what does it mean by give your answer in 'terms of pi' ??
please help me and thanks

The number of elements will always be the same as the number of observations.

Mean is the ratio of the sum of the values of the data set to the total number of values available in the data set.

Thus, we get;

[tex]\rm Mean = \dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}}[/tex]

We are given that;

the number of elements=number

Now,

From observation we can say that the number of elements is equal to the number of observations.

Therefore, by mean the answer will be observation.

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Ounces per cup is a measure of volume used in cooking; a standard measuring cup holds 8 fluid ounces.

Ounces per cup is a proportion of volume utilized in preparing and food planning. It alludes to the quantity of liquid ounces that can be held in a standard cup measure. In the US, a standard estimating cup holds 8 liquid ounces, so when somebody alludes to a specific number of ounces per cup, they are normally alluding to the number of liquid ounces that are expected to fill one cup.

Understanding ounces per cup is significant in cooking and baking, as recipes frequently call for fixings to be estimated in cups or liquid ounces. It is additionally essential to take note of that ounces per cup can change contingent upon the kind of fixing being estimated, as certain fixings have various densities or loads per volume.

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210 lbs is approximately equal to 95.2544 kg  ( rounded to four decimal places )

The conversion factor to convert lbs to kilogram is 0.453592

1 lbs = 0.453592 kg

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in kg = The mass in lbs × conversion factor

Substitute the values in the equation

1 lbs = 0.453592 kg

210 lbs = 210 × 0.453592

Multiply the numbers

= 95.2544 kg ( rounded to four decimal places )

Therefore, 210 lbs is 95.2544 kg

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2. The area of the cabin's window is 196 square inches.

3. The area of the doghouse is  32.5 square ft.

4. The farmer should purchase 2 begs of soil.

5. The artist needs 161.5 square in material to make the kite.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

Trapezoids are defined differently by different people. A trapezoid can have one and only one pair of parallel sides, according to one school of mathematics, while another contends that a trapezoid can have multiple pairs of parallel sides. If we take into account the second definition, then a parallelogram is also a trapezoid by that definition. However, the first definition excludes parallelograms from the definition of a trapezoid since it is one of the quadrilateral types that we have already mentioned.

2. The formula for the area of a trapezoid is 1/2 × (sum of parallel side) × height.

The length of one parallel side is 10 inches. The length of the other parallel side is (10+4+4) inches = 18 inches.

The height of the trapezoid is 14 inches

The area of the trapezoid is 1/2 ×(10 + 18) × 14

= 196 square inches.

3.

The formula for the area of a trapezoid is 1/2 × (sum of parallel side) × height.

The length of one parallel side is 5 ft. The length of the other parallel side is (5+3) ft = 8 ft.

The height of the trapezoid is 5 ft.

The area of the trapezoid is 1/2 ×(5 + 8) × 5

= 32.5 square ft.

4.

The area of a parallelogram is the product of height and base.

The length of the base is (2.5 yards + 6.5 yard) = 9 yards

The height of the parallelogram is 6 yards.

The area of the parallelogram is 9 yards × 6 yards

= 54 square yards

Each beg can cover 40 square yards field.

The number of begs that the farmer need is 56/40 = 1.4  ≈2

5.

The area of the kite is half of the product of diagonals.

The length of diagonals are (8.5 in + 8.5 in) = 17 in and (6 in  + 13 in) = 19 in

The area of the kite is (17×19)/2 = 161.5 square in.

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Therefore , the solution of the given problem of linear equation comes out to be Emily used 8.1 pints of blue paint to paint her bedroom walls.

A straightforward regression curve is created using the equation y=mx+b. The y-intercept is m, and the slope is B. The previous line is usually referred to as a "math equation mixing numerous variables," even though y / y represent independent components. Only two variables are present in bivariate linear equations. There are no known solutions to application issues involving linear equations.

Here,

If 4/5 of the total paint used is white paint, then 1/5 of the total paint used is blue paint. We can use this information to find the amount of blue paint Emily used.

Let x be the total amount of paint used in pints. Then:

4/5 x = 8.1 (the amount of white paint used)

1/5 x = ?

To solve for the amount of blue paint, we can multiply both sides of the equation by 5:

1/5 x = ?

1/5 x * 5 = ? * 5

x = 40.5

So Emily used a total of 40.5 pints of paint. To find the amount of blue paint, we can multiply the total amount of paint by the fraction that represents the amount of blue paint:

1/5 * 40.5 = 8.1

Therefore, Emily used 8.1 pints of blue paint to paint her bedroom walls.

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The question is, "Jada earns twice as much money per hour as Diego. Diego earns twice as much money per hour as Lin. Select all the graphs that could represent how much Jada, Diego, and Lin earn for different amounts of time worked."

The graphs that could represent how much Jada, Diego, and Lin earn for different amounts of time worked are:

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The solutions to the original equation are x = ±sqrt(10) or x = ±1.

What is quadratic expression ?
A quadratic expression is a polynomial expression of degree two, meaning that it contains one or more terms in which the variable is raised to the second power (or squared). The general form of a quadratic expression is:

ax^2 + bx + c

Explanation:
The given equation, x^4 - 11x^2 + 10 = 0, is a quadratic equation in terms of x^2.This can simplify the equation and make it easier to solve.

Let's make the substitution u = x^2. Then, the equation becomes:

u^2 - 11u + 10 = 0

This is a standard quadratic equation, which can be solved using the quadratic formula:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -11, and c = 10. Substituting these values into the formula, we get:

u = (11 ± sqrt(121 - 40)) / 2

u = (11 ± sqrt(81)) / 2

u = (11 ± 9) / 2

u = 10 or 1

Now, we substitute back u = x^2 to get:

x^2 = 10 or x^2 = 1

Taking the square root of both sides, we get:

x = ±sqrt(10) or x = ±1

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Using compound interest Arnold will have $412,102.63 in his IRA when he retires at age 67.

To find out how much Arnold will have in his IRA when he retires at age 67, we can use the formula for the future value of an annuity:

FV = PMT × ([tex](1 + r/n)^{(n*t)}[/tex] - 1) / (r/n)

Where:

Here are the steps to solve the future value of Arnold's IRA:

Convert the annual interest rate to a monthly rate and express it as a decimal:

r = 2.75% / 12 = 0.00229167

Determine the number of compounding periods per year:

n = 12 (since the interest is compounded monthly)

Calculate the number of years until Arnold retires:

t = 67 - 44 = 23

Plug in the values into the formula and solve for FV:

FV = 850 × ([tex](1 + 0.00229167/12)^{(12 * 23)}[/tex] - 1) / (0.00229167/12)

FV = $412,102.63

Therefore, Arnold will have $412,102.63 in his IRA when he retires at age 67.

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Answer:

75.4 (rounded)

Step-by-step explanation:

V= πr² h/3

V= π x 3² x 8/3

 = 75.3982236862

If you need any more help just ask :)

Answer:

(e) It means that your grade is 2 standard deviations above the mean for this exam.

Step-by-step explanation:

Z-score describes the number of standard deviations away from the mean. In this case, a z-score of +2.0 would be 2 standard deviations above the mean.

Answer:

Step-by-step explanation:

You can create a vector both by enclosing the elements in square brackets like v=[1 2 3 4 5] or using commas, like v=[1,2,3,4,5]. They mean the very same: a vector (matrix) of 1 row and 5 columns.

The given system of equations, option C. The system has a nontrivial solution.

When given a system of three equations with three unknowns, it is possible to determine if the system has a nontrivial solution by using row operations and Gaussian elimination. Nontrivial solutions are solutions that are not all 0.

In the given system of equations, the left-hand side of each equation consists of 3 variables, 4x₁-6x₂+13x₃, 4x₁-10x₂-x₃, and 8x₁+4x₂+14x₃. By performing row operations on the equations, the augmented matrix can be reduced to the form of the identity matrix.

The first row operation performed is to subtract the first row from the second row, resulting in

=> 4x₁-10x₂-x₃ = -2x₁-2x₂+13x₃.

The second row operation is to subtract twice the first row from the third row, resulting in

=> 8x₁+4x₂+14x₃ = 0.

The third row operation is to divide the second row by -2, resulting in

=> 4x₁-10x₂-x₃ = x₁+x₂-13x₃.

This reduced form of the augmented matrix can then be rearranged to the form of the identity matrix, indicating that the system of equations has a nontrivial solution.

Therefore, the answer to the question is that the system has a nontrivial solution

Hence the option (c) is correct.

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The converted value representing in grams and ounce is given by 30 grams is equal to 1.05822 ounce.

Conversion factor representing the relation between ounce and grams is given by :

28 grams equal to one ounce

Substitute the required grams value to be converted into ounce we have,

⇒ 28 grams = 1 ounce

⇒ 1gram = ( 1 / 28 ) ounce

⇒ 30 gram = ( 30 ) × ( 1 / 28 ) ounce

⇒ 30 gram =  ( 1.05822 ) ounce

Therefore, the value after conversion grams into ounce is given by            30 gram =  ( 1.05822 ) ounce .

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Using the conversion factor, 3 1/3 yards is equal to 120 inches

To convert yards to inches, we need to know the conversion factor between these two units. One yard is equal to 36 inches.

Therefore, to convert 3 1/3 yards to inches, we can use the following steps:

Convert the whole number of yards to inches: 3 yards x 36 inches/yard = 108 inches

Convert the remaining fraction of a yard to inches: 1/3 yard x 36 inches/yard = 12 inches

Add the results of steps 1 and 2 to get the total number of inches: 108 inches + 12 inches = 120 inches

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Answer:

Since there are (12) inches in 1 yard (divide) 3 1/3 by (36)

so 3 1/3 yards = (16) inches.

Step-by-step explanation:

when you see (   ) it means it's the Answer

The date which is 100 days ago from 12 February 2023  is equal to

November 04, 2022 .

Present date is equal to 12 February 2023.

Date which is 100 days is written as :

January month has 31 days.

December month has 31 days.

November month has 26 days.

Total days equal to :

( 31 + 31 + 26 + 12 ) days = 100 days

100 days ago from 12 February 2023 is equal to :

12 February 2023  minus 100 days is 04 days 2022.

Therefore, the day which is 100 days ago from 12 February 2023 is given by   November 04, 2022 .

The above question is incomplete , the complete question :

What is 100 days ago from 12 February 2023 ?

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more information needed.

In total he walked 6.3 kilometers, from the information you gave.

Formula:

(A+B/2)H

A=base

B=Base

H=height

A. 100 cm (i think not to sure about this one)

B. 174 cm

C. 240cm

Answer:

Step-by-step explanation:Formula:

(A+B/2)H

A=base

B=Base

H=height

A. 100 cm (i think not to sure about this one)

B. 174 cm

C. 240cm

In reference to the given question, the pairs of polygons that  are congruent is  pairs 1 and 3. Hence, the correct answer is D, pairs 1 and 3.

Congruent polygons are polygons that have the same size and shape.

Pair 1 has two same L-shaped shapes, which are not congruent to any other pair.

Pair 2 has two T-shaped shapes with unequal height, which are not congruent to any other pair.

Pair 3 has two same triangles, which are congruent to each other.

Pair 4 has two unequal triangles, which are not congruent to each other or to any other pair.

Therefore, the only pairs of polygons that are congruent are pair 3, which has two same triangles, and pair 1, which has two L-shaped shapes that are the same. So the correct answer is D, pairs 1 and 3.

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The population of the town in the year 2001 according to the equation; ý = 135.23x - 245 is; 270,350.

since the given equation is;

ý = 135.23x - 245

Therefore, in year 2001; the population, y is;

y = 135.23 (2001) - 245

y = 270,595.23 - 245

y = 270,350.23

y = 270,350 (nearest whole number).

Ultimately, the population of the town in 2001 is; 270,350.

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Answer:

(-4, 1)

Step-by-step explanation:

x - 5(x + 5) = -9

x - 5x - 25 = -9

-4x - 25 = -9

-4x = 16

x = -4

y = -4 + 5

y = 1

The domain is 0 ≤ x ≤ 52. The maximum number of lawns she can mow with 13 gallons is 52, and the minimum is 0 lawns.

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {0, 52}.

Range = {0, 13}.

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Let A be a symmetric matrix, which means that A is equal to its own transpose, i.e., A = Aᵀ. We want to prove that if A is invertible, then its inverse A⁻¹ is also symmetric.

To show that A⁻¹ is symmetric, we need to show that (A⁻¹)ᵀ = A⁻¹.

We know that A is invertible, so A⁻¹ exists. Taking the transpose of both sides of the equation A = Aᵀ, we get:

(Aᵀ)ᵀ = A

which simplifies to:

A = Aᵀ

Multiplying both sides of this equation by A⁻¹, we get:

A⁻¹ A = A⁻¹ Aᵀ

Using the property of transpose (i.e., (AB)ᵀ = Bᵀ Aᵀ), we can rewrite the right-hand side of the equation as:

A⁻¹ Aᵀ = (A A⁻¹)ᵀ = Iᵀ = I

where I is the identity matrix.

Substituting this back into the original equation, we get:

A⁻¹ A = I

Taking the transpose of both sides of this equation, we get:

(A⁻¹ A)ᵀ = Iᵀ

which simplifies to:

Aᵀ (A⁻¹)ᵀ = I

Using the property of transpose again, we can rewrite the left-hand side of the equation as:

(A⁻¹)ᵀ Aᵀ = (A A⁻¹)ᵀ = Iᵀ = I

Substituting this back into the equation, we get:

(A⁻¹)ᵀ Aᵀ = I

which can be rearranged as:

(A⁻¹)ᵀ = (Aᵀ)⁻¹

Since we know that A = Aᵀ, we can substitute this into the equation to get:

(A⁻¹)ᵀ = A⁻¹

which shows that A⁻¹ is symmetric. Therefore, if a symmetric matrix is invertible, then its inverse is symmetric also.

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The first digit in both numbers is 2, so we can move to the next digit. In 2.218, the digit in the second decimal place is 2, while in 2.21, the digit in the second decimal place is 1. Since 2 is greater than 1, 2.218 is longer than 2.21.

When comparing the length of two decimal numbers, it's important to consider the value of each digit in the number. Let's take the example of 2.218 inches and 2.21 inches.

To begin, we can compare the first digit of each number, which is 2 in both cases. Since the first digit is the same, we need to look at the next digit to determine which number is longer. In 2.218, the second digit is 2, while in 2.21, the second digit is 1. The second digit in a decimal number represents the tenths place, so we can conclude that 2.218 is longer than 2.21.

It's important to note that this method of comparing decimal numbers applies to numbers with the same number of decimal places. If we were comparing 2.218 inches to 2.2 inches, for example, we wouldn't be able to simply look at the second digit. Instead, we would need to compare the numbers digit by digit, starting from the leftmost digit.

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The value of 136 kilograms to pounds ( using conversion factor ) is equal  to  ( 299.8283 ) pounds ( round off to four decimals value ) .

Conversion factor used to convert kilograms to pounds is equal to :

One kilograms is equal to 2.20462 pounds

In mathematical notation we can write ,

1 kilograms = 2.20462 pounds

Multiply both the side of the relation by 136 we get,

⇒ ( 1 × 136 ) kilograms = ( 136 × 2.20462 ) pounds

⇒ 136 kilograms = ( 299.82832 ) pounds

⇒ 136 kilograms = ( 299.8283 ) pounds (round off to four decimals value )

Therefore, the using conversion factor the required 136 kilograms is equal to ( 299.8283 ) pounds ( round off to four decimals value ) .

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Thus, the value displayed by Point K is roughly 373.

A number line in mathematics is a continuous straight line with numerals spaced equally apart along that line. Some stories will have a defined beginning and conclusion. We refer to these as closed number lines.

The distance between 367 and 377 can be split into five equal portions because the number line has 5 increments. Two components make up each section.

So, starting at 367, we must move 2 units to the right for each component until we reach Point K in order to determine the number represented by Point K.

We arrive at 369 by adding 2 units to the right of 367. From 369, we deduct another 2 units to arrive at 371. Following the same pattern, we arrive at 373, 375, and ultimately 377.

Point K is closest to 373 because it lies between 373 and 375. Thus, the value displayed by Point K is roughly 373.

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To avoid unnecessary penalties, and stress and to get benefits from the government in time like financial aid we need to file tax returns on time.

The tax return is a process of reporting your income, expenses, and other financial information to the government for the purpose of calculating your tax liability.

It involves filling out a set of forms provided by a tax authority, such as the Internal Revenue Service (IRS) in the United States.

When you file a tax return, you report your income, deductions, and credits for the year. The tax authority uses this information to determine if you owe any taxes or if you are entitled to a refund.    

There are several reasons why it is important to file your tax return on time and the following are some of them

Therefore,

To avoid unnecessary penalties, and stress and to get benefits from the government in time like financial aid we need to file tax returns on time.  

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P is located at the point (31/13, 44/13).

How to determine?

Let A and B be two points on a line segment, and let P be the point that divides AB in the ratio 3:10. We can find the coordinates of P as follows:

Suppose that the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2). Then the coordinates of P can be found using the following formula:

P = ( (10 * x1 + 3 * x2) / (10 + 3), (10 * y1 + 3 * y2) / (10 + 3) )

In other words, we add 10 parts of x-coordinates of A to 3 parts of x-coordinates of B, and divide by the sum of the parts (10 + 3 = 13) to get the x-coordinate of P. Similarly, we add 10 parts of y-coordinates of A to 3 parts of y-coordinates of B, and divide by the sum of the parts (10 + 3 = 13) to get the y-coordinate of P.

So if we know the coordinates of A and B, we can plug them into the formula above to find the coordinates of P.

For example, suppose that A has coordinates (1, 2) and B has coordinates (7, 8). Then the coordinates of P can be found as follows:

P = ( (10 * 1 + 3 * 7) / (10 + 3), (10 * 2 + 3 * 8) / (10 + 3) )

= ( (10 + 21) / 13, (20 + 24) / 13 )

= (31/13, 44/13)

Therefore, P is located at the point (31/13, 44/13).

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We know that Angle-side-angle is one of the criterias to find congruent triangles, then with the given information we can make only one unique triangle.

Here we know two of the angles of a triangles and the length of the side between these two angles.

This can be written as an: Angle-Side-Angle.

Remember that this is one of the conditions for congruent triangles.

This means that A-S-A defines completely a single triangle, thus, there is only one triangle that we can make with that information.

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Answer: look at the image for the answer and explanation

Step-by-step explanation: