The rectangular rug is similar to the rectangular floor. If the floor of the room measures 32 feet in length and 26 feet in width, what is the width of the rug?

The value of x is approximately equals to 30.4 and the value of r is approximately 9.24.

What is circle ?

In geometry, a circle is a two-dimensional shape consisting of all points that are a fixed distance (called the radius) from a given point (called the center). A circle is a set of points that are equidistant from the center.

Is DE tangent to circle C?

Yes, DE is tangent to circle C. This is because a tangent to a circle is a line that intersects the circle at exactly one point, and in this case, DE intersects circle C at point E and only touches the circle at that point.

ST is tangent to circle Q. Find the value of r.

Since ST is tangent to circle Q at point T, the radius of the circle Q is perpendicular to ST at T. Therefore, triangle SRT is a right triangle, where RS is the hypotenuse and ST is the adjacent side to the angle at S. We can use the Pythagorean theorem to find the length of the hypotenuse:

We know that ST = 10 and RT = r, so we can substitute these values to get:

[tex]RS^{2}[/tex] = 100+ [tex]r^{2}[/tex]

We also know that RS = 2r, so we can substitute this value to get:

4[tex]r^{2}[/tex]= 100 + [tex]r^{2}[/tex]

3[tex]r^{2}[/tex] = 100

[tex]r^{2}[/tex] = 100/3

r ≈ 9.24

Therefore, the value of r is approximately 9.24.

Find the value(s) of x.

Since AB is a diameter of circle C, triangle ABC is a right triangle with right angle at B. Therefore, we can use the Pythagorean theorem to find the length of BC:

We know that AB = 26 and AC = x + 8, so we can substitute these values to get:

[tex](x + 8)^{2}[/tex]= 676 + [tex]BC^{2}[/tex]

We also know that BC = x - 2, so we can substitute this value to get:

[tex](x + 8)^{2}[/tex]= 676 + [tex](x - 2)^{2}[/tex]

[tex]x^{2}[/tex]+ 16x + 64 = 676 + [tex]x^{2}[/tex]- 4x + 4

20x = 608

x = 30.4

Therefore, the value of x is 30.4.

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Answer: The pool is 40 feet long.

Step-by-step explanation:  60ft) = 2 x 100ft = 200ft. Answer. The pool is    40 feet long.

Answer:

5cm^3

Step-by-step explanation:

Answer:

y = 5

Step-by-step explanation:

3(3y-8)=21

expand:

9y - 24 = 21

+24 to both sides to get 9y on its own.

9y = 45

divide both sides by 9 to get y on its own.

therefore

y = 5

hope this makes sense!

Answer: Solve for

y

by simplifying both sides of the equation, then isolating the variable.    

y≈−1.21698677,2.94165923

Step-by-step explanation:

Answer:

277.5

Step-by-step explanation:

first you multiply 37 * 90 then you get 3330 then you divide it by 12 and you get 277.5

Therefore, the rotated triangle has vertices at (-5, -10), (-3, -1), and (-4, -2), which forms a new triangle.

In mathematics, a vertex refers to a point where two or more lines, edges, or curves meet. In geometry, a vertex is a point where two or more edges of a polygon or polyhedron intersect. For example, in a triangle, each of the three points where the sides meet is a vertex.

A vertex is a fundamental unit of a graph, which is a collection of vertices connected by edges. Each vertex represents an entity or object, and the edges represent the relationships or connections between them. For example, in a social network graph, the vertices could represent individual users, and the edges could represent their friendships or connections with other users.

To perform a 270° counterclockwise rotation of a point about a center point, we can use the following formula:

[tex](x', y') = (x - a) * cos(theta) - (y - b) * sin(theta) + a, (x - a) * sin(theta) + (y - b) * cos(theta) + b[/tex]

where (x, y) is the original point, (x', y') is the rotated point, (a, b) is the center point, and theta is the angle of rotation in radians.

Let's first find the center point C(-5, -4) of the rotation. Then, we'll apply the formula to each vertex of the triangle to find its new location after the rotation.

[tex]Center point C = (-5, -4)[/tex]

Vertex P(-13, -3):

[tex]x' = (-13 - (-5)) * cos(270^{0} ) - (-3 - (-4)) * sin(270^{0} ) + (-5) = -5[/tex]

[tex]y' = (-13 - (-5)) * sin(270) + (-3 - (-4)) * cos(270) + (-4) = -10[/tex]

So, after the rotation, vertex P is at (-5, -10).

Vertex Q(-7, 3):

[tex]x' = (-7 - (-5)) * cos(270) - (3 - (-4)) * sin(270) + (-5) = -3[/tex]

[tex]y' = (-7 - (-5)) * sin(270) + (3 - (-4)) * cos(270) + (-4) = -1[/tex]

So, after the rotation, vertex Q is at (-3, -1).

Vertex R (-6, 2):

[tex]x' = (-6 - (-5)) * cos(270) - (2 - (-4)) * sin(270) + (-5) = -4\\y' = (-6 - (-5)) * sin(270) + (2 - (-4)) * cos(270) + (-4) = -2[/tex]

So, after the rotation, vertex R is at (-4, -2).

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Answer:

Step-by-step explanation:

In the proportion, Gear A makes 120 turns when Gear B makes 90 turns.

What is Proportion?

A proportion is a statement that two ratios or fractions are equal. It shows the relationship between two or more quantities that are proportional to each other.

The gears have a fixed ratio of rotations, which is determined by the number of teeth on each gear.

To find out how many turns Gear A makes when Gear B makes 90 turns, we can set up a proportion:

=> [tex]\frac{36}{27} =\frac{ x}{90}[/tex]

where x is the number of turns Gear A makes.

To solve for x, we can cross-multiply:

=> 36 × 90 = 27 × x

=> 3240 = 27x

=> x = 120

Therefore, Gear A makes 120 turns when Gear B makes 90 turns.

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Based on the general properties of the MAD and the characteristics of the data sets, these matches seem reasonable.

In statistics, a dataset is a collection of data that is organized in a specific way. Typically, a dataset consists of multiple data points, where each data point represents an observation or measurement of a particular variable or set of variables.

We can make some general observations to match the data sets to the appropriate MAD value without actually calculating them:

The MAD measures the average distance between each data point and the median of the data set.

Therefore, the larger the MAD value, the more spread out the data set is.

Data set 1 will have the smallest MAD value, since it is the most tightly clustered around the median.

Data set 3 will have the largest MAD value, since it is the most spread out around the median.

Data set 2 will have a MAD value between those of data sets 1 and 3.

Based on these observations, we can match the data sets to the appropriate MAD value as follows:

Data set 1 has the smallest MAD value (7).

Data set 2 has a medium MAD value (9).

Data set 3 has the largest MAD value (11).

Of course, without actually calculating the MAD values, we can't say for certain whether these matches are correct.

Therefore, based on the general properties of the MAD and the characteristics of the data sets, these matches seem reasonable.

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Scott Salman's net pay after subtracting all of his deductions is $1,620.26.

How To calculate Scott Salman's net pay?

To calculate Scott Salman's net pay, we need to first calculate his commission earnings and then subtract all of his deductions.

Commission Earnings:

3% of the first $20,000 in sales = $600

4% of the next $10,000 in sales = $400

6% of all sales over $30,000 = 6% × ($45,550 - $30,000) = $930

Total commission earnings = $600 + $400 + $930 = $1,930

Now we can calculate his gross pay by adding his commission earnings to his base salary:

Gross Pay:

Base salary = 0 (not given)

Commission earnings = $1,930

Total gross pay = $1,930

Next, we need to calculate his deductions. We'll assume the following rates for each deduction:

FICA: 7.65%

Medicare: 1.45%

Federal withholding: based on the IRS tax tables (not provided)

State disability insurance: 1%

State withholding: based on the state tax tables (not provided)

Retirement contribution: $45

Savings bond: $50

Charitable contributions: $20

Deductions:

FICA = 7.65% × $1,930 = $147.45

Medicare = 1.45% × $1,930 = $27.99

Federal withholding = based on the IRS tax tables (not provided)

State disability insurance = 1%×$1,930 = $19.30

State withholding = based on the state tax tables (not provided)

Retirement contribution = $45

Savings bond = $50

Charitable contributions = $20

Total deductions = $147.45 + $27.99 + $19.30 + $45 + $50 + $20 = $309.74

Finally, we can calculate Scott Salman's net pay by subtracting his total deductions from his gross pay:

Net Pay:

Gross pay = $1,930

Total deductions = $309.74

Net pay = $1,930 - $309.74 = $1,620.26

Therefore, Scott Salman's net pay after subtracting all of his deductions is $1,620.26.

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Since it is less than 5, we do not round up, and our final answer is 2.00.

Decimal rounding is a process of changing a number to a certain number of decimal places, based on a specified rounding rule. In decimal rounding, the digits to the right of the specified decimal place are examined to determine whether rounding is necessary. If the digit immediately to the right of the specified decimal place is 5 or greater, the number is rounded up by adding 1 to the last digit of the specified decimal place. If the digit is less than 5, the number is rounded down by simply dropping the digits to the right of the specified decimal place.

(a).   To round 1 to 1 significant figure, we only keep the leftmost digit, which is 1. Therefore, 1 rounded to 1 significant figure is 1.

(b) . To write 2 as a decimal rounded to 3 significant figures, we start by identifying the leftmost significant digit. In this case, it is the digit 2. We then count two more digits to the right, which gives us 2.00. Finally, we look at the next digit, which is 0. Since it is less than 5, we do not round up, and our final answer is 2.00.

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Answer: i'm going to assume, this needs to be a full answer

meaning this would be

43.9823 inches (or 44 if fully rounded)

basically, to find arc length, you take the given degrees shown (210) and divide it over the full length of the circle (360)

dividing this gives us 58.333333 (repeated forever) or 7/12

then we need to find the circumference, which is c=pid (or c=pi times diameter)

so we would do 24 multiplied by 3.14159 (this is standard amount of numbers for naturally calculating pi in equations) and we get 75.39816

finally, we need to multiply 75.39816 to 7/12, and we will get 43.98226

which when rounded to the 4th digit will give us 43.9823

Answer with step-by-step explanation:

The formula to find the arc length of a circle is:

[tex]\sf \red {Arc\: length = \frac{\theta}{360} *2 \pi r}[/tex]

PQ major arc length

[tex]\sf Arc\: length = \frac{\theta}{360} *2 \pi r\\\\\sf Arc\: length = \frac{210}{360} *2 \pi*12\\\\\sf Arc\: length = \frac{15825.6}{360} \\\\\sf Arc\: length = 43.96\: in[/tex]

PQ minor arc length

[tex]\sf Arc\: length = \frac{\theta}{360} *2 \pi r\\\\\sf Arc\: length = \frac{150}{360} *2 \pi*12\\\\\sf Arc\: length = \frac{11304}{360} \\\\\sf Arc\: length = 31.4\: in[/tex]

Scatterplots and correlation never prove causation. Causation may only be determined by well-designed experiments.

A scatterplot is a type of graph commonly used to observe and visually represent the relationships between variables. Variable values ​​are represented by dots. The position of the points on the vertical and horizontal axes indicates the value of each data point. Therefore, scatterplots use Cartesian coordinates to display the values ​​of the variables in the dataset. A scatterplot is also called a scatter graphs, scatter charts, or scattergrams.

Correlation means association, and more specifically, it measures how well two variables are related. Correlation analysis have three possible outcomes: Positive correlation, negative correlation, no correlation.

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Step-by-step explanation:

So what this question is asking is the volume of the cube. volume can be found with V=lwh or V=l^3 because it is a cube. So

V=(8)^3
V=512

The cube can fit 512 cubic inches.

Answer: Let's denote the length, width, and height of the cuboid as l, w, and h, respectively. We know that the shaded face is a square, which means that two of its dimensions are the same. Without loss of generality, let's assume that the dimensions of the square face are l and w.

Since the volume of the cuboid is 4900 cm³, we have:

lwh = 4900

Substituting l = 25 - w (since the length of the cuboid is 25 cm) and simplifying, we get:

(25 - w)w h = 4900

Now, we use the fact that the shaded face is a square. Since two of its dimensions are the same, we have:

l = w

Substituting this into the equation above, we get:

(25 - l)l h = 4900

Simplifying further, we have:

25l^2 - 4900 = 0

Solving for l using the quadratic formula, we get:

l = 14 or -14/5

Since the length of the cuboid cannot be negative, we have l = 14. Therefore, the length of one side of the square face is 14 cm.

Step-by-step explanation:

The total rainfall is given as 16

Average rainfall is given as 1.23

The average temperature is given as 22.8

we would add all of the weekly rain values

2.6 + 1.6 + 10.2 + 1.4 + 0.2 = 16

The total rainfall is 16

The average rainfall would be 16 divided by the total number of days that we have here:

16 / 13

= 1.23

The average rainfall is 1.23

total temperature

22.9 + 28.5 + 24.6 + 36.2 + 19 + 20.8 + 19.4 + 22.8 + 22.6 + 21.6 + 19.6 + 19.9 + 18.3

= 296.2

average = 296.2 / 13

= 22.8

average temperature is given as 22.8

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Answer:

x = 5;

[tex]y = \frac{5 \sqrt{2} }{2} [/tex]

Step-by-step explanation:

Use trigonometry:

[tex]y = \tan(45°) = \frac{ \frac{5 \sqrt{2} }{2} }{y} [/tex]

Use the property of proportion to find y:

[tex]y = \frac{ \frac{5 \sqrt{2} }{2} }{ \tan(45°) } = \frac{ \frac{5 \sqrt{2} }{2} }{1} = \frac{5 \sqrt{2} }{2} [/tex]

Use the Pythagorean theorem to find x:

[tex] {x}^{2} = {y}^{2} + { (\frac{5 \sqrt{2} }{2}) }^{2} [/tex]

[tex] {x}^{2} = {( \frac{5 \sqrt{2} }{2}) }^{2} + { (\frac{5 \sqrt{2} }{2}) }^{2} = \frac{25 \times 2}{4} + \frac{25 \times 2}{4} = \frac{50}{4} + \frac{50}{4} = \frac{100}{4} = 25[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{25} = 5[/tex]

Answer:

C. -7

Step-by-step explanation:

A rational expression will always be undefined when the denominator = 0 because we can't divide by 0.

-7 + 7 = 0 so -7 is the only number which makes the expression undefined

5. The value of angle LNM in the given circle is 54 degrees. 7. The value of angle ABC is 51 degrees.

A circle is a two-dimensional shape made up of a collection of points that are spaced uniformly apart from one another (called the radius) on a plane. The fixed point is referred to as the circle's origin or centre, and the fixed distance between each point and the origin is referred to as the radius. The centre, the radius, and the diameter of a circle may be seen in the following illustration.

5. The angle subtended by the two chords is half the measure of the angle at the center.

Thus,

angle LNM = 1/2 (angle LPM)

Substitute the value of angle LPM = 108, thus:

angle LNM = 1/2(108) = 54 degrees.

Hence, the value of angle LNM in the given circle is 54 degrees.

7. For measure angle ABC we have:

16x-26 = 2(5x+11)

16x-10x = 22+26

6x=48

x = 8

Substituting the value of x we have:

5(8) + 11 = 40 + 11 = 51

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Answer:

Step-by-step explanation:

Sorry, i can't "add up to five attachments" because i say only answer.

1.(−24,8)

2.[−3,1]

3.[−3,4]

4. (−3,5)

5 and 6 no answer (check my attachments)

7. (−∞,−8)v(4,+∞)

8 (−∞,1)v(7,+∞)

9. (−∞,−3]v[6,+∞)

10. (−∞,−3]v[2,+∞)

11. (−∞,∞)

12. (−∞,∞)

13. (−∞,−[tex]\frac{21}{4}[/tex]]v[[tex]\frac{15}{4}[/tex],+∞)

14.[-[tex]\frac{4}{5}[/tex],[tex]\frac{8}{5}[/tex]]

15. (-[tex]\frac{17}{3}[/tex];5)

16. (−∞,−14]v[22,+∞)

17. no answer (how 5 and 6)

18. (−∞,∞)

19. (−2,[tex]\frac{2}{3}[/tex])

20. (−∞,−4)v(−[tex]\frac{2}{3}[/tex],+∞)

The possible range of scores is given as follows:

Anything from 21% to 59%.

The percentage that is typically assigned is given as follows:

40%.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The parameters for this problem are given as follows:

[tex]\pi = 0.4, n = 25[/tex]

Then the lower bound of the confidence interval is given as follows:

0.4 - 1.96 x sqrt(0.4 x 0.6/25) = 0.21.

The upper bound of the confidence interval is given as follows:

0.4 + 1.96 x sqrt(0.4 x 0.6/25) = 0.59.

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Answer:

y = -2x + 5

Step-by-step explanation:

slope = rise/run = 2/-1 = -2

b = y-intercept = 5

y = -2x + 5

When p = 0. 1, the mean of the sampling distribution would be 65. 5 and the standard deviation would be 7.6769.

When p = 0.5, the mean of the sampling distribution would be 327.5 and the standard deviation would be 12.7984 .

To find the mean and standard deviation of the sampling distribution of the sample proportion, we can use the following formulas:

p = 0.1

Mean:

μ p = n x p = 655 x 0.1 = 65.5

Standard Deviation:

σ_p = √(n x p x  (1 - p)) = √(655 x 0.1 x (1 - 0.1)) = √(655 x 0.1 x 0.9) = √(58.95)

σp = 7.6769

When p = 0.5

Mean:

μ p = n x p = 655 x 0.5 = 327.5

Standard Deviation:

σ p = √(n x p x (1 - p)) = √(655 x 0.5 x (1 - 0.5)) = √(655 x 0.5 x 0.5) = √(163.75)

σp = 12.7984

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2091 square meters represents the total area of the figure.

What is the example polygon?

A polygon is any two-dimensional shape formed by straight lines. Triangles, hexagons, pentagons, and quadrilaterals are examples of polygons.

                               Polygons are flat two-dimensional shapes with straight sides that are completely closed. The sides should be straight, not curved. However, polygons can have any number of sides. The word polygon comes from the Greek word "polgonos". 

This figure is called a pentagon and has the shape of a trapezoid.

To find its area, we can calculate the area of the trapezoid, which is given by:

A = (b1 + b2)/2 * h

where b1 and b2 are the lengths of the parallel sides and h is the height.

In this case, the length of b1 is 43 meters and the length of b2 is 18 meters, and the height is 34 meters, so the area of the trapezoid is:

A = (43 + 16)/2 * 34 + (43 + 21) * 34

A = 1003 + 1088

A = 2091 square meters.

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The Greatest Common Factor of 7x^4y^3 - 15x^3y^5 is 27x^3y^3.

Answer: its A

Step-by-step explanation:

i did the test

Jasmine makes $2.08 more per hour cleaning a larger house compared to a smaller house.

Pricing strategies refer to the methods and techniques used by businesses or companies to set the prices of their products or services.

Let's first calculate the hourly rate Jasmine charges for cleaning a house with 2 bathrooms:

She charges $50 for a house with 3 bedrooms and 2 bathrooms, and it takes her 3 hours to clean it, so her hourly rate is:

⇒ $50 ÷ 3 hours = $16.67/hour

Now let's calculate the hourly rate she charges for cleaning a house with 3 or 4 bathrooms:

She charges $75 for a house with 3 to 4 bathrooms, and it takes her 4 hours to clean it, so her hourly rate is:

⇒ $75 ÷ 4 hours = $18.75/hour

Therefore, Jasmine makes $18.75/hour cleaning a larger house compared to $16.67/hour cleaning a smaller house.

To find out how much more Jasmine makes per hour cleaning a larger house compared to a smaller house, we can subtract the hourly rate for a smaller house from the hourly rate for a larger house:

⇒ $18.75/hour - $16.67/hour = $2.08/hour

So, Jasmine makes $2.08 more per hour cleaning a larger house compared to a smaller house.

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All real numbers make up the domain of a linear function, hence the domain of  [tex]f(x)=-5x+20x-7[/tex] is  [tex](-\infty , \infty )[/tex]  . The range of a linear function is also the set of all real numbers, hence   [tex]f(x)=-5x+20x-7[/tex] has a range of (-[tex]\infty[/tex], [tex]\infty[/tex]).

For the formula, [tex]y = 4x2 + 24x + 13[/tex]

All real numbers make up the domain of a polynomial function, hence the domain of y=4x2+24x+13 is [tex](-\infty , \infty )[/tex]

We can use calculus or the square root method to determine the function's range. At x=-3, where y=1, the function's minimal value is found. As a result, the function's range is  [tex][1, \infty )[/tex].

Using the formula [tex]f(x)=-5x+20x-7:[/tex]

Using related words together, we obtain [tex]f(x)=15x-7.[/tex]

Therefore, All real numbers make up the domain of a linear function, hence the domain of  [tex]f(x)=-5x+20x-7[/tex] is  [tex](-\infty , \infty )[/tex]  . The range of a linear function is also the set of all real numbers, hence   [tex]f(x)=-5x+20x-7[/tex] has a range of (-[tex]\infty[/tex], [tex]\infty[/tex]).

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0.20 is percent of observations fall between 0.7 and 0.9.

What use does percentage serve?

The simplest way to use percentages is to compare two numbers, with the second number being rebased to 100. Consider that we are curious about the proportion of employed women who are female. If this proportion is equal to 1/2, then generally speaking, there is one employed woman for every two men.

Density curve consists of two line segments .

   first line goes from the point (0,1) to the points (0.7 , 1) . second line goes from (0.7 , 1) to (0.9 , 2 ) in the xy plane .

   then percentage of observation fall below 0.20 and is 0.20.

        percentage = 20% = 0.20

area of rectangle = ab

                        = 0.2 * 1

                        = 0.20

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