Assume 0 is an acute angle.
cot 0 =
4
3

As per the given data, the area of the rectangular field is approximately 204 square meters.

To find the area of the rectangular field, we need to multiply its length by its width.

Given that the length is 18 2/5 m and the width is 11 2/23 m, we need to convert these mixed fractions into improper fractions for easier calculation.

Length: 18 2/5 m = (5 * 18 + 2)/5 = 92/5 m

Width: 11 2/23 m = (23 * 11 + 2)/23 = 255/23 m

Now, we can calculate the area of the rectangular field:

Area = Length * Width

     = (92/5) m * (255/23) m

     = (92 * 255)/(5 * 23) m^2

     = 23460/115 m^2

     = 204 m^2 (rounded to the nearest whole number)

Therefore, the area of the rectangular field is approximately 204 square meters.

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Your question seems incomplete, the probable complete question is:

A rectangular field is 18 2/5 m long and 11 2/23 m wide. Find its area. ​

The function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.

The given table is

Days After                        Number of

Release Date                   Games sold

       0                                   1024

       1                                     512

       2                                     256

       3                                     128

Here, the common ratio = 512/1024

= 1/2

The formula to find nth term of the geometric sequence is aₙ=arⁿ⁻¹. Where, a = first term of the sequence, r= common ratio and n = number of terms.

Here, [tex]G(t)= 1024(0.5)^{t-1[/tex]

Therefore, the function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.

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The best representation of the number of tiles that will be needed to cover the Floor is 80 tiles.

The number of tiles needed to cover the floor, we can calculate the total area of the floor and divide it by the area of each tile.

The area of the floor is given by the product of its length and width: 15 feet * 12 feet = 180 square feet.

The area of each tile is given by the product of its length and width: 1.5 feet * 1.5 feet = 2.25 square feet.

To find the number of tiles needed, we divide the total area of the floor by the area of each tile:

Number of tiles = (Total area of the floor) / (Area of each tile) = 180 square feet / 2.25 square feet = 80 tiles.

therefore, the best representation of the number of tiles that will be needed to cover the floor is 80 tiles.

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Answer: C

Step-by-step explanation:

|-8| = 8

x+77=180

x=180-77=103°

x+5y-98=180

=> 103+5y-98=180

=> 5y=180-5

=> y=175/5=35°

To determine the radius of each wheel, we can use the formula for the circumference of a circle:

Circumference = 2πr,

where "Circumference" represents the circumference of the wheel and "r" represents the radius of the wheel.

Given that the circumference of each wheel is 22 inches, we can set up the equation as follows:

22 = 2πr.

To solve for the radius, we'll isolate "r" by dividing both sides of the equation by 2π:

22 / (2π) = r.

Using a calculator for the approximation, we get:

r ≈ 3.5 inches.

Therefore, to the nearest length, the radius of each wheel is approximately 3.5 inches.

Answer:

C) 3.5 inch

Step-by-step explanation:

"dom(R) ⊂ UU R" means that the domain of relation R is a subset of the universal set associated with relation R

The notation "dom(R) ⊂ UU R" refers to the domain of a relation R being a subset of the universal set U.

Let me help you to break it down

1. dom(R): This represents the domain of the relation R. The domain of a relation is the set of all elements that appear as the first component in any ordered pair of the relation.

2. ⊂: This symbol indicates a subset relationship, meaning that the set on the left-hand side is a subset of the set on the right-hand side. In this case, "dom(R) ⊂ U" implies that the domain of relation R is a subset of the universal set U.

3. "UU R": The term "UU R" likely represents the universal set associated with relation R. It indicates the set that contains all possible elements that can be related by R.

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41.

Out of the 18 parts, we shade 5 parts

Out of the 27 parts, we shade 4 parts

42.

There are 60 pieces.

43.

The fractional part for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

We have,

41.

a.

1/3 x 5/6

= 5/18

This means,

Out of the 18 parts, we shade 5 parts

b.

2/9 x 2/3

= 4/27

This means,

Out of the 27 parts, we shade 4 parts

42.

String = 15 feet

Length of each piece = 1/4 feet

Now,

The number of 1/4 feet pieces.

= 15/(1/4)

= 15 x 4

= 60 pieces

43.

Original pizza = 1

Half pizza = 1/2

Number of people = 3

Now,

The fractional part for each person.

= 1/2 ÷ 3

= 1/6

44.

a.

7/6 x 9

= 7/2 x 3

= 21/2

= 10(1/2)

b.

1/7 ÷ 3

= 1/(7 x 3)

= 1/21

c.

4/5 x 3(2/3)

= 4/5 x 11/3

= 44/15

= 2(14/15)

d.

2 ÷ 1/9

= 2 x 9/1

= 18

Thus,

41.

Out of the 18 parts, we shade 5 parts

Out of the 27 parts, we shade 4 parts

42.

There are 60 pieces.

43.

The fractional part for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

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The test statistic χ² is approximately 1.47.

We have,

To test independence for the contingency table, we need to calculate the test statistic.

The most commonly used test statistic for testing independence in a 2x2 contingency table is the chi-square test statistic.

The chi-square test statistic (χ²) is calculated using the formula:

χ² = Σ [(Observed - Expected)² / Expected]

Where:

Σ represents the sum over all cells of the contingency table.

Observed is the observed frequency in each cell.

Expected is the expected frequency in each cell if the variables were independent.

First, we calculate the expected frequencies for each cell. To do this, we use the formula:

Expected frequency = (row total x column total) / grand total

Grand total = sum of all frequencies = 36 + 17 + 15 + 11 = 79

Expected frequency for the cell "Closed roof - Win" = (53 * 51) / 79 = 34.49

Expected frequency for the cell "Closed roof - Loss" = (53 * 28) / 79 = 18.51

Expected frequency for the cell "Open roof - Win" = (26 * 51) / 79 = 16.51

Expected frequency for the cell "Open roof - Loss" = (26 * 28) / 79 = 9.49

Now, we can calculate the test statistic using the formula:

χ² = [(36 - 34.49)² / 34.49] + [(17 - 18.51)² / 18.51] + [(15 - 16.51)² / 16.51] + [(11 - 9.49)² / 9.49]

Calculating each term and summing them up:

χ² ≈ 0.058 + 0.482 + 0.58 + 0.35 ≈ 1.47

Therefore,

The test statistic χ² is approximately 1.47.

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In the excerpt, Li's crush gave his girl   friend a rose. The text states: Li's crush gave his girl   friend a rose. She was so happy!

Li's mother was upset about the gift later because she thought it was too expensive.

The text states: Li's mother was upset when she found out how much the rose cost. She thought it was too much money to spend on a gift.

Li's mother's reaction is understandable. Roses are expensive flowers, and it is possible that Li's mother did not have the money to spend on such a gift. However, it is also important to remember that Li's crush was trying to do something nice for his girl friend, and the rose was a symbol of his love for her. In the end, it is up to Li and his girl friend to decide whether or not the rose was worth the money.

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The answer to this question: B

We can deduce here that in the diagram the ratios  AD : DB  and  AE : EC  are equal.

Triangles that resemble one another but may differ in size are said to be similar triangles. They have equal corresponding angles and proportional corresponding sides, in other words.

Two triangles are similar if and only if the following conditions are met:

The corresponding sides of two triangles that are comparable are proportionate. The length of the comparable side in the other triangle can be obtained by multiplying the length of a side in one triangle by the same factor.

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Answer:

Step-by-step explanation:

To find the measure of angle A

This is not a question. Next time, please add a question so that others might be able to help you with it

a = 30°

b = 180-135 = 45°

total angle inside triangle = 180°

x = 180-(30+45) = 105°

Answer: The Mode

Step-by-step explanation:

The mode is the data value that occurs the most often in a data set

The required reverse Euclidean algorithm is the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Given that (5*x) mod 91 =32.

To solve the modular equation (5*x) mod 91 =32 using reverse Euclidean algorithm is to find the modular inverse of 5 modulo 91.

Consider  (5*x) mod 91 =32.

5x = 32(mod 91)

Apply the Euclidean algorithm to find GCD of 5 and 91 is

91 = 18 * 5 + 1.

Rewrite it in congruence form,

1 = 91 - 18 *5

On simplifying the equation,

1 = 91 (mod 5)

The modular inverse of 5 modulo 91 is 18.

Multiply equation by 18 on both sides,

90x = 576 (mod91)

To obtain the smallest positive  solution,

91:576 = 6 (mod 91)

Divide both sides by the coefficient of x:

x = 6 * 90^(-1).

Apply the Euclidean algorithm,

91 = 1*90 + 1.

Simplify the equation,

1 + 1 mod (90)

The modular inverse of 90 modulo 91 is 1.

Substitute the modular inverse in the given question gives,

x = 6*1(mod 91)

x= 6 (mod91)

Therefore, the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

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The solution to the given differential equation is y(x) = (C1 + C2x) * e^(3x), where C1 and C2 are arbitrary constants.

To solve the given differential equation, we need to find the function y(x) that satisfies the equation:

(D^2 - 6D + 9)y(x) = 0,

where D represents the differentiation operator.

Let's break down the solution process step by step:

Characteristic Equation

First, we'll find the characteristic equation associated with the given differential equation. For a second-order linear homogeneous differential equation of the form aD^2y + bDy + cy = 0, the characteristic equation is obtained by replacing D with λ:

λ^2 - 6λ + 9 = 0.

Solving the Characteristic Equation

Now, we solve the characteristic equation to find the values of λ. Factoring the equation, we get:

(λ - 3)^2 = 0.

From this, we see that λ = 3 (with a multiplicity of 2).

General Solution

The general solution of the differential equation is given by:

y(x) = C1e^(λ1x) + C2xe^(λ2*x),

where C1 and C2 are arbitrary constants, and λ1, λ2 are the distinct roots of the characteristic equation.

In our case, since we have repeated roots, the general solution simplifies to:

y(x) = C1e^(3x) + C2xe^(3*x).

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Let's denote the total number of books on the shelf as 'total_books', and the number of new books as 'new_books'.

The number of used books can be calculated as the difference between the total number of books and the number of new books:

used_books = total_books - new_books

To find the ratio of used books to all books on the shelf, we divide the number of used books by the total number of books:

Ratio of used books to all books = used_books / total_books

Substituting the expression for used_books, we have:

Ratio of used books to all books = (total_books - new_books) / total_books

Simplifying further:

Ratio of used books to all books = 1 - (new_books / total_books)

Therefore, the ratio of used books to all books on the shelf is equal to 1 minus the ratio of new books to total books.

The average fourth grader is about three times as tall as the average newborn baby. If babies are on average 45 cm 7 mm when they are born,  137 cm 1 mm is the height of the average fourth grader.

Given information,

Baby height is typically 45 cm. 7 mm 45 cm Since there are 10 millimeters in a centimeter, 7 mm is equal to 45.7 cm.

Assume that a fourth-grader is x inches tall.

The average height of a newborn baby (x) = 3 times the height of a fourth-grader.

A fourth-grader's height (x) is equal to 3 x 45.7.

A fourth-grader's height is equal to (x)=137.

Fourth-grader height (x) = 137 cm 1 millimeter

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log 161 can be expressed as log 7 + log 23 in the form of loga + logb.

To express log 161 in the form of loga + logb, first we need to find suitable values for a and b such that their logarithmic product is equal to log 161.

Let's find the factors of 161 :

161 = 7 * 23

Now, we can express log 161 as product of two logarithms :

log 161 = log (7 + 23)

Using the logarithmic property log(a*b) = log a + log b :

log 161 = log 7 + log 23

Therefore, log 161 can be expressed as log 7 + log 23.

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Answer: Distribute the 10 on the left side of the equation:

10n + 30 = 1,000,000

Subtract 30 from both sides of the equation to isolate the term with n:

10n = 1,000,000 - 30

10n = 999,970

Divide both sides of the equation by 10 to solve for n:

n = 999,970 / 10

n = 99,997

Therefore, the value of the variable n that satisfies the equation 10(n + 3) = 1,000,000 is n = 99,997.

Step-by-step explanation:

" Sum of area of Trapezoid and Semicircle "

its " 1/2 times (sum of parallel sides) times (perpendicular distance between them) "

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times ( 8+ 12) \times (5.5)[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times (20) \times (5.5)[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 10 \times 5.5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 55 \: \: cm {}^{2} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi {r}^{2} }{2} [/tex]

[tex] \textsf{[ diameter (d) = 8 cm, radius (r) = d/2 = 8/2 = 4 cm ]} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{3.14 \times ( {4)}^{2} }{2}[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 1.57 \times 16[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 25.12 \: \: cm {}^{2} [/tex]

- Area of Trapezoid + Area of Semicircle

[tex]\qquad\displaystyle \tt \dashrightarrow \: 55 + 25.12 = 80.12 \: cm²[/tex]

Answer:
To find the volume of a cone with radius 9 feet and height 4 feet, we can use the formula:

V = (1/3) * π * r^2 * h

Plugging in the values:

V = (1/3) * π * (9^2) * 4

Calculating:

V = (1/3) * π * 81 * 4

V ≈ 108.19 cubic feet

Therefore, the volume of the cone is approximately 108.19 cubic feet (rounded to two decimal places)

The coordinates of the vertices of the image F'G'H' after reflecting FGH across the y-axis are:

F' = (2, -1)

G' = (-2, 2)

H' = (-4, -3)

We have,

When reflecting a point across the y-axis, the x-coordinate of the point is negated while the y-coordinate remains the same.

Applying this transformation to each vertex, we get:

F' = (-(-2), -1) = (2, -1)

G' = (-(2), 2) = (-2, 2)

H' = (-(4), -3) = (-4, -3)

Therefore,

The coordinates of the vertices of the image F'G'H' after reflecting FGH across the y-axis are:

F' = (2, -1)

G' = (-2, 2)

H' = (-4, -3)

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The formulas that represent the linear function in this problem are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The line has a slope of 2/3, hence:

y = 2x/3 + b.

When x = 1, y = 2, hence the intercept b is obtained as follows:

2/3 + b = 2

b = 6/3 - 2/3

b = 4/3.

Hence the slope-intercept equation of the line is given as follows:

f(x) = 2x/3 + 4/3.

The line goes through points (1,2) and (4,4), hence the point-slope equations to the line are given as follows:

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