2} }[/tex]

√144

12

12 is the equivalent expression of  [tex](144^{3}) ^{\frac{1}{6} }[/tex]

Expression is 2(3t+4)

Apply distributive property

6t+8

6t+8 is equivalent expression of  2(3t+4).

Hence, x⁶y¹⁴ is the expression equivalent to (x³y⁷)², 12 is the equivalent expression of  [tex](144^{3}) ^{\frac{1}{6} }[/tex] and 6t+8 is equivalent expression of  2(3t+4).

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The value of the constant rate of change of y with respect to x is 20.

A formula that expresses change in y in terms of change in x is y = kx.

Suppose that y = 1.5 when x = 1, a formula that expresses y in terms of x is k = 1.5.

In Geometry, the rate of change of any straight line simply refers to its gradient or slope and it can be calculated by using this mathematical expression;

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

Assuming that both the x-axis and the y-axis have a scale of 1:20, the constant rate of change is given by:

Constant rate of change = 20/1 = 20.

When y = 1.5 and x = 1, a formula that expresses y in terms of x is given by:

y = kx

k = y/x

k = 1.5/1

k = 1.5.

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The equation does not define a linear function

From the question, we have the following parameters that can be used in our computation:

y = -x³ - 11

As a general rule, a linear equation is any equation that has a degree of 1

The given equation above has a degree of 3

Hence, it is not a linear equation

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Answer:

C)  To know whether 2 triangles are similar, it is enough to know the measure of 2 angles in each triangle.

Step-by-step explanation:

Two triangles are said to be similar if:

As there are three interior angles in a triangle, and the sum of the interior angles is always 180°, we need to know the measure of at least 2 angles in each triangle to determine if they are similar.  The known angles don't have to be corresponding angles, as we can calculate the third angle and then compare all three angles to determine if the triangles are similar.

With regards to the sides of a triangle, it is not enough to know the measure of 2 sides to determine if they are similar. We would need to know at least one interior angle in this case.

Since the MCQ test has twelve questions with each question having four possible answers, the number of ways in which the test can be answered are 16777216.

There are 12 questions in the given test. It has an MCQ test and every question in the test has 4 options, that is, 4 possible answers.

There are multiple possibilities by which the given test can be answered as we can select a different option every time while answer a question. To calculate the different amount of possibilities,

By the fundamental principle of counting,

The amount of possible ways to answer one question are

4¹ = 4

The amount of possible ways to answer 12 questions are

4¹² = 16777216

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The joint frequency of adults who voted for chocolate is given as follows:

0.1148.

A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.

A joint frequency is calculated considering a combination of two events.

In the context of this problem, we have that out of 122 people, there are 14 adults who voted for chocolate, hence the joint frequency of adults who voted for chocolate is obtained as follows:

14/122 = 0.1148.

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Based on the ratio of the largest angle of the triangle with 180°, the degrees of the largest angle is 77°.

The ratio is the proportion of one value to the whole.

Ratios compare the relative sizes of components.

Ratios are computed as the quotients resulting from division operations.

The ratio of the measures of the angels of a triangle = 5:7:9

The sum of ratios = 21

The ratio of the largest angle = 9/21

We know that the total angles of a triangle = 180°

The angle (degrees) of the largest angle = 77° (180° x 9/21)

Thus, the degree of the largest angle is 77°.

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Answer:

in break-even point

C=R

20n+134000=160n

134000= 160n-20n

140n=134000

n=134000/140

n=957.14

n=957 ( nearest whole number)

C= 20(957.14) + 134000

= 153142.8

= 153143 (nearest whole number)

R= 160(957.14)

=153142.4

= 153142 (nearest whole number)

Answer:

Step-by-step explanation:

Given that akua is 3 years older than yaboah and the sum of their ages is 23, you want the age of yaboah and the product of their ages.

Let 'a' and 'y' represent the ages of akua and yaboah, respectively. The given relations are ...

  a + y = 23

  a - y = 3

Adding these equations gives ...

  2a = 26

  a = 13

Using this in the second equation, we find ...

  y = a -3 = 13 -3 = 10

The product of their ages is ...

  a·y = 13·10 = 130

Yaboah is 10 and the product of their ages is 130.

Using percentages we know that he read for 945 minutes over two months, covering pages. If Oliver accomplishes his goal of reading for 19% more minutes next month.

Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

So, this month, Oliver read for 450 minutes.

He has promised to read for 10% extra minutes the following month.

Next month, he spent minutes reading pages:

450 + 10% * 450 = 450 + 45 = 945

He, therefore, read for pages at a time for two months = 450+495=945

Hence He read for 945 minutes over two months, covering pages.

Therefore, using percentages we know that he read for 945 minutes over two months, covering pages. If Oliver accomplishes his goal of reading for 19% more minutes next month.

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The quantity of ounce of pate they should order for the 296 people which will be present for their wedding reception would be = 411.1 ounce.

The quantity of ounce ordered for 36 people = 50 ounce.

Therefore the quantity of ounce that will be enough for 296 people = X ounce.

Make X ounce the subject of formula;

X ounce = 296 × 50 /36

= 14800/36

= 411.1 ounce.

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The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.

The base will be calculated as:-

tan(38.6) = P / B

tan(38.6) = 67.7 / B

B = 67.7 / tan(38.6)

B = 54.8 ft

The height will be calculated as:-

Cos(42.4) = B / H

H = 84.8 / Cos(42.4)

H = 114.83 ft

Therefore, If someone were to look down from above, they would be 114.83 feet from the object and 84.8 feet away.

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The improper integrals are i and ii.

An improper integral is the limit of a definite integral in mathematical analysis when either one endpoint of the interval of integration approaches a limit, such as a real number, positive or negative infinity, or, in rare cases, when both endpoints approach limits.

According to the question

The first integral, the integral from 2 to 5 of dx over amount x squared minus 1, is incorrect because the denominator x2-1 becomes 0 at x=1, meaning the integrand expands to infinity at these places and the integral is not convergent across the range [2,5]. Since the interval of integration extends from 1 to infinity and the function is not limited, the second integral, the integral from 1 to infinity of amount x minus 1 dx, is incorrect. The integrals I and ii are both incorrect. The third integral, which is a standard integral and is the integral from negative 2 to 3 of dx over amount x + 1, is convergent.

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The equation is as follows: Q = a - bP^2.Nonlinear demand curve like this can be found in luxury goods and Veblen goods. Where the luxury goods are the goods whose demand increases as the price increases and Veblen goods are the goods whose demand increases with an increase in the consumer's income.

The equation is as follows: Q = a - bP^2.

To derive a demand schedule, we can plug in different values of P (price) and solve for Q (quantity demanded). For example:

Q = a - bP^2

Q = a - (b * 10^2)

Q = a - 1000b

Q = a - (b * 9^2)

Q = a - 810b

Q = a - (b * 8^2)

Q = a - 640b

and so on.

To derive a demand curve, we can plot the different points from the demand schedule on a graph, with P on the x-axis and Q on the y-axis. The demand curve will be a downward-sloping parabola.

Nonlinear demand curve like this can be found in luxury goods and Veblen goods. Where the luxury goods are the goods whose demand increases as the price increases and Veblen goods are the goods whose demand increases with an increase in the consumer's income.

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The probability of selecting a 9 and the coin landing on tails is 1/26.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Here,

The probability of selecting a card 9 is

Total number of outcomes =52

Number of favourable outcomes =4

Now, probability = 4/52

= 1/13

The probability of coin landing on tails is

1/2

Probability of an event = 1/13 × 1/2

= 1/26

Therefore, the probability of selecting a 9 and the coin landing on tails is 1/26.

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The circumference of the outer circle, greater, 12.57 feet, than the circumference of the inner​ circle.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

Given:

The circumference of the inner circle is 64 feet.

The radius of the inner circle,

2πr = 64

r = 32 x 7/22

r = 112/11 feet.

The distance between the inner circle and the outer circle is 2 ft.

The radius of the outer circle,

= 112/11 + 2

= 134/11 feet.

The circumference of the outer circle,

= 2 x 22/7 x 134/11

= 76.57 feet.

Now, 76.57 - 64 = 12.57 feet.

Therefore, the circumference of the outer circle is greater than 12.57 feet.

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