What is the area of this figure

Therefore, the dimensions of the square are 5 yards by 5 yards, and the dimensions of the rectangle are 40 yards by 5 yards.

Let's denote the width of the rectangle as "w". According to the problem, the length of the rectangle is 8 times the width, so the length would be 8w.

The area of the rectangle is given by length times width, which in this case is 8w * w = 8w^2.

The area of the square is given by side length squared, which is w^2.

The combined area of the square and rectangle is given as 225 square yards:

8w^2 + w^2 = 225

Combining like terms:

9w^2 = 225

Dividing both sides of the equation by 9:

w^2 = 25

Taking the square root of both sides:

w = 5

So the width of the rectangle is 5 yards. Since the length of the rectangle is 8 times the width, the length would be 8 * 5 = 40 yards.

The side length of the square is the same as the width of the rectangle, which is 5 yards.

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Two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs

The two-sample t-test defined as the method used to test whether the unknown population means of two groups are equal. The two sample t-test is also called independent samples t-test. Because the two samples of the data are statistically independent.

A paired t-test is used to find the difference between two variables usually separated by time for the same subject. By using the paired t-test  we can find the mean difference between pairs of measurements is zero or not. So  paired t-test is used, when data is in the form of matched pairs

Hence, two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs

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The given system of equations is expressed as

y = x + 5

y = x + 1

We would apply the method of substitution. It means that

x + 5 = x + 1

x - x = 1 - 5

0 = - 4

We know that 0 is not equal to - 4. Therefore, there is no solution

28

Step-by-step explanation:

To calculate the approximate area that will be painted on each lamp shade, we need to use the formula for finding the area of a circle: A = πr^2, where r is the radius of the circle. The diameter of the lamp shade is given as 6 inches, which means the radius is half of that, or 3 inches. Therefore, the area of the lamp shade that will be painted is approximately 3.14 x 3^2, which equals 28.26 square inches. So, the answer we select from the drop-down menu would be "28 square inches."

The average height of the students, the range of heights, and any other trends or patterns that may be present within the data. This information can be used to better understand the physical characteristics of the students in his class."

In order to answer the student question about Mr. Stoner's data on the heights of students in his first period physical

education class,

1. Look at the data chart provided by Mr. Stoner to analyze the heights of the students.

2. Identify any trends or patterns within the data, such as the average height, the range of heights, or the most common

height.

3. Summarize your findings in a concise and accurate manner, focusing on the key points that are relevant to the

question.

"Mr. Stoner measured the heights of students in his first period physical education class and organized

the data in a chart. By analyzing the chart, we can determine the average height of the students, the range of heights,

and any other trends or patterns that may be present within the data. This information can be used to better

understand the physical characteristics of the students in his class."

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the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.

There are no factors of 24 that are prime numbers. A factor of a number is a whole number that divides that number without leaving a remainder. Prime numbers, on the other hand, are numbers that are divisible only by 1 and themselves, and cannot be expressed as the product of any other numbers.

The prime factors of 24 are 2, 2, and 3. We can factorize 24 as 2 × 2 × 2 × 3 or 2^3 × 3. Here, 2 and 3 are both prime numbers, but they are not factors of 24 in isolation. They are only prime factors of 24 when combined in the manner shown.

This fact highlights an important concept in number theory: the uniqueness of prime factorization. Every composite number can be expressed as a unique product of prime numbers. This fundamental theorem of arithmetic is crucial in many areas of mathematics, including cryptography, where it is used to secure communications and protect sensitive information.

In summary, there are no factors of 24 that are prime numbers. However, the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.

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The domain and range of function  f(x) = 9 - x² are:

Domain: (-∞, ∞) {x | x ∈ R}

Range: (−∞, 9) {y | y ≤ 9}

What are the domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

f(x) = 9 - x²

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation: (-∞, ∞)

Notation: {x | x ∈ R}

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation: (−∞, 9)

Notation:  {y | y ≤ 9}

Hence, the domain and range of function  f(x) = 9 - x² are:

Domain: (-∞, ∞) {x | x ∈ R}

Range: (−∞, 9) {y | y ≤ 9}

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The equation of circle for both the parts will be as,

(a)  (x-3)² +(y-2)²= 4

(b)   x²+y² = 1

What is circle?

A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.

Main Body:

(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.

Circle centered at (h, k) with radius r:

(x -h)² +(y -k)² = r²

The given circle is ...

(x -2)² +(y -2)² =2²

(x -2)² +(y -2)² = 4

__

(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:

x²+y² = 1

Hence the equation of circle is such.

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Given:

There are given that the triangle ABC.

Where,

Explanation:

According to the question:

We need to find the value for BC:

So,

To find the value of BC, we need to use the cosine rule:

From the cosine rule:

Then,

Put the all values into the given formula:

Then,

Then,

Final answer:

Hence, the value of BC is 6.016 km.

Answer with Step-by -step explanation:

Sequence A;4,7,10,13,16

\(a_2-a_1=7-4=3\)

\(a_3-a_2=10-7=3\)

The difference between two consecutive terms is equal. Therefore, it forms arithmetic sequence.

Common difference, d=3

a=4

\(a_n=a+(n-1)d\)

\(a_6=a+5d=4+5\times 3=19\)

\(a_7=a+6d=4+6(3)=22\)

\(a_8=a+7d=4+7(3)=25\)

Sequence B: 5,10,20,40,80,...

\(a_1=5,a_2=10,a_3=20\)

\(\frac{a_2}{a_1}=\frac{10}{2}=2\)

\(\frac{a_3}{a_2}=\frac{20}{10}=2\)

The ratio  of two consecutive terms is equal. Therefore, it forms geometric sequence.

Common ratio, r=2

a=5

\(a_n=a r^{n-1}\)

\(a_6=ar^5=5(2)^5=160\)

\(a_7=ar^6=5(2^6)=320\)

\(a_8=ar^7=5(2^7)=640\)

Sequence C:2,5,10,17,26,..

a1=2

\(a_2=5=2+3=a_1+3\)

\(a_3=10=5+5=a_2+5\)

\(a_4=17=10+7=a_3+7\)

\(a_5=26=17+9=a_4+9\)

From the following pattern

We can get

\(a_6=a_5+11=26+11=37\)

\(a_7=a_6+13=37+13=50\)

\(a_8=a_7+15=50+15=65\)

Step-by-step explanation:

1kL = 100 dal

x = 470 dal .... you will criss cross it

1 kl × 470 dal = x ×100dal

470 dal kl = 100dal x ... then you will divide 100 dal from both side

4.7 kl = x

x = 4.7 kl

so our result is 4.7kl which is equal to 470 dal

Step-by-step explanation:

470 dal = 4.7 kl

because 1 kl = 100 dal

\( \frac{1}{x} = \frac{100}{470} \\ \\ 100x = 470 \\ x = \frac{470}{100} \\ x = 4.7\)

Answer:

y = 9\(\sqrt{2}\) inches

Step-by-step explanation:

Since the base angles are congruent then the triangle is isosceles with both legs being equal.

Using Pythagoras' identity in the right triangle

y² = 9² + 9² = 81 + 81 = 162 ( take the square root of both sides )

y = \(\sqrt{162}\) = \(\sqrt{81(2)}\) = 9\(\sqrt{2}\)

The calculated measure of the angle EJK is 20 degrees

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

The regular nonagon ABCDEFGHI

This shape is inscribed in a circle

So, we start by calculating the measure of the angle at each vertex from the center of the circle/nonagon

A nonagon has 9 sides

So, we have

Angle = 360/9

Evaluate

Angle = 40

Next, we have

Angle EJK = 1/2 * Angle

This gives

Angle EJK = 1/2 * 40

Evaluate

Angle EJK = 2 0

Hence, the measure of the angle EJK is 20 degrees

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Complete question

Regular nonagon ABCDEFGHI is inscribed in a circle. Find the mEJK

Answer:

The answer is ≈3 to the nearest whole number

Step-by-step explanation:

using SOH CAH TOA

BCA

sin0=opp/hyp

sin0=7.9/11

0=sin‐¹(7.9/11)

0=46 to the nearest degree

<A=<D

so,<EDF=46°

tan0=adj/hyp

tan46=x/3.3

x=tan46×3.3

x=3 to the nearest whole number

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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One or more of the mean differences are statistically significant, but not the precise location of the group differences.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, might be an independent variable.

Dependent variables are so-called because, during an experiment, their values are examined on the assumption or presumption that they are governed by the values of other variables.

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Answer:

8c

Step-by-step explanation:

5c + 2c + c the same as doing 5 + 2 + 1 = 8

the c without a number before means 1c but it's easier to write just c

these are all like terms and can be added together

Answer:

Step-by-step explanation:

\((g+f)(x)=g(x)+f(x)=x-1+x^2 +4=x^2 +x+3\)\(x^2 +x+3\)

The surface area and the volume of each solid are listed below:

Case 23

A = 216 + 153√3 cm² = 481 cm², V = 324√3 cm³ = 561.18 cm³

Case 13

A = 575π m² = 1806.42 m², V = 4000π / 3 m³ = 4188.79  m³

In this problem we must determine the surface area and the volume of each of the two solids, the following area and volume formulas are listed below:

Triangles

A = 0.5 · w · h

Rectangle

A = w · h

Circle

A = π · r²

Surface of a hemisphere

A = 2π · r²

Surface of the inclined section of a cone

A = π · r · l

Lateral surface of a cylinder

A = 2π · r · l

Volume of a prism

V = A' · l

Volume of a hemisphere

V = (2π / 3) · r³

Volume of a pyramid

V = (1 / 3) · A' · l

Where:

Now we proceed to determine the surface area and the volume of each solid:

Case 23

Surface area

A = (9 cm) · (8 cm) + (9√3 cm) · (8 cm) + (18 cm) · (8 cm) + (9 cm) · (9√3 cm)

A = 72 cm² + 72√3 cm² + 144 cm² + 81√3 cm²

A = 216 + 153√3 cm²

A = 481 cm²

V = 0.5 · (9 cm) · (9√3 cm) · (8 cm)

V = 324√3 cm³

V = 561.18 cm³

Case 13

Surface area

A = 2π · (5 m)² + 2π · (5 m) · (45 m) + π · (5 m) · (15 m)

A = 575π m²

A = 1806.42 m²

Volume

V = (2π / 3) · (5 m)³ + π · (5 m)² · (45 m) + (π / 3) · (5 m)² · (15 m)

V = 4000π / 3 m³

V = 4188.79  m³

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Roman has a certain amount of money. if he spends 15, then he has 14 of the original amount left. Roman had originally 20.

To find out how much money Roman had originally, you can follow these steps:
Step 1: Let the original amount of money be "x".
Step 2: According to the problem, if Roman spends $15, he has 1/4 of the original amount left.

So, after spending 15, he has (1/4)x left.
Step 3: Since he spent $15, we can write the equation as: x - 15 = (1/4)x.
Step 4: To solve for x, first multiply both sides of the equation by 4 to get rid of the fraction:

4(x - 15) = 4(1/4)x => 4x - 60 = x.
Step 5: Subtract "x" from both sides:

4x - x - 60 = 0 => 3x - 60 = 0.
Step 6: Add 60 to both sides:

3x = 60.
Step 7: Divide both sides by 3 to find the value of x:

x = 60 / 3 => x = 20.

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Answer:

Can't properly see the question mate

Step-by-step explanation:

Answer:

165

Step-by-step explanation:

A whole line equals to 180 degrees.

180-15=165

Hope this helps plz mark brainliest!

As I explained before, first we need to move the point in the divisor until it gets to the last number in the divisor. As you can see, the point moved 2 spaces to the right.

Therefore, the point in the number of dividends has to move 2 spaces to the right too.

Then, 1000 cannot divide 0, so we put a 0 in the first space above the line. In the second space, we put another 0 again, and in the third space 1000 cannot divide 64, therefore we have to write another 0.

Then, we need to write a 0 right beside the 64, getting a new number 640, but still, 1000 cannot divide 640 so we have to write another 0.

Now we have to add another 0 to the 640, getting 6400 and that now can be divided by 1000.

Answer:

v=-1

Step-by-step explanation:

15x - 21v = 51---------(mutiply by 3) (Equaltion-1)

-15x -10v = -20 ------- (mutiply by -5) (Equation-20

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

-31v=31 (Cancel 15x and 15x because Equation 1   15x is positive and equation 2      15x is netgative.

v=-1

Answer:

IM DIEING INSIDEEEEEEEEEEEEEEEEEEEE AS WE SPEAK AS I RIDE TOWARDS THE SUNSET AS WE SPEAK IM DIEING SLOWLYYYYYYYYYYYYYYYYYYYY OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH AS SPEAK IM LEAVING THIS PLANET OH OH OHHHHHHHHHHHHHHHH

~ I wrote this song UwU

Step-by-step explanation:

When written as an expression, the product of 17 and 487 would be 17 × 487.

A math expression is an assemblage of numbers, symbols, and operations that are combined for forming a value or thought about mathematics. What makes an expression unique is that there is no equal sign. If there was to be an equal sign, it becomes an equation.

The product of 17 and 487 can be written as an expression by simply using the multiplication symbol between the two numbers:

17 × 487

In conclusion, the expression representing the product of 17 and 487 is 17 × 487.

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