Russo is trying to find the area of the lake in his neighborhood. He sees a duck (point C) and uses a tape measure to find that the duck is 16 feet from the point of tangency (point B). He also measures out that the duck is 8 feet away from the edge of the lake (in the direction of A).



Using this information, what is the radius of the lake?

Answer:

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Answer:

for the first one it is 96 cents

for the second one it is 96 cents

and for the third one it is also 96 cents

Step-by-step explanation:

use long division.

11/10.56

.96 * 11 = 10.56

same for the rest of them

Answer:

(x,y)=(-2,-1)

Step-by-step explanation:

4x - y = -7: 8x-2y=-14

8x-2y=-14

-8x + 4y = 12

add these two:

2y=-2

y=-1

plug in the y:

-8x-4=12

-8x=16

x=-2

Answer:

2/5

Step-by-step explanation:

Answer:

Given:

To Find:

Solution:

First, we have to find the Circumference of the Wheel:

As, we know:

\( \bigstar \:{\boxed{ \rm{Circumference_{(Circle)} = 2 \pi r }}} \: \bigstar\)

where,

So, the Circumference of wheel will be:

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = 2 \times \frac{22}{7} \times 1.75 }}}} \)

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{2 \times 22}{7} \times 1.75}}}}\)

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{44}{7} \times 1.75 }}}}\)

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{44 \times 1.75}{7} }}}}\)

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{77}{7} }}}}\)

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} ={ \boxed{ \rm{ \red{11m}}}}}}}}\)

Hence, the circumference of the wheel is 11m.

Now, we have to convert distance covered km into m:

\({\leadsto{\large{\rm{ \: Distance \: Covered = 22km}}}}\)

\({\leadsto{\large{\rm{ \: Distance \: Covered =(22 \times 1000)m }}}}\)

\({\leadsto{\large{\rm{ \: Distance \: Covered = {\boxed{\rm{\red{22000m}}}}}}}}\)

Hence, the distance covered is 22000m.

Now, we have to find the number of revolution:

Given:

According to the question by using the formula, we get:

\( \bigstar \: { \boxed{ \large{ \rm{Number \: of \: Revolution \: = \: \frac{Distance \: Covered}{Circumference }}}}}\)

\({ \large{ \longrightarrow{ \rm{Number \: of \: Revolution = \frac{22000}{11} }}}}\)

\({ \large{ \longrightarrow{ \rm{Number \: of \: Revolution = { \boxed{\red{2000}}}}}}}\)

Answer:

2(x-10)+4=-6x+2

2x-20+4= -6x+2

2x-16=-6x+2

2x+6x=2+16

8x=18

x=18/8

x=9/4

Answer:

i = 0.06

n = 108

Step-by-step explanation:

Rate per period:

This is the interest rate, as a decimal.

In this question, the interest rate is 6%. As a decimal, this is 0.06.

So i = 0.06

Number of periods:

The compounding happens monthly.

So 1 period is 1 month.

The payments are made for 9 years, and each year has 12 months.

9*12 = 108

So n = 108R

The mean and standard deviation of the sample proportion are 0.2 and 0.04. The correct option is 0.2 and 0.04.

Based on the information provided, we can infer that the random samples of size 100 were taken from an infinite population with a population proportion of 0.2. This means that 20% of the population exhibits a certain trait or characteristic of interest.

The mean of the sample proportion is also 0.2, which is the same as the population proportion. This suggests that the sample is representative of the population and that the sample was drawn randomly.

The standard deviation of the sample proportion is 0.04, or 4%. This indicates that there is some variability in the sample proportions. However, it is not too high and suggests that the sample is reliable and consistent.

In conclusion, based on the mean and standard deviation of the sample proportion, we can say that the sample is representative of the population and that the estimates obtained from the sample are reliable and accurate. It is important to note that the size of the sample is relatively large (100) and this helps to increase the accuracy and precision of the estimates. The correct option is 0.2 and 0.04.

The complete question is;

Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are

0.2 and .04

0.2 and 0.2

20 and .04

20 and 0.2

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After interpreting the given data we come to the conclusion that the conversion of the given standard form to vertex form is y = 2(x - 2)² - 4.

In order to convert the quadratic equation from standard form to vertex form, we have to complete the square.
2x² - 8x + 4 = 2(x² - 4x) + 4
Now we have to add and subtract a constant inside the parenthesis so that we can factorize it into a perfect square.
The constant we need to add is (b/2a)².
For this case,
a = 2 and b = -8.
2(x² - 4x + 4) - 8 + 4 = 2(x - 2)² - 4
Hence, the vertex form of the quadratic equation is:
y = 2(x - 2)² - 4
The vertex of this parabola is (2,-4).
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Answer:

4

Step-by-step explanation:

Answer:

The answer is D. 4

Step-by-step explanation:

plz mark brainliest

The inverse function of f(x) = 2x + 12 is: f⁻¹(x) = (x - 12)/2

The inverse function of f(x) = 5x - 1/2 is: f⁻¹(x) = (2x + 1)/10

Given the functions are,

f(x) = 2x + 12

f(x) = 5x - 1/2

We have to find the inverse function for the each given functions.

For f(x) = 2x + 12:

Let f(x) = y

2x + 12 = y

2x = y - 12

x = (y - 12)/2

So, f⁻¹(y) = (y - 12)/2

Therefore, f⁻¹(x) = (x - 12)/2

For f(x) = 5x - 1/2:

Let f(x) = y

5x - 1/2 = y

(10x - 1)/2 = y

10x - 1 = 2y

10x = 2y + 1

x = (2y + 1)/10

So, f⁻¹(y) = (2y + 1)/10

Therefore, f⁻¹(x) = (2x + 1)/10

Hence the required inverse functions are:

f⁻¹(x) = (x - 12)/2

f⁻¹(x) = (2x + 1)/10 respectively.

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The complex number -4 + 4√3i can be written in a trigonometric form as \(8(cos(-\pi/3) + isin(-\pi/3)).\) Option D.

To convert the complex number to trigonometric form, we need to find its magnitude and argument.

The magnitude (r) can be calculated using the formula r = \(\sqrt(a^2 + b^2),\) where a and b are the real and imaginary parts of the complex number, respectively.

In this case, a = -4 and b = 4√3.

So, r = \(\sqrt((-4)^2 + (4\sqrt3)^2) = \sqrt(16 + 48) = \sqrt64\)

= 8.

The argument (θ) can be found using the formula θ = arctan(b/a). In this case, θ = arctan((4√3)/-4) = arctan(-√3) = -π/3.

Therefore, the complex number -4 + 4√3i can be written in a trigonometric form as \(8(cos(-\pi/3) + isin(-\pi/3)).\) Option D.

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Answer:

The length of arc PRQ is 16.7 in.

Step-by-step explanation:

So,

arc length = 2πr × (θ/360)

arc length = 2(3.14)(8) × (120/360)

arc length = 2(3.14)(8) × (120/360)

arc length = 50.24 × (1/3)

arc length = 16.7 inches

Thus, The length of arc PRQ is 16.7 in.

Answer:

(x - 1)² + (y - 1)² = 8

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (1, 1 ) and r has to be found

the radius r is the distance from the centre to any point on the circle

calculate r using the distance formula

r = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = P (1, 1 ) and (x₂, y₂ ) = B (- 1, 3 )

r = \(\sqrt{(-1-1)^2+(3-1)^2}\)

  = \(\sqrt{(-2)^2+2^2}\)

  = \(\sqrt{4+4}\)

  = \(\sqrt{8}\)

then equation of circle is

(x - 1 )² + (y - 1)² = (\(\sqrt{8}\) )² , that is

(x - 1)² + (y - 1)² = 8

Answer:

b, and c

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

\(tan \: A = \frac{2 \sqrt{a} }{a - 1} ...(given) \\ \because \: {sec}^{2} \: A = 1 + {tan}^{2}\: A \\ \therefore\: {sec}^{2} \: A = 1 + \bigg(\frac{2 \sqrt{a} }{a - 1} \bigg)^{2} \\\\ \hspace{38 pt} = 1 + \frac{4a}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{(a - 1)^{2} + 4a}{ {(a - 1)}^{2} } \\ \\\hspace{38 pt} = \frac{a^{2} - 2a + 1+ 4a}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{a^{2} + 2a+ 1}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{(a + 1)^{2}}{ {(a - 1)}^{2} } \\ \\ \therefore {sec}^{2} \: A = \bigg(\frac{a + 1}{ {a - 1}} \bigg) ^{2} \\ \\ \therefore \: {sec} \: A = \pm \bigg(\frac{a + 1}{ {a - 1}} \bigg)\\ \\ \)

In the question It is not mentioned that in which quadrant does angle A lie, so we will assume it to be in first quadrant.

\( \therefore \: {sec} \: A = \bigg(\frac{a + 1}{ {a - 1}} \bigg)\\ \\

\red{ \boxed{ \bold{\therefore \: {cos} \: A = \bigg(\frac{a - 1}{ {a + 1}} \bigg)}}} \\ \\ {sin} \: A ={cos} \: A \times {tan} \: A \\ \\ \hspace{25 pt}=\bigg(\frac{a - 1}{ {a + 1}} \bigg) \times \frac{2 \sqrt{a} }{a - 1} \\ \\ \purple {\boxed { \bold{{sin} \: A = \frac{2 \sqrt{a} }{a + 1}}}}\)

la respuesta es b. 9/100

Answer:

\(-\frac{1}{5} t^{15}\)

Step-by-step explanation:

sry if im wrong

Answer:

$35,000.00 - $1,000.00 = 34,000.00

(a) The domain of the function y = f(x) + 2 is D = (7, 11], R = [6, 16]

(b) The domain of the function y = f(x + 2) is D = (5, 9], R = [4, 14]

(a) The domain of the function y = f(x) + 2 is the same as the domain of the function f(x), which is (7, 11]. The range of the function y = f(x) + 2 is obtained by adding 2 to the endpoints of the range of f(x), which is [4, 14]. Therefore, the range of y = f(x) + 2 is [6, 16].

(b) The domain of the function y = f(x + 2) is obtained by subtracting 2 from the endpoints of the domain of f(x), which is (7, 11]. So the domain of y = f(x + 2) is (5, 9]. The range of the function y = f(x + 2) is the same as the range of the function f(x), which is [4, 14]. Therefore, the range of y = f(x + 2) is [4, 14].

In summary, for the function y = f(x) + 2, the domain is (7, 11] and the range is [6, 16]. For the function y = f(x + 2), the domain is (5, 9] and the range is [4, 14].

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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A) The corresponding unit rate for each package is,

For Cannie cakes;

⇒ $1.85

Bark bits;

⇒ $2.25

Woofy Waffles;

⇒ $1.9

B) The best buy by the units rates is, Cannie cakes.

We have to given that;

Jeremiah needed dog food for his new pippy.

Now, We get;

A) The corresponding unit rate for each package is,

For Cannie cakes;

⇒ 74/40

⇒ $1.85

Bark bits;

⇒ 27/12

⇒ $2.25

Woofy Waffles;

⇒ 76 / 40

⇒ $1.9

Hence, We get;

B) The best buy by the units rates is, Cannie cakes.

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Marginal relative frequency of customers liking hamburgers is 53.66%, calculated by dividing 110 customers by 205, resulting in a value of 0.5366.

To find the marginal relative frequency of all customers that like hamburgers, we need to divide the number of customers who like hamburgers by the total number of customers.

According to the given data, there are 110 people who like hamburgers out of a total of 205 people.

Marginal relative frequency of customers who like hamburgers = (Number of customers who like hamburgers) / (Total number of customers)
= 110 / 205

To calculate the exact value, we divide 110 by 205:
Marginal relative frequency of customers who like hamburgers = 0.5366

Therefore, the marginal relative frequency of all customers who like hamburgers is approximately 0.5366 or 53.66%.

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Answer:

original price was 64 dollars

Step-by-step explanation:

Answer:

$15.80

Step-by-step explanation:

20% of 16, or 1/5 of 16, is 3.2. So we subtract 3.2 from 16

16 - 3.2 = 15.8

So, in dollar form, it is $15.80

So the final cost of the pair of gloves is $15.80

Answer:

please see photo attached for detailed analysis.

The dimension of the subspace is 3 which is a basis for the subspace spanned by the given vectors from exercises 13 and 14.

An augmented matrix in linear algebra is a matrix that is created by adding the columns of two specific matrices, often to resolve the achievement of the identical fundamental row operations on each of the particular matrices. The subspace covered by the provided vectors and its dimension need to have a basis.

Every basis of a subspace S contains exactly the same number of vectors; this quantity is the subspace's dimension. Write the vectors as rows of a matrix, then row reduce the matrix to determine the basis for the span of the collection of vectors. The row space of a matrix is the distance between its rows. The solution can be seen on the attached image.

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Question correction:

See on one of the attached image.

Using Mathematica, we can find the roots of the function y = x^3 Exp[-x] Sin[2x] by substituting x = 3t and evaluating the expression for t in the range [0,1]. The roots correspond to the values of t where the function crosses the x-axis.

To find the roots of the given function, we substitute x = 3t into the expression y = x^3 Exp[-x] Sin[2x]. This gives us y = (3t)^3 Exp[-3t] Sin[2(3t)]. Simplifying further, we have y = 27t^3 Exp[-3t] Sin[6t].

Using Mathematica, we can evaluate this expression for t values ranging from 0 to 1. The roots of the function correspond to the values of t where y equals zero, indicating that the function crosses the x-axis. By plotting the function or using numerical methods such as FindRoot or NSolve in Mathematica, we can determine the values of t where y = 0, thus finding the roots of the function.

In summary, by substituting x = 3t and evaluating the expression y = x^3 Exp[-x] Sin[2x] for t in the range [0,1] using Mathematica, we can find the roots of the function, which represent the values of t where the function crosses the x-axis.

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In a case, 96 is the only maximal element. In b case, 2 is the only minimal element, in c case, there is no greatest element, in d case, there is no least element and in e case, the greatest lower bound of {48, 60} is 12.

To answer these questions, let's first create the Hasse diagram for the poset ({2, 6, 8, 12, 18, 36, 48, 60, 96}, ∣), where "I" represents the "divides" relation:

markdown

Copy code

                  96

                 /  \

               48   60

                |    |

                18   |

                 \  /

                  12

                  |

                   6

                  / \

                 2   8

a. Maximal elements: Maximal elements are the elements that have no elements greater than them in the poset. In this case, 96 is the only maximal element.

b. Minimal elements: Minimal elements are the elements that have no elements smaller than them in the poset. In this case, 2 is the only minimal element.

c. Greatest element: A greatest element is an element that is greater than or equal to every other element in the poset. In this case, there is no greatest element.

d. Least element: A least element is an element that is smaller than or equal to every other element in the poset. In this case, there is no least element.

e. Upper bounds of {8, 12}: An upper bound of a set is an element that is greater than or equal to every element in the set. In this case, the upper bounds of {8, 12} are 18, 36, 48, 60, 96.

f. Least upper bound of {8, 12}: The least upper bound (also known as the supremum) of a set is the smallest element that is greater than or equal to every element in the set. In this case, the least upper bound of {8, 12} is 18.

g. Lower bounds of {48, 60}: A lower bound of a set is an element that is smaller than or equal to every element in the set. In this case, the lower bounds of {48, 60} are 2, 6.

h. Greatest lower bound of {48, 60}: The greatest lower bound (also known as the infimum) of a set is the largest element that is smaller than or equal to every element in the set. In this case, the greatest lower bound of {48, 60} is 12.

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