How do you find the mean and standard deviation of data in R?.

Due to its peculiar ratio of 1:2:3  , the  30-60-90 triangle is referred to as a special right triangle. Any triangle with a ° angle is considered to be a right triangle in this context.

A unique type of right triangle known as  30-60-90 a  triangle always has angles of

30-60 and -90 ,

The length of the hypotenuse is twice the length of the shortest side and the length of the other side is √ times the length of the shortest side in a  30-60-90  Triangle.

The above theorem can be written mathematically as the 30-60-90  Triangle Formula as

√  which is the ratio of the three sides of the  30-60-90 Triangle.

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The function y whose graph is a horizontal shrink of f(x) = 5x + 8 by a factor of 1/5 is given as follows:

y = 25x + 8.

The function for this problem is defined as follows:

f(x) = 5x + 8.

For the horizontal shrink by a factor of a, the function is defined as follows:

f(x/a).

The parameter a for this problem is given as follows:

a = 1/5.

Hence the shrunk function is defined as follows:

y = f(x/(1/5)) = f(5x) = 5(5x) + 8 = 25x + 8.

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Answer:

If you're looking for the equivalent of m then it is -390

Step-by-step explanation:

-30 = m divided by 13 is the same as -30 times 13 = m

Finally m is equal to -390

Answer:

m = -390

Step-by-step explanation:

Given statement,

→ -30 = m divided by 13.

Forming the equation,

→ -30 = m/13

Now the value of m will be,

→ -30 = m/13

→ m/13 = -30

→ m = -30 × 13

→ [ m = -390 ]

Hence, value of m is -390.

Trigonometric ratios depend only on angles as they remain constant no matter what.

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides relate to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. The sin, cos, and tan functions can be used to obtain the other significant trigonometric ratios, cosec, sec, and cot.

Even if the sides of the triangle increases or decreases in a specific ratio, the angles of the triangle will always remain the same no matter what.

Trigonometric ratios in right triangles are therefore independent of the side lengths  and solely depend on the magnitude of the angles.

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A 3x4 matrix is ​​a matrix with 3 rows and 4 columns is a rectangular matrix. The number of solutions in a matrix depends on the context in which it is used.

When the matrix is ​​used to represent a system of linear equations, the number of solutions to the system depends on the rank of the matrix, which is the number of linearly independent rows or columns.

A 3x4 matrix has no solutions because it is not a square matrix and does not have a well-defined inverse. A square matrix has the same number of rows and columns and can be inverted if and only if its determinant is nonzero. A non-square matrix, on the other hand, has no inverse and cannot be inverted.

It should be noted that in the case of the rectangular matrix, the solution depends on the context of the problem and by using other techniques, such as the linear least squares method.

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Answer:

8:00

Step-by-step explanation:

This is probably extremely late

distance between their ends greater at 8.00

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Answer: f(2) = g(2)

Step-by-step explanation:

Well, this is kind of a comparison so you can do this by putting "2" as x value for both functions.

If you do that for both functions:

[tex]f(x) = 4x^{5}\\f(2) = 128 = (2^{7}) \\----------\\g(x) = 8.4^{x} = 2^{2x + 3}\\g(2) = 128[/tex]

So, this shows that f(2) = g(2).

Answer:

Obtuse

Step-by-step explanation:

An angle that is measured more than 90 degrees is an obtuse angle. Although an angle that measures 180 degrees is a straight angle or a half angle, and an angle that measures 360 degrees is a straight angle or a complete angle. However, when it's 360 degrees it's a full circle because a circle measures 360 degrees. If you want to measure an angle to determine which one it is, you must use a protractor.

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Answer:

Step-by-step solution:

Let's first familiarize ourselves with the basic types of angles out there.

The simplest angles are:

In a nutshell, acute angles are angles whose measure is less than 90 degrees, right angles are the ones whose measure is exactly 90 degrees, and obtuse angles are the ones whose measure is greater than 90 degrees.

Here's what an obtuse angle looks like.

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\linethickness{.4mm}\qbezier(1,1)(1,1)(5.5,1)\qbezier(1,1)(1,1)( -1,4)\qbezier(0.65,1.55)(1.5,1.8)(2,1)\put(3,3){\rm Obtuse Angle :}\put(3,2.5){\it measures more than}\put(3,2){\sf 90 degrees}\end{picture}[/tex]

--

Now, since 140 measures more than 90 degrees, it's an obtuse angle.

[tex]\therefore\quad\underline{\boxed{\sf{The~angle~is~obtuse}}}[/tex]

The quadratic formula, factoring, using the square roots, and completing the square are the four methods for solving a quadratic equation.

The quadratic formula x = [-b(b2 - 4ac)] / (2a) provides the solutions of the quadratic equation ax2 + bx + c = 0. Therefore, to use the quadratic formula to solve a quadratic equation, simply transform the equation into its standard form, ax2 + bx + c = 0, and then apply the quadratic formula.

A quadratic equation is a second-order equation written as ax2 + bx + c = 0, where a is a real number and b and c are real number coefficients.

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Find the x and y-intercepts of the line. Let y and solve for x. Let x and solve for y. Find a third solution to the equation. Plot these three coordinates and check that they line up. Draw the line.

Let the equation be y = Px + Qz. P and Q are constants, and x and z are 2 variables.

Firstly, make one variable 0, z = 0. This implies that you are dealing with only two variables, so you can make a graph(1) on X and Y axis. A simple line passes through the origin. Now take z = 1, and plot on the same plane, i.e., Plot y = Px + Q (this will be graph 2). Similarly, for all z. You will get a set of parallel lines separated by B.

Then you realize that only Graph(1) belongs to the z = 0 plane. and Graph(2) belongs to z = 1 plane and so on for z = 2, 3, 4….

So all you get is a Plane with slope P with respect to the x-axis and slope Q with respect to slope Q.

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A 45-45-90 triangle is an isosceles right triangle, meaning that it has two congruent sides and one right angle. To find the area and perimeter of a 45-45-90 triangle, use the following formulas:

Area:

(1/2) * (side length)^2

Perimeter:

2 * (side length) + (side length) * √2

Note that the perimeter of a 45-45-90 triangle is equal to twice the length of one of its sides plus the length of the hypotenuse.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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Your monthly payment for this house will be $1689.5 if your mortgage payment is $1345, your annual insurance premium is $678, and your real estate taxes are $3456.

Describe the mortgage payments in brief?

Principal and interest payments make up your monthly mortgage payments. You must purchase private mortgage insurance if your down payment is less than 20%, which raises your monthly payment. Real estate or property taxes are also included in some payments. Early on in the mortgage, the borrower pays more interest, whereas the principle balance is favored in the latter stages. A greater down payment will directly increase your home's equity.

To find the total monthly payment for the home, we need to divide the annual costs by 12.

Total monthly payment = Mortgage payment + (Annual insurance premium / 12) + (Annual real estate taxes / 12)

= $1345 + ($678 / 12) + ($3456 / 12)

= $1345 + $56.5 + $288

= $1689.5

So the total monthly payment for the home is $1689.5

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Your monthly payment for this house will be $1689.5 if your mortgage payment is $1345, your annual insurance premium is $678, and your real estate taxes are $3456.

Principal and interest payments make up your monthly mortgage payments. You must purchase private mortgage insurance if your down payment is less than 20%, which raises your monthly payment. Real estate or property taxes are also included in some payments. Early on in the mortgage, the borrower pays more interest, whereas the principle balance is favored in the latter stages. A greater down payment will directly increase your home's equity.

To find the total monthly payment for the home, we need to divide the annual costs by 12.

Total monthly payment = Mortgage payment + (Annual insurance premium / 12) + (Annual real estate taxes / 12)

= $1345 + ($678 / 12) + ($3456 / 12)

= $1345 + $56.5 + $288

= $1689.5

So the total monthly payment for the home is $1689.5

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In a perfect square trinomial, two of your terms will be perfect squares. If you do not have two perfect square terms, then this trinomial is not a perfect square trinomial.

The general shape of a really perfect rectangular trinomial is (x + y)^2, in which x and y are the roots of the trinomial. to check if a trinomial is perfectly rectangular, we will try to the component it into the rectangular binomial. We also can whole the square technique, which involves adding and subtracting the rectangular of 1/2 of the x-coefficient of the linear time period after which grouping the resulting phrases.

It's far essential to note that for a trinomial to be a super rectangular trinomial, the regular time period has to be a square of an integer and the linear time period should be an excellent variety.

Perfect rectangular trinomials are used in fixing quadratic equations and expertise their solutions, they also have programs in algebra, geometry, and trigonometry. Factoring them is an essential talent in algebra and is utilized in solving exceptional types of mathematical troubles.

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The value of x for the two expressions will be 0.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two equations are (-x+2y= 6) and 6y =x+18. The equations can be solved as below,

-x+2y= 6 or x = 2y - 6

6y = x + 18

Substitute the value of x in the second equation,

6y = 2y - 6 + 18

4y = 12

y = 3

x = 2y - 6

x = ( 2 x 3 ) - 6

x = 0

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Answer:74 blue beads and 90 purple beads

Step-by-step explanation:

first you need to take the total number of beads 164 divide by the 2 colors so 164÷2=86 then you subtract the 8 more purple from 1/2 of 86 and you get 74 then you add 8 more to the other half of 82 and get 90 purple and 74 blue.

Answer:

Step-by-step explanation:

(a) 1.653 x 10^12 / 87 * 10^6

= (1.653 / 87) x (10^12 / 10^6)

= 0.019 x 10^6

= 1.9 x 10^4

or 19,000 days.

(b) 6 billion / 87 million

= 6,000,000,000 / 87,000,000

= 6000/87

= 69 days.

  The mathematical function known as a logarithm expresses the degree to which a base number must be raised in order to obtain a specific value. The symbol logb(x), where b is the logarithm's base and x is the value being evaluated, stands for the logarithm of a number. The natural logarithm, which has a base of e, is the most widely used logarithm (approximately 2.71828). The inverse function of exponentiation is the logarithm, according to this definition. The exponent to which we must raise b in order to obtain a number x is its logarithm to base b.

       It reads log2(3x + 8) = 5.

logb(a^n) = n * logb(a) where b is the base of the logarithm, is a property of logarithms that can be used to rewrite expressions. Since the base in this instance is 2, we obtain log2(3x + 8) = 5.

 corresponding to 2^5 = 3x + 8

Now that x is on one side of the equation, we can solve for it.

32 = 3x + 8

After deducting 8 from both sides, we arrive at 24 = 3x, which we then multiply both sides by to get 8

 Thus, x = 8 is the corresponding equation.

and the solution is 8.

     Therefore, the x=8 is the solution of this problem .

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Answer:

1. a 2. 8

Step-by-step explanation:

A 20 degree angle called an acute angle.

Any angle which is less than 90 degree but greater than 0 degree is called an acute angle. For example - 20, 30, 40 , 50 etc are acute angles.

Polygons with at least one acute angle include triangles, parallelograms, trapezoids, and so on.The acute angle that are present in the triangle they are known as acute angle triangle.

Properties of acute angle triangles:

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We can demonstrate the solution set in a number of different ways. Number line, interval notation, and set notation are all options for accomplishing this.

Depending on the question, these methods may or may not be used.

There are two ways to write the interval notation solution set.

The closed interval is the first. The solution is enclosed by square brackets and includes the endpoints in a closed interval.

The form [a, b] is used to indicate this. The set notation, on the other hand, is x a x b. This indicates that the solution set runs from a to b, with the second interval being open. The endpoints are not included in the solution when an open interval is enclosed by round brackets ().

The format used for this is (a, b). The set notation, on the other hand, is x a x b. The solution set is therefore situated between a and b.

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$12034 is the worth of the car after 4 years.

Percentage, a relative value indicating hundredth parts of any quantity.

Given that we purchased a  car for $22,000

Every year your car depreciates by 14%

We have to find the worth of the car after 4 years.

[tex]A=P(1-r)^{t}[/tex]

P is the principal amount=$12000

r is rate of interest =14%=0.14

t is time =4 years

A=22000(1-0.14)⁴

A=22000(0.86)⁴

A=22000×0.547

A=$12034

Hence, $12034 is the worth of the car after 4 years.

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Radical 3, also known as the cube root of 3, is a number that when multiplied by itself three times equals 3. It is denoted as ∛3. To find the value of radical 3, one way is to use a calculator with a cube root function.

Another way to find the value of radical 3 is to use a process called prime factorization. It involves breaking the number down into its prime factors and then taking the cube root of the result. In the case of ∛3, we have:

∛3 = ∛(3)

Since 3 is a prime number, we don't need to factor it further, and thus the cube root of 3 is just 3^(1/3) = 3^(1/3) = ∛3.

It's important to note that cube roots can be negative or positive and in this case, ∛3 is positive.

∛3 is an irrational number, which means that it cannot be expressed as a ratio of two integers, and its decimal representation is non-repeating and non-terminating. But it can be approximated to some decimal values.

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The second step required to solve the given system of equations using elimination method is to add or subtract the modified system of equations.

As given in the question,

Steps required to solve the given system of equations by elimination method :

Let us consider two system of equations are :

2x + 3y = 1  __(1)

3x + 2y = 1  __(2)

1. Multiply 3 to (1) and 2 to (2)  to eliminate the x-term.

6x + 9y = 3  __(3)

6x + 4y = 2   __(4)

2. Now in second step subtract (4) from (3) to get the value of y.

6x + 9y = 3  

6x + 4y = 2

0x + 5y = 1

⇒ y = 1/5

3.  Multiply 2 to (1) and 3 to (2)  to eliminate the x-term

4x + 6y = 2 __(5)

9x + 6y = 3  __(6)

4. Now in subtract (5) from (6) to get the value of x.

9x + 6y = 3

4x + 6y = 2

5x = 1

⇒ x = 1/5

Therefore, the second step in the given system of equation using elimination method is add or subtract the modified equations.

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The y-intercept of y =- 2/3x + 7 is 7.

The equation, y = mx + b, is the slope-intercept form of a straight line.

Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.

The value of b is equal to y when x = 0, and m shows how steep the line is. The slope of the line is also called the gradient.

Thus, The y-intercept of y =- 2/3x + 7 is 7.

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Step-by-step explanation:

22 pounds for $11.

we could now calculate how many pounds we can buy for $1.

that would be 22/11 = 2 pounds.

or we can calculate as requested how much (how many $) he needed to pay for 1 pound.

that would be 11/22 = 1/2 = $0.50

and as you can see, both answers work prefectly together. they are just different views of the same basic problem.

we have to pay $0.50 per pound, and so we can buy 2 pounds with $1.

In this situation, it is true that the population who go to the movie theater, and the sample is the first 150 people of the theater.

In statistics and related fields, the population can be considered as the whole or the complete group that is being studied. On the other hand, the sample is a fraction taken from the whole population.

The purpose of a sample is to make the process of studying the population easier as studying every individual of the population is too complicated.

Based on this, the population are all customers going to the theater but the sample are the 150 people.

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Beatrice made 11 sales this week. The solution has been obtained using linear equations.

What is linear equation?

A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.

Let the sales of Beatrice be 'x'.

Since, Marshall made 5 more sales than Beatrice, we get

Sales of Marshall= x+5

Thus, Earnings of Beatrice = $276 + $11x

Earnings of Marshall = $29 + $23(x+5)

We are given that Beatrice and Marshall have earned the same amount this week, therefore,

⇒$276 + $11x = $29 + $23(x+5)

⇒$276 + $11x = $29 + $23x + $115

⇒$12x = $132

⇒x = $132/$12

⇒x = 11

Hence, Beatrice made 11 sales this week.

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Answer:

24 children

Step-by-step explanation:

Given ratios:

Multiply the first ratio by 2 and the second ratio by 3 so that the ratios of children are the same:

Therefore the combined ratio is:

So the ratio of Adult Males to Adult Females is 22 : 15.

If the difference between the number of Adult Males and Adult Females is 28 then:

[tex]\implies \dfrac{22}{22+15}x-\dfrac{15}{22+15}x=28[/tex]

[tex]\implies \dfrac{22}{37}x-\dfrac{15}{37}x=28[/tex]

[tex]\implies \dfrac{7}{37}x=28[/tex]

[tex]\implies 7x=1036[/tex]

[tex]\implies x=148[/tex]

Therefore:

[tex]\implies \textsf{Adult Males}=\dfrac{22}{37} \times 148=88[/tex]

[tex]\implies \textsf{Adult Females}=\dfrac{15}{37} \times 148=60[/tex]

If the original ratio of Adult Males to Children is 11 : 3, and the number of Adult Males is 88:

[tex]\implies 11:3=88:c[/tex]

[tex]\implies \dfrac{11}{3}=\dfrac{88}{c}[/tex]

[tex]\implies 11c=264[/tex]

[tex]\implies c=24[/tex]

Therefore, the number of children in the village is 24.

Part A: percent of 70 is 10.

x% of 70 = 10

70x / 100 = 10

x = 1000 / 70

x = 14.28 %.

Part B: percent of 2.8 is 20.

x% of 2.8 = 20

2.8x/ 100 = 20

x = 2000/ 2.8

x = 714.28%

Part C: percent of 90 is 18.

x% of 90 = 18

90x/100 = 18

x = 1800 / 90

x = 2 %

Part D: percent of 10 is 55.

x% of 10 = 55

10x / 100 = 55

x = 5500/ 10

x = 550%.

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A system of equations is an arrangement of one or more equations with many variables.

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The equivalent fractions of 3/4 are 6/8, 9/12, 12/16, and 15/20.

Equivalent fractions are fractions that represent the same value, even though they look different. For example, if you have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake. If you cut a cake into eight equal pieces and eat four of them, you will still have eaten half the cake. These are equivalent fractions.

To find the equivalent fractions for any given fraction, multiply the numerator and the denominator by the same number. For example, to find an equivalent fraction of 3/4, multiply the numerator 3 and the denominator 4 by the same number, say, 2. Thus, 6/8 is an equivalent fraction of 3/4. We can find some other equivalent fractions by multiplying the numerator and the denominator of the given fraction by the same number.

3/4= 3×3/4×3

=9/12.

3/4=

3/4= 3×4/4×4

=12/16

3/4= 3×5/4×5

=15/20

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